Wave

Three-Dimensional Simulations of Subaerial Landslide-Generated Waves: Comparing OpenFOAM and FLOW-3D HYDRO Models

지표 산사태로 발생한 파랑의 3차원 시뮬레이션: OpenFOAM과 FLOW-3D HYDRO 모델 비교

Ramtin Sabeti, Mohammad Heidarzadeh, Alessandro Romano, Gabriel Barajas Ojeda & Javier L. Lara

Abstract

The recent destructive landslide tsunamis, such as the 2018 Anak Krakatau event, were fresh reminders for developing validated three-dimensional numerical tools to accurately model landslide tsunamis and to predict their hazards. In this study, we perform Three-dimensional physical modelling of waves generated by subaerial solid-block landslides, and use the data to validate two numerical models: the commercial software FLOW-3D HYDRO and the open-source OpenFOAM package. These models are key representatives of the primary types of modelling tools—commercial and open-source—utilized by scientists and engineers in the field. This research is among a few studies on 3D physical and numerical models for landslide-generated waves, and it is the first time that the aforementioned two models are systematically compared. We show that the two models accurately reproduce the physical experiments and give similar performances in modelling landslide-generated waves. However, they apply different approaches, mechanisms and calibrations to deliver the tasks. It is found that the results of the two models are deviated by approximately 10% from one another. This guide helps engineers and scientists implement, calibrate, and validate these models for landslide-generated waves. The validity of this research is confined to solid-block subaerial landslides and their impact in the near-field zone.

1 Introduction and Literature Review

Subaerial landslide-generated waves represent major threats to coastal areas and have resulted in destruction and casualties in several locations worldwide (Heller et al., 2016; Paris et al., 2021). Interest in landslide-generated tsunamis has risen in the last decade due to a number of devastating events, especially after the December 2018 Anak Krakatau tsunami which left a death toll of more than 450 people (Grilli et al., 2021; Heidarzadeh et al., 2020a). Another significant subaerial landslide tsunami occurred on 16 October 1963 in Vajont dam reservoir (Northern Italy), when an impulsive landslide-generated wave overtopped the dam, killing more than 2000 people (Heller & Spinneken, 2013; Panizzo et al., 2005). The largest tsunami run-up (524 m) was recorded in Lituya Bay landslide tsunami event in 1958 where it killed five people (Fritz et al., 2009).

To achieve a better understanding of subaerial landslide tsunamis, laboratory experiments have been performed using two- and three-dimensional (2D, 3D) set-ups (Bellotti & Romano, 2017; Di Risio et al., 2009; Fritz et al., 2004; Romano et al., 2013; Sabeti & Heidarzadeh, 2022a). Results of physical models are essential to shed light on the nonlinear physical phenomena involved. Furthermore, they can be used to validate numerical models (Fritz et al., 2009; Grilli & Watts, 2005; Liu et al., 2005; Takabatake et al., 2022). However, the complementary development of numerical tools for modelling of landslide-generated waves is inevitable, as these models could be employed to accelerate understanding the nature of the processes involved and predict the detailed outcomes in specific areas (Cremonesi et al. 2011). Due to the high flexibility of numerical models and their low costs in comparison to physical models, validated numerical models can be used to replicate actual events at a fair cost and time (e.g., Cecioni et al., 2011; Grilli et al., 2017; Heidarzadeh et al., 2020b, 2022; Horrillo et al., 2013; Liu et al., 2005; Løvholt et al., 2005; Lynett & Liu, 2005).

Table 1 lists some of the existing numerical models for landslide tsunamis although the list is not exhaustive. Traditionally, Boussinesq-type models, and Shallow water equations have been used to simulate landslide tsunamis, among which are TWO-LAYER (Imamura and Imteaz,1995), LS3D (Ataie-Ashtiani & Najafi Jilani, 2007), GLOBOUSS (Løvholt et al., 2017), and BOUSSCLAW (Kim et al., 2017). Numerical models that solve Navier–Stokes equations showed good capability and reliability to simulate subaerial landslide-generated waves (Biscarini, 2010). Considering the high computational cost of solving the full version of Navier–Stokes equations, a set of methods such as RANS (Reynolds-averaged Navier–Stokes equations) are employed by some existing numerical models (Table 1), which provide an approximate averaged solution to the Navier–Stokes equations in combination with turbulent models (e.g., k–ε, k–ω). Multiphase flow models were used to simulate the complex dynamics of landslide-generated waves, including scenarios where the landslide mass is treated as granular material, as in the work by Lee and Huang (2021), or as a solid block (Abadie et al., 2010). Among the models listed in Table 1, FLOW-3D HYDRO and OpenFOAM solve Navier–Stokes equations with different approaches (e.g., solving the RANS by IHFOAM) (Paris et al., 2021; Rauter et al., 2022). They both offer a wide range of turbulent models (e.g., Large Eddy Simulation—LES, k–ε, k–ω model with Renormalization Group—RNG), and they both use the VOF (Volume of Fluid) method to track the water surface elevation. These similarities are one of the motivations of this study to compare the performance of these two models. Details of governing equations and numerical schemes are discussed in the following.

Numerical modelsApproachDeveloper
FLOW-3D HYDROThis CFD package solves Navier–Stokes equations using finite-difference and finite volume approximations, along with Volume of Fluid (VOF) method for tracking the free surfaceFlow Science, Inc. (https://www.flow3d.com/)
MIKE 21This model is based on the numerical solution of 2D and 3D incompressible RANS equations subject to the assumptions of Boussinesq and hydrostatic pressureDanish Hydraulic Institute (DHI) (https://www.mikepoweredbydhi.com/products/mike-21-3)
OpenFOAM (IHFOAM solver)IHFOAM is a newly developed 3D numerical two-phase flow solver. Its core is based on OpenFOAM®. IHFOAM can also solve two-phase flow within porous media using RANS/VARANS equationsIHCantabria research institute (https://ihfoam.ihcantabria.com/)
NHWAVENHWAVE is a 3D shock-capturing non-Hydrostatic model which solves the incompressible Navier–Stokes equations in terrain and surface-following sigma coordinatesKirby et al. (2022) (https://sites.google.com/site/gangfma/nhwave, https://github.com/JimKirby/NHWAVE)
GLOBOUSSGloBouss is a depth-averaged model based on the standard Boussinesq equations including higher order dispersion terms, Coriolis terms, and numerical hydrostatic correction termsLøvholt et al. (2022) (https://www.duo.uio.no/handle/10852/10184)
BOUSSCLAWBoussClaw is a new hybrid Boussinesq type model which is an extension of the GeoClaw model. It employs a hybrid of finite volume and finite difference methods to solve Boussinesq equationsClawpack Development Team (http://www.clawpack.org/)Kim et al. (2017)
THETIS-MUITHETIS is a multi-fluid Navier–Stokes solver which can be considered a one-fluid model as only one velocity is defined at each point of the mesh and there is no mixing between the three considered fluids (water, air, and slide). It applies VOF methodTREFLE department of the I2M Laboratory at Bordeaux, France (https://www.i2m.u-bordeaux.fr/en)
LS3DA 2D depth-integrated numerical model which applies a fourth-order Boussinesq approximation for an arbitrary time-variable bottom boundaryAtaie-Ashtiani and Najafi Jilani (2007)
LYNETT- Mild-Slope Equation (MSE)MSE is a depth-integrated version of the Laplace equation operating under the assumption of inviscid flow and mildly varying bottom slopesLynett and Martinez (2012)
Tsunami 3DA simplified 3D Navier–Stokes model for two fluids (water and landslide material) using VOF for tracking of water surfaceHorrillo et al. (2013)Kim et al. (2020)
(Cornell Multi-grid Coupled Tsunami Mode (COMCOT)COMCOT adopts explicit staggered leap-frog finite difference schemes to solve Shallow Water Equations in both Spherical and Cartesian CoordinatesLiu et al. (1998); Wang and Liu (2006)
TWO-LAYERA mathematical model for a two-layer flow along a non-horizontal bottom. Conservation of mass and momentum equations are depth integrated in each layer, and nonlinear kinematic and dynamic conditions are specified at the free surface and at the interface between fluidsImamura and Imteaz (1995)
Table 1 Some of the existing numerical models for simulating landslide-generated waves

In this work, we apply two Computational Fluid Dynamic (CFD) frameworks, FLOW-3D HYDRO, and OpenFOAM to simulate waves generated by solid-block subaerial landslides in a 3D set-up. We calibrate and validate both numerical models using our physical experiments in a 3D wave tank and compare the performances of these models systematically. These two numerical models are selected among the existing CFD solvers because they have been reported to provide valuable insights into landslide-generated waves (Kim et al., 2020; Romano et al., 2020a, b ; Sabeti & Heidarzadeh, 2022a). As there is no study to compare the performances of these two models (FLOW-3D HYDRO and OpenFOAM) with each other in reproducing landslide-generated waves, this study is conducted to offer such a comparison, which can be helpful for model selection in future research studies or industrial projects. In the realm of tsunami generation by subaerial landslides, the solid-block approach serves as an effective representative for scenarios where the landslide mass is more cohesive and rigid, rather than granular. This methodology is particularly relevant in cases such as the 2018 Anak Krakatau or 1963 Vajont landslides, where the landslide’s nature aligns closely with the characteristics simulated by a solid-block model (Zaniboni & Tinti, 2014; Heidarzadeh et al., 2020a, 2020b).

The objectives of this research are: (i) To provide a detailed implementation and calibration for simulating solid-block subaerial landslide-generated waves using FLOW-3D HYDRO and OpenFOAM, and (ii) To compare the performance of these two numerical models based on three criteria: free surface elevation of the landslide-generated waves, capabilities of the models in simulating 3D features of the waves in the near-field, velocity fields, and velocity variations at different locations. The innovations of this study are twofold: firstly, it is a 3D study involving physical and numerical modelling and thus the data can be useful for other studies, and secondly, it compares the performance of two popular CFD models in modelling landslide-generated waves for the first time. The validated models such as those reported in this study and comparison of their performances can be useful for engineers and scientists addressing landslide tsunami hazards worldwide.

2 Data and Methods

2.1 Physical Modelling

To validate our numerical models, a series of three-dimensional physical experiments were carried out at the Hydraulic Laboratory of the Brunel University London (UK) in a 3D wave tank 2.40 m long, 2.60 m wide, and 0.60 m high (Figs. 1 and 2). To mitigate experimental errors and enhance the reliability of our results, each physical experiment was conducted three times. The reported data in the manuscript reflects the average of these three trials, assuming no anomalous outliers, thus ensuring an accurate reflection of the experimental tests. One experiment was used for validation of our numerical models. The slope angle (α) and water depth (h) were 45° and 0.246 m, respectively for this experiment. The movement of the sliding mass was recorded by a digital camera with a sampling frequency of 120 frames per second, which was used to calculate the slide impact velocity (vs). The travel distance (D), defined as the distance from the toe of the sliding mass to the water surface, was D=0.045 m. The material of the solid block used in our study was concrete with a density of 2600 kg/m3. Table 2 provides detailed information on the dimensions and kinematics of this solid block used in our physical experiments.

Figure 1. The geometrical and kinematic parameters of a subaerial landslide tsunami. Parameters are: h, water depth; aM, maximum wave amplitude; α, slope angle;vs, slide velocity; ls, length of landslide; bs, width of landslide; s, thickness of landslide; SWL, still water level; D, travel distance (the distance from the toe of the sliding mass to the water surface); L, length of the wave tank; and W, width of the wave tank and H, is the hight of the wave tank

Figure 2. a Wave tank setup of the physical experiments of this study. b Numerical simulation setup for the FLOW-3D HYDRO Model. c The numerical set-up for the OpenFOAM model. The location of the physical wave gauge (represented by numerical gauge WG-3 in the numerical simulations) is at X = 1.03 m, Y = 1.21 m, and Z = 0.046 m. d Top view showing the locations of numerical wave gauges (WG-1, WG-2, WG-3, WG-4, WG-5)
Parameter, unitValue/type
Slide width (bs), m0.26
Slide length (ls), m0.20
Slide thickness (s), m0.10
Slide volume (V), m32.60 × 10–3
Specific gravity, (γs)2.60
Slide weight (ms), kg6.86
Slide impact velocity (vs), m/s1.84
Slide Froude number (Fr)1.18
MaterialConcrete
Table 2 Geometrical and kinematic information of the sliding mass used for physical experiments in this study

We took scale effects into account during physical experiments by considering the study by Heller et al. (2008) who proposed a criterion for avoiding scale effects. Heller et al. (2008) stated that the scale effects can be negligible as long as the Weber number (W=ρgh2/σ; where σ is surface tension coefficient) is greater than 5.0 × 103 and the Reynolds number (R=g0.5h1.5/ν; where ν is kinematic viscosity) is greater than 3.0 × 105 or water depth (h) is approximately above 0.20 m. Considering the water temperature of approximately 20 °C during our experiments, the kinematic viscosity (ν) and surface tension coefficient (σ) of water become 1.01 × 10–6 m2/s and 0.073 N/m, respectively. Therefore, the Reynolds and Weber numbers were as R= 3.8 × 105 and W= 8.1 × 105, indicating that the scale effect can be insignificant in our experiments. To record the waves, we used a twin wire wave gauge provided by HR Wallingford (https://equipit.hrwallingford.com). This wave gauge was placed at X = 1.03 m, Y = 1.21 m based on the coordinate system shown in Fig. 2a.

2.2 Numerical Simulations

The numerical simulations in this work were performed employing two CFD packages FLOW-3D HYDRO, and OpenFOAM which have been widely used in industry and academia (e.g., Bayon et al., 2016; Jasak, 2009; Rauter et al., 2021; Romano et al., 2020a, b; Yin et al., 2015).

2.2.1 Governing Equations and Turbulent Models

2.2.1.1 FLOW-3D HYDRO

The FLOW-3D HYDRO solver is based on the fundamental law of mass, momentum and energy conservation. To estimate the influence of turbulent fluctuations on the flow quantities, it is expressed by adding the diffusion terms in the following mass continuity and momentum transport equations:

quation (1) is the general mass continuity equation, where u is fluid velocity in the Cartesian coordinate directions (x), Ax is the fractional area open to flow in the x direction, VF is the fractional volume open to flow, ρ is the fluid density, R and ξ are coefficients that depend on the choice of the coordinate system. When Cartesian coordinates are used, R is set to unity and ξ is set to zero. RDIF and RSOR are the turbulent diffusion and density source terms, respectively. Uρ=Scμ∗/ρ, in which Sc is the turbulent Schmidt number, μ∗ is the dynamic viscosity, and ρ is fluid density. RSOR is applied to model mass injection through porous obstacle surfaces.

The 3D equations of motion are solved with the following Navier–Stokes equations with some additional terms:

where t is time, Gx is accelerations due to gravity, fx is viscous accelerations, and bx is the flow losses in porous media.

According to Flow Science (2022), FLOW-3D HYDRO’s turbulence models differ slightly from other formulations by generalizing the turbulence production with buoyancy forces at non-inertial accelerations and by including the influence of fractional areas/volumes of the FAVOR method (Fractional Area-Volume Obstacle Representation) method. Here we use k–ω model for turbulence modelling. The k–ω model demonstrates enhanced performance over the k-ε and Renormalization-Group (RNG) methods in simulating flows near wall boundaries. Also, for scenarios involving pressure changes that align with the flow direction, the k–ω model provides more accurate simulations, effectively capturing the effects of these pressure variations on the flow (Flow Science, 2022). The equations for turbulence kinetic energy are formulated as below based on Wilcox’s k–ω model (Flow Science, 2022):

where kT is turbulent kinetic energy, PT is the turbulent kinetic energy production, DiffKT is diffusion of turbulent kinetic energy, GT is buoyancy production, β∗=0.09 is closure coefficient, and ω is turbulent frequency.

2.2.1.2 OpenFOAM

For the simulations conducted in this study, OpenFOAM utilizes the Volume-Averaged RANS equations (VARANS) to enable the representation of flow within porous material, treated as a continuous medium. The momentum equation incorporates supplementary terms to accommodate frictional forces from the porous media. The mass and momentum conservation equations are linked to the VOF equation (Jesus et al., 2012) and are expressed as follows:

where the gravitational acceleration components are denoted bygj. The term u¯i=1Vf∫Vf0ujdV represents the volume averaged ensemble averaged velocity (or Darcy velocity) component, Vf is the fluid volume contained in the average volumeV,τ is the surface tension constant (assumed to be 1 for the water phase and 0 for the air phase), and fσi is surface tension, defined as fσi=σκ∂α∂xi, where σ (N/m) is the surface tension constant and κ (1/m) is the curvature (Brackbill et al., 1992). μeff is the effective dynamic viscosity that is defined as μeff=μ+ρνt and takes into account the dynamic molecular (μ) and the turbulent viscosity effects (ρνt). νt is eddy viscosity, which is provided by the turbulence closure model. n is the porosity, defined as the volume of voids over total volume, and P∗=1Vf∫∂Vf0P∗dS is the ensemble averaged pressure in excess of hydrostatic pressure. The coefficient A accounts for the frictional force induced by laminar Darcy-type flow, B considers the frictional force under turbulent flow conditions, and c accounts for the added mass. These coefficients (A,B, and c) are defined based on the work of Engelund (1953) and later modified by Van Gent (1995) as given below:

where D50 is the mean nominal diameter of the porous material, KC is the Keulegan–Carpenter number, a and b are empirical nondimensional coefficients (see Lara et al., 2011; Losada et al., 2016) and γ = 0.34 is a nondimensional parameter as proposed by Van Gent (1995). The k-ω Shear Stress Transport (SST) turbulence is employed to capture the effect of turbulent flow conditions (Zhang & Zhang, 2023) with the enhancement proposed by Larsen and Fuhrman (2018) for the over-production of turbulence beneath surface waves. Boundary layers are modelled with wall functions. The reader is referred to Larsen and Fuhrman (2018) for descriptions, validations, and discussions of the stabilized turbulence models.

2.2.2 FLOW-3D HYDRO Simulation Procedure

In our specific case in this study, FLOW-3D HYDRO utilizes the finite-volume method to numerically solve the equations described in the previous Sect. 2.2.1.1, ensuring a high level of accuracy in the computational modelling. The use of structured rectangular grids in FLOW-3D HYDRO offers the advantages of easier development of numerical methods, greater transparency in their relation to physical problems, and enhanced accuracy and stability of numerical solutions. (Flow Science, 2022). Curved obstacles, wall boundaries, or other geometric features are embedded in the mesh by defining the fractional face areas and fractional volumes of the cells that are open to flow (the FAVOR method). The VOF method is employed in FLOW-3D HYDRO for accurate capturing of the free-surface dynamics (Hirt and Nichols 1981). This approach then is upgraded to method of the TruVOF which is a split Lagrangian method that typically produces lower cumulative volume error than the alternative methods (Flow Science, 2022).

For numerical simulation using FLOW-3D HYDRO, the entire flow domain was 2.60 m wide, 0.60 m deep and 2.50 m long (Fig. 2b). The specific gravity (γs) for solid blocks was set to 2.60 in our model, aligning closely with the density of the actual sliding mass, which was approximately determined in our physical experiments. The fluid medium was modelled as water with a density of 1000 kg/m3 at 20 °C. A uniform grid comprising of one single mesh plane was applied with a grid size of 0.005 m. The top, front and back of the mesh areas were defined as symmetry, and the other surfaces were of wall type with no-slip conditions around the walls.

To simulate turbulent flows, k-ω model was used because of its accuracy in modelling turbulent flows (Menter 1992). Landslide movement was replicated in simulations using coupled motion objects, which implies that the movement of landslides is based on gravity and the friction between surfaces rather than a specified motion in which the model should be provided by force and torques. The time intervals of the numerical model outputs were set to 0.02 s to be consistent with the actual sampling rates of our wave gauges in the laboratory. In order to calibrate the FLOW-3D HYDRO model, the friction coefficient is set to 0.45, which is consistent with the Coulombic friction measurements in the laboratory. The Courant Number (C=UΔtΔx) is considered as the criterion for the stability of numerical simulations which gives the maximum time step (Δt) for a prespecified mesh size (Δx) and flow speed (U). The Courant number was always kept below one.

2.2.3 OpenFOAM Simulation Procedure

OpenFOAM is an open-source platform containing several C++ libraries which solves both 3D Reynolds-Averaged Navier–Stokes equations (RANS) and Volume-Averaged RANS equations (VARANS) for two-phase flows (https://www.openfoam.com/documentation/user-guide). Its implementation is based on a tensorial approach using object-oriented programming techniques and the Finite Volume Method (McDonald 1971). In order to simulate the subaerial landslide-generated waves, the IHFOAM solver based on interFoam (Higuera et al., 2013a, 2013b), and the overset mesh framework method are employed. The implementation of the overset mesh method for porous mediums in OpenFOAM is described in Romano et al. (2020a, b) for submerged rigid and impermeable landslides.

The overset mesh technique, as outlined by Romano et al. (2020a, b), uses two distinct domains: a moving domain that captures the dynamics of the rigid landslide and a static background domain to characterize the numerical wave tank. The overlapping of these domains results in a composite mesh that accurately depicts complex geometrical transformations while preserving mesh quality. A porous media with a very low permeability (n = 0.001) was used to simulate the impermeable sliding surfaces. RANS equations were solved within the porous media. The Multidimensional Universal Limiter with Explicit Solution (MULES) algorithm is employed for solving the (VOF) equation, ensuring precision in tracking fluid interfaces. Simultaneously, the PIMPLE algorithm is employed for the effective resolution of velocity–pressure coupling in the Eqs. 7 and 8. A background domain was created to reproduce the subaerial landslide waves with dimensions 2.50 m (x-direction) × 2.60 m (y-direction) × 0.6 m (z-direction) (Fig. 2c). The grid size is set to 0.005 m for the background mesh. A moving domain was applied in an area of 0.35 m (x-direction) × 0.46 m (y-direction) × 0.32 m (z-direction) with a grid spacing of 0.005 m and applying a body-fitted mesh approach, which contains the rigid and impermeable wedges. Wall condition with No-slip is defined as the boundary for the four side walls (left, right, front and back, in Fig. 1). Also, a non-slip boundary condition is specified to the bottom, whereas the top boundary is defined as open. The experimental slide movement time series is used to model the landslide motion in OpenFOAM. The applied equation is based on the analytical solution by Pelinovsky and Poplavsky (1996) which was later elaborated by Watts (1998). The motion of a sliding rigid body is governed by the following equation:

where, m represents the mass of the landslide, s is the displacement of the landslide down the slope, t is time elapsed, g stands for the acceleration due to gravity, θ is the slope angle, Cf is the Coulomb friction coefficient, Cm is the added mass coefficient, m0 denotes the mass of the water displaced by the moving landslide, A is the cross-sectional area of the landslide perpendicular to the direction of motion, ρ is the water density, and Cd is the drag coefficient.

2.2.4 Mesh Sensitivity Analysis

In order to find the most efficient mesh size, mesh sensitivity analyses were conducted for both numerical models (Fig. 3). We considered the influence of mesh density on simulated waveforms by considering three mesh sizes (Δx) of 0.0025 m, 0.005 m and 0.010 m. The results of FLOW-3D HYDRO revealed that the largest mesh deviates 9% (Fig. 3a, Δx = 0.0100 m) from two other finer meshes. Since the simulations by FLOW-3D HYDRO for the finest mesh (Δx = 0.0025 m) do not show any improvements in comparison with the 0.005 m mesh, therefore the mesh with the size of Δx = 0.0050 m is used for simulations (Fig. 3a). A similar approach was followed for mesh sensitivity of OpenFOAM mesh grids. The mesh with the grid spacing of Δx = 0.0050 m was selected for further simulations since a satisfactory independence was observed in comparison with the half size mesh (Δx = 0.0025 m). However, results showed that the mesh size with the double size of the selected mesh (Δx = 0.0100 m) was not sufficiently fine to minimize the errors (Fig. 3b).

Figure 3. a, b Sensitivity of numerical simulations to the sizes of the mesh (Δx) for FLOW-3D HYDRO, and OpenFOAM, respectively. The location of the wave gauge 3 (WG-3) is at X = 1.03 m, Y = 1.21 m, and Z = -0.55 m (see Fig. 2d)

In terms of computational cost, the time required for 2 s simulations by FLOW-3D HYDRO is approximately 4.0 h on a PC Intel® Core™ i7-8700 CPU with a frequency of 3.20 GHz equipped with a 32 GB RAM. OpenFOAM requires 20 h to run 2 s of numerical simulation on 2 processors on a PC Intel® Core™ i9-9900KF CPU with a frequency of 3.60 GHz equipped with a 364 GB RAM. Differences in computational time for simulations run with FLOW-3D HYDRO and OpenFOAM reflect the distinct characteristics of each numerical methods, and the specific hardware setups.

2.2.5 Validation

We validated both numerical models based on our laboratory experimental data (Fig. 4). The following criterion was used to assess the level of agreement between numerical simulations and laboratory observations:

where ε is the mismatch error, Obsi is the laboratory observation values, Simi is the simulation values, and the mathematical expression |X| represents the absolute value of X. The slope angle (α), water depth (h) and travel distance (D) were: α = 45°, h = 0.246 m and D = 0.045 m in both numerical models, consistent with the physical model. We find the percentage error between each simulated data point and its corresponding observed value, and subsequently average these errors to assess the overall accuracy of the simulation against the observed time series. Our results revealed that the mismatch errors between physical experiments and numerical models for the FLOW-3D HYDRO and OpenFOAM are 8% and 18%, respectively, indicating that our models reproduce the measured waveforms satisfactorily (Fig. 4). The simulated waveform by OpenFOAM shows a minor mismatch at t = 0.76 s which resulted from a droplet immediately after the slide hits the water surface in the splash zone. In term of the maximum negative amplitude, the simulated waves by OpenFOAM indicates a relatively better performance than FLOW-3D HYDRO, whereas the maximum positive amplitude (aM) simulated by FLOW-3D HYDRO is closer to the experimental value. The recorded maximum positive amplitude in physical experiment is 0.022 m, whereas it is 0.020 m for FLOW-3D HYDRO and 0.017 m for OpenFOAM simulations. In acknowledging the deviations observed, it is pertinent to highlight that while numerical models offer robust insights, the difference in meshing techniques and the distinct computational methods to resolve the governing equations in FLOW-3D HYDRO and OpenFOAM have contributed to the variance. Moreover, the intrinsic uncertainties associated with the physical experimentation process, including the precision of wave gauges and laboratory conditions, are non-negligible factors influencing the results.

Figure 4. Validation of the simulated waves (brown line for FLOW-3D HYDRO and green line for OpenFOAM) using the laboratory-measured waves (black solid diamonds). This physical experiment was conducted for wave gauge 3 (WG-3) located at X = 1.03 m, Y = 1.21 m, and Z = -0.55 m (see Fig. 2d). Here, 
ε shows the errors between simulations and actual physical measurements using Eq. (13)

3 Results

Following the validations of the two numerical models (FLOW-3D HYDRO and OpenFOAM), a series of simulations were performed to compare the performances of these two CFD solvers. The generation process of landslide waves, waveforms, and velocity fields are considered as the basis for comparing the performance of the two models (Figs. 5, 6, 7 and 8).

Figure 5.Comparison between the simulated waveforms by FLOW-3D HYDRO (black) and OpenFOAM (red) at four different locations in the near-field zone (WG-1,2,4 and 5). WG is the abbreviation for wave gauge. The mismatch (Δ) between the two models at each wave gauge is calculated using Eq. (14)
Figure 6. Comparison of water surface elevations produced by solid-block subaerial landslides for the two numerical models FLOW-3D-HYDRO (a–c) and OpenFOAM (e–g) at different times
Figure 7. Snapshots of the simulations at different times for FLOW-3D HYDRO (a–c) and OpenFOAM (e–g) showing velocity fields (colour maps and arrows). The colormaps indicate water particle velocity in m/s, and the lines indicate the velocities of water particles
Figure 8. Comparison of velocity variations at (WG-3) for FLOW-3D HYDRO (light blue) and OpenFOAM (brown)

3.1 Comparison of Waveforms

Five numerical wave gauges were placed in our numerical models to measure water surface oscillations in the near-field zone (Fig. 5). These gauges offer an azimuthal coverage of 60° (Fig. 2d). Figure 5 reveals that the simulated waveforms from two models (FLOW-3D HYDRO and OpenFOAM) are similar. The highest wave amplitude (aM) is recorded at WG-3 for both models, whereas the lowest amplitude is recorded at WG-5 and WG-1 which can be attributed to the longer distances of these gauges from the source region as well as their lateral offsets, resulting in higher wave energy dissipation at these gauges. The sharp peaks observed in the simulated waveforms, such as the red peak between 0.8–1.0 s in Fig. 5a from OpenFOAM, the red peak between 0.6–0.8 s in Fig. 5b also from OpenFOAM, and the black peak between 1.4–1.6 s in Fig. 5d from FLOW-3D HYDRO, are due to the models’ spatial and temporal discretization. They reflect the sensitivity of the models to capturing transient phenomena, where the chosen mesh and time-stepping intervals are key factors in the models’ ability to track rapid changes in the flow field. To quantify the deviations of the two models from one another, we apply the following equation for mismatch calculation:

where Δ is the mismatch error, Sim1 is the simulation values from FLOW-3D HYDRO, Sim2 is the simulation values from OpenFOAM, and the mathematical expression |X| implies the absolute value of X. We calculate the percentage difference for each corresponding pair of simulation results, then take the mean of these percentage differences to determine the average deviation between the two simulation time series. Using Eq. (14), we found a deviation range from 9 to 11% between the two models at various numerical gauges (Fig. 5), further confirming that the two models give similar simulation results.

3.2 Three-Dimensional Vision of Landslide Generation Process by Numerical Models

A sequence of four water surface elevation snapshots at different times is shown in Fig. 6 for both numerical modes. In both simulations, the sliding mass travels a constant distance of 0.045 m before hitting the water surface at t = 0.270 s which induces an initial change in water surface elevation (Figs. 6a and e). At t = 0.420 s, the mass is fully immersed for both simulations and an initial dipole wave is generated (Figs. 6b and f). Based on both numerical models, the maximum positive amplitude (0.020 m for FLOW-3D HYDRO, and 0.017 m for OpenFOAM) is observed at this stage (Fig. 6). The maximum propagation of landslide-simulated waves along with more droplets in the splash zone could be seen at t = 0.670 s for both models (Fig. 6c and g). The observed distinctions in water surface elevation simulations as illustrated in Fig. 6 are rooted in the unique computational methodologies intrinsic to each model. In the OpenFOAM simulations, a more diffused water surface elevation profile is evident. Such diffusion is an outcome of the simulation’s intrinsic treatment of turbulent kinetic energy dissipation, aligning with the solver’s numerical dissipation characteristics. These traits are influenced by the selected turbulence models and the numerical advection schemes, which prioritize computational stability, possibly at the expense of interface sharpness. The diffusion in the wave pattern as rendered by OpenFOAM reflects the application of a turbulence model with higher dissipative qualities, which serves to moderate the energy retained during wave propagation. This approach can provide insights into the potential overestimation of energy loss under specific simulation conditions. In contrast, the simulations from FLOW-3D HYDRO depict a more localized wave pattern, indicative of a different approach to turbulent dissipation. This coherence in wave fronts is a function of the model’s specific handling of the air–water interface and its targeted representation of the energy dynamics resulting from the landslide’s interaction with the water body. They each have specific attributes that cater to different aspects of wave simulation fidelity, thereby contributing to a more comprehensive understanding of the phenomena under study.

3.3 Wave Velocity Analysis

We show four velocity fields at different times during landslide motion in Fig. 7 and one time series of velocity (Fig. 8) for both numerical models. The velocity varies in the range of 0–1.9 m/s for both models, and the spatial distribution of water particle velocity appears to be similar in both. The models successfully reproduce the complex wavefield around the landslide generation area, which is responsible for splashing water and mixing with air around the source zone (Fig. 7). The first snapshot at t = 0.270 s (Fig. 7a and e) shows the initial contact of the sliding mass with water surface for both numerical models which generates a small elevation wave in front of the mass exhibiting a water velocity of approximately 1.2 m/s. The slide fully immerses for the first time at t = 0.420 s producing a water velocity of approximately 1.5 m/s at this time (Fig. 7b and f). The last snapshot (t = 0.670 s) shows 1.20 s after the slide hits the bottom of the wave tank. Both models show similar patterns for the propagation of the waves towards the right side of the wave tank. The differences in water surface profiles close to the slope and solid block at t = 0.67 s, observed in the FLOW-3D HYDRO and OpenFOAM simulations (Figs. 6 and 7), are due to the distinct turbulence models employed by each (RNG and k-ω SST, respectively) which handle the complex interactions of the landslide-induced waves with the structures differently. Additionally, the methods of simulating landslide movement further contribute to this discrepancy, with FLOW-3D HYDRO’s coupled motion objects possibly affecting the waves’ initiation and propagation unlike OpenFOAM’s prescribed motion from experimental data. In addition to the turbulence models, the variations in VOF methodologies between the two models also contribute to the observed discrepancies.

For the simulated time series of velocity, both models give similar patterns and close maximum velocities (Fig. 8). For both models the WG-3 located at X = 1.03 m, Y = 1.21 m, and Z = − 0.55 m (Fig. 2d) were used to record the time series. WG-3 is positioned 5 mm above the wave tank bottom, ensuring that the measurements taken reflect velocities very close to the bottom of the wave tank. The maximum velocity calculated by FLOW-3D HYDRO is 0.162 m/s while it is 0.132 m/s for OpenFOAM, implying a deviation of approximately 19% from one another. Some oscillations in velocity records are observed for both models, but these oscillations are clearer and sharper for OpenFOAM. Although it is hard to see velocity oscillations in the FLOW-3D HYDRO record, a close look may reveal some small oscillations (around t = 0.55 s and 0.9 s in Fig. 8). In fact, velocity oscillations are expected due to the variations in velocity of the sliding mass during the travel as well as due to the interferences of the initial waves with the reflected wave from the beach. In general, it appears that the velocity time series of the two models show similar patterns and similar maximum values although they have some differences in the amplitudes of the velocity oscillations. The differences between the two curves are attributed to factors such as difference in meshing between the two models, turbulence models, as well as the way that two models record the outputs.

4 Discussions

An important step for CFD modelling in academic or industrial projects is the selection of an appropriate numerical model that can deliver the task with satisfactory performance and at a reasonable computational cost. Obviously, the major drivers when choosing a CFD model are cost, capability, flexibility, and accessibility. In this sense, the existing options are of two types as follows:

  • Commercial models, such as FLOW-3D HYDRO, which are optimised to solve free-surface flow problems, with customer support and an intuitive Graphical User Interface (GUI) that significantly facilitates meshing, setup, simulation monitoring, visualization, and post-processing. They usually offer high-quality customer support. Although these models show high capabilities and flexibilities for numerical modelling, they are costly, and thus less accessible.
  • Open-source models, such as OpenFOAM, which come without a GUI but with coded tools for meshing, setup, parallel running, monitoring, post-processing, and visualization. Although these models offer no customer support, they have a big community support and online resources. Open-source models are free and widely accessible, but they may not be necessarily always flexible and capable.

OpenFOAM provides freedom for experimenting and diving through the code and formulating the problem for a user whereas FLOW-3D HYDRO comes with high-level customer supports, tutorial videos and access to an extensive set of example simulations (https://www.flow3d.com/). While FLOW-3D-HYDRO applies a semi-automatic meshing process where users only need to input the 3D model of the structure, OpenFOAM provides meshing options for simple cases, and in many advanced cases, users need to create the mesh in other software (e.g., ANSYS) (Ariza et al., 2018) and then convert it to OpenFOAM format. Auspiciously, there are numerous online resources (https://www.openfoam.com/trainings/about-trainings), and published examples for OpenFOAM (Rauter et al., 2021; Romano et al., 2020a, b; Zhang & Zhang, 2023).

The capabilities of both FLOW-3D HYDRO and OpenFOAM to simulate actual, complex landslide-generated wave events have been showcased in significant case studies. The study by Ersoy et al. (2022) applied FLOW-3D HYDRO to simulate impulse waves originating from landslides near an active fault at the Çetin Dam Reservoir, highlighting the model’s capacity for detailed, site-specific modelling. Concurrently, the work by Alexandre Paris (2021) applied OpenFOAM to model the 2017 Karrat Fjord landslide tsunami events, providing a robust validation of OpenFOAM’s utility in capturing the dynamics of real-world geophysical phenomena. Both instances exemplify the sophisticated computational approaches of these models in aiding the prediction and analysis of natural hazards from landslides.

As for limitations of this study, we acknowledge that our numerical models are validated by one real-world measured wave time series. However, it is believed that this one actual measurement was sufficient for validation of this study because it was out of the scope of this research to fully validate the FLOW-3D HYDRO and OpenFOAM models. These two models have been fully validated by more actual measurements by other researchers in the past (e.g., Sabeti & Heidarzadeh, 2022b). It is also noted that some of the comparisons made in this research were qualitative, such as the 3D wave propagation snapshots, as it was challenging to develop quantitative comparisons for snapshots. Another limitation of this study concerns the number of tests conducted here. We fixed properties such as water depth, slope angle, and travel distance throughout this study because it was out of the scope of this research to perform sensitivity analyses.

5 Conclusions

We configured, calibrated, validated and compared two numerical models, FLOW-3D HYDRO, and OpenFOAM, using physical experiments in a 3D wave tank. These validated models were used to simulate subaerial solid-block landslides in the near-field zone. Our results showed that both models are fully compatible with investigating waves generated by subaerial landslides, although they use different approaches to simulate the phenomenon. The properties of solid-block, water depth, slope angle, and travel distance were kept constant in this study as we focused on comparing the performance of the two models rather than conducting a full sensitivity analysis. The findings are as follows:

  • Different settings were used in the two models for modelling landslide-generated waves. In terms of turbulent flow modelling, we used the Renormalization Group (RNG) turbulence model in FLOW-3D HYDRO, and k-ω (SST) turbulence model in OpenFOAM. Regarding meshing techniques, the overset mesh method was used in OpenFOAM, whereas the structured cartesian mesh was applied in FLOW-3D HYDRO. As for simulation of landslide movement, the coupled motion objects method was used in FLOW-3D HYDRO, and the experimental slide movement time series were prescribed in OpenFOAM.
  • Our modelling revealed that both models successfully reproduced the physical experiments. The two models deviated 8% (FLOW-3D HYDRO) and 18% (OpenFOAM) from the physical experiments, indicating satisfactory performances. The maximum water particle velocity was approximately 1.9 m/s for both numerical models. When the simulated waveforms from the two numerical models are compared with each other, a deviation of 10% was achieved indicating that the two models perform approximately equally. Comparing the 3D snapshots of the two models showed that there are some minor differences in reproducing the details of the water splash in the near field.
  • Regarding computational costs, FLOW-3D HYDRO was able to complete the same simulations in 4 h as compared to nearly 20 h by OpenFOAM. However, the hardware that were used for modelling were not the same; the computer used for the OpenFOAM model was stronger than the one used for running FLOW-3D HYDRO. Therefore, it is challenging to provide a fair comparison for computational time costs.
  • Overall, we conclude that the two models give approximately similar performances, and they are both capable of accurately modelling landslide-generated waves. The choice of a model for research or industrial projects may depend on several factors such as availability of local knowledge of the models, computational costs, accessibility and flexibilities of the model, and the affordability of the cost of a license (either a commercial or an open-source model).

Reference

  1. Abadie, S., Morichon, D., Grilli, S., & Glockner, S. (2010). Numerical simulation of waves generated by landslides using a multiple-fluid Navier–Stokes model. Coastal Engineering, 57(9), 779–794. https://doi.org/10.1016/j.coastaleng.2010.04.002
  2. Ariza, C., Casado, C., Wang, R.-Q., Adams, E., & Marugán, J. (2018). Comparative evaluation of OpenFOAM® and ANSYS® Fluent for the modeling of annular reactors. Chemical Engineering & Technology, 41(7), 1473–1483. https://doi.org/10.1002/ceat.201700455
  3. Ataie-Ashtiani, B., & Najafi Jilani, A. (2007). A higher-order Boussinesq-type model with moving bottom boundary: Applications to submarine landslide tsunami waves. Pure and Applied Geophysics, 164(6), 1019–1048. https://doi.org/10.1002/fld.1354
  4. Bayon, A., Valero, D., García-Bartual, R., & López-Jiménez, P. A. (2016). Performance assessment of OpenFOAM and FLOW-3D in the numerical modeling of a low Reynolds number hydraulic jump. Environmental Modelling & Software, 80, 322–335. https://doi.org/10.1016/j.envsoft.2016.02.018
  5. Bellotti, G., & Romano, A. (2017). Wavenumber-frequency analysis of landslide-generated tsunamis at a conical island. Part II: EOF and modal analysis. Coastal Engineering, 128, 84–91. https://doi.org/10.1016/j.coastaleng.2017.07.008
  6. Biscarini, C. (2010). Computational fluid dynamics modelling of landslide generated water waves. Landslides, 7(2), 117–124. https://doi.org/10.1007/s10346-009-0194-z
  7. Brackbill, J. U., Kothe, D. B., & Zemach, C. (1992). A continuum method for modeling surface tension. Journal of computational physics, 100(2), 335–354.
  8. Cecioni, C., Romano, A., Bellotti, G., Di Risio, M., & De Girolamo, P. (2011). Real-time inversion of tsunamis generated by landslides. Natural Hazards & Earth System Sciences, 11(9), 2511–2520. https://doi.org/10.5194/nhess-11-2511-2011
  9. Cremonesi, M., Frangi, A., & Perego, U. (2011). A Lagrangian finite element approaches the simulation of water-waves induced by landslides. Computers & Structures, 89(11–12), 1086–1093.
  10. Del Jesus, M., Lara, J. L., & Losada, I. J. (2012). Three-dimensional interaction of waves and porous coastal structures: Part I: Numerical model formulation. Coastal Engineering, 64, 57–72. https://doi.org/10.1016/J.COASTALENG.2012.01.008
  11. Di Risio, M., De Girolamo, P., Bellotti, G., Panizzo, A., Aristodemo, F., Molfetta, M. G., & Petrillo, A. F. (2009). Landslide-generated tsunamis runup at the coast of a conical island: New physical model experiments. Journal of Geophysical Research: Oceans. https://doi.org/10.1029/2008JC004858
  12. Engelund, F., & Munch-Petersen, J. (1953). Steady flow in contracted and expanded rectangular channels. La Houille Blanche, (4), 464–481.
  13. Ersoy, H., Oğuz Sünnetci, M., Karahan, M., & Perinçek, D. (2022). Three-dimensional simulations of impulse waves originating from concurrent landslides near an active fault using FLOW-3D software: A case study of Çetin Dam Reservoir (Southeast Turkey). Bulletin of Engineering Geology and the Environment, 81(7), 267. https://doi.org/10.1007/s10064-022-02675-8
  14. Flow Science. (2022). FLOW-3D HYDRO version 12.0 user’s manual. Santa Fe, NM, USA. Retrieved from https://www.flow3d.com/. 6 Aug 2023.
  15. Fritz, H. M., Hager, W. H., & Minor, H. E. (2004). Near field characteristics of landslide generated impulse waves. Journal of waterway, port, coastal, and ocean engineering, 130(6), 287–302.
  16. Fritz, H. M., Mohammed, F., & Yoo, J. (2009). Lituya bay landslide impact generated mega-tsunami 50th anniversary. In: Tsunami science four years after the 2004 Indian Ocean Tsunami (pp. 153–175). Birkhäuser Basel, Switzerland.
  17. Grilli, S. T., Shelby, M., Kimmoun, O., Dupont, G., Nicolsky, D., Ma, G., Kirby, J. T., & Shi, F. (2017). Modelling coastal tsunami hazard from submarine mass failures: Effect of slide rheology, experimental validation, and case studies off the US East Coast. Natural Hazards, 86(1), 353–391. https://doi.org/10.1007/s11069-016-2692-3
  18. Grilli, S. T., & Watts, P. (2005). Tsunami generation by submarine mass failure. I: Modelling, experimental validation, and sensitivity analyses. Journal of Waterway, Port, Coastal, and Ocean Engineering, 131(6), 283–297. https://doi.org/10.1061/(ASCE)0733-950X
  19. Grilli, S. T., Zhang, C., Kirby, J. T., Grilli, A. R., Tappin, D. R., Watt, S. F. L., et al. (2021). Modeling of the Dec. 22nd, 2018, Anak Krakatau volcano lateral collapse and tsunami based on recent field surveys: Comparison with observed tsunami impact. Marine Geology. https://doi.org/10.1016/j.margeo.2021.106566
  20. Heidarzadeh, M., Gusman, A., Ishibe, T., Sabeti, R., & Šepić, J. (2022). Estimating the eruption-induced water displacement source of the 15 January 2022 Tonga volcanic tsunami from tsunami spectra and numerical modelling. Ocean Engineering, 261, 112165. https://doi.org/10.1016/j.oceaneng.2022.112165
  21. Heidarzadeh, M., Ishibe, T., Sandanbata, O., Muhari, A., & Wijanarto, A. B. (2020a). Numerical modeling of the subaerial landslide source of the 22 December 2018 Anak Krakatoa volcanic tsunami, Indonesia. Ocean Engineering, 195, 106733. https://doi.org/10.1016/j.oceaneng.2019.106733
  22. Heidarzadeh, M., Putra, P. S., Nugroho, H. S., & Rashid, D. B. Z. (2020b). Field survey of tsunami heights and runups following the 22 December 2018 Anak Krakatau volcano tsunami, Indonesia. Pure and Applied Geophysics, 177, 4577–4595. https://doi.org/10.1007/s00024-020-02587-w
  23. Heller, V., Bruggemann, M., Spinneken, J., & Rogers, B. D. (2016). Composite modelling of subaerial landslide–tsunamis in different water body geometries and novel insight into slide and wave kinematics. Coastal Engineering, 109, 20–41. https://doi.org/10.1016/j.coastaleng.2015.12.004
  24. Heller, V., Hager, W. H., & Minor, H. E. (2008). Scale effects in subaerial landslide generated impulse waves. Experiments in Fluids, 44(5), 691–703. https://doi.org/10.1007/s00348-007-0427-7
  25. Heller, V., & Spinneken, J. (2013). Improved landslide-tsunami prediction: Effects of block model parameters and slide model. Journal of Geophysical Research: Oceans, 118(3), 1489–1507. https://doi.org/10.1002/jgrc.20099
  26. Higuera, P., Lara, J. L., & Losada, I. J. (2013a). Realistic wave generation and active wave absorption for Navier–Stokes models: Application to OpenFOAM®. Coastal Engineering, 71, 102–118. https://doi.org/10.1016/j.coastaleng.2012.07.002
  27. Higuera, P., Lara, J. L., & Losada, I. J. (2013b). Simulating coastal engineering processes with OpenFOAM®. Coastal Engineering, 71, 119–134. https://doi.org/10.1016/j.coastaleng.2012.06.002
  28. Hirt, C.W. and Nichols, B.D., 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of computational physics, 39(1), 201–225.
  29. Horrillo, J., Wood, A., Kim, G.-B., & Parambath, A. (2013). A simplified 3-D Navier–Stokes numerical model for landslide-tsunami: Application to the Gulf of Mexico. Journal of Geophysical Research, 118(12), 6934–6950. https://doi.org/10.1002/2012JC008689
  30. Imamura, F., & Imteaz, M. A. (1995). Long waves in two-layers: Governing equations and numerical model. Science of Tsunami Hazards, 13(1), 3–24.
  31. Jasak, H. (2009). OpenFOAM: Open source CFD in research and industry. International Journal of Naval Architecture and Ocean Engineering, 1(2), 89–94. https://doi.org/10.2478/IJNAOE-2013-0011
  32. Kim, G. B., Cheng, W., Sunny, R. C., Horrillo, J. J., McFall, B. C., Mohammed, F., Fritz, H. M., Beget, J., & Kowalik, Z. (2020). Three-dimensional landslide generated tsunamis: Numerical and physical model comparisons. Landslides, 17(5), 1145–1161. https://doi.org/10.1007/s10346-019-01308-2
  33. Kim, J., Pedersen, G. K., Løvholt, F., & LeVeque, R. J. (2017). A Boussinesq type extension of the GeoClaw model-a study of wave breaking phenomena applying dispersive long wave models. Coastal Engineering, 122, 75–86. https://doi.org/10.1016/j.coastaleng.2017.01.005
  34. Kirby, J. T., Grilli, S. T., Horrillo, J., Liu, P. L. F., Nicolsky, D., Abadie, S., Ataie-Ashtiani, B., Castro, M. J., Clous, L., Escalante, C., Fine, I., et al. (2022). Validation and inter-comparison of models for landslide tsunami generation. Ocean Modelling, 170, 101943. https://doi.org/10.1016/j.ocemod.2021.101943
  35. Lara, J. L., Ruju, A., & Losada, I. J. (2011). Reynolds averaged Navier–Stokes modelling of long waves induced by a transient wave group on a beach. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 467(2129), 1215–1242.
  36. Larsen, B. E., & Fuhrman, D. R. (2018). On the over-production of turbulence beneath surface waves in Reynolds-averaged Navier–Stokes models. Journal of Fluid Mechanics, 853, 419–460.
  37. Lee, C. H., & Huang, Z. (2021). Multi-phase flow simulation of impulsive waves generated by a sub-aerial granular landslide on an erodible slope. Landslides, 18(3), 881–895. https://doi.org/10.1007/s10346-020-01560-z
  38. Liu, P. L. F., Woo, S. B., & Cho, Y. S. (1998). Computer programs for tsunami propagation and inundation. Technical Report. Cornell University, Ithaca, New York.
  39. Liu, F., Wu, T.-R., Raichlen, F., Synolakis, C. E., & Borrero, J. C. (2005). Runup and rundown generated by three-dimensional sliding masses. Journal of Fluid Mechanics, 536(1), 107–144. https://doi.org/10.1017/S0022112005004799
  40. Losada, I. J., Lara, J. L., & del Jesus, M. (2016). Modeling the interaction of water waves with porous coastal structures. Journal of Waterway, Port, Coastal, and Ocean Engineering, 142(6), 03116003
  41. Løvholt, F., Harbitz, C. B., & Haugen, K. (2005). A parametric study of tsunamis generated by submarine slides in the Ormen Lange/Storegga area off western Norway. In: Ormen Lange—An integrated study for safe field development in the Storegga submarine area (pp. 219–231). Elsevier. https://doi.org/10.1016/B978-0-08-044694-3.50023-8
  42. Løvholt, F., Bondevik, S., Laberg, J. S., Kim, J., & Boylan, N. (2017). Some giant submarine landslides do not produce large tsunamis. Geophysical Research Letters, 44(16), 8463–8472
  43. Løvholt, F. J. M. R., Griffin, J., & Salgado-Gálvez, M. A. (2022). Tsunami hazard and risk assessment on the global scale. Complexity in Tsunamis, Volcanoes, and their Hazards, 213–246
  44. Lynett, P., & Liu, P. L. F. (2005). A numerical study of the run-up generated by three-dimensional landslides. Journal of Geophysical Research: Oceans. https://doi.org/10.1029/2004JC002443
  45. Lynett, P. J., & Martinez, A. J. (2012). A probabilistic approach for the waves generated by a submarine landslide. Coastal Engineering Proceedings, 33, 15–15. https://doi.org/10.9753/icce.v33.currents.15
  46. McDonald, P. W. (1971). The computation of transonic flow through two-dimensional gas turbine cascades (Vol. 79825, p. V001T01A089). American Society of Mechanical Engineers
  47. Menter, F. R. (1992). Improved two-equation k-omega turbulence models for aerodynamic flows (No. A-92183). https://ntrs.nasa.gov/citations/19930013620
  48. Panizzo, A., De Girolamo, P., Di Risio, M., Maistri, A., & Petaccia, A. (2005). Great landslide events in Italian artificial reservoirs. Natural Hazards and Earth System Sciences, 5(5), 733–740. https://doi.org/10.5194/nhess-5-733-2005
  49. Paris, A. (2021). Comparison of landslide tsunami models and exploration of fields of application. Doctoral dissertation, Université de Pau et des Pays de l’Adour.
  50. Paris, A., Heinrich, P., & Abadie, S. (2021). Landslide tsunamis: Comparison between depth-averaged and Navier–Stokes models. Coastal Engineering, 170, 104022. https://doi.org/10.1016/j.coastaleng.2021.104022
  51. Pelinovsky, E., & Poplavsky, A. (1996). Simplified model of tsunami generation by submarine landslides. Physics and Chemistry of the Earth, 21(1–2), 13–17. https://doi.org/10.1016/S0079-1946(97)00003-7
  52. Rauter, M., Hoße, L., Mulligan, R. P., Take, W. A., & Løvholt, F. (2021). Numerical simulation of impulse wave generation by idealized landslides with OpenFOAM. Coastal Engineering, 165, 103815. https://doi.org/10.1016/j.coastaleng.2020.103815
  53. Rauter, M., Viroulet, S., Gylfadóttir, S. S., Fellin, W., & Løvholt, F. (2022). Granular porous landslide tsunami modelling–the 2014 Lake Askja flank collapse. Nature Communications, 13(1), 678. https://doi.org/10.1038/s41467-022-28356-2
  54. Romano, A., Bellotti, G., & Di Risio, M. (2013). Wavenumber–frequency analysis of the landslide-generated tsunamis at a conical island. Coastal Engineering, 81, 32–43. https://doi.org/10.1016/j.coastaleng.2013.06.007
  55. Romano, A., Lara, J., Barajas, G., Di Paolo, B., Bellotti, G., Di Risio, M., Losada, I., & De Girolamo, P. (2020a). Tsunamis generated by submerged landslides: Numerical analysis of the near-field wave characteristics. Journal of Geophysical Research: Oceans, 125(7), e2020JC016157. https://doi.org/10.1029/2020JC016157
  56. Romano, M., Ruggiero, A., Squeglia, F., Maga, G., & Berisio, R. (2020b). A structural view of SARS-CoV-2 RNA replication machinery: RNA synthesis, proofreading and final capping. Cells, 9(5), 1267.
  57. Sabeti, R., & Heidarzadeh, M. (2022a). Numerical simulations of water waves generated by subaerial granular and solid-block landslides: Validation, comparison, and predictive equations. Ocean Engineering, 266, 112853. https://doi.org/10.1016/j.oceaneng.2022.112853
  58. Sabeti, R., & Heidarzadeh, M. (2022b). Numerical simulations of tsunami wave generation by submarine landslides: Validation and sensitivity analysis to landslide parameters. Journal of Waterway, Port, Coastal, and Ocean Engineering, 148(2), 05021016. https://doi.org/10.1061/(ASCE)WW.1943-5460.0000694
  59. Takabatake, T., Han, D. C., Valdez, J. J., Inagaki, N., Mäll, M., Esteban, M., & Shibayama, T. (2022). Three-dimensional physical modeling of tsunamis generated by partially submerged landslides. Journal of Geophysical Research: Oceans, 127(1), e2021JC017826. https://doi.org/10.1029/2021JC017826
  60. Van Gent, M. R. A. (1995). Porous flows through rubble-mound material. Journal of waterway, port, coastal, and ocean engineering, 121(3), 176–181.
  61. Wang, X., & Liu, P. L. F. (2006). An analysis of 2004 Sumatra earthquake fault plane mechanisms and Indian Ocean tsunami. Journal of Hydraulic Research, 44, 147–154. https://doi.org/10.1080/00221686.2006.9521671
  62. Watts, P. (1998). Wavemaker curves for tsunamis generated by underwater landslides. Journal of Waterway, Port, Coastal, and Ocean Engineering, 124(3), 127–137. https://doi.org/10.1061/(ASCE)0733-950X(1998)124:3(127)
  63. Yin, Y., Zhang, C., Imamura, F., Harris, J. C., & Li, Z. (2015). Numerical analysis on wave generated by the Qianjiangping landslide in Three Gorges Reservoir. China. Landslides, 12(2), 355–364. https://doi.org/10.1007/s10346-015-0564-7
  64. Zaniboni, F., & Tinti, S. (2014). Numerical simulations of the 1963 Vajont landslide, Italy: application of 1D Lagrangian modelling. Natural hazards, 70, 567–592.
  65. Zhang, C., & Zhang, M. (2023). Numerical investigation of solitary wave attenuation and mitigation caused by vegetation using OpenFOAM. Coastal Engineering Journal, 65(2), 198–216. https://doi.org/10.1080/21664250.2022.2163844
Weir

Discharge Formula and Hydraulics of Rectangular Side Weirs in the Small Channel and Field Inlet

소규모 수로 및 유입구에서의 직사각형 측면 위어의 유량 공식 및 수리학

Yingying Wang, Mouchao Lv, Wen’e Wang, Ming Meng

Abstract

In this study, experimental investigations were conducted on rectangular side weirs with different widths and heights. Corresponding simulations were also performed to analyze hydraulic characteristics including the water surface profile, flow velocity, and pressure. The relationship between the discharge coefficient and the Froude number, as well as the ratios of the side weir height and width to upstream water depth, was determined. A discharge formula was derived based on a dimensional analysis. The results demonstrated good agreement between simulated and experimental data, indicating the reliability of numerical simulations using FLOW-3D software (version 11.1). Notably, significant fluctuations in water surface profiles near the side weir were observed compared to those along the center line or away from the side weir in the main channel, suggesting that the entrance effect of the side weir did not propagate towards the center line of the main channel. The proposed discharge formula exhibited relative errors within 10%, thereby satisfying the flow measurement requirements for small channels and field inlets.

1. Introduction

Sharp crested weirs are used to obtain discharge in open channels by solely measuring the water head upstream of the water. Side weirs, as a kind of sharp-crested weir, are extensively used for flow measurement, flow diversion, and flow regulation in open channels. Side weirs can be placed directly in the channel direction or field inlet, without changing the original structure of the channel. Thus, side weirs have certain advantages in the promotion and application of flow measurement facilities in small channels and field inlets. The rectangular sharp-crested weir is the most commonly available, and many scholars have conducted research on it.
Research on side weirs started in 1934. De Marchi studied the side weir in the rectangular channel and derived the theoretical formula based on the assumption that the specific energy of the main flow section of the rectangular channel in the side weir section was constant [1]. Ackers discussed the existing formulas for the prediction of the side weir discharge coefficient [2]. Chen concluded that the momentum theorem was more suitable for the analytical calculation of the side weir based on the experimental data [3]. Based on previous theoretical research, more and more scholars began to carry out experimental research on side weirs. Uyumaz and Muslu conducted experiments under subcritical and supercritical flow regimes and derived expressions for the side weir discharge and water surface profiles for these regimes by comparing them with experimental results [4]. Borghei et al. developed a discharge coefficient equation for rectangular side weirs in subcritical flow [5]. Ghodsian [6] and Durga and Pillai [7] developed a discharge coefficient equation of rectangular side weirs in supercritical flow. Mohamed proposed a new approach based on the video monitoring concept to measure the free surface of flow over rectangular side weirs [8]. Durga conducted experiments on rectangular side weirs of different lengths and sill heights and discussed the application of momentum and energy principles to the analysis of spatially varied flow under supercritical conditions. The results showed that the momentum principle was fitting better [7]. Omer et al. obtained sharp-crested rectangular side weirs discharge coefficients in the straight channel by using an artificial neural network model for a total of 843 experiments [9]. Emiroglu et al. studied water surface profile and surface velocity streamlines, and developed a discharge coefficient formula of the upstream Froude number, the ratios of weir length to channel width, weir length to flow depth, and weir height to flow depth [10]. Other investigators [11,12,13,14] have conducted experiments to study flow over rectangular side weirs in different flow conditions.
Numerous studies have been conducted in laboratories to this day. Compared to experimental methods, the numerical simulation method has many attractive advantages. We can easily obtain a wide range of hydraulic parameters of side weirs using numerical simulation methods, without investing a lot of manpower and resources. In addition, we can conduct small changes in inlet condition, outlet condition, and geometric parameters, and study their impact on the flow characteristics of side weirs. Therefore, with the development and improvement of computational fluid dynamics, the numerical simulation method has begun to be widely applied on side weirs. Salimi et al. studied the free surface changes and the velocity field along a side weir located on a circular channel in the supercritical regime by numerical simulation [15]. Samadi et al. conducted a three-dimensional simulation on rectangular sharp-crested weirs with side contraction and without side contraction and verified the accuracy of numerical simulation compared with the experimental results [16]. Aydin investigated the effect of the sill on rectangular side weir flow by using a three-dimensional computational fluid dynamics model [17]. Azimi et al. studied the discharge coefficient of rectangular side weirs on circular channels in a supercritical flow regime using numerical simulation and experiments [18]. The discharge coefficient over the two compound side weirs (Rectangular and Semi-Circle) was modeled by using the FLOW-3D software to describe the flow characteristics in subcritical flow conditions [19]. Safarzadeh and Noroozi compared the hydraulics and 3D flow features of the ordinary rectangular and trapezoidal plan view piano key weirs (PKWs) using two-phase RANS numerical simulations [20]. Tarek et al. investigated the discharge performance, flow characteristics, and energy dissipation over PK and TL weirs under free-flow conditions using the FLOW-3D software [21].
As evident from the aforementioned, the majority of studies have primarily focused on determining the discharge coefficient, while comparatively less attention has been devoted to investigating the hydraulic characteristics of rectangular side weirs. Numerical simulations were conducted on different types of side weirs, including compound side weirs and piano key weirs, in different cross-section channels under different flow regimes. It is imperative to derive the discharge formula and investigate other crucial flow parameters such as depth, velocity, and pressure near side weirs for their effective implementation in water measurement. In this study, a combination of experimental and numerical simulation methods was employed to examine the relationship between the discharge coefficient and its influencing factors; furthermore, a dimensionless analysis was utilized to derive the discharge formula. Additionally, water surface profiles near side weirs and pressure distribution at the bottom of the side channel were analyzed to assess safety operation issues associated with installing side weirs.

2. Principle of Flow Measurement

Flow discharge over side weirs is a function of different dominant physical and geometrical quantities, which is defined as

where Q is flow discharge over the side weir, b is the side weir width, B is the channel width, P is the side weir height, v is the mean velocity, h1 is water depth upstream the side weir in the main channel, g is the gravitational acceleration, μ is the dynamic viscosity of fluid, ρ is fluid density, and i is the channel slope (Figure 1).

Figure 1. Definition sketch of parameters of rectangular side weir under subcritical flow. Note: h1 and h2 represent water depth upstream and downstream of the side weir in the main channel, respectively; y1 and y2 represent weir head upstream and downstream of the side weir in the main channel, respectively.

In experiments when the upstream weir head was over 30 mm, the effects of surface tension on discharge were found to be minor [22]. The viscosity effect was far less than the gravity effect in a turbulent flow. Hence μ and σ were excluded from the analysis [23,24]. In addition, the channel width, the channel slope, and the fluid density were all constant, so the discharge formula can be simplified as:

According to the Buckingham π theorem, the following relationship among the dimensionless parameters is established:

Selected h1 and g as basic fundamental quantities, and the remaining physical quantities were represented in terms of these fundamental quantities as follows:

In which

Based on dimensional analysis, the following equations were derived.

Namely

So the discharge formula can be simplified as:

In a sharp-crested weir, discharge over the weir is proportional to 𝐻1.51H11.5 (H1 is the upstream total head above the crest, namely H1 = y1 + v2/2 g), so Equation (6) can be transformed as follows:

Consequently, the discharge formula over rectangular side weirs is defined as follows, in which 𝑚=𝑓(𝑏ℎ1m=f(bh1,𝑃ℎ1,𝐹𝑟1)Ph1,Fr1). Parameter m represents the dimensionless discharge coefficient. Parameter Fr1 represents the Froude number at the upstream end of the side weir in the main channel.

3. Experiment Setup

The experimental setup contained a storage reservoir, a pumping station, an electromagnetic flow meter, a control valve, a stabilization pond, rectangular channels, a side weir, and a sluice gate. The layout of the experimental setup is shown in Figure 2. Water was supplied from the storage reservoir using a pump. The flow discharge was measured with an electromagnetic flow meter with precision of ±3‰. Water depth was measured with a point gauge with an accuracy of ±0.1 mm. The flow velocity was measured with a 3D Acoustic Doppler Velocimeter (Nortek Vectrino, manufactured by Nortek AS in Rud, Norway). In order to eliminate accidental and human error, multiple measurements of the water depth and flow velocity at the same point were performed and the average values were used as the actual water depth and flow velocity of the point. The main and side channels were both rectangular open channels measuring 47 cm in width and 60 cm in height. The geometrical parameters of rectangular side weirs are shown in Table 1.

Figure 2. Layout of the test system.
Table 1. The geometrical parameters of rectangular side weirs.

When water passes through a side weir, its quality point is affected not only by gravity but also by centrifugal inertia force, leading to an inclined water surface within that particular cross-section before reaching the weir. In order to examine water profiles adjacent to side weirs, cross-sectional measurements were conducted at regular intervals of 12 cm both upstream and downstream of each side weir, denoted as sections ① to ⑩, respectively. Measuring points were positioned near the side weir (referred to as “Side I”), along the center line of the main channel (referred to as “Side II”), and far away from the side weir (referred to as “Side III”) for each cross-section. The schematic diagram illustrating these measuring points is presented in Figure 3.

Figure 3. Schematic diagram of measurement points.

4. Numerical Simulation Settings

4.1. Mathematical Model

4.1.1. Governing Equations

Establishing the controlling equations is a prerequisite for solving any problem. For the flow analysis problem of water flowing over a side weir in a rectangular channel, assuming that no heat exchange occurs, the continuity equation (Equation (9)) and momentum equation (Equation (10)) can be used as the controlling equations as follows:

The continuity equation:

Momentum equation:

where: ρ is the fluid density, kg/m3; t is time, s; ui, uj are average flow velocities, u1, u2, u3 represent average flow velocity components in Cartesian coordinates x, y, and z, respectively, m/s; μ is dynamic viscosity of fluid, N·s/m2; p is the pressure, pa; Si is the body force, S1 = 0, S2 = 0, S3 = −ρg, N [24].

4.1.2. RNG k-ε Model

The water flow in the main channel is subcritical flow. When the water flows through the side weir, the flow line deviates sharply, the cross section suddenly decreases, and due to the blocking effect of the side weir, the water reflects and diffracts, resulting in strong changes in the water surface and obvious three-dimensional characteristics of the water flow [25]. Therefore the RNG k–ε model is selected. The model can better handle flows with greater streamline curvature, and its corresponding k and ε equation is, respectively, as follows:

where: k is the turbulent kinetic energy, m2/s2; μeff is the effective hydrodynamic viscous coefficient; Gk is the generation item of turbulent kinetic energy k due to gradient of the average flow velocity; C∗1εC1ε*, C2ε are empirical constants of 1.42 and 1.68, respectively; ε is turbulence dissipation rate, kg·m2/s2.

4.1.3. TruVOF Model

Because the shape of the free surface is very complex and the overall position is constantly changing, the fluid flow phenomenon with a free surface is a typical flow phenomenon that is difficult to simulate. The current methods used to simulate free surfaces mainly include elevation function method, the MAC method [26] and the VOF (Volume of Fluid) method [27]. The VOF method is a method proposed by Hirt and Nichols to deal with the complex motion of the free surface of a fluid, which can describe all the complexities of the free surface with only one function. The basic idea of the method is to define functions αw and αa, which represent the volume percentage of the calculation area occupied by water and air, respectively. In each unit cell, the sum of the volume fractions of water and air is equal to 1, i.e.,

The TruVOF calculation method can accurately track the change of free liquid level and accurately simulate the flow problems with free interface. Its equation is:

where: u_¯m is the average velocity of the mixture; t is the time; F is the volume fraction of the required fluid.

4.2. Parameter Setting and Boundary Conditions

To streamline the iterative calculation and minimize simulation time, we selected a main channel measuring 7.5 m in length and a side channel measuring 2.5 m in length for simulation. Three-dimensional geometrical models were developed using the software AutoCAD (version 2016-Simplified Chinese). The spatial domain was meshed using a constructed rectangular hexahedral mesh and each cell size was 2 cm. A volume flow rate was set in the channel inlet with an auto-adjusted fluid height. An outflow–outlet condition was positioned at the end of the side channel. A symmetry boundary condition was set in the air inlet at the top of the model, which represented that no fluid flows through the boundary. The lower Z (Zmin) and both of the side boundaries were treated as a rigid wall (W). No-slip conditions were applied at the wall boundaries. Figure 4 illustrates these boundary conditions.

Figure 4. Diagram of boundary conditions.

5. Results

5.1. Water Surface Profiles

Water surface profiles were crucial parameters for selecting water-measuring devices. Upon analyzing the consistent patterns observed in different conditions, one specific condition was chosen for further analysis. To validate the reliability of numerical simulation, measured and simulated water depths of rectangular side weirs with different widths and heights at a discharge rate of 25 L/s were extracted for comparison (Table 2 and Figure 5). The results in Table 2 and Figure 5 indicate a maximum absolute relative error value of 9.97% and all absolute relative error values within 10%, demonstrating satisfactory agreement between experimental and simulated results.

Figure 5. Comparison between measured and simulated flow depth.
P/cmSection Positionb = 20 cmb = 30 cmb = 40 cmb = 47 cm
hm/cmhs/cmR/%hm/cmhs/cmR/%hm/cmhs/cmR/%hm/cmhs/cmR/%
7④21.4919.49.7317.7416.94.7416.0714.519.7113.7912.509.35
④′20.4819.056.9817.7816.149.2215.6914.318.80
⑥20.7119.028.1617.8216.318.4715.9214.538.7315.2313.809.39
⑧′22.0020.228.0918.2716.748.3716.5914.969.83
⑧22.3720.179.8317.7316.805.2516.2715.087.3115.3614.366.51
10④24.1522.66.4219.9618.845.6119.0318.582.3616.8315.855.82
④′24.2122.058.9219.4918.196.6718.7518.352.13
⑥24.0121.789.2919.6518.346.6718.9518.631.6917.5216.098.16
⑧′24.8822.49.9720.6519.216.9720.1219.294.13
⑧24.0322.964.4521.1619.348.6019.7119.431.4218.3917.365.60
15④28.8527.564.4725.8624.096.8424.0521.898.9822.7320.808.49
④′28.4926.975.3425.1923.845.3623.4221.468.37
⑥28.8526.986.4825.7223.996.7323.2321.826.0723.1021.058.87
⑧′28.9627.305.7326.3824.198.3024.1822.277.90
⑧29.1827.964.1826.5724.547.6424.5722.339.1223.2021.109.05
20④33.2932.342.8530.6329.025.2628.4926.875.6926.9925.814.37
④′33.1431.953.5929.7528.623.8028.1126.794.70
⑥33.3231.794.5930.0428.455.2928.9926.867.3527.4226.722.55
⑧′34.0232.394.7930.6928.955.6729.5927.257.91
⑧34.6232.845.1431.4429.296.8429.5127.317.4628.2127.004.29
Table 2. Comparison of measured and simulated water depths on Side I of each side weir at a discharge of 25 L/s

Due to the diversion caused by the side weir, there was a rapid variation in flow near the side weir in the main channel. In order to investigate the impact of the side weir on water flow in the main channel, water surface profiles on Side I, Side II, and Side III were plotted with a side weir width and height both set at 20 cm at a discharge rate of 25 L/s (Figure 6). As depicted in Figure 6, within a certain range of the upstream end of the main channel, water depths on Side I, Side II, and Side III were nearly equal with almost horizontal profiles. As the distance between the location of water flow and the upstream end of the weir crest decreased gradually, there was a gradual decrease in water depth on Side I along with an inclined trend in its corresponding profile; however, both Side II and Side III still maintained almost horizontal profiles. When approaching closer to the side weir area with flowing water, there was an evident reduction in water depth on Side I accompanied by a significant downward trend visible across an expanded decline range. The minimum point occurred near the upstream end of the weir crest before gradually increasing again towards downstream sections. At the crest section of the side weir, there is an upward trend observed in the water surface. The water surface tended to stabilize downstream of the main channel within a certain range from the downstream end of the weir crest. There was no significant change in the water surface profiles of Side Ⅱ and Side Ⅲ in the crest section. It can be inferred that the side weir entrance effect occurred only between Side Ⅰ and Side Ⅱ. M. Emin reported the same pattern [10].

Figure 6. Water surface profiles on Side I, Side II, and Side III with a side weir width of 20 cm and height of 15 cm at a discharge of 25 L/s.

For a more accurate study on the entrance effect of the side weir on the Water Surface Profile (WSP) for Side I; a comparative analysis conducted using different widths but the same height (15 cm) at a discharge rate of 25 L/s is presented through Figure 7, Figure 8, Figure 9 and Figure 10.

Figure 7. Water surface profile on Side Ⅰ with a side weir width of 20 cm and height of 15 cm at a discharge of 25 L/s.
Figure 8. Water surface profile on Side Ⅰ with a side weir width of 30 cm and height of 15 cm at a discharge of 25 L/s.
Figure 9. Water surface profile on Side Ⅰ with a side weir width of 40 cm and height of 15 cm at a discharge of 25 L/s.
Figure 10. Water surface profile on Side Ⅰ with a side weir width of 47 cm and height of 15 cm at a discharge of 25 L/s.

According to Figure 7, Figure 8, Figure 9 and Figure 10, the water depth upstream of the main channel started to decrease as it approached the upstream end of the weir crest and then gradually increased at the weir crest section. In other words, the water surface profile exhibited a backwater curve along the length of the weir crest. The water depth remained relatively stable downstream of the main channel within a certain range from the downstream end of the weir crest. Additionally, there was a higher water depth downstream of the main channel compared to that upstream of the main channel. Furthermore, an increase in the width of the side weir led to a gradual reduction in fluctuations on its water surface.

5.2. Velocity Distribution

The law of flow velocity distribution near the side weir is the focus of research and analysis, so the simulated and measured values of flow velocity near the side weir were compared and analyzed. Take the discharge of 25 L/s, the height of 15 cm, and the width of 30 cm of the side weir as an example to illustrate. Figure 11 shows the measured and simulated velocity distribution in the x-direction of cross-section ④. As can be seen from Figure 11, the diagrams of the measured and simulated velocity distribution were relatively consistent, and the maximum absolute relative error between the measured and simulated values at the same measurement point was 9.37%, and the average absolute relative error was 3.97%, which indicated a satisfactory agreement between the experimental and simulated results.

Figure 11. Velocity distribution in the x-direction of section ④: when the discharge is 25 L/s, the height of the side weir is 15 cm and the width of the side weir is 30 cm. (a) Measured velocity distribution; (b) Simulated velocity distribution.

From Figure 11, it can be seen that the flow velocity gradually increased from the bottom of the channel towards the water surface in the Z-direction, and the flow velocity gradually increased from Side Ⅲ to Side Ⅰ in the Y-direction. The maximum flow velocity occurred near the weir crest.

Figure 12 shows the distribution of flow velocity at different depths (z/P = 0.3, z/P = 0.8, z/P = 1.6) with a side weir width of 30 cm and height of 15 cm at a discharge of 25 L/s. The water flow line began to bend at a certain point upstream of the main channel, and the closer it was to the upstream end of the weir crest, the greater the curvature. The maximum curvature occurred at the downstream end of the weir crest. The flow patterns at the bottom, near the side weir crest, and above the side weir crest were significantly different. There was a reverse flow at the bottom of the main channel, where the forward and reverse flows intersect, resulting in a detention zone. The maximum flow velocity at the bottom layer occurred at the upstream end of the side weir crest. When the location of water flow approached the weir crest, the maximum flow velocity occurred at the upstream end of the weir crest. The maximum flow velocity on the water surface occurred at the downstream end of the weir crest. As the water depth decreased, the position of the maximum flow velocity gradually moved from the upstream end of the side weir to the downstream end of the side weir.

Figure 12. Distribution of flow velocity at different depths with a side weir width of 30 cm and height of 15 cm at a discharge of 25 L/s. (a) z/P = 0.3; (b) z/P = 0.8; (c) z/P = 1.6.

5.3. Side Channel Pressure Distribution

When water flowed through the side weir, an upstream water level was formed, resulting in a pressure zone at the junction with the side channel. This pressure zone led to increased water pressure on the floor of the side channel, which affected its stability and durability. In small channels or fields where erosion resistance is weak, excessive pressure can cause scour holes. Therefore, analyzing the pressure distribution in the side channel is necessary to select an appropriate height and width for the side weir that effectively reduces its impact on the bottom plate.

To investigate the impact of side weir width on hydraulic characteristics, pressure data was collected at a discharge rate of 25 L/s for side weirs with heights of 20 cm and widths ranging from 20 cm to 47 cm. The pressure distribution map was drawn, as shown in Figure 13.

Figure 13. Comparison of pressure distribution on the bottom plate of the side channel with different widths of side weirs when the discharge is 25 L/s and the height of side weirs is 20 cm. (a) P = 20 cm, b = 20 cm; (b) P = 20 cm, b = 30 cm; (c) P = 20 cm, b = 40 cm; (d) P = 20 cm, b = 47 cm.

As can be seen from Figure 13, the pressure at the bottom of the side channel decreased as the width of the side weir increased. This uneven distribution of water flow on the weir was caused by the sharp bending of water flow lines and the influence of centrifugal inertia force over a short period. After passing through the side weir, the water flow became symmetrically distributed with respect to the axis of the side channel, leaning towards the right bank at a certain distance. As we increased the width of the side weir, we noticed that its position gradually approached the side weir and maximum pressure decreased at this location where the water tongue formed due to flowing through it (Figure 13). For a constant height (20 cm) but varying widths (20 cm, 30 cm, 40 cm, and 47 cm), we measured maximum pressures at these positions as follows: 103,713 Pa, 103,558 Pa, 103,324 Pa, and 103,280 Pa, respectively. Consequently, increasing width reduced the impact on the side channel from water flowing through it while changing pressure distribution from concentration to dispersion in a vertical direction. In the practical application of side weirs, appropriate height should be selected based on the bottom plate’s capacity to withstand the pressure exerted by flowing water within channels.

To investigate how height affects the hydraulic characteristics of rectangular side weirs further (Figure 14), we extracted pressures on bottom plates when discharge was fixed at 25 L/s while varying heights were set as follows: 7 cm, 10 cm, 15 cm, and 20 cm, respectively.

Figure 14. Comparison of pressure distribution on the bottom plate of the side channel with different heights of side weirs when discharge is 25 L/s and the width of side weirs is 20 cm. (a) P = 7 cm, b = 20 cm; (b) P = 10 cm, b = 20 cm; (c) P = 15 cm, b = 20 cm; (d) P = 20 cm, b = 20 cm.

As shown in Figure 14, when the width of the side weir was constant, the pressure at the bottom of the side channel increased with the height of the side weir. As the height of the side weir increased, the water tongue formed by flow through the side weir gradually moved away from it in a downstream direction. In terms of vertical water flow, as the height of the side weir increased, the position of maximum pressure at which the water tongue falls shifted closer to the axis of the side channel from its right bank. Moreover, an increase in height resulted in higher maximum pressure at this falling point. For a constant width (20 cm) and varying heights (7 cm, 10 cm, 15 cm, and 20 cm), corresponding maximum pressures at this landing point were measured as 102,422 Pa, 102,700 Pa, 103,375 Pa, and 103,766 Pa, respectively. Consequently, increasing width led to a greater impact on both flow through and pressure distribution within the side channel; transforming it from scattered to concentrated along its lengthwise direction. Therefore, when applying such weirs practically one should select an appropriate width based on what pressure can be sustained by their respective channel bottom plates.

5.4. Discharge Coefficient

Based on dimensionless analysis, the influencing parameters of the discharge coefficient were obtained. To study the effect of parameters Fr1, b/h1, and P/h1, discharge coefficient values were plotted against Fr1, b/h1, and P/h1, shown in Figure 15, Figure 16 and Figure 17. The discharge coefficient decreased as parameters Fr1 and b/h1 increased. The discharge coefficient increased as parameter P/h1 increased. As Uyumaz and Muslu reported in a previous study, the variation of the discharge coefficient with respect to the Froude number showed a second-degree curve for a subcritical regime [4].

Figure 15. Variation of discharge coefficient values against Froude number.
Figure 16. Variation of discharge coefficient values against the percentage of the side weir width to the upstream flow depth over the side weir.
Figure 17. Variation of discharge coefficient values against the percentage of the side weir height to the upstream flow depth over the side weir.

Quantitative analysis between discharge coefficient values and parameters Fr1, b/h1, and P/h1 was conducted using data analysis software (IBM SPSS Statistics 19). The various coefficients obtained are shown in Table 3.

ModelUnstandardized CoefficientsStandardized CoefficientstSig
BStd. ErrorBeta (β)
Constant−1.2940.155−8.3690.000
Fr13.4300.2863.40112.0130.000
b/h1−0.0040.004−0.045−0.9440.348
P/h12.4010.1674.06414.3940.000
Table 3. Coefficient.

The value of t and Sig are the significance results of the independent variable, and the value of Sig corresponding to the value of t is less than 0.05, indicating that the independent variable has a significant impact on the dependent variable. Therefore, the values of Sig corresponding to the parameters Fr1 and P/h1 were less than 0.05, indicating that the parameters Fr1 and P/h1 have a significant impact on the discharge coefficient. On the contrary, the parameter b/h1 has less impact on the discharge coefficient. Therefore, quantitative analysis between discharge coefficient values and parameters Fr1, and P/h1 was conducted using data analysis software by removing factor b/h1. The model summary, ANOVA, and coefficient obtained are shown respectively in Table 4, Table 5 and Table 6. R and adjusted R square in Table 4 were approaching 1, which indicated the goodness of fit of the regression model was high. The value of Sig corresponding to the value of F in Table 5 was less than 0.05, which indicated that the regression equation was useful. The values of Sig corresponding to the parameters Fr1 and P/h1 in Table 6 were less than 0.05, indicating that the parameters Fr1 and P/h1 have a significant impact on the discharge coefficient.

ModelRR SquareAdjusted R SquareStd. Error of the Estimate
10.913 a0.8330.8290.03232
Table 4. Model Summary b. Note: a. Predictors:(Constant), Fr1, P/h1; b. Discharge coefficient.
ModelSum of SquaresdfMean SquareFSig
1Regression0.40220.201192.5450.000 a
Residual0.080770.001
Total0.48379
Table 5. ANOVA b. Note: a. Predictors:(Constant), Fr1, P/h1; b. Discharge coefficient.
ModelUnstandardized CoefficientsStandardized CoefficientstSig
BStd. ErrorBeta (β)
Constant−1.3260.151−8.7960.000
Fr13.4790.2813.44912.3960.000
P/h12.4270.1644.10814.7650.000
Table 6. Coefficient a. Note: a. Predictors:(Constant), Fr1, P/h1.

Based on the above analysis, the flow coefficient formula has been obtained, shown as follows:

Discharge formula were obtained by substituting Equation (15) into Equation (12), as shown in Equation (16).

where Q ∈ [0.006, 0.030], m3/s; b ∈ [0.20, 0.47], m; P ∈ [0.07, 0.20], m.

Figure 18 showed the measured discharge coefficient values with those calculated from discharge formulas in Table 3. The scatter of the data with respect to perfect line was limited to ±10%.

Figure 18. Comparison of the measured discharge coefficient values with those calculated from discharge formulas in Table 3.

6. Discussions

Determining water surface profile near the side weir in the main channel is one of the tasks of hydraulic calculation for side weirs. As the water flows through the side weir, discharge in the main channel is gradually decreasing, namely dQ/ds<0. According to the Equation (17) derived from Qimo Chen [3], it can be inferred that the value of 𝑑ℎ/𝑑𝑠 is greater than zero in subcritical flow (Fr < 1), that is, the water surface profile near the side weir in the main channel is a backwater curve. Due to the side weir entrance effect at the upstream end, water surface profiles drop slightly at the upstream end of the side weir crest, as EI-Khashab [28] and Emiroglu et al. [29] reported in previous experimental studies.

In this study, the water surface profile exhibited a backwater curve along the length of the weir crest. Therefore, during side weir application, it is crucial to ensure that downstream water levels do not exceed the highest water level of the channel.

The head on the weir is one of the important factors that flow over side weirs depends on. At the same time, the head depends on the water surface profile near the side weir in the main channel. Therefore, further research on the quantitative analysis of water surface profile needs to be conducted. Mohamed Khorchani proposed a new approach based on the video monitoring concept to measure the free surface of flow over side weirs. It points out a new direction for future research [8].

The maximum flow velocity, a key parameter in assessing the efficiency of a weir, occurs at the upstream end of the weir crest, typically near the crest. This is attributed to the convergence of the flow as it approaches the crest, resulting in a significant increase in velocity. It was found that in this study the minimum flow velocity occurred at the bottom of the main channel away from the side weir. Under such conditions, the accumulation of sediments could lead to siltation, which in turn can affect the accuracy of flow measurement through side weirs. This is because the presence of sediments can alter the flow patterns and cause errors in the measurement. Therefore, it becomes crucial to explore methods to optimize the selection of side weirs in order to minimize or eliminate the effects of sedimentation on flow measurement.

Pressure distribution plays a crucial role in ensuring structural safety for side weirs since small channels and field inlets have relatively limited pressure-bearing capacities. Therefore, it is important to select an appropriate geometrical parameter of rectangular side weirs based on their ability to withstand the pressure exerted on their bottom combined with pressure distribution data at the bottom of the side channel we have obtained in this study.

The discharge coefficient formula (Equation (15)), which incorporates Fr1 and P/h1, was derived based on dimensional analysis. However, it is worth noting that previous research has contradicted this formula by suggesting that the discharge coefficient solely depends on the Froude number. This conclusion can be observed in this study such as in Equations (18)–(23) in Table 7 of the manuscript [30,31,32,33,34,35], which clearly demonstrate the dependency of the discharge coefficient on the Froude number. In contrast, our derived discharge coefficient formula (Equation (15)) offers a more streamlined and simplified approach compared to Equation (25) [36] and Equation (29) [10]—making it easier to comprehend and apply—an advantageous feature particularly valuable in fluid dynamics where intricate calculations can be time-consuming. Furthermore, our derived discharge coefficient formula (Equation (15)) exhibits a broader application scope than that of Equation (24) [37] as shown in Table 8. Equation (26) [38] and Equation (27) [5] are specifically applicable under high flow discharge conditions. Conversely, our derived discharge coefficient formula (Equation (15)) is better suited for low-flow discharge conditions.

Table 7. Discharge coefficient formulas of rectangular side weirs presented in previous studies.
Discharge/(L·s−1)Width of Side Weir/cmHeight of Side Weir/cmNumber of Formula
10~1410~206~12(24)
35–10020~751~19(26), (27)
6~3020~477~20(15)
Table 8. Application scope of discharge coefficient formulas.

In addition to the factors studied in the paper, factors such as the sediment content in the flow, the bottom slope, and the cross-section shape of the channel also have a certain impact on the hydraulic characteristics of the side weir. Further numerical simulation methods can be used to study the hydraulic characteristics and the influencing factors of the side weir. Water measurement facilities generally require high accuracy of water measurement, the flow of sharp-crested side weirs is complex, and the water surface fluctuates greatly. While conducting numerical simulations, experimental research on prototype channels is necessary to ensure the reliability of the results and provide reference for the body design and optimization of side weirs in small channels and field inlets.

7. Conclusions

This paper presents a comprehensive study that encompasses both experimental and numerical simulation research on rectangular side weirs of varying heights and widths within rectangular channels. A thorough analysis of the experimental and numerical simulation results has been conducted, leading to the derivation of several notable conclusions:

  1. A comparative analysis was conducted on the measured and simulated values of water depth and flow velocity. Both of the maximum absolute relative errors were within 10%, which indicated that the numerical simulation of the side weir was feasible and effective.
  2. The water surface profile exhibited a backwater curve along the length of the weir crest. The side weir entrance effect occurred only between Side Ⅰ and Side Ⅱ. This indicates that flow patterns and associated hydraulic forces at the weir entrance play a crucial role in determining water level distribution along the weir crest.
  3. The maximum flow velocity of the cross-section at the upstream end of the weir crest occurred near the weir crest, while the minimum flow velocity occurred at the bottom of the main channel away from the side weir. As the water depth decreased, the position of the maximum flow velocity gradually moved from the upstream end of the side weir to the downstream end of the side weir.
  4. When the height of the side weir remains constant, an increase in the width of the side weir leads to a decrease in pressure at the bottom of the side channel. Conversely, when the width of the side weir is kept constant, an increase in its height results in an increase in pressure at the bottom of the side channel. Therefore, during practical applications involving side weirs, it is crucial to select an appropriate weir width based on the maximum pressure that can be sustained by the channel’s bottom plate.
  5. The discharge coefficient was found to depend on the upstream Froude number Fr1 and the percentage of the side weir height to the upstream flow depth over the side weir P/h1. The relationship between the discharge coefficient and parameters Fr1 and P/h1 was obtained using multiple regression analysis, which was of linear form and provided an easy means to estimate the discharge coefficient. The discharge formula is of high accuracy with relative errors within 10%, which met the water measurement accuracy requirements of small channels in irrigation areas.

Reference

  1. De Marchi, G. Essay on the performance of lateral weirs. L’Energ Electr. 1934, 11, 849.
  2. Ackers, P. A theoretical consideration of side weirs as storm water overflows. Proc. Inst. Civ. Eng. 1957, 6, 250–269.
  3. Chen, Q.M.; Xie, P.Z.; Chen, Q.R. Experiment on hydraulic characteristics of side weir. J. Fuzhou Univ. 1979, 19, 26–29.
  4. Uyumaz, A.; Muslu, Y. Flow over side weir in circular channels. ASCE J. Hydraul. Eng. 1985, 111, 144–160.
  5. Borghei, M.; Jalili, M.R.; Ghodsian, M. Discharge coefficient for sharp-crested side weir in subcritical flow. ASCE J. Hydraul. Eng. 1999, 125, 1051–1056.
  6. Ghodsian, M. Supercritical flow over rectangular side weir. Can. J. Civ. Eng. 2003, 30, 596–600.
  7. Durga Rao, K.H.V.; Pillai, C.R.S. Study of Flow Over Side Weirs Under Supercritical Conditions. Water Resour Manag. 2008, 22, 131–143.
  8. Khorchani, M.; Blanpain, O. Free surface measurement of flow over side weirs using the video monitoring concept. Flow Meas. Instrum. 2004, 15, 111–117.
  9. Bilhan, O.; Emiroglu, M.E.; Kisi, O. Application of two different neural network techniques to lateral outflow over rectangular side weirs located on a straight channel. Adv. Eng. Softw. 2010, 41, 831–837.
  10. Emiroglu, M.E.; Agaccioglu, H.; Kaya, N. Discharging capacity of rectangular side weirs in straight open channels. Flow Meas. Instrum. 2011, 22, 319–330.
  11. Azza, N.; Al-Talib, A.N. Flow over oblique side weir. J. Damascus Univ. 2012, 28, 15–22.
  12. Bagheri, S.; Kabiri-Samani, A.R.; Heidarpour, M. Discharge coefficient of rectangular sharp-crested side weirs part i: Traditional weir equation, Flow Measure. Instrumentation 2014, 35, 109–115.
  13. Shariq, A.; Hussain, A.; Ansari, M.A. Lateral flow through the sharp crested side rectangular weirs in open channels. Flow Measure. Instrumentation 2018, 59, 8–17.
  14. Li, G.D.; Shen, G.Y.; Li, S.S.; Lu, Q.N. Prediction Model of Side Weir Discharge Capacity Based on LS-SVM. J. Basic Sci. Eng. 2023, 4, 843–851.
  15. Shabanlou, S.; Salimi, M.S. Free surface and velocity field in a circular channel along the side weir in supercritical flow conditions. Flow Meas. Instrum. 2014, 38, 108–115.
  16. Samadi, A.; Arvanaghi, H.; Abbaspour, A. Three-Dimensional Simulation of Free Surface Flow over Rectangular Sharp crested Weirs. Int. J. Agric. Biosci. 2015, 4, 83–86.
  17. Aydin, M.C. Investigation of a Sill Effect on Rectangular Side-Weir Flow by Using CFD. J. Irrig. Drain. Eng. 2016, 142.
  18. Azimi, H.; Shabanlou, S.; Ebtehaj, I.; Bonakdari, H. Discharge Coefficient of Rectangular Side Weirs on Circular Channels. Int. J. Nonlinear Sci. Numer. Simul. 2016, 17, 391–399.
  19. Khassaf, S.I.; Attiyah, A.N.; Al-Yousify, H.A. Experimental investigation of compound side weir with modeling using computational fluid dynamic. Energy Environ. 2018, 7, 169–178.
  20. Safarzadeh, A.; Noroozi, B. 3D Hydrodynamics of Trapezoidal Piano Key Spillways. Int. J. Civ. Eng. 2017, 15, 89–101.
  21. Selim, T.; Hamed, A.K.; Elkiki, M.; Eltarabily, M.G. Numerical investigation of flow characteristics and energy dissipation over piano key and trapezoidal labyrinth weirs under free-flow conditions. Model. Earth Syst. Environ. 2023, 10, 1253–1272.
  22. Novak, P.; Cabelka, J. Models in Hydraulic Engineering; Pitman: London, UK, 1981.
  23. Henderson, F.M. Open Channel Flow; Prentice-Hall: Englewood Cliffs, NJ, USA, 1966.
  24. Wang, F.J. Computational Fluid Dynamics Analysis-Theory and Application of CFD; Tsinghua University Press: Beijing, China, 2004.
  25. Zhu, Y.L.; Ma, X.Y.; Zhan, G.L.; Lv, J.W. Numerical simulation of flow in flat V-weir. Yellow River 2010, 32, 99–100.
  26. Harlow, F.H.; Welch, J.E. Numberical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 1965, 8, 2182–2189.
  27. Hirt, C.W.; Nichols, B.D. Volume of fluid (VOF) method for dynamics of free boundaries. Phys. Fluids 1981, 39, 201–221.
  28. El-Khashab, A.M.M. Hydraulics of Flow over Side Weirs. Ph.D. Thesis, University of Southampton, Southampton, UK, 1975.
  29. Emiroglu, M.E.; Kaya, N.; Agaccioglu, H. Discharge capacity of labyrinth side-weir located on a straight channel. ASCE J. Irrig. Drain. Eng. 2010, 136, 37–46.
  30. Subramanya, K.; Awasthy, S.C. Spatially varied flow over side weirs. ASCE J. Hydraul. Div. 1972, 98, 1–10.
  31. Nandesamoorthy, T.; Thomson, A. Discussion of spatially varied flow over side weir. ASCE J. Hydraul. Eng. 1972, 98, 2234–2235.
  32. Yu-Tech, L. Discussion of spatially varied flow over side weir. ASCE J. Hydraul. Div. 1972, 98, 2046–2048.
  33. Ranga Raju, K.G.; Prasad, B.; Grupta, S.K. Side weir in rectangular channel. ASCE J. Hydraul. Div. 1979, 105, 547–554.
  34. Hager, W.H. Lateral outflow over side weirs. ASCE J. Hydraul. Eng. 1987, 113, 491–504.
  35. Cheong, H.F. Discharge coefficient oflateral diversion from trapezoidal channel. ASCE J. Irrig. Drain. Eng. 1991, 117, 321–333.
  36. Swamee, P.K.; Santosh, K.P.; Masoud, S.A. Side weir analysis using elementary discharge coefficient. ASCE J. Irrig. Drain. Eng. 1994, 120, 742–755.
  37. Singh, R.; Manivannan, D.; Satyanarayana, T. Discharge coefficient of rectangular side weirs. ASCE J. Irrig. Drain. Eng. 1994, 120, 814–819.
  38. Jalili, M.R.; Borghei, S.M. Discussion of Discharge coefficient of rectangular side weir. ASCE J. Irrig. Drain. Eng. 1996, 122, 132.

Three-dimensional flow structure in a confluence-bifurcation unit

합류 분기 유닛의 3차원 유동 구조

Di Wang, Xiaoyong Cheng, Zhixuan Cao, Jinyun Deng

Abstract

Enhanced understanding of flow structure in braided rivers is essential for river regulation, flood control, and infrastructure safety across the river. It has been revealed that the basic morphological element of braided rivers is confluence-bifurcation units. However, flow structure in these units has so far remained poorly understood with previous studies having focused mainly on single confluences/bifurcations. Here, the flow structure in a laboratory-scale confluence-bifurcation unit is numerically investigated based on the FLOW–3D® software platform. Two discharges are considered, with the central bars submerged or exposed respectively when the discharge is high or low. The results show that flow convergence and divergence in the confluence-bifurcation unit are relatively weak when the central bars are submerged. Based on comparisons with a single confluence/bifurcation, it is found that the effects of the upstream central bar on the flow structure in the confluence-bifurcation unit reign over those of the downstream central bar. Concurrently, the high-velocity zone in the confluence-bifurcation unit is less concentrated than that in a single confluence while being more concentrated than that observed in a single bifurcation. The present work unravels the flow structure in a confluence-bifurcation unit and provides a unique basis for further investigating morphodynamics in braided rivers.

1 Introduction

Confluences and bifurcations commonly exist in alluvial rivers and usually are important nodes of riverbed planform (Szupiany et al., 2012; Hackney et al., 2018). Flow convergence and divergence in these junctions result in highly three-dimensional (3D) flow characteristics, which greatly influence sediment transport, and hence riverbed evolution and channel formation (Le et al., 2019; Xie et al., 2020). Braided rivers, characterized by unstable networks of channels separated by central bars (Ashmore, 2013), have confluence-bifurcation units as their basic morphological elements (Ashmore, 1982; 1991; 2013; Federici & Paola, 2003; Jang & Shimizu, 2005). In particular, confluence-bifurcation units exhibit a distinct morphology from single confluences/bifurcations and bifurcation-confluence regions because two adjacent central bars are included. Within a confluence-bifurcation unit, two tributaries converge at the upstream bar tail and soon diverge to two anabranches again at the downstream bar head. Therefore, the flow structure in the unit may be significantly influenced by both the two central bars, and thus considerably different from that in single confluences, single bifurcations, and bifurcation-confluence regions, where the flow is affected by only one central bar. Enhanced understanding of flow structure in confluence-bifurcation units is urgently needed, which is essential for water resources management, river regulation, flood control, protection of river ecosystems and the safety of infrastructures across the rivers such as bridges, oil pipelines and communication cables (Redolfi et al., 2019; Ragno et al., 2021).

The flow dynamics, turbulent coherent structures, and turbulent characteristics in single confluences have been widely studied since the 1980s (Yuan et al., 2022). Flow dynamics at river channel confluences have been systematically and completely analyzed, which can be characterized by six major regions of flow stagnation, flow deflection, flow separation, maximum velocity, flow recovery and distinct shear layers (Best, 1987). For example, the field observation of Roy et al. (1988) and Roy and Bergeron (1990) highlighted the flow separation zones and recirculation at downstream natural confluence corners. Ashmore et al. (1992) measured the flow field in a natural confluence and found flow accelerates suddenly at the confluence junction with two separated high-velocity cores merging into one single core at the channel centre. De Serres et al. (1999) investigated the three-dimensional flow structure at a river confluence and identified the existence of the mixing layer, stagnation zones, separation zones and recovery zones. Sharifipour et al. (2015) numerically studied the flow structure in a 90° single confluence and found that the size of the separation zone decreases with the width ratio between the tributary and the main channel. Recently, three main classes of large-scale turbulent coherent structures (Duguay et al., 2022) have been presented, i.e. vertical-orientated vortices or Kelvin-Helmholtz instabilities (Rhoads & Sukhodolov, 2001; Constantinescu et al., 2011; 2016; Biron et al., 2019), channel-scale ‘back-to-back’ helical cells, (Mosley, 1976; Ashmore, 1982; Ashmore et al., 1992; Ashworth, 1996; Best, 1987; Rhoads & Kenworthy, 1995; Bradbrook et al., 1998; Lane et al., 2000), and smaller, strongly coherent streamwise-orientated vortices (Constantinescu et al., 2011; Sukhodolov & Sukhodolova, 2019; Duguay et al., 2022). However, no consensus on a universal turbulent coherent structure mode has been reached so far (Duguay et al., 2022). In addition, some studies (Ashworth, 1996; Constantinescu et al., 2011; Sukhodolov et al., 2017; Le et al., 2019; Yuan et al., 2023) have focused on turbulent characteristics, e.g. turbulent kinetic energy, turbulent dissipation rate and Reynolds stress, which can be critical parameters to further explaining the diversity of these turbulent coherent structure modes.

Investigations on the flow structure in single bifurcations have mainly focused on hydrodynamics in anabranches (Hua et al., 2009; van der Mark & Mosselman, 2013; Iwantoro et al., 2022) and around bifurcation bars (McLelland et al., 1999; Bertoldi & Tubino, 2005; 2007; Marra et al., 2014), whereas few studies have considered the effects of bifurcations on the upstream flow structure. Thomas et al. (2011) found that the velocity core upstream of the bifurcation is located near the water surface and towards the channel center in experimental investigations of a Y-shaped bifurcation. Miori et al. (2012) simulated flow in a Y-shaped bifurcation and found two circulation cells upstream of the bifurcation with flow converging at the water surface and diverging near the bed. Szupiany et al. (2012) reported velocity decreasing and back-to-back circulation cells upstream of the bifurcation junction in the field observation of a bifurcation of the Rio Parana River. These investigations provide insight into how bifurcations affect the flow patterns upstream, yet there is a need for further research on the dynamics of flow occurring immediately before the bifurcation junction.

Generally, the findings of studies on bifurcation-confluence regions are similar to those concerning single confluences and bifurcations. Hackney et al. (2018) measured the hydrodynamic characteristics in a bifurcation-confluence of the Mekong River and found the velocity cores located at the channel centre and strong secondary current occurring under low discharges. Le et al. (2019) reported a high-turbulent-kinetic-energy (high-TKE) zone located near the bed in their numerical simulation of flow in a natural bifurcation-confluence region. Moreover, a stagnation zone was found upstream of the confluence and back-to-back secondary current cells were detected at the confluence according to Xie et al. (2020) and Xu et al. (2022). Overall, these studies have further unraveled the flow patterns in river confluences and bifurcations.

Unfortunately, limited attention has been paid to the flow structure in confluence-bifurcation units. Parsons et al. (2007) investigated a large confluence-bifurcation unit in Rio Parana, Argentina, and no classical back-to-back secondary current cells were observed under a discharge of 12000 m3·s−1. To date, the differences in flow structure between confluence-bifurcation units and single confluences/bifurcations have remained far from clear. In addition, although the effects of discharge on flow structure have been investigated in several studies on single confluences/bifurcations, (Hua et al., 2009; Le et al., 2019; Luz et al., 2020; Xie et al., 2020; Xu et al., 2022), cases with fully submerged central bars were not considered, which is typical in braided rivers during floods. In-depth studies concerning these issues are urgently needed to gain better insight into the flow structure in confluence-bifurcation units of braided rivers.

This paper aims to (1) reveal the 3D flow structure in a confluence-bifurcation unit under different discharges and (2) elucidate the differences in the flow structure between confluence-bifurcation units and single confluence/bifurcation cases. Using the commercial computational fluid dynamics software FLOW-3D® (Version 11.2; https://www.flow3d.com; Flow Science, Inc.), fixed-bed simulations of a laboratory-scale confluence-bifurcation unit are conducted, and cases of a single confluence/bifurcation are also included for comparison. Two discharges are considered, with the central bars fully submerged or exposed respectively when the discharge is high or low. Based on the computational results, the 3D flow structure in the confluence-bifurcation unit conditions is analyzed from various aspects including free surface elevation, time-averaged flow velocity distribution, recirculation vortex structure, secondary current, and turbulent kinetic energy and dissipation rate. In particular, the flow structure in the confluence-bifurcation unit is compared with that in the single confluence/bifurcation cases to unravel the differences.h

2. Conceptual flume and computational cases

2.1. Conceptual flume

In this paper, a laboratory-scale conceptual flume is designed and used in numerical simulations. Figure 1(a–d) shows the morphological characteristics of the flume. To ensure that the conceptual flume reflects morphology features of natural braided channels, key parameters governing the flume morphology, e.g. unit length, width, and channel width-depth ratio, are determined according to studies on morphological characteristics of natural confluence-bifurcation units (Hundey & Ashmore, 2009; Ashworth, 1996; Orfeo et al., 2006; Parsons et al., 2007; Sambrook Smith et al., 2005; Kelly, 2006; Ashmore, 2013; Egozi & Ashmore, 2009; Redolfi et al., 2016; Ettema & Armstrong, 2019).

Figure 1. The sketch of the conceptual flume: (a) the original flume, (b) the central bar: (c) the sketch of cross-section C-C, (d) the sketch of cross-section D-D, (e) the modified part for the single confluence, (f) the modified part for the single bifurcation, (g) the position of different cross-sections. The red dashed boxes denote the regions of primary concern.

Figure 1. The sketch of the conceptual flume: (a) the original flume, (b) the central bar: (c) the sketch of cross-section C-C, (d) the sketch of cross-section D-D, (e) the modified part for the single confluence, (f) the modified part for the single bifurcation, (g) the position of different cross-sections. The red dashed boxes denote the regions of primary concern.

2.1.1. Length and width scales of the confluence-bifurcation unit

The length and width scales of the flume are first determined. The inner relation among the length LCB and average width B of a confluence-bifurcation unit and the average width Bi of a single branch was statistically studied by Hundey and Ashmore (2009), which indicates the following relations:
𝐿CB =(4∼5)⁢𝐵 (1)
𝐵 =1.41⁢𝐵𝑖 (2)
In addition, Ashworth (1996) gave B = 2Bi in his experimental research on mid-bar formation downstream of a confluence, while the confluence-bifurcation unit of Rio Parana, Argentina has a relation of B≈1.71Bi (Orfeo et al., 2006; Parsons et al., 2007). Accordingly, the following relations are used in the present paper:
𝐿CB =4⁢𝐵 (3)
𝐵 =1.88⁢𝐵𝑖 (4)
where LCB = 6 m, B = 1.5 m and Bi = 0.8 m.

2.1.2. Central bar morphology

The idealized plane pattern of central bars in braided rivers is a slightly fusiform leaf shape with a short upstream side and a long downstream side (Ashworth, 1996; Sambrook Smith et al., 2005; Kelly, 2006; Ashmore, 2013). To simplify the design, the bar is approximated as a combination of two different semi-ellipses (Figure 1(b)). The major axis Lb is two to ten times longer than the minor axis Bb according to the statistical data in Kelly’s study, and the regression equation is given as (Kelly, 2006):
𝐿𝑏=4.62⁢𝐵0.96𝑏 (5)
In this study, the bar width Bb is set as 0.8 m, whilst the lengths of downstream (LT1) and upstream sides (LT2) are 2 and 1.5 m, respectively (Figure 1(b)). Thus, the relation of Lb and Bb is given as:
𝐿𝑏=(𝐿𝑇⁢1+𝐿𝑇⁢2)=4.375⁢𝐵𝑏 (6)
The lengths of the inlet and outlet parts are determined as Lin = Lout = 8 m, which ensures negligible effects of boundary conditions without exceptional computational cost.

2.1.3. Width-depth ratio

Channel flow capacity can be significantly affected by cross-section shapes. For natural rivers, cross-section shapes can be generalized into three sorts based on the following width-depth curve (Redolfi et al., 2016):
𝐵=𝜓⁢𝐻𝜑(7)
Braided rivers usually have ψ = 5∼50 and φ>1, which indicates a rather wide and shallow cross-section. The central bar form should also be taken into account, so a parabolic cross-section shape is used here with ψ = 8 and φ>1 (Figure 1(c,d)).

2.1.4. Bed slope

In addition, natural braided rivers are usually located in mountainous areas and thus have a relatively large bed slope. According to flume experiments and field observations, the bed slope Sb is mostly in the range of 0.01∼0.02, and a few are below 0.01 (Ashworth, 1996; Egozi & Ashmore, 2009; Ashmore, 2013; Redolfi et al., 2016; Ettema & Armstrong, 2019). In this study, Sb takes 0.005.

2.1.5. Complete sketch of the conceptual flume

In summary, the flume is 29 m long, 2.4 m wide, and 0.6 m high. The plane coordinates (x-direction and y-direction) used in the calculation process are shown in Figure 1
(a). Note that the inlet corresponds to x = 0 m, and the centreline of the flume is located at y = 1.3 m. Besides, the thalweg elevation of the outlet is set as z = 0 m.

2.2. Computational cases

As stated before, the first aim of this paper is to reveal the flow structure in the confluence-bifurcation unit under different discharges. Therefore, two basic cases are set first: (1) case 1a under a low discharge (0.05 m3·s−1) with exposed central bars and (2) case 2a under a high discharge (0.30 m3·s−1) with fully submerged central bars. A total of 22 cross-sections are identified to examine the results (Figure 1(g)).

Further, cases of a single confluence/bifurcation are generated by splitting the original confluence-bifurcation unit into two parts. Part 1 only includes the upstream central bar and focuses on the flow convergence downstream of CS04 (Figure 1(e)), while Part 2 only includes the downstream central bar and focuses on the flow divergence upstream of CS19 (Figure 1(f)). Notably, the numbers of corresponding cross-sections in the original flume are reserved to facilitate comparison. The outlet section of the single confluence as well as the inlet section of the single bifurcation is extended to make the total length equivalent to the original flume (29 m). Also, two discharge conditions (0.05 and 0.30 m3·s−1), which correspond to exposed and fully submerged central bars, are considered for the single confluence/bifurcation. In total, six computational cases are conducted, as listed in Table 1. As the conceptual flume is designed to be symmetrical about the centreline, the momentum flux ratio (Mr) of the two branches should be 1 in all six cases. This is confirmed by further examining the computational results.

CaseConfigurationQin (m3·s−1)Zout (m)MrCondition of bars
1aCBU0.050.151Exposed
1bSC0.050.151Exposed
1cSB0.050.151Exposed
2aCBU0.300.341Submerged
2bSC0.300.341Submerged
2cSB0.300.341Submerged
Table 1. Computational cases with inlet and outlet boundary conditions.

3. Numerical method

In this section, the 3D Large Eddy Simulation (LES) model integrated in the FLOW-3D® (Version 11.2; https://www.flow3d.com; Flow Science, Inc.) software platform is introduced, including governing equations and boundary conditions. Information on computational meshes with mesh independence test can be found in the Supplementary material.

3.1. Governing equations

The LES model was applied in the present paper to simulate flow in the laboratory-scale confluence-bifurcation unit. The LES model has been proven to be effective in simulating turbulent flow in river confluences and bifurcations (Constantinescu et al., 2011; Le et al., 2019). The basic idea of the LES model is that one should directly compute all turbulent flow structures that can be resolved by the computational meshes and only approximate those features that are too small to be resolved (Smagorinsky, 1963). Therefore, a filtering operation is applied to the original Navier-Stokes (NS) equations for incompressible fluids to distinguish the large-scale eddies and small-scale eddies (Liu et al., 2018). The filtered NS equations are then generated, which can be expressed in the form of a Cartesian tensor as (Liu, 2012):

(10) where ¯𝑢𝑖 is the resolved velocity component in the i – direction (i goes from 1 to 3, denoting the x-, y – and z-directions, respectively); t is the flow time; ρ is the density of the fluid; ¯𝑝 is the pressure; ν is the kinematic viscosity; τij is the sub-grid scale (SGS) stress; ¯𝐺𝑖 is the body acceleration. In FLOW–3D®, the full NS equations are discretized and solved using the finite-volume/finite-difference method (Bombardelli et al., 2011; Lu et al., 2023).

Due to the filtering process, the velocity can be divided into a resolved part (¯𝑢⁡(𝑥,𝑡)) and an approximate part (𝑢′⁡(𝑥,𝑡)) which is also known as the SGS part (Liu, 2012). To achieve model closure, the standard Smagorinsky SGS stress model is introduced here (Smagorinsky, 1963):
𝜏ij−13⁢𝜏kk⁢𝛿ij=−2⁢𝜈SGS⁢¯𝑆ij(11)
 where νSGS is the SGS turbulent viscosity, and ¯𝑆ij is the resolved rate-of-strain tensor for the resolved scale defined by (Smagorinsky, 1963):
¯𝑆ij=12⁢(∂¯𝑢𝑖∂𝑥𝑗+∂¯𝑢𝑗∂𝑥𝑖)(12) 
In the standard Smagorinsky SGS stress model, the eddy viscosity is modelled by (Smagorinsky, 1963):
𝜈SGS=(𝐶𝑠⁢¯𝛥)2⁢∣¯𝑆∣,∣¯𝑆∣=√2⁢¯𝑆ij⁢¯𝑆ij(13)
¯𝛥=(ΔxΔyΔz⁢)1/3(14) 
where Cs is the Smagorinsky constant, Δx, Δy, and Δz are mesh scales. In FLOW–3D®, Cs is between 0.1 to 0.2 (Smagorinsky, 1963).
One of the key problems in simulating 3D open channel flow is the calculation of free surface. FLOW–3D® uses the Volume of Fluid (VOF) method (Hirt & Nichols, 1981) to track the change of free surface. The VOF method introduces a fluid phase fraction function f to characterize the proportion of a certain fluid in each mesh cell. In that case, the surface position can be precisely located if the mesh cell is fine enough. To monitor the change of f with time and space, the following convection equation is added:

For open channel flow, only two kinds of fluids are involved: water and air. If f is the fraction of water, the state of the fluid in each mesh cell can be defined as:

In FLOW–3D®, the interface between water and air is assumed to be shear-free, which means that the drag force on the water from the air is negligible. Moreover, in most cases, the details of the gas motion are not crucial for the heavier water motion so the computational processes will be more efficient.

3.2. Boundary conditions

Six boundary conditions need to be preset in the 3D numerical simulation process. Discharge boundary conditions are used for the inlet of the flume, where the free surface elevation is automatically calculated based on the free surface elevation boundary conditions set for the outlet. The specific information on the inlet and outlet boundary conditions for all computational cases is shown in Table 1. Moreover, because the free surface moves temporally, the free surface boundary conditions are just set as no shear stress and having a normal pressure, and the position of the free surface will be automatically adjusted over time by the VOF method in FLOW–3D®. Furthermore, the bed and two side walls are all set to be no-slip for fixed bed conditions, and a standard wall function is employed at the wall boundaries for wall treatment.

The inlet turbulent boundary conditions also need to be considered. They are set by default here. The turbulent velocity fluctuations V’ are assumed to be 10% of the mean flow velocity with the turbulent kinetic energy (TKE) (per unit mass) equaling 0.5V’2. The maximum turbulent mixing length is assumed to be 7% of the minimum computational domain scale, and the turbulent dissipation rate is evaluated automatically from the TKE.

4. Results and discussion

4.1. Flow structure in the confluence-bifurcation unit

4.1.1. Free surface elevation

Figure 2 shows the free surface elevation at five different longitudinal profiles (i.e. α = 0.2, 0.4, 0.5, 0.6, 0.8) for cases 1a and 2a. The parameter α was defined as follows:𝛼=𝑠𝐵(17) where s is the transverse distance between a certain profile and the left boundary of the flume. In general, the longitudinal change of free surface in the two cases is very similar despite different discharge levels. The free surface elevation decreases as the channel narrows from the upstream bifurcation to the front of the confluence-bifurcation unit. On the contrary, when the flow diverges again at the end of the confluence-bifurcation unit, the free surface elevation increases with channel widening. However, whether the fall or rise of free surface elevation in case 1a is much sharper than that in case 2a, especially at profiles with α = 0.2 and 0.8 (Figure 2(a)), which indicates there may be distinct flow states between the two cases. To further illustrate this finding, the Froude number Fr at different cross-sections (CS08∼CS15) is examined. In case 2a, the flow remains subcritical within the confluence-bifurcation unit. By contrast, in case 1a, a local supercritical flow is observed near the side banks of CS09 (i.e. α = 0.2 and 0.8), with Fr being about 1.2. This local supercritical flow can lead to a hydraulic drop followed by a hydraulic jump, which accounts for the sharp change of the free surface. The foregoing reveals that when central bars are exposed under relatively low discharge, supercritical flow is more likely to occur near the side banks of the confluence junction due to flow convergence.

Figure 2. Five time-averaged free surface elevation profiles in the confluence-bifurcation unit, in which α denotes the lateral position of the certain profile. Note that the black dashed line denotes the position of CS09, where Fr is about 1.2 near the side banks (α = 0.2 and 0.8) in case 1a. Z’ = z/h2, X’ = x/B, h2 is the maximum flow depth at the outlet boundary of cases 2a, 2b and 2c, h2 = 0.34 m.

Moreover, in both cases 1a and 2a, the free surface is higher at the channel centre than near the side banks, whether at the front or the end of the confluence-bifurcation unit. Thus, lateral free surface slopes from the centre to the side banks are generated. For example, the lateral free surface slopes at CS09 are 0.022 and 0.016 respectively for cases 1a and 2a. These lateral slopes can lead to lateral pressure gradient force whose direction is from the channel centreline to the side banks. Notably, the lateral surface slope in case 1a is steeper than that in case 2a, which may also result from the effect of the supercritical flow.

4.1.2. Time-averaged streamwise flow velocity

Figure 3. Time-averaged flow velocity distribution at three different slices over z-direction in the confluence-bifurcation unit: (a)∼(c) case 1a, (d)∼(f) case 2a. The flow direction is from the left to the right. StZ = Stagnation Zones, MiL = Mixing Layer. X’ = x/B, Y’ = y/B, Ui’ = Ui/Uti, Ui denotes the time-averaged streamwise flow velocity in case series i (i = 1,2), Uti denotes the cross-section-averaged streamwise flow velocity in case series i, Ut1 = 0.385 m/s, for case 2a Ut2 = 0.714 m/s.
Figure 4. Time-averaged flow velocity contours at eight different cross-sections in the confluence-bifurcation unit: (a) case 1a, (b) case 2a.

Besides the shared features described above, some differences between the two cases are also identified. First, flow stagnation zones at the upstream bar tail are found exclusively in case 1a as the central bars are exposed (Figure 3
(a–c)). Second, in case 1a the mixing layer is obvious in both the lower or upper flows (Figure 3
(a–c)), while in case 2a the mixing layer can be inconspicuous in the upper flow (Figure 3
(f)). Third, in case 1a, two high-velocity cores gradually transform into one single core downstream of the confluence [Figure 4
(a), CS08∼CS11] and are divided into two cores again at the downstream bar head [Figure 4
(a), CS15]. By contrast, in case 2a, the two cores merge much more rapidly [Figure 4
(a), CS08∼CS09], and no obvious reseparation of the merged core is found at the downstream bar head (Figure 3
(d–f)). The latter two differences between cases 1a and 2a indicate that the flow convergence and divergence are relatively weak when the central bars are fully submerged. It is noticed that when the central bars are exposed, the flow in branches needs to steer around the central bar, which can cause a large angle between the two flow directions at the confluence, and thus relatively strong flow convergence and divergence may occur. By contrast, when the central bars are fully submerged, the flow behavior resembles that of a straight channel, with flow predominantly moving straight along the main axis of the central bars. Therefore, a small angle between two tributary flow forms, and thus flow convergence and divergence are relatively mild.

4.1.3. Recirculation vortex

A recirculation vortex with a vertical axis is a typical structure usually found where flow steers sharply, and is generated from flow separation (Lu et al., 2023). This vortex structure is found in the confluence-bifurcation unit in the present study, marking several significant flow separation zones. Figure 5 shows the recirculation vortex structure at the bifurcation junction of the confluence-bifurcation unit. In both cases 1a and 2a, two recirculation vortices BV1 and BV2 are found at the bifurcation junction corner. Moreover, BV1 and BV2 seem well-established near the bed but tend to transform into premature ones in the upper flow, and there is also a tendency for the cores of BV1 and BV2 to shift downstream as they transition from the lower to the upper flow (Figure 5(a–c,d–f)). This finding indicates that flow separation zones exist at the bifurcation junction corner, and the vortex structure is similar in the separation zones under low and high discharges. These flow separation zones are generated due to the inertia effect as flow suddenly diverges and steers towards the curved side banks of the channel (Xie et al., 2020). Notably, two additional vortices BV3 and BV4 are found at both sides of the downstream bar in case 1a (Figure 5(a–c)), but no such vortices exist in case 2a. This difference shows that flow separation zones at both sides of the downstream bar are hard to form when the bars are completely submerged under the high discharge.

Figure 5. Recirculation vortices at the bifurcation junction (streamline view at three different slices over z-direction): (a)∼(c) case 1a, (d)∼(f) case 2a. The red solid line marked out the position of these vortices (BV1∼BV4).

Similarly, Figure 6 shows the recirculation vortex structure at the confluence junction of the confluence-bifurcation unit. No noteworthy similarities but a key difference between the two cases are observed at this site. Two vortices CV1 and CV2 are found downstream of the confluence junction corner in case 1a (Figure 6(c)), which mark two separation zones. Conversely, no such separation zones are found in case 2a. In fact, separation zones were reported at similar sites under relatively low discharges in some previous studies (Ashmore et al., 1992, Luz et al., 2020, Sukhodolov & Sukhodolova, 2019; Xie et al., 2020). Nevertheless, the flow separation zones at the confluence corner are very restricted in the present study (Figure 6(c)). Ashmore et al. (1992) also reported that no, or very restricted flow separation zones occur downstream of natural river confluence corners, primarily because of the relatively slow change in bank orientation compared with the sharp corners of laboratory confluences where separation is pronounced (Best & Reid, 1984; Best, 1988). In the present study, the bank orientation also changes slowly, which may explain why flow separation zones are inconspicuous at the confluence corner.

Figure 6. Recirculation vortices at the confluence junction (streamline view at three different slices over z-direction): (a)∼(c) case 1a, (d)∼(f) case 2a. The red solid line marked out the position of these vortices (CV1 & CV2).

The differences in the distribution of recirculation vortices discussed above may be mainly attributed to the difference in the angle between the tributary flows under different discharges. Some previous studies have reported that the confluence/bifurcation angle can significantly influence the flow structure at confluences/bifurcations (Best & Roy, 1991; Ashmore et al., 1992; Miori et al., 2012). Although the confluence/bifurcation angle is fixed due to the determined central bar shape in the present study, the angle between two tributary flows is affected by the varying discharge. When the central bars are exposed under the low discharge, the flow is characterized by a more pronounced curvature of the streamlines, and a large angle between the two tributary flows is noted (Figure 6(b)), causing strong flow convergence and divergence. By contrast, a small angle forms as the central bars are submerged, thereby leading to relatively weak flow convergence/divergence (Figure 6(e)). Overall, the differences mentioned above can be attributed to the differences in the intensity of flow convergence and divergence under different discharges.

It should be noted that some previous studies (Constantinescu et al., 2011; Sukhodolov & Sukhodolova, 2019) presented that there is a wake mode in the mixing layer of two streams at the confluence junction. The wake mode means that in the mixing layer, multiple streamwise coherent vortices moving downstream will form, which is similar to the flow structure around a bluffing body (Constantinescu et al., 2011). However, no such structure has been found within the confluence-bifurcation unit in this study. According to the numerical simulations of Constantinescu et al. (2011), a wake mode was found at a river confluence with a concordant bed and a momentum flux ratio of about 1. The confluence has a much larger angle (∼60°) between the two streams when compared to the confluence junction of the confluence-bifurcation unit in the present study where the angle is about 25°. As flow mechanics at river confluences may include several dominant mechanisms depending on confluence morphology, momentum ratio, the angle between the tributaries and the main channel, and other factors (Constantinescu et al., 2011), the relatively small confluence angle in the present study may explain why the wake mode is absent. The possible effects of the confluence/bifurcation angle are reserved for future study. Additionally, flow separation can lead to reduced local sediment transport capacity, thus causing considerable sediment deposition under natural conditions. Hence, the bank may migrate towards the inner side of the channel at the positions of CV1, CV2, BV1, and BV2, while the bar may expand laterally at the positions of BV3 and BV4.

4.1.4. Secondary current

Secondary current is the flow perpendicular to the mainstream axis (Thorne et al., 1985) and can be categorized into two primary types based on its origin: (1) Secondary current generated by the interaction between centrifugal force and pressure gradient force; (2) Secondary current resulting from turbulence heterogeneity and anisotropy (Lane et al., 2000). There are some widely recognized definitions of secondary current strength (SCS) (Lane et al., 2000). In this paper, the secondary current cells are identified by visible vortex with a streamwise axis, and the definition of SCS proposed by Shukry (1950) is used:

where ux, uy, and uz are flow velocities in x, y, and z directions and ux represents the mainstream flow velocity.

Figure 7 presents contour plots of SCS and the secondary current structure at key cross-sections of the study area. When the central bars are exposed, at the upstream bar tail (CS08), intense transverse flow occurs with flow converging to the centreline, but no secondary current cell is formed (Figure 7(a)). This is consistent with the findings of Hackney et al. (2018). At the confluence junction (CS09), transverse flow still plays a major role in the secondary current structure, with flow converging to the centreline at the surface and diverging to side banks near the bed (Figure 7(b)). Moreover, ‘back-to-back’ helical cells, which are two vortices rotating reversely, tend to generate at CS09 with their cores located near the side banks (Figure 7(b)) (Mosley, 1976; Ashmore, 1982; Ashmore et al., 1992), yet their forms are rather premature. As the flow goes downstream, the cores of the helical cells gradually rise to the upper flow and approach towards the centreline, and the helical cells become well-established (Figure 7(c–e)). When the flow diverges again at the downstream bar head (CS15), the helical cells attenuate rapidly, and the secondary current structure is once again characterized predominantly by transverse flow (Figure 7(f)).

Figure 7. Distribution of secondary current strength and secondary current cells at six different cross-sections: (a)∼(f) case 1a, (g)∼(l) case 2a. The secondary current cells are identified by visible lateral vortices (streamline view). The zero distance of each cross-section is located on the right bank.

When the central bars are fully submerged under the high discharge, the secondary current structure at the upstream bar tail and the confluence junction exhibits a resemblance to that under the low discharge (Figure 7(g,h)). However, at CS09, two pairs of cells with different scales tend to form under the high discharge (Figure 7(h)). The large and premature helical cells are similar to those under the low discharge, whereas the small helical cells are located near side banks possibly due to wall effects. As the flow moves downstream, the large helical cells tend to diminish rapidly and merge with the small ones near both side walls (Figure 7(i–k)). Moreover, the secondary current structure is once again characterized predominantly by transverse flow at CS14 under the high discharge, which occurs earlier than that under the low discharge (Figure 7(k)). At the downstream bar head, transverse flow still takes a dominant place, while the helical cells seem to become premature with increased scale (Figure 7(l)).

In general, in both cases 1a and 2a, the lateral distribution of SCS at all cross-sections is symmetrical about the channel centreline, where SCS is relatively small. A relatively high SCS is detected at both the upstream bar tail and the downstream bar head due to the effects of centrifugal force caused by flow steering. SCS decreases rapidly from the upstream bar tail (CS08) to the entrance of the downstream bifurcation junction (CS14), followed by a sudden increase at the downstream bar head (CS15) (Figure 7
(a–e, g–k)). However, the distribution of high-SCS zones is different between the two discharges. Under the low discharge, high-SCS zones appear along the bottom near the centerline and at the free surface on both sides of the centreline. Although similar high-SCS zones are found along the bottom near the centerline under the high discharge, the high-SCS zones are not found at the free surface. Furthermore, it is noticed that more obvious high-SCS zones appear under the low discharge compared with the high discharge, especially at CS09. This may be attributed to the differences in the intensity of flow convergence and divergence under different submerging conditions of the central bars. When the central bars are exposed, flow convergence and divergence are strong and sharp flow steering occurs, thereby causing large SCS. By contrast, when the central bars are fully submerged, flow convergence and divergence are relatively weak, and thus small SCS is observed.

4.1.5. Turbulent characteristics

Turbulent characteristics reflect the performance of energy and momentum transfer activities in flow (Sukhodolov et al., 2017). Comprehensive analysis of turbulent characteristics is crucial as they greatly impact the incipient motion, settling behavior, diffusion pattern, and transport process of sediment. Here, the TKE and turbulent dissipation rate (TDR) of flow in the confluence-bifurcation unit are analyzed.

Figure 8 shows the distribution of TKE on various cross-sections in cases 1a and 2a. In the same way, Figure 10 shows the distribution of TDR. The values of TKE and TDR are nondimensionalized with mid-values of TKE = 0.005 m2·s−2 and TDR = 0.007 m3·s−2. In both cases 1a and 2a, the distributions of TKE and TDR show symmetrical patterns concerning the channel centreline. High-TKE and high-TDR zones exhibit a belt distribution near the channel bottom (McLelland et al., 1999; Ashworth, 1996; Constantinescu et al., 2011), indicating that turbulence primarily originates at the channel bottom due to the influence of bed shear stress. A sudden increase of TKE (Weber et al., 2001) and TDR occurs near the channel bottom at the confluence junction [Figure 8 and 9, CS08∼CS09] and from the entrance of the bifurcation junction (CS14) to the downstream bar head (CS15) (Figures 8 and 9).

Figure 8. Turbulent kinetic energy contours at eight different cross-sections in the confluence-bifurcation unit: (a) case 1a, (b) case 2a. TKE = turbulent kinetic energy. TKE’ =  dimensionless value of TKE, with regard to a mid-value of TKE = 0.005 m2·s−2.
Figure 9. Turbulent dissipation rate contours at eight different cross-sections in the confluence-bifurcation unit: (a) case 1a, (b) case 2a. TDR = turbulent dissipation rate. TDR’ =  dimensionless value of TDR, with regard to a mid-value of TDR = 0.007 m3·s−2.
Figure 10. Comparison of the distribution of time-averaged streamwise flow velocity along the flow depth at different cross-sections between the confluence-bifurcation unit and the single confluence. (a)∼(f) 1a vs. 1b, (g)∼(l) 2a vs. 2b.

Despite the common turbulent characteristics between cases 1a and 2a, additional high-TKE zones are found in the upper flow at the upstream bar tail (CS08), the confluence junction (CS09) and the downstream bar head (CS15) (Figure 8) when the central bars are fully submerged. The formation mechanism of these high-TKE zones near the water surface is more complicated, which may result from interactions of velocity gradient, secondary current structure and wall shear stress (Engel & Rhoads, 2017; Lu et al., 2023).

4.2. Comparison with single confluence/bifurcation cases

In this section, the results of a single confluence (cases 1b and 2b) and a single bifurcation (cases 1c and 2c) are compared with those of the confluence-bifurcation unit (cases 1a and 2a) under two discharges. Flow structure at CS08∼CS15 is mainly concerned below.

4.2.1. Comparison with single confluence cases

First, the patterns of time-averaged streamwise velocity, TKE and TDR within the single confluence (presented by contour plots in the supplementary materials) are assessed and then compared with those within the confluence-bifurcation unit (Figures 4, 8, and 9). It is found that distributions of these parameters are similar in the confluence-bifurcation unit and the single confluence from the upstream bar tail (CS08) to the entrance of the bifurcation junction (CS14), despite varying discharges. As the existence of the downstream central bar is the main difference between the single confluence and the confluence-bifurcation unit, this finding indicates that the downstream bar may have limited influence on the flow structure in the confluence-bifurcation unit. In other words, the flow structure in the confluence-bifurcation unit appears to be mainly shaped by the presence of the upstream bar, with its impact potentially reaching as far as the entrance of the bifurcation (CS14). Moreover, under the low discharge, the two high-velocity cores seem to merge later (at CS11) in the single confluence than in the confluence-bifurcation unit (at CS10), which indicates the convergence of two tributary flows may achieve a steady state faster in the confluence-bifurcation unit. To further elucidate the differences, results on the distribution of time-averaged streamwise velocity and TKE along the flow depth are discussed below.

4.2.1.1. Time-averaged streamwise velocity

Figure 10 shows the distribution of time-averaged streamwise flow velocity along the flow depth at different cross-sections. Note that α = 0.5 denotes the channel centreline and α = 0.7 denotes a position near the side banks. As only marginal differences are found at α = 0.3 and 0.7, only profiles at α = 0.7 are displayed for clarity.

Under the low discharge, no obvious difference in the distribution of time-averaged streamwise flow velocity is observed at the upstream bar tail (Figure 10(a)). At the confluence junction (Figure 10(b)), the velocities near the side banks (α = 0.7) are larger than those at the centre (α = 0.5) in both the confluence-bifurcation unit and the single confluence, which suggests that the two tributary flows have not sufficiently merged. The two tributary flows achieve convergence at CS11 in both the confluence-bifurcation unit and the single confluence (Figure 10(c)), with the velocity at the centre (α = 0.5) is larger than that near the side banks. Nevertheless, the velocities at the centre (α = 0.5) and near the side banks (α = 0.7) are closer to each other in the confluence-bifurcation unit than those in the single confluence, which represents less sufficient flow convergence in the confluence-bifurcation unit than in the single confluence. Therefore, it can be inferred that the convergence of two tributary flows may achieve a steady state faster in the confluence-bifurcation unit. After reaching the steady state, the velocity near the side banks (α = 0.7) is smaller in the single confluence than in the confluence-bifurcation unit despite close values at the centre (α = 0.5) (Figure 10(d,e)). This leads to a more pronounced disparity between velocities at the centre and near the side banks in the single confluence than that observed in the confluence-bifurcation unit. In other words, the high-velocity zone is more concentrated on the channel centreline in the single confluence, while the lateral distribution of flow velocity tends to be more uniform in the confluence-bifurcation unit. This may be attributed to the influence of the downstream central bar, which is further proved by comparing the velocity profiles at CS15 (Figure 10(e)).

As for the high discharge condition, from CS08 to CS14, the quantitative differences in velocity distribution between the confluence-bifurcation unit and the single confluence seem small. This indicates that the effect of morphology appears to be subdued when the central bars are fully submerged under the high discharge. It should be also noted that under both the low and high discharge, velocity profiles at the corresponding location exhibit the same shapes in the confluence-bifurcation unit and the single confluence, which indicates that the upstream confluence may dominate the flow structure in the confluence-bifurcation unit.

4.2.1.2. Secondary current

Figure 11 shows contour plots of SCS and the secondary current structure for single confluence cases. Compared with Figure 7, under both low and high discharge conditions, the distribution of SCS and the structure of helical cells in the confluence-bifurcation unit and the single confluence are very similar from CS08 to CS12 (Figure 7(a–d, g–j) and Figure 11(a–d, g–j)]. This indicates that the secondary current structure in the confluence-bifurcation unit exhibits certain consistent features when compared to those in the single confluence, thus proving that the effects of the upstream central bar may dominate the flow structure in the confluence-bifurcation unit. However, the secondary current structure at CS14 and CS15 is different between the confluence-bifurcation unit and the single confluence (Figure 7 and 11(e, f, k,l)). Under the low discharge, transverse flow is from the side banks to the centre and relatively high SCS is found near the side banks at CS14 in the single confluence, while the transverse flow is always from the centre to the side banks and SCS is relatively low at the corresponding sites in the confluence-bifurcation unit (Figure 11(e)). Under the high discharge, the helical cells near the side walls almost diminish in the single confluence, while they still exist in the confluence-bifurcation unit at CS14 (Figure 11(k)). Under both low and high discharges, the secondary current pattern at CS15 is similar to that at CS14 in the single confluence, while they are different in the confluence-bifurcation unit due to the existence of the downstream central bar. This comparison indicates that the existence of the downstream central bar can influence the upstream secondary current structure, nevertheless, the effects are fairly limited.

Figure 11. Secondary current at different cross-sections in the single confluence condition: (a)∼(f) case 1b, (g)∼(l) case 2b. The zero distance of each cross-section is located on the right bank.
4.2.1.3. Turbulent kinetic energy

Figure 12 shows TKE distribution along the flow depth at different cross-sections. Under the low discharge, in general, the maximum TKE tends to appear near the channel bottom in both the confluence-bifurcation unit and the single confluence. No obvious difference is observed at the upstream bar tail (CS08) (Figure 12(a)). Downstream this site (at CS09), the maximum TKE near the side banks (α = 0.7) is larger than that at the channel centre in the single confluence, while they are close to each other in the confluence-bifurcation unit (Figure 12(b)). This can also be attributed to the insufficient convergence of the two tributary flows. At CS11, flow convergence achieves a steady state in the confluence-bifurcation unit, while it remains insufficient in the single confluence. As flow convergence reaches a steady state at CS12, the maximum TKE in the single confluence exhibits a more concentrated distribution on the channel centre than that in the confluence-bifurcation unit (Figure 12(d)). This effect becomes more obvious downstream at CS14 (Figure 12(e)). The less-concentrated distribution of the maximum TKE in the confluence-bifurcation unit can be owing to the effects of the downstream central bar as well, which appears analogous to that mentioned in 4.2.1.1.

Figure 12. Comparison of the distribution of TKE along the flow depth at different cross-sections between the confluence-bifurcation unit and the single confluence. (a)∼(f) 1a vs. 1b, (g)∼(l) 2a vs. 2b.

Under the high discharge condition, two peaks of TKE appear in both the confluence-bifurcation unit and the single confluence (Figure 12(g–l)). Moreover, in both the confluence-bifurcation unit and the single confluence, from the upstream bar tail to the downstream bar head, the peak of TKE in the upper flow is larger at the channel centre (α = 0.5), while the peak of TKE in the lower flow is larger near the side banks (α = 0.7). However, the disparity between the TKE near the side banks and at the channel centre seems to be larger in the single confluence, while the TKE in the confluence-bifurcation unit takes a more uniform distribution. Even though, TKE profiles at the corresponding location exhibit highly similar shapes in the confluence-bifurcation unit and the single confluence, suggesting that the effects of channel morphology seem to be inhibited when the central bars are submerged under the high discharge.

4.2.2. Comparison with single bifurcation cases

Distributions of time-averaged streamwise velocity, TKE and TDR at corresponding cross-sections are also compared between the single bifurcation (see the Supplementary material) and the confluence-bifurcation unit (Figures 4, 8 and 9). Unlike the high similarity in flow characteristics exhibited between the confluence-bifurcation unit and the single confluence, significant differences are found between the confluence-bifurcation unit and the single bifurcation, especially at CS08∼CS14. On the one hand, the high-velocity zones are broader and asymmetrical concerning the channel centreline in the single bifurcation, with a belt-like and an approximately elliptic-like distribution respectively under the low and high discharges. By contrast, the high-velocity zone is a core that concentrates on the channel centre in the confluence-bifurcation unit. Moreover, the maximum velocity seems smaller in the single bifurcation than that in the confluence-bifurcation unit. On the other hand, the high-TKE belt near the channel bottom appears to be narrower in the single bifurcation than in the confluence-bifurcation unit, especially at CS08∼CS14 under the low discharge. Furthermore, additional high-TKE zones are found near the side walls at CS08∼CS11 in the single bifurcation, of which the scale is obviously smaller than those in the confluence-bifurcation unit. In addition, TKE at the channel centre is smaller near the free surface in the single bifurcation than that in the confluence-bifurcation unit. Nevertheless, the distributions of velocity, TKE and TDR seem to be similar in the confluence-bifurcation unit and the single bifurcation at CS15. As the existence of the upstream central bar is the main difference between the single confluence and the confluence-bifurcation unit, all the above findings indicate that the upstream central bar greatly influences the flow structure in the confluence-bifurcation unit. On the other hand, the downstream central bar may have a restricted influence on the flow structure in the confluence-bifurcation unit, whose impact may be limited to a range between the entrance of the bifurcation (CS14) and the downstream bar head (CS15). To further elucidate the differences, results on the distribution of time-averaged streamwise velocity and TKE along the flow depth are discussed below.

4.2.2.1. Time-averaged streamwise velocity

Figure 13 shows the distribution of time-averaged streamwise velocity along the flow depth at different cross-sections. Under the low discharge, distinct distribution patterns of flow velocity between the confluence-bifurcation unit and the single bifurcation are found at CS08, CS09 and CS11, which can be attributed to the effects of upstream flow convergence (Figure 13(a–c)). However, when the flow convergence reaches a steady state in the confluence-bifurcation unit (Figure 13(d–f)), the high-velocity zone is more concentrated in the confluence-bifurcation unit than in the single bifurcation due to to the significant influence of the upstream central bar on the flow structure. The velocity profiles at the downstream bar head can be a shred of evidence as well, with the maximum velocity larger at the channel centre but smaller near the side banks in the confluence-bifurcation unit than in the single bifurcation.

Figure 13. Comparison of the distribution of time-averaged streamwise flow velocity along the flow depth at different cross-sections between the confluence-bifurcation unit and the single bifurcation. (a)∼(f) 1a vs. 1c, (g)∼(l) 2a vs. 2c.

Under the high discharge, the distribution of velocity seems to exhibit limited differences between the two kinds of morphology, which indicates that the effects of channel morphology may be less noticeable when the central bars are fully submerged under the high discharge. Nevertheless, the velocity in the lower flow (below a relative depth of 0.45) shows a uniform lateral distribution in the single bifurcation, as the velocity profile at the channel centreline (α = 0.5) is in line with that near the side banks (α = 0.7) (Figure 13(g–l)). However, in the confluence-bifurcation unit, different velocity distributions in the lower flow can be observed at the channel centreline (α = 0.5) and near the side banks (α = 0.7). The foregoing results indicate that when the central bars are fully submerged, the high-velocity zones are more concentrated on the channel centreline in the confluence-bifurcation unit, while the lateral distribution of flow velocity within the single bifurcation tends to be more uniform, especially near the bifurcation junction (Figure 13(j,k)). This can also be attributed to the dominant influence of the upstream central bar over the downstream central bar.

It is also noted that the flow velocity distribution along the flow depth in the confluence-bifurcation unit is of a similar pattern despite varying discharges. As a critical point, the maximum velocity appears in the upper flow. The distribution above the critical point is approximately linear whereas it appears logarithmic below. By contrast, despite the similarity observed under the low discharge, the flow velocity distribution along the flow depth within the single bifurcation exhibits a distinct pattern under the high discharge, especially near the side banks (Figure 13(e–h)). On the one hand, the critical point in the upper flow no longer corresponds to the maximum velocity. On the other hand, the velocity distribution deviates from logarithmic below the critical point, with the maximum velocity appearing at a relative depth of 0.45. Succinctly, the distribution of streamwise velocity along the flow depth may retain the same pattern regardless of discharge levels in the confluence-bifurcation unit, while it may exhibit distinct patterns under different discharge levels in the single bifurcation.

4.2.2.2. Secondary current

Figure 14 shows contour plots of SCS and the distribution of secondary current for single bifurcation cases. In general, the value of SCS near the side banks at CS08∼CS14 (Figure 14(a–d, g–j)) in the single bifurcation seems smaller than that in the confluence-bifurcation unit (Figure 7(a–d, g–j)), especially under the low discharge. SCS distribution at CS14 is similar in the confluence-bifurcation unit and the single bifurcation under both low and high discharges. This difference in SCS distribution between the confluence-bifurcation unit and the single bifurcation indicates that the downstream bifurcation may have a restricted influence on the flow structure in the confluence-bifurcation unit. This influence is limited to a range between the entrance of the bifurcation (CS14) and the downstream bar head (CS15).

Figure 14. Secondary current at different cross-sections in the single bifurcation condition: (a)∼(f) case 1c, (g)∼(l) case 2c. The zero distance of each cross-section is located on the right bank.

In addition, the secondary current structure may also present different patterns in response to varying channel morphologies and discharge conditions. Under the low discharge condition, multiple unstable helical cells with asymmetrical distribution are formed from CS08 to CS12 in the single bifurcation (Figure 14(a–d)), while no obvious helical cells are found at CS14 and CS15 (Figure 14(d,e)). These findings are quite different from the stable and symmetrical helical cells at all cross-sections shown in the confluence-bifurcation unit (Figure 7). This difference may be attributed to the significant influence of the upstream central bar and the limited influence of the downstream central bar. Under the high discharge condition, only one pair of premature helical cells are found from CS08 to CS12 in the single bifurcation with their cores located near the side banks (Figure 14(e,f)). As the flow moves downstream, the helical cells gradually develop and become well-established (Figure 14(g,h)). These helical cells in the single bifurcation show symmetric cross-sectional distribution and a similar longitudinal development as in the confluence-bifurcation unit. However, in the confluence-bifurcation unit, two pairs of helical cells appear upstream of CS12 and CS14 and gradually fuse to one pair under the high discharge. As the ‘two-pairs’ structure in the confluence-bifurcation unit origins from the upstream confluence, the differences in the secondary current structure between the single bifurcation and the confluence-bifurcation unit under the high discharge can also be owing to the effects of the upstream central bar in excess of those of the downstream central bar.

4.2.2.3. Turbulent kinetic energy

Figure 15 shows the TKE distribution along the flow depth at different cross-sections. Under the low discharge, when the two tributary flows have not achieved sufficient convergence in the confluence-bifurcation unit, the maximum TKE is more concentrated in the single bifurcation (Figure 15(a–c)). As flow convergence achieves a steady state, more concentrated high-TKE zones appear at the channel centre within the confluence-bifurcation unit, confirming the finding that the effects of the upstream central bar reign over those of the downstream central bar in the confluence-bifurcation unit. However, things can be very complicated under the high discharge. For TKE distribution at the channel centreline, two peaks appear in the confluence-bifurcation unit with one close to the free surface and the other near the bed (Figure 15(g–l)). By contrast, only one peak near the bed is present in the single bifurcation. Therefore, a larger TKE can be found in the upper flow of the channel centreline in the confluence-bifurcation unit. For TKE distribution near the side banks, two peaks appear in both the confluence-bifurcation unit and the single bifurcation at CS09∼CS14 (Figure 15(h–l)). The upper peak is larger but the lower peak is smaller within the single bifurcation than those within the confluence-bifurcation unit. These significant discordances in TKE distribution under the high discharge further prove that the effects of the upstream bar on the flow structure in the confluence-bifurcation unit are more prominent than those of the downstream central bar.

Figure 15. Comparison of the distribution of TKE along the flow depth at different cross-sections between the confluence-bifurcation unit and the single bifurcation. (a)∼(f) 1a vs. 1c, (g)∼(l) 2a vs. 2c.

4.2.3. Further discussion of the comparisons

The above subsections have revealed significant differences in flow structure within the confluence-bifurcation unit and the single confluence and bifurcation, which directly result from the distinct channel morphologies and vary with the discharge conditions as well. These differences are summarized and further discussed below.

The distinctive morphology of a confluence-bifurcation unit plays a pivotal role in governing streamwise flow velocity distribution, secondary current structure, and turbulent kinetic energy distribution within the channel. Generally, from the upstream bar tail (CS08) to the entrance of the bifurcation (CS14), the flow structure in the confluence-bifurcation unit is highly similar to that in the single confluence, while it exhibits great differences (as shown in 4.2.2) between the confluence-bifurcation unit and the single bifurcation. This indicates that the upstream central bar greatly influences the flow structure in the confluence-bifurcation unit, with the effects spreading to the entrance of the bifurcation. At the downstream bar head (CS15), the flow structure (e.g. the transverse flow patterns) in the confluence-bifurcation unit exhibits high similarity to that in the single bifurcation. However, these similarities do not spread to upstream cross-sections, suggesting that the influence of the downstream central bar is limited at the bifurcation junction. In a word, the effects of the upstream central bar on the flow structure in the confluence-bifurcation unit are in excess of those of the downstream central bar.

However, despite the influence of channel morphology, discharge may also have some important effects on the streamwise flow velocity distribution. On the one hand, when the central bars are exposed under the low discharge, the high-velocity zone is less concentrated in the confluence-bifurcation unit than in the single confluence, while it is more concentrated in the confluence-bifurcation unit than in the single bifurcation. On the other hand, it is noticed that when the central bars are fully submerged under the high discharge, reduced differences in flow structure between the confluence-bifurcation unit and the single confluence/bifurcation are witnessed, and thus the morphology effect seems to be subdued.

4.3. Implications

The present work unravels the flow structure in a laboratory-scale confluence-bifurcation unit and takes the first step to further investigating morphodynamics in such channel morphology. Based on the comparison with a single confluence/bifurcation, the findings provide insight into the complex 3D interactions between water flow and channel morphology. The distinct flow structure in the laboratory-scale confluence-bifurcation unit may appreciably alter sediment transport and morphological evolution, of which research is underway. As the basic morphological element of braided river planform is confluence-bifurcation units, the present work should have direct implications for flow structure in natural braided rivers. This is pivotal for the sustainable management of braided rivers which deals with water and land resources planning, eco-hydrological well-being, and infrastructure safety such as cross-river bridges and oil pipelines (Redolfi et al., 2019; Ragno et al., 2021).

Notably, braided rivers worldwide (e.g. in the Himalayas, North America, and New Zealand) have undergone increased pressures and will continue to evolve due to forces of global climate change and intensified anthropogenic activities (Caruso et al., 2017; Hicks et al., 2021; Lu et al., 2022). In particular, channel aggradation caused by increased sediment supply as well as exploitation of braidplain compromise space for flood conveyance, making the rivers prone to flooding. In this sense, an enhanced understanding of the flow structure under high discharge when central bars are fully submerged is essential for mitigating flooding hazards.

5. Conclusions

This study has numerically investigated the 3D flow structure in a laboratory-scale confluence-bifurcation unit based on the LES model integrated in the FLOW–3D® software platform. Two different discharges are considered with the central bars fully submerged or exposed respectively when the discharge is high or low. Cases of a single confluence/bifurcation are included for comparison. The key findings of this paper are as follows:

  1. Several differences are highlighted in the comparison of the flow structure in the confluence-bifurcation unit between the two discharges. When the central bars are fully submerged under the high discharge, the mixing layer of two tributary flows is less obvious, and two high-velocity cores merge more rapidly as compared with those under the low discharge. Besides, flow separation zones are found neither at the confluence corner nor on both sides of the downstream bar when the central bars are fully submerged. Moreover, SCS seems to be smaller near the side banks under the high discharge than under the low discharge. Therefore, it is suggested that flow convergence/divergence is relatively weak in the confluence-bifurcation unit when central bars are fully submerged under the high discharge.
  2. From the upstream bar tail to the entrance of the bifurcation, the flow structure in the confluence-bifurcation unit is highly similar to that in the single confluence, while it exhibits great differences from that in the single bifurcation. Only at the downstream bar head does the flow structure in the confluence-bifurcation unit exhibit high similarity to that in the single bifurcation. Consequently, the effects of the upstream central bar on the flow structure in the confluence-bifurcation unit reign over those of the downstream central bar.
  3. Despite the influence of channel morphology, discharge may also have significant effects on the distribution of streamwise flow velocity. On the one hand, when the central bars are exposed under the low discharge, the high-velocity zone is less concentrated in the confluence-bifurcation unit than in the single confluence, while it is more concentrated in the confluence-bifurcation unit than in the single bifurcation. On the other hand, when the central bars are fully submerged under the high discharge, reduced differences in flow structure between the confluence-bifurcation unit and the single confluence/bifurcation are witnessed, and thus the morphology effect seems to be subdued.

It is noticed that the effects of other factors (e.g. confluence and bifurcation angles, bed discordance) on the flow structure in the confluence-bifurcation unit are not discussed here. Studies on these issues are warranted and reserved for future work.

Reference

  1. Ashmore, P. E. (1982). Laboratory modelling of gravel braided stream morphology. Earth Surface Processes and Landforms, 7(3), 201–225. https://doi.org/10.1002/esp.3290070301
  2. Ashmore, P. E. (1991). How do gravel-bed rivers braid? Canadian Journal of Earth Sciences, 28(3), 326–341. https://doi.org/10.1139/e91-030
  3. Ashmore, P. E. (2013). Morphology and dynamics of braided rivers. In J. Shroder, & (Editor in Chief) E. Wohl (Eds.), Treatise on geomorphology (Vol. 9, pp. 289–312). https://doi.org/10.1016/B978-0-12-374739-6.00242-6
  4. Ashmore, P. E., Ferguson, R. I., Prestegaard, K. L., Ashworth, P. J., & Paola, C. (1992). Secondary flow in anabranch confluences of a braided, gravel-bed stream. Earth Surface Processes and Landforms, 17(3), 299–311. https://doi.org/10.1002/esp.3290170308
  5. Ashworth, P. J. (1996). Mid channel bar growth and its relationship to local flow strength and direction. Earth Surface Processes and Landforms, 21(2), 103–123.
  6. Bertoldi, W., & Tubino, M. (2005). Bed and bank evolution of bifurcating channels. Water Resources Research, 41(7), W07001. https://doi.org/10.1029/2004WR003333
  7. Bertoldi, W., & Tubino, M. (2007). River bifurcations: Experimental observations on equilibrium configurations. Water Resources Research, 43(10), W10437. https://doi.org/10.1029/2007WR005907
  8. Best, J. L. (1987). Flow dynamics at river channel confluences: Implications for sediment transport and bed morphology. In F. G. Ethridge, R. M. Flores, & M. D. Harvey (Eds.), Recent developments in fluvial sedimentology (pp. 27–35).
  9. Best, J. L. (1988). Sediment transport and bed morphology at river channel confluences. Sedimentology, 35(3), 481–498. https://doi.org/10.1111/j.1365-3091.1988.tb00999.x
  10. Best, J. L., & Reid, I. (1984). Separation zone at open-channel junctions. Journal of Hydraulic Engineering, 110(11), 1588–1594. https://doi.org/10.1061/(ASCE)0733-9429(1984)110:11(1588)
  11. Best, J. L., & Roy, A. G. (1991). Mixing-layer distortion at the confluence of channels of different depth. Nature, 350(6317), 411–413. https://doi.org/10.1038/350411a0
  12. Biron, P. M., Buffin-Bélanger, T., & Martel, N. (2019). Three-dimensional turbulent structures at a medium-sized confluence with and without an ice cover. Earth Surface Processes and Landforms, 44(15), 3042–3056. https://doi.org/10.1002/esp.4718
  13. Bombardelli, F. A., Meireles, I., & Matos, J. (2011). Laboratory measurements and multi-block numerical simulations of the mean flow and turbulence in the nonaerated skimming flow region of steep stepped spillways. Environmental Fluid Mechanics, 11(3), 263–288. https://doi.org/10.1007/s10652-010-9188-6
  14. Bradbrook, K. F., Biron, P. M., Lane, S. N., Richards, K. S., & Roy, A. G. (1998). Investigation of controls on secondary circulation in a simple confluence geometry using a three-dimensional numerical model. Hydrological Processes, 12(8), 1371–1396. https://doi.org/10.1002/(SICI)1099-1085(19980630)12:8<1371::AID-HYP620>3.0.CO;2-C
  15. Caruso, B., Newton, S., King, R., & Zammit, C. (2017). Modelling climate change impacts on hydropower lake inflows and braided rivers in a mountain basin. Hydrological Sciences Journal, 62(6), 928–946. https://doi.org/10.1080/02626667.2016.1267860
  16. Constantinescu, G., Miyawaki, S., Rhoads, B., & Sukhodolov, A. (2016). Influence of planform geometry and momentum ratio on thermal mixing at a stream confluence with a concordant bed. Environmental Fluid Mechanics, 16(4), 845–873. https://doi.org/10.1007/s10652-016-9457-0
  17. Constantinescu, G., Miyawaki, S., Rhoads, B., Sukhodolov, A., & Kirkil, G. (2011). Structure of turbulent flow at a river confluence with momentum and velocity ratios close to 1: Insight provided by an eddy-resolving numerical simulation. Water Resources Research, 47(5), W05507. https://doi.org/10.1029/2010WR010018
  18. De Serres, B., Roy, A. G., Biron, M. P., & Best, J. L. (1999). Three-dimensional structure of flow at a confluence of river channels with discordant beds. Geomorphology, 26(4), 313–335. https://doi.org/10.1016/S0169-555X(98)00064-6
  19. Duguay, J., Biron, P., & Buffin-Bélanger, T. (2022). Large-scale turbulent mixing at a mesoscale confluence assessed through drone imagery and eddy-resolved modelling. Earth Surface Processes and Landforms, 47(1), 345–363. https://doi.org/10.1002/esp.5251
  20. Egozi, R., & Ashmore, P. E. (2009). Experimental analysis of braided channel pattern response to increased discharge. Journal of Geophysical Research: Earth Surface, 114, F02012. https://doi.org/10.1029/2008JF001099
  21. Engel, F. L., & Rhoads, B. L. (2017). Velocity profiles and the structure of turbulence at the outer bank of a compound meander bend. Geomorphology, 295, 191–201. https://doi.org/10.1016/j.geomorph.2017.06.018
  22. Ettema, R., & Armstrong, D. L. (2019). Bedload and channel morphology along a braided, sand-bed channel: Insights from a large flume. Journal of Hydraulic Research, 57(6), 822–835. https://doi.org/10.1080/00221686.2018.1555557
  23. Federici, B., & Paola, C. (2003). Dynamics of channel bifurcations in noncohesive sediments. Water Resources Research, 39(6), 1162. https://doi.org/10.1029/2002WR001434
  24. Hackney, C. R., Darby, S. E., Parsons, D. R., Leyland, J., Aalto, R., Nicholas, A. P., & Best, J. L. (2018). The influence of flow discharge variations on the morphodynamics of a diffluence-confluence unit on a large river. Earth Surface Processes and Landforms, 43(2), 349–362. https://doi.org/10.1002/esp.4204
  25. Hicks, D. M., Baynes, E. R. C., Measures, R., Stecca, G., Tunnicliffe, J., & Fredrich, H. (2021). Morphodynamic research challenges for braided river environments: Lessons from the iconic case of New Zealand. Earth Surface Processes and Landforms, 46(1), 188–204. https://doi.org/10.1002/esp.5014
  26. Hirt, C. W., & Nichols, B. D. (1981). Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 39(1), 201–225. https://doi.org/10.1016/0021-9991(81)90145-5
  27. Hua, Z. L., Gu, L., & Chu, K. J. (2009). Experiments of three-dimensional flow structure in braided rivers. Journal of Hydrodynamics, 21(2), 228–237. https://doi.org/10.1016/S1001-6058(08)60140-7
  28. Hundey, E. J., & Ashmore, P. E. (2009). Length scale of braided river morphology. Water Resources Research, 45(8), W08409. https://doi.org/10.1029/2008WR007521
  29. Iwantoro, A. P., van der Vegt, M., & Kleinhans, M. G. (2022). Stability and asymmetry of tide-influenced river bifurcations. Journal of Geophysical Research: Earth Surface, 127(6), e2021JF006282. https://doi.org/10.1029/2021JF006282
  30. Jang, C. L., & Shimizu, Y. (2005). Numerical simulation of relatively wide, shallow channels with erodible banks. Journal of Hydraulic Engineering, 131, 565–575.
  31. Kelly, S. (2006). Scaling and hierarchy in braided rivers and their deposits: Examples and implications for reservoir modelling. In G. H. Smith, J. L. Best, C. S. Bristow, & G. E. Petts (Eds.), Braided rivers: Process, deposits, ecology and management (pp. 75–106).
  32. Lane, S. N., Bradbrook, K. F., Richards, K. S., Biron, P. M., & Roy, A. G. (2000). Secondary circulation cells in river channel confluences: Measurement artefacts or coherent flow structures? Hydrological Processes, 14(11-12), 2047–2071. https://doi.org/10.1002/1099-1085(20000815/30)14:11/12<2047::AID-HYP54>3.0.CO;2-4
  33. Le, T. B., Khosronejad, A., Sotiropoulos, F., Bartelt, N., Woldeamlak, S., & Dewall, P. (2019). Large-eddy simulation of the Mississippi River under base-flow condition: Hydrodynamics of a natural diffluence-confluence region. Journal of Hydraulic Research, 57(6), 836–851. https://doi.org/10.1080/00221686.2018.1534282
  34. Liu, C. B., Li, J., Bu, W. Y., Ma, W. X., Shen, G., & Yuan, Z. (2018). Large eddy simulation for improvement of performance estimation and turbulent flow analysis in a hydrodynamic torque converter. Engineering Applications of Computational Fluid Mechanics, 12(1), 635–651. https://doi.org/10.1080/19942060.2018.1489896
  35. Liu, Z. (2012). Investigation of flow characteristics around square cylinder with inflow turbulence. Engineering Applications of Computational Fluid Mechanics, 6(3), 426–446. https://doi.org/10.1080/19942060.2012.11015433
  36. Lu, G. W., Liu, J. X., Cao, Z. X., Li, Y. W., Lei, X. T., & Li, Y. (2023). A computational study of 3D flow structure in two consecutive bends subject to the influence of tributary inflow in the middle Yangtze River. Engineering Applications of Computational Fluid Mechanics, 17(1), 2183901. https://doi.org/10.1080/19942060.2023.2183901
  37. Lu, H. Y., Li, Z. W., Hu, X. Y., Chen, B., & You, Y. C. (2022). Morphodynamic processes in a large gravel–bed braided channel in response to runof change: A case study in the Source Region of Yangtze River. Arabian Journal of Geosciences, 15(5), 377. https://doi.org/10.1007/s12517-022-09641-y
  38. Luz, L. D., Szupiany, R. N., Parolin, M., Silva, A., & Stevaux, J. C. (2020). Obtuse-angle vs. confluent sharp meander bends: Insights from the Paraguay-Cuiabá confluence in the tropical Pantanal wetlands, Brazil. Geomorphology, 348, 106907. https://doi.org/10.1016/j.geomorph.2019.106907
  39. Marra, W. A., Parsons, D. R., Kleinhans, M. G., Keevil, G. M., & Thomas, R. E. (2014). Near-bed and surface flow division patterns in experimental river bifurcations. Water Resources Research, 50(2), 1506–1530. https://doi.org/10.1002/2013WR014215
  40. McLelland, S. J., Ashworth, P. J., Best, J. L., Roden, J., & Klaassen, G. J. (1999). Flow structure and transport of sand-grade suspended sediment around an evolving braid bar, Jamuna River, Bangladesh. Fluvial Sedimentology VI, 28, 43–57. https://doi.org/10.1002/9781444304213.ch4
  41. Miori, S., Hardy, R. J., & Lane, S. N. (2012). Topographic forcing of flow partition and flow structures at river bifurcations. Earth Surface Processes and Landforms, 37(6), 666–679. https://doi.org/10.1002/esp.3204
  42. Mosley, M. P. (1976). An experimental study of channel confluences. The Journal of Geology, 84(5), 535–562. https://doi.org/10.1086/628230
  43. Orfeo, O., Parsons, D. R., Best, J. L., Lane, S. N., Hardy, R. J., Kostaschuk, R., Szupiany, R. N., & Amsler, M. L. (2006). Morphology and flow structures in a large confluence-diffluence: Rio Parana, Argentina. In R. M. L. Ferreira, C. T. L. Alves, G. A. B. Leal, & A. H. Cardoso (Eds.), River Flow 2006 (pp. 1277–1282).
  44. Parsons, D. R., Best, J. L., Lane, S. N., Orfeo, O., Hardy, R. J., & Kostaschuk, R. (2007). Form roughness and the absence of secondary flow in a large confluence–diffluence, Rio Paraná, Argentina. Earth Surface Processes and Landforms, 32(1), 155–162. https://doi.org/10.1002/esp.1457
  45. Ragno, N., Redolfi, M., & Tubino, M. (2021). Coupled morphodynamics of river bifurcations and confluences. Water Resources Research, 57(1), e2020WR028515. https://doi.org/10.1029/2020WR028515
  46. Redolfi, M., Tubino, M., Bertoldi, W., & Brasington, J. (2016). Analysis of reach-scale elevation distribution in braided rivers: Definition of a new morphologic indicator and estimation of mean quantities. Water Resources Research, 52(8), 5951–5970. https://doi.org/10.1002/2015WR017918
  47. Redolfi, M., Zolezzi, G., & Tubino, M. (2019). Free and forced morphodynamics of river bifurcations. Earth Surface Processes and Landforms, 44(4), 973–987. https://doi.org/10.1002/esp.4561
  48. Rhoads, B. L., & Kenworthy, S. T. (1995). Flow structure at an asymmetrical stream confluence. Geomorphology, 11(4), 273–293. https://doi.org/10.1016/0169-555X(94)00069-4
  49. Rhoads, B. L., & Sukhodolov, A. N. (2001). Field investigation of three-dimensional flow structure at stream confluences: 1. Thermal mixing and time-averaged velocities. Water Resources Research, 37(9), 2393–2410. https://doi.org/10.1029/2001WR000316
  50. Roy, A. G., & Bergeron, N. (1990). Flow and particle paths at a natural river confluence with coarse bed material. Geomorphology, 3(2), 99–112. https://doi.org/10.1016/0169-555X(90)90039-S
  51. Roy, A. G., Roy, R., & Bergeron, N. (1988). Hydraulic geometry and changes in flow velocity at a river confluence with coarse bed material. Earth Surface Processes and Landforms, 13(7), 583–598. https://doi.org/10.1002/esp.3290130704
  52. Sambrook Smith, G. H., Ashworth, P. J., Best, J. L., Woodward, J., & Simpson, C. J. (2005). The morphology and facies of sandy braided rivers: Some considerations of scale invariance. In M. D. Blum, S. B. Marriott, & S. F. Leclair (Eds.), Fluvial sedimentology VII. International association of sedimentologists. Special Publication No. 35 (pp. 145–158). Blackwell.
  53. Sharifipour, M., Bonakdari, H., Zaji, A. H., & Shamshirband, S. (2015). Numerical investigation of flow field and flowmeter accuracy in open-channel junctions. Engineering Applications of Computational Fluid Mechanics, 9(1), 280–290. https://doi.org/10.1080/19942060.2015.1008963
  54. Shukry, A. (1950). Flow around bends in an open flume. Transactions of the American Society of Civil Engineers, 115(1), 751–778. https://doi.org/10.1061/TACEAT.0006426
  55. Smagorinsky, J. (1963). General circulation experiments with the primitive equations. Monthly Weather Review, 91(3), 99–164. https://doi.org/10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2
  56. Sukhodolov, A. N., Krick, J., Sukhodolova, T. A., Cheng, Z. Y., Rhoads, B. L., & Constantinescu, G. S. (2017). Turbulent flow structure at a discordant river confluence: Asymmetric jet dynamics with implications for channel morphology. Journal of Geophysical Research: Earth Surface, 122(6), 1278–1293. https://doi.org/10.1002/2016JF004126
  57. Sukhodolov, A. N., & Sukhodolova, T. A. (2019). Dynamics of flow at concordant gravel bed river confluences: Effects of junction angle and momentum flux ratio. Journal of Geophysical Research: Earth Surface, 124(2), 588–615. https://doi.org/10.1029/2018JF004648
  58. Szupiany, R. N., Amsler, M. L., Hernandez, J., Parsons, D. R., Best, J. L., Fornari, E., & Trento, A. (2012). Flow fields, bed shear stresses, and suspended bed sediment dynamics in bifurcations of a large river. Water Resources Research, 48(11), W11515. https://doi.org/10.1029/2011WR011677.
  59. Thomas, R. E., Parsons, D. R., Sandbach, S. D., Keevil, G. M., Marra, W. A., Hardy, R. J., Best, J. L., Lane, S. N., & Ross, J. A. (2011). An experimental study of discharge partitioning and flow structure at symmetrical bifurcations. Earth Surface Processes and Landforms, 36(15), 2069–2082. https://doi.org/10.1002/esp.2231
  60. Thorne, C. R., Zevenbergen, L. W., Pitlick, J. C., Rais, S., Bradley, J. B., & Julien, P. Y. (1985). Direct measurements of secondary currents in a meandering sand-bed river. Nature, 315, 746–747. https://doi.org/10.1038/315746a0.
  61. van der Mark, C. F., & Mosselman, E. (2013). Effects of helical flow in one-dimensional modelling of sediment distribution at river bifurcations. Earth Surface Processes and Landforms, 38(5), 502–511. https://doi.org/10.1002/esp.3335
  62. Wang, X. G., Yan, Z. M., & Guo, W. D. (2007). Three-dimensional simulation for effects of bed discordance on flow dynamics at Y-shaped open channel confluences. Journal of Hydrodynamics, 19(5), 587–593. https://doi.org/10.1016/S1001-6058(07)60157-7
  63. Weber, L. J., Schumate, E. D., & Mawer, N. (2001). Experiments on flow at a 90° open-channel junction. Journal of Hydraulic Engineering, 127(5), 340–350. https://doi.org/10.1061/(ASCE)0733-9429(2001)127:5(340)
  64. Xie, Q. C., Yang, J., & Lundström, T. S. (2020). Flow and sediment behaviours and morpho-dynamics of a diffluence−Confluence unit. River Research and Applications, 36(8), 1515–1528. https://doi.org/10.1002/rra.3697
  65. Xu, L., Yuan, S. Y., Tang, H. W., Qiu, J. J., Whittaker, C., & Gualtieri, C. (2022). Mixing dynamics at the large confluence between the Yangtze River and Poyang Lake. Water Resources Research, 58(11), e2022WR032195. https://doi.org/10.1029/2022WR032195
  66. Yuan, S. Y., Xu, L., Tang, H. W., Xiao, Y., & Gualtieri, C. (2022). The dynamics of river confluences and their effects on the ecology of aquatic environment: A review. Journal of Hydrodynamics, 34(1), 1–14. https://doi.org/10.1007/s42241-022-0001-z
  67. Yuan, S. Y., Yan, G. H., Tang, H. W., Xiao, Y., Rahimi, H., Aye, M. N., & Gualtieri, C. (2023). Effects of tributary floodplain on confluence hydrodynamics. Journal of Hydraulic Research, 61(4), 552–572. https://doi.org/10.1080/00221686.2023.2231413
Download PDF

stencil

Experimental and numerical investigation of the squeegee process during stencil printing of thick adhesive sealings

두꺼운 접착제 실링의 스텐실 인쇄 중 스퀴지 프로세스에 대한 실험적 및 수치적 조사

 Fabiano I. Indicatti, Bo Cheng, Michael Rädler, Elisabeth Stammen, Klaus Dilger

ABSTRACT

To reliably compensate fuel cell stack tolerances, sealings with a layer thickness of at least 500 µm are necessary. Additionally, threads positioned at the upper region of the stencil apertures need to be integrated to print closed-loop designs under cycle times of as low as 3 seconds. All these requirements can intensify the occurrence of print defects and diminish the process stability. This paper addresses the issues of incomplete regions and air bubbles emerging during the squeegee process. It was detected that the cleanliness state of the stencil directly impacts the formation of incomplete regions by affecting venting conditions inside the aperture. Moreover, it was identified that bubbles are either transferred from the adhesive roll into the aperture or created due to interactions between the moving adhesive and stencil threads. Further, it was shown that bubbles cannot be completely eliminated using a stencil with threads but their size can remain smaller than 300 µm when printing with a new adhesive roll. Finally, distinct strategies were derived and verified experimentally to successfully print a basic sealing design. By introducing a small local gap between substrate and stencil, the entire sealing aperture was reliably filled without the need of a cleaning step.

1. Introduction

The structure of a single low temperature proton exchange membrane fuel cell (LT-PEMFC) fundamentally consists of a membrane electrode assembly (MEA) sandwiched between bipolar plates (BPPs) with sealings between these elements.[Citation1] Up to hundreds of cells can be combined into a stack to provide the required power output, which demands highly reliable manufacturing processes since a single defective cell can compromise the entire stack safety and performance.[Citation2] In light of this, the sealing is one specific component that has been receiving increased attention in the last years. Besides impeding gas and coolant leakages, the sealing is a crucial element in the overall stack concept for compensating assembly tolerances, which can reach up to 300 µm.[Citation3]

To achieve projected market volumes, stencil printing was identified as an attractive technique to meet cycle time requirements for the sealing production, which should be as low as 3 seconds.[Citation4–6] Despite that simple deposit structures achieving heights of up to 500 µm have been reported using solder pastes and conductive adhesives,[Citation7,Citation8] stencil printing is typically not adopted to apply layer thicknesses higher than 200 µm. In comparison, fuel cell sealing concepts demand a minimum layer thickness of 500 µm to safely offset the mentioned stack tolerances under compression ratios of up to 40%.[Citation9–12] Additionally, the sealings are characterized by significantly more complex contour designs to effectively seal ports, flow field and distribution channels of BPPs.

To print closed-loop designs, a so-called double-layer stencil can be adopted to apply the desired structure using a single print cycle.[Citation12–15] As shown in Figure 1, it consists of an upper layer with patterned threads that link different regions of the stencil and provide sufficient mechanical stability. These threads also support the second lower layer, which delineates the print design. This same stencil concept was previously tested using distinct configurations for the threads to print sealings for fuel cells.[Citation5,Citation6] These studies were mainly focused on investigating phenomena and print inconsistencies occurring during the separation process, such as the formation of air bubbles, filaments and excessive spreading. In contrast, print defects emerging during the squeegee process have not been thoroughly explored using this stencil concept.

Figure 1. Schematic of the stencil printing process consisting of a squeegee process (a) and a separation process (b). Perspective view of an aperture segment of a double-layer stencil made from stainless steel, based on.[Citation5,Citation6]

In this paper, a basic sealing design was used to identify relevant printing problems during the squeegee process, as shown in Figure 2. It presents approximate dimensions of 60 mm x 60 mm that should resemble the sealing design in the ports region of typical fuel cells. The squeegee direction corresponds to the indicated x-direction and the three sealing lines perpendicular to the squeegee direction were marked with the letters A, B and C for the sake of better differentiation. With this design, potential printing difficulties closer to the real application can be identified and evaluated more effectively. Based on preliminary experiments, two main print defects during the squeegee process were identified: incomplete regions and bubble formation.

Figure 2. Representative specimen of the basic sealing design with highlighted print defects (printed at 160 mm/s using condition SS–R1). The used squeegee direction corresponds to the indicated positive x-direction.

Incomplete regions are a known issue in stencil printing.[Citation16–20] Typically, small aperture dimensions and an insufficient pressure inside the print material are the main reported reasons for the emergence of this defect. In contrast, the formation of bubbles during the squeegee process is a less recognized phenomenon in stencil printing but can considerably impact the process reproducibility. In the field of screen printing, the presence of bubbles inside specimens was already reported by several studies.[Citation20–27] The mechanical agitation of the print material before the squeegee process and inherent interactions with the mesh were indicated as driving mechanisms for bubbles to appear.[Citation24–28] Yet, there is still very little consensus and a general lack of correlation with experimental data on describing how these bubbles are produced. Several computational fluid dynamics (CFD) simulations were developed to estimate the pressure distribution within the print material in front of the moving squeegee[Citation29–32] and the filling completeness of a given aperture volume,[Citation17,Citation18,Citation33,Citation34] where the latter has the additional advantage of being experimentally measurable. However, more comprehensive simulative approaches demonstrating the print material motion are still missing in the literature, which could provide valuable information to optimize the aperture filling behaviour and avoid print defects.

Based on this scenario, comprehensive print experiments were conducted to determine how print and stencil parameters influence the formation of incomplete regions and bubbles during the squeegee process. Characterisation methods using microscope images and micro-CT scans were applied to quantify and analyse these defects. Here, a stencil containing a lines design with and without threads was adopted, which allows to isolate the impact of threads in the print results. In addition, a new CFD model of the squeegee process was developed in FLOW–3D[Citation35] to visualize how these print defects emerge. The squeegee process was recorded in slow motion to analyse the adhesive roll behaviour and provide additional validation for the simulations. Based upon the combined experimental and simulation results, potential approaches to avoid these printing problems using the basic sealing design were derived and tested. Ultimately, the collected findings in this paper should enhance the understanding on decisive process and stencil parameters during the squeegee step, increasing the attractiveness of this technique for the application of sealings and adhesives in the industry.

2. Materials and methods

All preparation steps and experiments were conducted in laboratory conditions, at 23°C.

2.1. Stencil design

Two different stencils made from stainless steel (Christian Koenen GmbH, Ottobrunn, Germany) were used for the experiments. As illustrated in Figure 3, both stencils presented apertures with a 680 µm thick step and 120 µm thick threads, resulting in a stencil thickness of 800 µm. Here, a thicker stencil than the minimum layer thickness of 500 µm is required since a certain degree of spreading (height loss) of the applied material over the substrate always occurs. A very similar configuration was previously used to reliably reach the same layer thickness using several distinct adhesives as print material.[Citation6] The first stencil (a) corresponds to the one used to print the mentioned sealing design, and the second stencil (b) consists of 80 mm length lines with two different widths: 1.52 and 2.34 mm, which correspond to aperture aspect ratios (AR = width/height) of 1.90 and 2.93, respectively. A second pair of lines without threads was included in this stencil to separately examine how the addition of threads influences the print results. The line orientation relative to the squeegee direction was primarily adjusted at 0°. This considerably reduces the modelling and computational effort for the numerical simulations but still allows to capture the basic formation mechanisms of desired print defects.

Figure 3. Schematic of used stencils and detailed views of the aperture threads design.

2.2. Adhesive selection and print parameters

An ultraviolet (UV) curable acrylic was selected for all experiments, and it corresponds to adhesive B3, which was thoroughly characterized and tested previously by Indicatti et al.[Citation6] It exhibited very good printability, and its transparency facilitates the characterisation of bubbles inside the specimen. Moreover, this adhesive presented a reduced filament-stretching tendency, which avoided the formation of bubbles during the separation process.

The rheological properties of this adhesive required for the simulation model are reported in Table 1. The viscosity values were obtained with a stepped flow approach using a rheometer (MCR 500, Anton-Paar GmbH, Ostfildern, Germany) equipped with a plate-plate setup (25 mm diameter) and a 0.4 mm gap. The adhesive surface tension was measured with the Wilhelmy plate method (K100 Force Tensiometer, KRÜSS GmbH, Hamburg, Germany) using a platin-iridium Wilhelmy-plate (10 × 20 x 0.2 mm). These measurements were carried out at a constant speed of 0.01 mm/s and an immersion depth of 2 mm. An optical contact angle measurement system (DSA 10, KRÜSS GmbH, Hamburg, Germany) was used to determine the adhesive equilibrium contact angle with the stencil surface. The surface tension and contact angle measurements were conducted with adhesive B3 without fumed silica since the filled one used for the print experiments exhibited an apparent yield stress that prevented wetting and thereby reliable measurements with these methods. For additional information about this adhesive and rheological characterisations, see reference.[Citation6]

Equilibrium surface tension [mN/m]28.6 ± 0.1
Equilibrium contact angle of the adhesive on the stencil surface (smooth untreated stainless steel) [°]20.0 ± 1.5
Density [g/cm3]0.970
Shear rate [1/s]Steady-state viscosity [Pa∙s]
1021.1
15.615.4
25.111.5
39.88.9
63.17.1
1005.8
Table 1. Average and corresponding standard deviation of the adhesive properties incorporated into the model. The contact angle and surface tension measurements were repeated five times. The viscosity standard deviation remained below 5%, based upon three measurements.

The print experiments were performed with a commercial stencil printer (EKRA STS E5, ASYS Group, Dornstadt, Germany). Squeegee speeds of 40 and 160 mm/s were tested, and the separation speed kept unchanged at 1 mm/s to minimize the risk of print defects emerging during separation. A squeegee pressure of 0.5 N/mm was adopted to leave the stencil topside completely free of adhesive remains after the squeegee process, which is a required condition to not affect the final layer thickness. The used squeegee (RKS Carbon S HQ/30 65 Shore, RK Siebdrucktechnik GmbH, Rösrath, Germany) presented a length of 120 mm and a 4 mm chamfer (45°) at the tip. A squeegee holder of 60° was adopted, resulting in a nominal squeegee angle of 15°. This squeegee configuration was selected based on previous experiments to enhance the aperture filling and process reproducibility.

An adhesive roll was manually dispensed over the stencil using an adhesive gun to ensure comparable initial conditions. Every new adhesive roll was completely free of bubbles and its height was always between 8 and 12 mm. Large adhesive residues on the squeegee after printing were also removed when a new roll was added to prevent any further sources of bubbles. Another additional parameter evaluated was the aperture state and cleanliness of the stencil underside before printing. Considering the adhesive roll state, four different print conditions were investigated, as illustrated in Figure 4
: cleaned aperture with cleaned stencil and a new adhesive roll (CA–R1), pre-wetted aperture with cleaned stencil and a new adhesive roll (CS–R1), pre-wetted aperture with smeared stencil and a new adhesive roll (SS–R1), and pre-wetted aperture with smeared stencil and a three-times used adhesive roll (SS–R3).

Figure 4. Simplified illustration of the aperture cross section describing the four tested print conditions considering the state of the aperture, stencil underside and adhesive roll.

With exception of condition CA–R1, these correspond to relevant operation modes that have direct impact on the production cycle time and process efficiency. The cleaning procedure of the stencil was conducted manually by hand using absorbent wipes. It is important to emphasize that the illustrated smearings in Figure 4 were not considered as a print defect since these remained roughly smaller than 0.2 mm throughout the performed experiments. Moreover, the extent of smearings observed did not cause instabilities during the separation process, nor did it significantly affect print resolution due to the relatively large dimensions of the printed structures.

2.3. Specimens characterisation

All specimens were scanned using a light microscope (VHX-2000, Keyence, Osaka, Japan) with a resolution of 5.2 µm/pixel. To analyse the bubbles inside the specimens, ImageJ[Citation36,Citation37] was used for image processing and extracting the quantity and area of bubbles, as depicted in Figure 5
. Since the majority of the bubbles exhibited a circular shape, the measured bubble area was converted to an equivalent bubble diameter, which is a more convenient indicator. Frequency distribution histograms of the bubble diameter were derived from this data by combining the quantity of bubbles of three different specimens printed at identical conditions. Furthermore, micro-CT measurements (voxel-size: 10 µm) were conducted with a few representative specimens to obtain the precise position of the bubbles along the specimen height, which could not be assessed using the microscope.

Figure 5. Developed approach using ImageJ to characterize bubbles formed during the squeegee process.

3. Experimental results and discussion

3.1. Incomplete regions

The gap between stencil and substrate was measured and set to zero in order to keep the smearings at a minimum. Prominent smearings were not observed during all experiments. However, it was identified that the cleanliness state of the stencil before printing was associated with the emergence of incomplete regions, as reported in Figure 6. When the stencil was not cleaned before printing (conditions SS–R1 and SS–R3), 95.8% of the specimens exhibited incomplete regions. In contrast, only 6.3% of the specimens printed with a cleaned stencil (conditions CA–R1 and CS–R1) presented this defect. The incomplete regions were located exclusively at the line extremity that was last filled by the squeegee and appeared either as a large bubble that extends almost throughout the entire line width (Figure 7(a)) or as an empty space (Figure 7(b)).

Figure 6. Number of specimens exhibiting incomplete regions printed at 40 and 160 mm/s.
Figure 7. Representative specimens with incomplete regions at the line extremity (last part to be filled by the squeegee).

The occurrence of this defect was attributed to the lack of air venting at the line extremity due to the smearings at the stencil underside. Despite being small, the smearings can act like an additional seal between the stencil and substrate that impedes air to be expelled from the aperture during the squeegee process. This deduction is supported by the fact that large air bubbles were transferred into the adhesive roll when printing with a smeared stencil whereas such bubbles were not observed when it was cleaned. Figure 8 displays this phenomenon with two image sequences from the squeegee process recorded at a frame rate of 120 fps using a cleaned (a) and a smeared stencil (b). As can be seen, both adhesive rolls are completely free of bubbles before reaching the line extremity. The gap between stencil and substrate is intended to be zero, however, it still allows air to escape when the stencil is cleaned, which most of the time is sufficient to avoid filling defects and the formation of bubbles inside the adhesive roll. This phenomenon was identified using all four print conditions and was consistently replicated using both squeegee speeds.

Figure 8. Image sequences of the squeegee process using a cleaned (a) and smeared stencil (b) to compare the formation of bubbles inside the adhesive roll when the squeegee (40 mm/s) passes through the line extremity.

The same effect was observed when printing the sealing design, where large bubbles formed inside the adhesive roll when it was passing by the T-intersections and the line C of the sealing. Here, the detection of these bubbles was correlated with the presence of incomplete regions as well. The T-intersections can be considered as a more critical part to be completely filled due to their geometry and larger volume compared to the lines. Thus, the aperture design and its orientation relative to the squeegee direction can be considered as an additional influencing parameter, which directly determine the available time for filling. For instance, a few small incomplete regions were also formed at lines A and B, as shown in Figure 2. In this case, large bubbles did not appear inside the adhesive roll when passing through these lines, and the formation of these incomplete regions can be further associated with an insufficient time for the adhesive to fill the aperture or air to be expelled from it. This is reinforced by the observation that lines A and B of sealing specimens printed at 40 mm/s exhibited a better or even complete filling of those lines. Therefore, additional approaches to provide sufficient venting and time for filling are required to reliably fill all critical regions, which will be discussed later in section 5.

Variations of the squeegee speed and aperture AR or the presence of stencil threads did not notably impact the formation of incomplete regions, see Figure 6. All specimens were printed with a nominal squeegee angle of 15°, and experiments performed with larger (30°) and shallower (5°) angles did not result in any significant improvement of the aperture filling completeness. Increasing the vertical squeegee pressure to minimize the extent of smearings at the stencil underside also did not avoid incomplete regions. Indeed, an excessive squeegee pressure (>1 N/mm) might even enhance the restriction on air flow between stencil and substrate, leading to the emergence of incomplete regions using a cleaned stencil as well. This description better indicates the ‘cleanliness state’ as the decisive parameter on the formation of the print defect.

3.2. Bubble formation

Figure 9 reports frequency distribution histograms of the bubble diameter from specimens printed at two different squeegee speeds and aperture ARs. The measured quantity of bubbles was normalized by the total considered length of three specimens (240 mm) to enhance comparability. The histograms of specimens printed without threads were included as well. Yet, the following explanations are only considered for the specimens printed with threads if not indicated.

Figure 9. Frequency histograms of the diameter of the bubbles produced during the squeegee process.

Overall, the diameter of the bubbles did not surpass 1000 µm and the majority of them remained below 300 µm. By increasing the squeegee speed from 40 to 160 mm/s, the quantity of bubbles more than doubled in average considering the four tested print conditions. When the aperture AR is increased from 1.90 to 2.93, the average quantity of bubbles increased about 44%. In all considered cases, the cleaned aperture (CA–R1) produced the smallest quantity of bubbles. The bubble formation drastically increased with a pre-wetted aperture, as represented by the profiles of the cleaned (CS–R1) and smeared stencil (SS–R1). Here, the quantity of bubbles stayed relatively constant independent of the cleanliness state of the stencil (CS–R1 or SS–R1), and the distribution of the bubble diameter maintained a similar range as well. In this case, the largest discrepancy was notable in bubbles of up to 50 µm in diameter. Specimens printed with a smeared stencil (SS–R1) presented about twice the quantity of bubbles of this size when compared to those printed with the cleaned stencil (CS–R1). When printing with the same adhesive roll for the third time (SS–R3), the quantity of bubbles kept in about the same level of specimens printed with a new adhesive roll (SS–R1). One exception here was observed using the larger aperture AR at 160 mm/s, which produced approximately 50% more bubbles with the three times used adhesive roll. In addition, SS–R3 specimens were the only ones that exhibited very large bubbles with more than 300 µm in diameter.

By combining the results from the diagrams with the recordings of the squeegee process and specimens characteristics, three main mechanisms for bubble formation were identified, as shown in Figure 10. The first mechanism corresponds to bubbles that are not created due to the stencil threads but transferred from the adhesive roll into the aperture during the squeegee process. These bubbles are in general smaller than 300 µm and they hardly interact with stencil threads due to their size. This was confirmed by the fact that lines printed with the aperture without threads still presented bubbles but in considerable smaller quantities. In this case, lines printed with a new adhesive roll did not exhibit a significant quantity of bubbles independent of the squeegee speed. However, if a new adhesive roll was not added, the quantity of bubbles increased with the number of print cycles. Figure 11 presents an adhesive roll free of air bubbles before the squeegee process (a) and the same adhesive roll after three print cycles (b). The visible bubbles in the roll correspond to the ones that can be transferred into the aperture during the squeegee process. These bubbles might be created by random local instabilities during filling, but the main sources appear to be the air entrapment due to the lack of venting at the aperture extremity, as mentioned earlier, and due to the first contact or recontact between the squeegee and the adhesive over the stencil.

Figure 10. Identified bubble formation mechanisms during the squeegee process. The shown specimen segments were printed with an aperture AR of 2.93.
Figure 11. Adhesive roll over the stencil free of air bubbles before printing (a) and after three print cycles (b). In this case, the aperture with threads was used but very similar bubble characteristics inside the adhesive roll were observed when printing with the aperture without threads.

The second mechanism is very similar to the first one, with the difference that the stencil threads interact with large bubbles from the adhesive roll (shown in Figure 11(b)) when these are entering the aperture. This was deduced considering the regular position of large bubbles coinciding with the threads pitch and by comparing specimens printed with and without threads. This mechanism was responsible for producing the largest bubbles identified (>300 µm), which solely emerged inside specimens printed with threads. Thus, it is plausible to say that the interactions with the threads might increase the final air volume of bubbles coming from the adhesive roll since the characteristics of bubbles produced inside the adhesive roll were very similar independent of the threads presence. Alternatively, the threads might also locally change flow conditions, which could facilitate the transfer of larger bubbles from the adhesive roll.

Finally, the third mechanism is exclusively related to the presence of stencil threads, as these bubbles presented a very uniform pattern correlated with the threads pitch. Here, bubbles having a broad size range between 50 and 300 µm appearing near the centreline were the main type responsible for increasing the quantity of bubbles when a higher squeegee speed was used. Moreover, bubbles typically smaller than 100 µm in diameter emerged very close to the aperture walls and mostly in pairs. These are the primary contributors to the increase of the bubbles quantity when printing with a pre-wetted aperture (CS–R1 and SS–R1) instead with a cleaned aperture (CA–R1). The formation mechanisms of these two types of bubbles could not be captured experimentally but were assessed by the numerical simulations.

During the experiments it was also observed that bubbles can disappear after the separation process, as shown in Figure 12. Bubbles close to the aperture walls and threads might stay in the aperture or break due to the separation process since filaments are stretched near these regions. However, this phenomenon happened only occasionally and has a considerable smaller impact than the mechanisms previously presented. Yet, this phenomenon should be still mentioned since these bubbles might remain inside the aperture after separation and reappear in the following printed specimen. Thus, considering this and the three bubble formation mechanisms shown in Figure 10, it can be stated that all bubbles inside specimens printed with condition CA–R1 emerge due to the presence of stencil threads (Mechanism 3). Specimens produced with conditions CS–R1 and SS–R1 present bubbles that are majorly originated from Mechanism 3 since a new adhesive roll is used for these two conditions as well. Finally, specimens printed with condition SS–R3 exhibit bubbles from all mechanisms described before. It is possible to infer that all bubbles larger than 300 µm emerge due to Mechanism 2. However, excepting the small bubbles (<100 µm) close to the lateral walls exhibiting a uniform relative distance (Mechanism 3), the remaining bubbles cannot be categorized into their corresponding formation mechanism with certainty.

Figure 12. Comparison of the aperture before the separation process (left) and the final specimen (right) demonstrating how bubbles can disappear when located near the aperture walls and threads. This specimen was printed using condition SS–R1.

4. Modelling approach

This numerical study is focused on reproducing the basic formation mechanisms of incomplete regions and bubbles during the squeegee process. The simulations were performed only at a constant squeegee speed of 40 mm/s since it was already sufficient for both print defects to emerge. As previously discussed, a higher squeegee speed solely increased the quantity of bubbles but did not drastically change other characteristics of these print defects. For validation, the position and relative size of these defects were assessed alongside real specimens using microscope images and micro-CT scans. In addition, recordings of the adhesive motion during the squeegee process were compared with the simulation results to identify possible similarities. The CFD model was implemented in the commercially available software FLOW–3D,[Citation35] which applies the finite volume method (FVM) to numerically solve the conservation equations for mass and momentum. By neglecting turbulence effects and mass generation, these two equations can be described by the following expressions, respectively:

∂𝜌∂t+∇⋅(𝜌⁢𝒖)=0 (1)

∂𝒖∂𝑡+(𝒖⋅∇)⁢𝒖=1𝜌∇𝑝+𝜈∇2𝒖+𝒇 (2)

where 𝜌 is the adhesive density, 𝑡 is the time, ∇ is the divergence, 𝒖 is the velocity vector, and 𝑝 is the static pressure. 𝜈 corresponds to the kinematic viscosity and 𝒇 to the external body forces, such as gravitational and surface tension forces. To describe the free interface between the two fluids (adhesive and air), the volume of fluid (VOF) method is used:

∂𝛼∂t+∇⋅(𝛼⁢𝒖)=0 (3)

The variable 𝛼 represents the proportion of the cell volume occupied by adhesive, with 𝛼=0 signifying a cell entirely filled with air and 𝛼=1 indicating a cell entirely filled with adhesive. Consequently, a partially filled cell is defined as 0<𝛼<1. At each step time, the interface between the fluids can be dynamically reconstructed based on this cell information and is iteratively recalculated considered the updated moving squeegee location. For further details about the model implementation, we refer here to the software’s user manual.[Citation38]

4.1. Model description and assumptions

The same squeegee and threads dimensions from the experiments were incorporated into the model. To reduce computational effort, the aperture with 2.34 mm width (AR = 2.93) was modelled using an axisymmetric geometry, and only a line segment with 9.96 mm length was considered, as shown in Figure 13. A 3D model was adopted since a 2D model is not able to capture the adhesive flow perpendicular to the squeegee direction, which is a decisive phenomenon inside the aperture during the filling process. In order to investigate the impact of venting on the formation of incomplete regions and bubbles, two different simulation cases were established. In the first case, a 50 µm gap between stencil and substrate was integrated to allow air to escape from the aperture during filling. This should be equivalent to condition CA–R1 tested experimentally. In the second case, the model did not include a gap and should correspond to condition SS–R1. Here, it is important to note that the simulation model did not contain pre-wetted aperture walls or threads, which has to be considered when comparing it with experimental results.

Figure 13. Model overview with relevant dimensions and mesh details.

The following assumptions have been further considered for the model:

  1. The simulation domain contains only two phases (adhesive and air) with constant volumes, where the adhesive motion is simulated as an incompressible and laminar fluid flow.
  2. The stencil and squeegee are modelled as rigid bodies and exhibit no-slip boundary conditions. A horizontal translational speed is given to the squeegee to simulate the filling process, and the stencil remains stationary. There is no gap between the squeegee tip and the stencil.
  3. The shear thinning viscosity of the adhesive was defined in a tabular form between the shear rates of 10 and 100 s−1, see Table 1.
  4. The measured adhesive surface tension and its equilibrium contact angle with the stencil surface were included in the material model. The same equilibrium contact angle was adopted for the squeegee surface in the simulation.

The entire simulation domain was meshed with regular block shaped cells adopting a commonly used meshing strategy, where the cells exhibit reducing dimensions towards the aperture region and remain unchanged throughout the entire simulation time, as shown in Figure 12. To minimize repeated calculations, the squeegee process was modelled using a two-step approach. In the first step, the adhesive over the stencil rolls for about 25 mm up to near the aperture, reproducing the initial conditions from the experiments. The rolling motion of the adhesive reduces the viscosity due its shear thinning properties, which can impact the filling behaviour. This step was identical in both simulation cases, and the adhesive roll remained free of air bubbles. A coarser mesh with cell sides of up to 750 µm was applied for this step resulting in a simulation domain with about 1.8 million cells. In the second step, the adhesive starts entering the aperture, which corresponds to the simulation stage of main interest. Inside the aperture, the cells exhibited equal sides of 40 µm, which was adopted as a balance between computational time and accuracy. Using this mesh approach, the second domain contained about 3 million cells. The time step was automatically adjusted and ranged from 1 × 103 to 1 × 104 s during the first step while in the second one it stayed between 1 × 10−4 and 1 × 10−5 s.

4.2. Simulation results and validation

Figure 14 shows two simultaneous views from the symmetry plane and aperture bottom over the simulation time during the aperture filling with (a) and without (b) a gap between stencil and substrate. As can be seen, the adhesive is able to completely fill the aperture when a gap for venting is available. When the gap is removed, the right aperture extremity remains unfilled due to the enclosed volume formed between substrate, aperture walls and adhesive (t = 1.44 s). In this case, the formation of an air bubble inside the adhesive roll (t = 1.53 s) was captured by the simulation as well, agreeing with the experiment results presented in Figure 8(b). Another important phenomenon observed in the experiments and replicated by the model was the adhesive infiltrating the gap between the stencil and substrate, resulting in the formation of smearings that remained smaller than 0.15 mm in the simulation.

Figure 14. Simultaneous views (∆t = 0.09 s) from the symmetry plane and aperture bottom of the simulated squeegee process with (a) and without (b) a gap between stencil and substrate.

The simulations were also able to reproduce the formation of bubbles due to the presence of threads, as previously described by the third mechanism shown in Figure 10
. In the simulation case without a gap, bubbles with size ranging between 50 and 100 µm formed at the aperture walls and substrate surface with their relative distance coinciding with the threads pitch. When entering the aperture, the adhesive front is split by the threads into two smaller fronts that entrap air when reencountering at the substrate surface (t = 1.35 s). As the squeegee advances, the air is pushed towards the lateral walls but remains inside the aperture due to lack of venting. From micro-CT scans, it was possible to verify that these bubbles are touching the substrate surface as well, see Figure 15(b)
. Thus, these simulation results correlate very well with real specimens printed using condition SS–R1. Here is important to stress that the bubbles in the simulation are directly touching the aperture walls and would disappear in a subsequent separation process. In the real specimens, these bubbles are not contacting the aperture walls before separation, as shown in Figure 12
. This difference can be explained by the fact that the aperture in the simulation is not pre-wetted with adhesive before being filled, which differs from real SS–R1 conditions. Hence, the formation of these bubbles near the aperture walls results from the interplay between the incoming adhesive pushed by the squeegee and the adhesive that is pre-wetting the aperture walls. For comparison, these bubbles near the aperture walls did not appear when venting was available in the simulation, which also correlates with real specimens printed with CA–R1 conditions.

Figure 15. Qualitative comparison of representative specimens (scanned with microscope and micro-CT) and corresponding simulation exhibiting the final state of the aperture after the squeegee process with (a) and without (b) a venting gap. Bubbles produced due to the presence of threads (Mechanism 3) are visible in both experimental and simulation results, as indicated by the arrows. Two additional views (perspective and symmetry plane showing mesh cell size) of the two last threads (aperture extremity) from the simulated cases were included with the adhesive showing transparent properties to better visualize the generated bubbles.

Bubbles along the aperture centreline were formed in both simulation cases as well, see Figure 15. These bubbles are located close to or on the threads and exhibited sizes in the range of 100 to 200 µm, which fairly correlates with the experimental results. In the model, these bubbles only remained at the two last threads of the aperture. However, it is possible to observe bubbles forming around the other threads during filling (t = 1.44 s) but are broken after the squeegee tip passes through them (t = 1.62 s). In the experiments, these bubbles were visible all along the line length using conditions CA–R1 and SS–R1. Hence, the formation of these bubbles is unaffected by whether the threads are pre-wetted with adhesive or not. This discrepancy can be related to the apparent higher difficulty for the bubbles to detach from the threads in the model, which might be associated with insufficient small cell elements or simplifications in the material model.

To better understand this behaviour, Figure 16 presents the resulting adhesive velocity during the aperture filling for the case with a venting gap. The bubbles around the threads are formed approximately 4 to 6 mm in front of the squeegee tip (t = 1.46 s) and remain attached up until the squeegee tip reaches them (t = 1.55 s). The generated adhesive flow around the bubbles is not sufficient to release these from the threads. About 1 mm in front of the squeegee tip, a region with practically zero velocity is formed due to the flow direction change inside the aperture (t = 1.46 s). Immediately below the squeegee tip, the adhesive flow follows the squeegee direction but is gradually reorientated towards the substrate surface up until reaching the opposite direction of the squeegee. This reorientation leads to the formation of a backflow behind the squeegee tip, which causes a local overfilling of the aperture and contributes to break the bubbles around the threads (t = 1.55 s). When approaching the aperture extremity, the backflow region is affected by the aperture wall, which can explain why these bubbles only formed near the last two threads in the simulation.

Figure 16. Detailed symmetry plane view (∆t = 0.03 s) showing the resulting adhesive velocity for the simulation case with a venting gap between the stencil and substrate. The velocity vectors and fields are represented for a stationary observer fixed on the stencil.

This backflow was also observed experimentally but not in the same intensity as in the simulations. This difference can be related to the reduced viscosity range adopted and calibrated for the model, which used the viscosity value at 10 s−1 for lower shear rates. In addition, the neglected thixotropic properties of the adhesive might also have an impact on this response. Simulations using a larger range for the shear thinning viscosity of up to 0.1 and 1 s−1 were carried out but the higher viscosity avoided the reliable filling of the aperture, preventing any assessment of bubble formation during this step. Thus, the model is sensitive to changes in the viscosity range and should be recalibrated when, for instance, the squeegee speed is considerably increased. Additional simulation cases were not conducted since the formation of incomplete regions and bubbles was already detected and an appropriate investigation of the mentioned models deviations would go beyond the scope of this paper.

5. Sealing design with optimized print conditions

In this section, new strategies based on the presented experimental and numerical results were assessed to enhance the print conditions of the sealing design. Primary focus was placed on minimizing the process cycle time and on reducing print defects. The exhibited findings indicate that bubbles cannot be completely eliminated when using a stencil with threads. However, when using a new adhesive roll, the bubble diameter generally did not surpass 300 µm independent of the squeegee speed. Therefore, for every new specimen, a new adhesive roll was used. Despite producing more bubbles, the higher squeegee speed of 160 mm/s was favoured since these marginally impacted the process reliability. Yet, it should be emphasized that the influence of such bubbles on other sealing characteristics still needs to be quantified experimentally. For instance, previous studies have shown that voids inside composite and polymeric materials can notably diminish gas permeability, which on the other hand might be also compensated by increasing the sealing width or altering material properties.[Citation39–43] Hence, systematic investigations should be conducted in the future to assess the real performance of sealings printed with stencil printing and determine how process parameters can be actively adjusted to control gas permeability.

It is possible to reduce the number of stencil threads and consequently the quantity of bubbles. However, the mechanical stability of the stencil must be re-evaluated when altering the threads design. In this case, the stencil was not changed but the orientation of the sealing design relative to the squeegee direction was rotated by 20°. This angle was selected based on previous experiments to shift the position of incomplete regions to the sealing edges highlighted in Figure 17. Yet, solely adjusting the sealing orientation was not sufficient to prevent all filling defects, which can be considered the major cause for print inconsistencies. For this reason, four different approaches were investigated to achieve a completely filled sealing, as reported in Table 2. Here, only approaches using the least amount of cleaning were considered since adding a cleaning step before printing every single specimen can substantially increase cycle time and production costs. Thus, all approaches were conducted using a pre-wetted aperture with a smeared stencil (SS–R1 condition), and three specimens were printed in sequence to confirm the observations. It is also important to note that, despite rotating the sealing design at 20° or adding a second squeegee stroke, the observed quantity and size of bubbles did not notably change compared to sealings printed at 0° with a single squeegee stroke. Thereby, further bubble characterisations were not conducted to analyse the influence of these parameters.

Figure 17. Illustration of the rotated stencil with the sealing design and indication of regions exhibiting filling problems.
Approach descriptionSnap-off distance [mm]Formation of incomplete regions
(a) Single squeegee stroke with snap-off distance0.2Yes
(b) Double squeegee stroke0Yes
(c) Double squeegee stroke with snap-off distance0.2Yes
(d) Single squeegee stroke with local tape pieces (0.2 mm)0.2No
Table 2. Overview of evaluated approaches to eliminate incomplete regions in the sealing design.

The first approach was based on introducing a gap of 0.2 mm between stencil and substrate, also sometimes referred as snap-off distance.[Citation44,Citation45] It was expected that this gap could provide sufficient venting to fill the aperture entirely. However, no significant improvement in avoiding incomplete regions was observed compared to sealings printed without a gap, see Figure 18(a)
. Here, the squeegee vertical pressure closes the gap when it advances towards the aperture, and the smearings at the stencil underside act, as previously described, as an additional seal that inhibit air being expelled through it. Additional tests including the cleaning of the stencil enhanced the filling completeness of the T-intersection, but the last sealing edge (at line C) still remained incomplete.

Figure 18. Representative specimens printed with four different approaches to avoid the formation of incomplete regions: (a) single squeegee stroke with snap-off distance, (b) double squeegee stroke, (c) double squeegee stroke with snap-off distance, and (d) single squeegee stroke with local tape pieces.

The second and third approaches relied on using two squeegee strokes moving forwards and backwards. The idea here was that a second squeegee stroke could eliminate the incomplete regions by pushing adhesive from the opposite direction. However, this approach was insufficient to completely prevent this print defect as well. Adding a gap of 0.2 mm between stencil and substrate also did not improve the filling completeness. Instead of an incomplete filling, large bubbles usually larger than 1000 µm formed at these regions, see cases (b) and (c) in Figure 18. The main disadvantage of this approach is that it requires at least twice the time for the squeegee process. Yet, an additional squeegee stroke can be considered to have a smaller impact on production efficiency compared to introducing a cleaning step before every single specimen.

For the fourth approach, local gaps of about 0.2 mm height were introduced between the stencil and substrate by adding a small piece of adhesive tape near the edges with filling problems. The main difference to the first approach is that the gap created by the piece of tape does not close due to the squeegee vertical pressure or due to smearings. Thus, a small venting channel is maintained during the squeegee process that allows air to escape the aperture at those edges, ensuring the complete filling of the entire sealing, see Figure 18(d)
. The use of a tape piece was solely a simple method to prove the effectiveness of a local gap and more sophisticated approaches can be used, such as integrating a local elevation or channel on the substrate or stencil.[Citation46–48]

6. Conclusions

The squeegee process to print a basic sealing including relevant design features close to real fuel cell applications was optimized using experimental and numerical approaches. First, incomplete regions and bubbles forming during the squeegee process were detected as the main print defects. An additional stencil containing only lines with and without threads was used to isolate the formation mechanisms of these two defects. It was shown that the stencil cleanliness state considerably impacts the venting conditions inside the aperture during filling and thereby is determinant on the emergence of incomplete regions. Moreover, three main formation mechanisms of bubbles were proposed, evidencing that pre-existing bubbles inside the adhesive roll might be transferred into the aperture by the squeegee movement or produced due to interactions between the adhesive and stencil threads. The developed numerical model presented an overall good agreement with experimental observations and was able to reproduce the formation of incomplete regions and bubbles as well.

By combining experiment and simulation results it was verified that bubbles cannot be completely avoided when using a stencil with threads. However, by adding a new adhesive roll for every new print cycle, the quantity of bubbles can be reduced, and their diameter remained generally smaller than 300 µm, which was considered to have a minor impact on the process reliability. Based on these findings, four different print strategies focused on minimizing the print cycle time were assessed to eliminate incomplete regions emerging in the sealing design. By reorienting the aperture relative to the squeegee direction and maintaining a local gap during the squeegee process, this printing issue was prevented and the reproducible filling of the entire sealing was successfully achieved.

References

  1. Mehta, V.; Cooper, J. S. Review and Analysis of PEM Fuel Cell Design and Manufacturing. J. Power Sources. 2003, 114(1), 32–53. DOI: 10.1016/S0378-7753(02)00542-6.
  2. Jörissen, L.; Garche, J. Polymer Electrolyte Membrane Fuel Cells. In Hydrogen and Fuel Cell, 1st ed.; Töpler, J. Lehmann, J., Eds.; Springer Vieweg: Berlin/Heidelberg, 2016; pp. 239–281.
  3. Bieringer, R.; Adler, M.; Geiss, S.; Viol, M. Gaskets: Important Durability Issues. In Polymer Electrolyte Fuel Cell Durability, Büchi, F., Inaba, M. Schmidt, T., Eds.; Springer: New York, 2009; pp. 271–281. DOI: 10.1007/978-0-387-85536-3_13.
  4. Heimes, H.; Kehrer, M.; Hagedorn, S.; Hausmann, J.; Krieger, G.; Müller, J. Production of fuel cell components, 2nd ed.; PEM of RWTH Aachen University and VDMA AG Fuel Cell: Aachen, 2022.
  5. Indicatti, F. I.; Rädler, M.; Günter, F.; Stammen, E.; Dilger, K. Stencil Printing of Adhesive-Based Fuel Cell Sealings: The Influence of Rheology on Bubble Formation During the Separation Step. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 2022, 238(7), 2552–2567. DOI: 10.1177/09544062221121991.
  6. Indicatti, F. I.; Rädler, M.; Stammen, E.; Dilger, K. Optimizing Adhesive Rheology for Stencil Printing of Fuel Cell Sealings Using Supervised Machine Learning. Int. J. Adhes. Adhes. 2024, 132, 103693. DOI: 10.1016/j.ijadhadh.2024.103693.
  7. Dušek, M.; Hunt, C. A Novel Measurement Technique for Stencil Printed Solder Paste. Solder. Surf. Mount. Technol. 2003, 15(2), 35–45. DOI: 10.1108/09540910310479512.
  8. Zou, L.; Dušek, M.; Wickham, M.; Hunt, C. Characterising Stencil Printing of Surface Mount and Conductive Adhesives; NPL Report. MATC(A)55, 2002.
  9. Freudenberg-NOK. Ice Cube Sealing Prototyping Sheets. https://www.fst.com/-/media/files/gated/solution-sheets/en/ice-cube-sealing_fst.pdf(open in a new window) (accessed Mar 24, 2024).
  10. Freudenberg-NOK. Elastomeric Seals for Bipolar Plates. https://www.fst.com/-/media/files/gated/solution-sheets/en/elastomeric-seals-for-bipolar-plates_fst.pdf(open in a new window) (accessed Mar 24, 2024).
  11. Xu, Q.; Zhao, J.; Chen, Y.; Liu, S.; Wang, Z. Effects of Gas Permeation on the Sealing Performance of PEMFC Stacks. Int. J. Hydrogen. Energy. 2021, 46(73), 36424–36435. DOI: 10.1016/j.ijhydene.2021.08.137.
  12. Zhao, J.; Guo, H.; Ping, S.; Guo, Z.; Lin, W.; Yang, Y.; Shi, W.; Wang, Z.; Ma, T. Research on Design and Optimization of Large Metal Bipolar Plate Sealing for Proton Exchange Membrane Fuel Cells. Sustainability. 2023, 15(15), 12002. DOI: 10.3390/su151512002.
  13. Tepner, S.; Lorenz, A. Printing Technologies for Silicon Solar Cell Metallization: A Comprehensive Review. Prog. Photovoltaics Res. Appl. 2023, 31(6), 557–590. DOI: 10.1002/pip.3674.
  14. Hoornstra, J.; Roberts, S.; Moor, H.; Bruton, T. First Experiences with Double Layer Stencil Printing for Low Cost Production Solar Cells. Vienna: 2nd World Conf Photovoltaic Solar Energy Conv. 1998, 1527–1530.
  15. Hoornstra, J.; Moor, H.; Weeber, A.; Wyers, P. Improved Front Side Metallization on Silicon Solar Cells with Stencil Printing. Glasgow: 16th Eur. Photovoltaic Solar Energy Conf. Exhib. 2000, 1, 5.
  16. Rösch, M. Potenziale und Strategien zur Optimierung des Schablonendruckprozesses in der Elektronikproduktion. Doctoral Dissertation, FAU, Erlangen, 2011.
  17. Seo, W.; Kim, J. Filling Analyses of Solder Paste in the Stencil Printing Process and Its Application to Process Design. Solder Surf. Mt. Technol 2013, 25(3), 145–154. DOI: 10.1108/SSMT-Oct-2012-0022.
  18. Rusdi, M. S.; Abdullah, M. Z.; Ishak, M. H. H.; Aziz, M. S. A.; Abdullah, M. K.; Rethinasamy, P.; Jalar, A. Three-Dimensional CFD Simulation of the Stencil Printing Performance of Solder Paste. Int. J. Adv. Manuf. Technol. 2020, 108(9–10), 3351–3359. DOI: 10.1007/s00170-020-05636-9.
  19. Kumar, S.; Mallik, S.; Ekere, N.; Jung, J. Stencil Printing Behavior of Lead-Free Sn-3Ag-0.5 Cu Solder Paste for Wafer Level Bumping for Sub-100 μm Size Solder Bumps. Met. Mater. Int. 2013, 19(5), 1083–1090. DOI: 10.1007/s12540-013-5025-z.
  20. Barlow, F. D.; Elshabini, A. Ceramic Interconnect Technology Handbook, 1st ed.; CRC Press: New York, NY, 2007; p. 227.
  21. Dittrich, S.; Reitz, E.; Schell, K. G.; Bucharsky, E. C.; Hoffmann, M. J. Development and Characterization of Inks for Screen Printing of Glass Solders for SOFCs. Int. J. Appl. Ceram. Technol. 2020, 17(3), 1304–1313. DOI: 10.1111/ijac.13461.
  22. Pennemann, H.; Dobra, M.; Wichert, M.; Kolb, G. Optimization of Wash-Coating Slurries As Catalyst Carrier for Screen Printing into Microstructured Reactors. Chem. Eng. & Technol. 2013, 36(6), 1033–1041. DOI: 10.1002/ceat.201200637.
  23. Sborikas, M.; Qiu, X.; Wirges, W.; Gerhard, R.; Jenninger, W.; Lovera, D. Screen Printing for Producing Ferroelectret Systems with Polymer-Electret Films and Well-Defined Cavities. Appl. Phys. A 2014, 114(2), 515–520. DOI: 10.1007/s00339-013-7998-3.
  24. Kamp, M.; Efinger, R.; Gensowski, K.; Bechmann, S.; Bartsch, J.; Glatthaar, M. Structuring of Metal Layers by Electrochemical Screen Printing for Back-Contact Solar Cells. IEEE J. Photovoltaics. 2018, 8(3), 676–682. DOI: 10.1109/JPHOTOV.2018.2802201.
  25. Hong, H.; Jiang, L.; Tu, H.; Hu, J.; Yan, X. Formulation of UV Curable Nano-Silver Conductive Ink for Direct Screen-Printing on Common Fabric Substrates for Wearable Electronic Applications. Smart Mater. Struc 2021, 30(4), 045001. DOI: 10.1088/1361-665X/abe4b3.
  26. Wilson, S.; Howison, S.; Parker, D. Void Elimination in Screen Printed Thick Film Dielectric Pastes. Math. Ind. Rep. 2021, 145, 1–12. DOI: 10.33774/miir-2021-vgnwr.
  27. Bommineedi, L. K.; Upadhyay, N.; Minnes, R. Screen Printing: An Ease Thin Film Technique. In Simple Chemical Methods for Thin Film Deposition: Synthesis and Applications, Sankapal, B., Ennaoui, A., Gupta, R. Lokhande, C., Eds.; Springer Nature: Singapore, 2023; pp. 449–507. DOI: 10.1007/978-981-99-0961-2_11.
  28. Riemer, D. E. Ein Beitrag zur Untersuchung der physikalisch-technischen Grundlagen des Siebdruckverfahrens. Doctoral Dissertation, TU, Berlin, Berlin, 1988.
  29. Krammer, O.; Al-Ma’aiteh, T. I.; Illes, B.; Bušek, D.; Dušek, K. Numerical Investigation on the Effect of Solder Paste Rheological Behaviour and Printing Speed on Stencil Printing. Solder Surf. Mt. Technol. 2020, 32(4), 219–223. DOI: 10.1108/SSMT-11-2019-0037.
  30. Glinski, G. P.; Bailey, C.; Pericleous, K. A. A Non-Newtonian Computational Fluid Dynamics Study of the Stencil Printing Process. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 2001, 215(4), 437–446. DOI: 10.1243/0954406011520869.
  31. Kay, R. W.; Stoyanov, S.; Glinski, G. P.; Bailey, C.; Desmulliez, M. P. Ultra-Fine Pitch Stencil Printing for a Low Cost and Low Temperature Flip-Chip Assembly Process. IEEE Trans. Compon. Packag. Technol. 2007, 30(1), 129–136. DOI: 10.1109/TCAPT.2007.892085.
  32. Durairaj, R.; Jackson, G. J.; Ekere, N. N.; Glinski, G.; Bailey, C. Correlation of Solder Paste Rheology with Computational Simulations of the Stencil Printing Process. Solder. Surf. Mount. Technol. 2002, 14(1), 11–17. DOI: 10.1108/09540910210416422.
  33. Ishak, M. H. H.; Ismail, M. I.; Mat, S.; Ismail, F.; Mohd Salleh, M. A. A. Influence of Squeegee Impact on Stencil Printing Process: CFD Approach. IOP Conf. Ser Mater. Sci. Eng. 2020, 957(1), 012065. DOI: 10.1088/1757-899X/957/1/012065.
  34. Choi, S. A.; Youn, J. T.; Mok, J. S.; Koo, C. W. Computer Simulation of Ink Transfer in the Different Printing Speed and Ink Viscosity in the Screen Printing. J Korean Graph. Arts Commun Soc. 2011, 29(1), 75–83.
  35. Flow Science, Inc. Santa Fe, NM, USA. FLOW-3D® Version 2023R1. 2023. https://www.flow3d.com/
  36. Schindelin, J.; Arganda-Carreras, I.; Frise, E.; Kaynig, V.; Longair, M.; Pietzsch, T.; Preibisch, S.; Rueden, C.; Saalfeld, S.; Schmid, B. Fiji: An Open-Source Platform for Biological-Image Analysis. Nat. Methods. 2012, 9(7), 676–682. DOI: 10.1038/nmeth.2019.
  37. Preibisch, S.; Saalfeld, S.; Tomancak, P. Globally Optimal Stitching of Tiled 3D Microscopic Image Acquisitions. Bioinformatics. 2009, 25(11), 1463–1465. DOI: 10.1093/bioinformatics/btp184.
  38. FLOW-3D® Version 2023R1 Users Manual. FLOW-3D [Computer Software]; Flow Science, Inc: Santa Fe, NM, 2023. https://www.flow3d.com
  39. Murray, B. R. Characterisation of Rotationally Moulded Polymer Liners for Low Permeability Cryogenic Applications in Composite Overwrapped Pressure Vessels. Doctoral Dissertation, National University of Ireland, Galway, 2016.
  40. Grimsley, B. W.; Cano, R. J.; Johnston, N. J. Hybrid Composites for LH2 Fuel Tank Structure; NASA Langley Research Center: Hampton, USA, 2001.
  41. Jackson, J. R.; Vickers, J.; Fikes, J. Composite Cryotank Technologies and Development 2.4 and 5.5m Out of Autoclave Tank Test Results. Composites and Advanced Materials Expo (CAMX); Dallas, USA, Oct 26–29, 2015.
  42. Guan, C.; Zhan, L.; Shi, H. Simulation and Experiment Analysis of Relationship Between Voids and Permeability of Composites. Proc. Inst. Mech. Eng. Part L J Mater. Des. Appl. 2022, 236(1), 23–36. DOI: 10.1177/14644207211026942.
  43. Saha, S.; Rani, W. S. A Review on Gas Permeability of Polymer Matrix Composites for Cryogenic Applications. J. Compos. Mater. 2024, 00219983241228550. DOI: 10.1177/00219983241228550.
  44. Yang, T.; Tsai, T. N. A Neurofuzzy-Based Quality-Control System for Fine Pitch Stencil Printing Process in Surface Mount Assembly. J. Intell. Manuf. 2004, 15, 711–721. DOI: 10.1023/B:JIMS.0000037719.35871.aa.
  45. Manessis, D.; Patzelt, R.; Ostmann, A.; Aschenbrenner, R.; Reichl, H. Technical Challenges of Stencil Printing Technology for Ultra Fine Pitch Flip Chip Bumping. Microelectron. Reliab. 2004, 44(5), 797–803. DOI: 10.1016/S0026-2714(03)00361-5.
  46. Indicatti, F. I.; Rädler, M. Device and Method for Printing a Substrate with a Sealant And/Or Adhesive. DE102022209195A1, German Patent and Trade Mark Office, 2024.
  47. Indicatti, F. I.; Rädler, M. Method for Printing a Substrate with a Sealant And/Or Adhesive, Electrochemical Cell with a Printed Seal. DE102022209196A1, German Patent and Trade Mark Office, 2024.
  48. Indicatti, F. I.; Rädler, M. Device and Method for Printing a Substrate with a Sealant And/Or Adhesive. DE102022209197A1, German Patent and Trade Mark Office. 2024.
View Page

WELD_Graph

Processing windows of Ni625 alloy fabricated using direct energy deposition

직접 에너지 증착을 이용한 Ni625 합금의 가공 범위

Yusufu Ekubaru, Takuya Nakabayashi, Tomoharu Fujiwara, Behrang Poorganji

Abstract

Herein, a process window is developed for Ni625 alloy fabricated using a Nikon Lasermeister laser powder direct energy deposition (LP-DED) unit. The process map illustrates the relationship between the laser power, scan speed, and effective energy density, established by examining the correlation between the microstructure and mechanical properties. All samples exhibit a bimodal microstructure comprising equiaxed and columnar dendrite grains, and the dendrite arm spacing decreases with increasing scan speed. The tensile behavior of each sample demonstrates minimal variation, and the values are comparable to those reported previously. The ultimate tensile and yield strengths range from 1008 ± 2 to 941 ± 9 and 682 ± 11 to 640 ± 7 MPa, respectively. This study highlights the remarkable manufacturability of Ni625 alloy for additive manufacturing across diverse parameter sets, demonstrating that a single ideal process set does not exist for each material and machine. Instead, multiple “recipes” may be employed to achieve similar outcomes.

1. Introduction

Metal additive manufacturing (AM) is an excellent technology for part fabrication, offering distinct advantages over conventional manufacturing methods. With significant cost and lead-time reductions and the capability to develop complex geometrical features,[1–3] metal AM has rapidly garnered interest from key industries such as aerospace, automotive, military, and biomedical sectors.[3–5] Metal AM entails various techniques, including material jetting, sheet lamination, laser powder bed fusion, binder jetting, and direct energy deposition.

Laser powder direct energy deposition (LP-DED) presents unique advantages over other AM processes, including alloy design, repair capabilities, surface modifications, and the synthesis of large-scale components with adequate dimensional accuracy.[6] These capabilities have been increasingly demonstrated and recognized in various fields, particularly in the aerospace industry.[4] The in-situ alloying of elemental powders offers an effective alternative to the use of pre-alloyed powders, which are cost- and time-intensive to produce using traditional atomization methods. By mixing pure elemental powders of Ni, Cr, Mo, Nb, and Fe, Wang et al.[7] demonstrated the high-quality fabrication of Ni625 alloy components using LP-DED and in situ alloying. Wilson et al.[8, 9] repaired defective voids in turbine blades, illustrating the effectiveness of LP-DED in repair. These studies highlight the adaptability of DED to a wide range of defective parts, as well as its capabilities in repair and maintenance. Balla et al.[10] applied a tantalum coating onto titanium using LP-DED, a notable achievement considering the extremely high melting point (>3000 °C) of Ta, which poses challenges for traditional melt-cast methods. Ta-coated Ti exhibits favorable interactions with bone cells, indicating promising biocompatibility. Gradl et al.[1, 2, 11] utilized LP-DED to manufacture a large-scale rocket nozzle for aerospace applications. The growing recognition of LP-DED is reflected in the significant increase in the number of patents and scientific publications dedicated to this technology, highlighting its importance in academia and industry.[5, 12]

Furthermore, the anticipation of an expanding market for AM has spurred intense competition among AM machine manufacturers, resulting in the development of various AM systems.[4] In this context, the Nikkon Advanced Manufacturing Department in Japan developed an LP-DED system named Lasermeister. Extensive empirical testing has been conducted on this machine with common AM materials, including Fe-, Ni-, and Ti-based alloys. Herein, we present our latest research findings, particularly focusing on the Ni625 alloy, also referred to as Alloy 625 or Inconel 625.

The Ni625 alloy has been utilized in various industries, including petrochemical, aerospace, chemical, marine, and nuclear sectors, due to its excellent strength and high corrosion and fatigue resistance.[12, 13] Moreover, its remarkable weldability has attracted considerable attention in AM, where it has been successfully produced using various process parameters in LP-DED, including laser power (P) (220–1500 W) and scan speed (V) (8.3–33.3 mm s−1), with the corresponding effective energy density (ED) ranging from 14 to 66 J mm−2.[7, 13–20]

The solidification microstructure of AM-produced Ni625 alloy is complex, featuring fine dendrites, micro-segregated elements, and various solidification phases.[21] The nickel-based superalloy, primarily strengthened by the solid hardening effects of refractory elements including niobium and molybdenum within a nickel–chromium matrix exhibits a face-centered cubic (FCC) structure.[14] These alloys are sensitive to the precipitation of strengthening intermetallic phases, including stable ordered FCC (L12)γ′-Ni3Al; metastable body-centered tetragonal γ″-Ni3Nb; stable orthorhombic δ-Ni3Nb; carbides (MC, M6C); and intergranular brittle Laves phases ((Nb, Mo)(NiCrFe)2) in the interdendritic region.[1, 12–14] The formation of these phases, particularly the Laves phases, consumes significant amounts of Nb and Mo, thereby reducing their content in the matrix, which diminishes solid solution and precipitation strengthening effects.[19] Further, the Laves phase induces crack nucleation and propagation, significantly deteriorating creep rupture properties and ductility.[19] Consequently, manufacturing components with reduced elemental segregation and fewer Laves phases has become critical.[22–24]

The mechanical properties of materials are primarily influenced by factors such as porosity, grain size, the behavior of precipitates, and dendrite spacing.[25] Generally, the mechanical properties can be improved by reducing their size, which essentially means creating a finer microstructure. Reducing porosity can enhance the material’s strength and durability as fewer pores mean less space for cracks to initiate. Smaller grain sizes often lead to increased hardness and strength due to the Hall–Petch relationship. Controlling the behavior of precipitates, such as reducing their size, can increase the material’s strength as smaller precipitates more effectively hinder dislocation movement.[25, 26] Lastly, smaller dendrite spacing can contribute to a more homogeneous microstructure, reducing segregation and enhancing various mechanical properties.[25, 26] One fundamental approach to achieving a finer microstructure is to increase the cooling rate, and it can be accomplished by using a smaller P, a higher V, or a combination of both.[27]

Based on this background, this study aimed to 1) develop the process windows for Ni625 alloy using the Lasermeister system and 2) establish a process window that expresses the relationship between P, V, and ED based on a series of simulations and experiments focusing on microstructural properties and mechanical performance.

This research demonstrated for the first time that using lower P values and smaller hatch spacings can significantly enhance the strength of Ni625 alloys by promoting substantial microstructure miniaturization. Additionally, DED process “recipes” for Ni625 in the lower P region were developed. These results are expected to significantly contribute to the DED fabrication of components such as precise, large, thin-walled structures that are vulnerable to thermal deformation, as well as the automation of gas turbine blade repairs, among other applications.

Advanced Engineering Materials

Research Article

Open Access

Processing Windows of Ni625 Alloy Fabricated Using Direct Energy Deposition

Yusufu Ekubaru, Takuya Nakabayashi, Tomoharu Fujiwara, Behrang Poorganji

First published: 21 June 2024

https://doi.org/10.1002/adem.202400962

Sections

PDF

Tools

Share

Abstract

Herein, a process window is developed for Ni625 alloy fabricated using a Nikon Lasermeister laser powder direct energy deposition (LP-DED) unit. The process map illustrates the relationship between the laser power, scan speed, and effective energy density, established by examining the correlation between the microstructure and mechanical properties. All samples exhibit a bimodal microstructure comprising equiaxed and columnar dendrite grains, and the dendrite arm spacing decreases with increasing scan speed. The tensile behavior of each sample demonstrates minimal variation, and the values are comparable to those reported previously. The ultimate tensile and yield strengths range from 1008 ± 2 to 941 ± 9 and 682 ± 11 to 640 ± 7 MPa, respectively. This study highlights the remarkable manufacturability of Ni625 alloy for additive manufacturing across diverse parameter sets, demonstrating that a single ideal process set does not exist for each material and machine. Instead, multiple “recipes” may be employed to achieve similar outcomes.

1 Introduction

Metal additive manufacturing (AM) is an excellent technology for part fabrication, offering distinct advantages over conventional manufacturing methods. With significant cost and lead-time reductions and the capability to develop complex geometrical features,[1–3] metal AM has rapidly garnered interest from key industries such as aerospace, automotive, military, and biomedical sectors.[3–5] Metal AM entails various techniques, including material jetting, sheet lamination, laser powder bed fusion, binder jetting, and direct energy deposition.

Laser powder direct energy deposition (LP-DED) presents unique advantages over other AM processes, including alloy design, repair capabilities, surface modifications, and the synthesis of large-scale components with adequate dimensional accuracy.[6] These capabilities have been increasingly demonstrated and recognized in various fields, particularly in the aerospace industry.[4] The in-situ alloying of elemental powders offers an effective alternative to the use of pre-alloyed powders, which are cost- and time-intensive to produce using traditional atomization methods. By mixing pure elemental powders of Ni, Cr, Mo, Nb, and Fe, Wang et al.[7] demonstrated the high-quality fabrication of Ni625 alloy components using LP-DED and in situ alloying. Wilson et al.[8, 9] repaired defective voids in turbine blades, illustrating the effectiveness of LP-DED in repair. These studies highlight the adaptability of DED to a wide range of defective parts, as well as its capabilities in repair and maintenance. Balla et al.[10] applied a tantalum coating onto titanium using LP-DED, a notable achievement considering the extremely high melting point (>3000 °C) of Ta, which poses challenges for traditional melt-cast methods. Ta-coated Ti exhibits favorable interactions with bone cells, indicating promising biocompatibility. Gradl et al.[1, 2, 11] utilized LP-DED to manufacture a large-scale rocket nozzle for aerospace applications. The growing recognition of LP-DED is reflected in the significant increase in the number of patents and scientific publications dedicated to this technology, highlighting its importance in academia and industry.[5, 12]

Furthermore, the anticipation of an expanding market for AM has spurred intense competition among AM machine manufacturers, resulting in the development of various AM systems.[4] In this context, the Nikkon Advanced Manufacturing Department in Japan developed an LP-DED system named Lasermeister. Extensive empirical testing has been conducted on this machine with common AM materials, including Fe-, Ni-, and Ti-based alloys. Herein, we present our latest research findings, particularly focusing on the Ni625 alloy, also referred to as Alloy 625 or Inconel 625.

The Ni625 alloy has been utilized in various industries, including petrochemical, aerospace, chemical, marine, and nuclear sectors, due to its excellent strength and high corrosion and fatigue resistance.[12, 13] Moreover, its remarkable weldability has attracted considerable attention in AM, where it has been successfully produced using various process parameters in LP-DED, including laser power (P) (220–1500 W) and scan speed (V) (8.3–33.3 mm s−1), with the corresponding effective energy density (ED) ranging from 14 to 66 J mm−2.[7, 13–20]

The solidification microstructure of AM-produced Ni625 alloy is complex, featuring fine dendrites, micro-segregated elements, and various solidification phases.[21] The nickel-based superalloy, primarily strengthened by the solid hardening effects of refractory elements including niobium and molybdenum within a nickel–chromium matrix exhibits a face-centered cubic (FCC) structure.[14] These alloys are sensitive to the precipitation of strengthening intermetallic phases, including stable ordered FCC (L12)γ′-Ni3Al; metastable body-centered tetragonal γ″-Ni3Nb; stable orthorhombic δ-Ni3Nb; carbides (MC, M6C); and intergranular brittle Laves phases ((Nb, Mo)(NiCrFe)2) in the interdendritic region.[1, 12–14] The formation of these phases, particularly the Laves phases, consumes significant amounts of Nb and Mo, thereby reducing their content in the matrix, which diminishes solid solution and precipitation strengthening effects.[19] Further, the Laves phase induces crack nucleation and propagation, significantly deteriorating creep rupture properties and ductility.[19] Consequently, manufacturing components with reduced elemental segregation and fewer Laves phases has become critical.[22–24]

The mechanical properties of materials are primarily influenced by factors such as porosity, grain size, the behavior of precipitates, and dendrite spacing.[25] Generally, the mechanical properties can be improved by reducing their size, which essentially means creating a finer microstructure. Reducing porosity can enhance the material’s strength and durability as fewer pores mean less space for cracks to initiate. Smaller grain sizes often lead to increased hardness and strength due to the Hall–Petch relationship. Controlling the behavior of precipitates, such as reducing their size, can increase the material’s strength as smaller precipitates more effectively hinder dislocation movement.[25, 26] Lastly, smaller dendrite spacing can contribute to a more homogeneous microstructure, reducing segregation and enhancing various mechanical properties.[25, 26] One fundamental approach to achieving a finer microstructure is to increase the cooling rate, and it can be accomplished by using a smaller P, a higher V, or a combination of both.[27]

Based on this background, this study aimed to 1) develop the process windows for Ni625 alloy using the Lasermeister system and 2) establish a process window that expresses the relationship between P, V, and ED based on a series of simulations and experiments focusing on microstructural properties and mechanical performance.

This research demonstrated for the first time that using lower P values and smaller hatch spacings can significantly enhance the strength of Ni625 alloys by promoting substantial microstructure miniaturization. Additionally, DED process “recipes” for Ni625 in the lower P region were developed. These results are expected to significantly contribute to the DED fabrication of components such as precise, large, thin-walled structures that are vulnerable to thermal deformation, as well as the automation of gas turbine blade repairs, among other applications.

2. Experimental Section

2.1 Ni625 Alloy Fabrication

Ni625 alloy powders were procured from Carpenter Additive Inc.; and their compositions and morphologies are summarized in Table 1 and Figure 1, respectively. An LP-DED unit (Nikon Lasermeister 100A, Japan) with a 915 nm 200 W laser diode module and a beam diameter (d) of 0.5 mm was utilized to fabricate the Ni625 alloy samples (Figure 1c). Two samples, namely, a 10 × 10 × 10 mm cube and a 10 × 10 × 55 mm rectangle, were fabricated along the x-, y-, and z-axes on a SUS304 substrate via the XY scanning strategy. Cubic samples were used for microstructural analysis, whereas rectangular samples were employed for tensile property testing (Figure 1d).[7, 20] The parameter values used for the experiment are listed in Table 3, where the laser hatch spacing was maintained at 0.2 mm.

PowderNiCrMoNb + TaFeAlTiCMn
Inconel625Bal.20–238–103.15–4.15≤5≤0.4≤0.4≤0.03≤0.01
Table 1. Chemical composition (wt%) of Ni625 alloy.
Figure 1 a) Morphology and b) powder size distribution of the Ni625 alloy powders used in laser powder direct energy deposition (LP-DED). c) Schematic of LP-DED and d) dimensions of the tensile test sample.

2.2 Microstructure Characterization and Mechanical Properties

Samples were cut from the substrate via electrical discharge machining to analyze their microstructures and mechanical properties. The YZ cross sections were first mechanically polished using emery paper up to a 4000 grade and subsequently chemically polished with colloidal silica to achieve mirror-polished sections for microstructural examination.

Optical microscopy (KEYENCE VHX8000) and scanning electron microscopy (SEM; Hitachi SU1500) were conducted to examine the microstructures. The bulk samples fabricated by the LP-DED Lasermeister were characterized via X-ray diffraction (XRD; Rigaku RINT2500) with Cu-K radiation at room temperature (RT). Crystallographic texture and elemental segregation were investigated using electron backscattered diffraction (EBSD) and energy-dispersive X-ray spectroscopy (EDS), respectively, with a scanning electron microscope (JEOL JSM-7900F). A tensile test (Minebea TGI-50KN) was conducted at RT, where the loading axis was parallel to the build direction (BD). The test was conducted thrice for each sample, and the results were averaged.

2.3 Simulations

The formation mechanism of the microstructure induced by LP-DED was explored through simulations focusing on thermal behavior and solidification characteristics. The thermal behavior calculations provided insights into the temperature distribution and the shape and size of the melt pool. Conversely, analyzing the solidification characteristics aided in understanding the development of grains, which could manifest as either equiaxed dendrites (ED) or columnar dendrites (CD).

These simulations were performed using the commercial software FLOW-3D v12.0 for a region measuring 10 × 7 × 3 mm in the X, Y, and Z directions. The region was discretized into a structural Eulerian mesh with a size of 0.025 mm.

2.3.1 Heat Source Model

where P0 is the laser power (100/120/160 W), r is the distance from the beam center, r is the laser radius (0.25 mm), rb is the effective laser radius (0.1 mm), hc is the heat transfer coefficient (9.5 W m−2 K),[28] T is the temperature, and T0 is the ambient temperature (298 K).

2.3.2 Powder Model

We employed the Lagrangian particle tracking method to model the powder particles. Particles entering the melt pool transformed into liquid cells upon surpassing the melting point. The amount of powder injected was calculated from the predetermined powder utilization efficiency. The powder was injected at a constant velocity from the vertical direction of the melt pool to ensure the melting of all particles.

2.3.3 Melt Pool (MP) Flow Governing Equations

The governing equations, which include mass, momentum, and energy conservation, are expressed in Equation (2), (3), and (4), respectively.

where ρ is density, t is time, v is flow velocity, RSOR is the amount of mass source due to powder particles, p is pressure, μ is viscosity, vp is particle velocity, Cv is specific heat, fs is the solidus rate, ISOR is the discharge of energy, and L is latent heat. The thermophysical parameters were calculated using the thermodynamic database of JmatPro (Sente Software) considering their temperature dependencies (Table 2).

Temperature intervalsThermal conductivitySpecific heatDensityViscositySurface tensionLatent heat of fusion
T [K]κ [W (m K)−1]Cv [J (kg K)−1]ρ [kg m−3]μ [kg (m s)−1]σ [N m−1]L [kJ kg−1]
29810.84068474––210
60015.94568373––
90020.95048253––
120025.85598117––
150030.171379311.39 × 10−21.84
180031.473774990.62 × 10−21.74
210035.874572350.38 × 10−21.62
240040.274869520.26 × 10−21.52
Table 2. Thermophysical properties of Ni625 calculated using JmatPro.

2.3.4 Solidification Parameter

The temperature gradient G and solidification velocity R represent spatial temperature variations and are expressed as:

where ε is the cooling rate, Ts is the solidus line temperature (1398 K), TL is the liquidus line temperature (1613 K), tS is the time below the solidus line temperature, tL is the time below the liquidus line temperature, and ∇ is the differential operator.

3 Results

3.1 Simulated Data

The aspect ratio (D/W), indicating the depth (D) to width (W) ratio of the MP, was assessed in both the experimental and simulated scenarios to verify the simulation model. Figure 2 displays the results of the single-track experiments and simulations at V values of 5 and 10 mm s−1, with constant P and powder feeding rate (Q) values of 120 W and 3 g min−1, respectively. The experimental dimensions of the MP were measured from the optical images, whereas the simulated sizes of the MP were determined by identifying a black solidus line on the temperature contour map. The aspect ratios decreased with increasing V, and the experimental aspect ratios were slightly higher than the simulated ones, with differences of <10%. It is considered that one possible reason for this difference is the thermal boundary conditions of the substrate in the simulation. Hence, this model was employed for additional simulations to generate a process map for the Ni625 alloy.

Figure 2 Comparison of the experimental and simulated MP: a,b) experimental optical images, a’,b’) simulated temperature contours, and c) aspect ratio. Scale bars: 200 μm.

Various conditions were simulated to assess fabrication feasibility using these process parameters. Figure3 illustrates the simulated temperature contour plots and the maximum temperature of the MPs under nine different conditions, accompanied by their respective sizes. As shown in Figure 3b,c, with an increase in P from 100 to 160 W (while V is constant at 5 mm s−1), the maximum temperature increases from 2335 to 2725 K, and the width of the MPs increases from 540 to 780 μm; by contrast, increasing V when P is constant causes both the maximum temperature and the width and depth of the MPs to remain almost constant. The highest temperatures and dimensions of the MPs indicated a significant dependence on P but less dependence on V. Consequently, MPs were formed under all conditions, and the maximum temperature exceeded the melting point of the Ni625 alloy at 1623 K,[29] which allowed us to proceed with the experiments.

Figure 3 Simulated MP of a) temperature contour plot, b) maximum temperature, and c) dimensions at varying process parameters.

3.2 Microstructural Analysis

The fabricated state, porosity, and cracks of the samples produced under the nine simulated conditions were investigated via cross-sectional image analysis using an optical microscope. All samples, except S7, were successfully manufactured, as shown in Figure 4a; however, S7 could not be completed because the powder adhered to the nozzle owing to the highest energy density input. The optical density shown in Figure 4b was measured from optical images of the polished surfaces of the samples. Five images were taken from different locations on the polished surface of each sample at 200× magnification. The optical density of these images was then measured using ImageJ software, and the average was calculated. As shown in Figure 4b, most samples, excluding S2 and S3, exhibited a dense structure without any visible cracks; this resulted in a satisfactory industrial density of over 99.5%.[3, 30, 31] However, samples S2 and S3 showed noticeably lower density values with irregularly shaped pores caused by the lack of fusion owing to the lower energy density input. It can be generally observed that densification increases with increasing P and decreases with increasing V. This behavior is more significant in samples S1 to S3 at 100 W, while it is less pronounced in samples S4 to S9 at 120 and 160 W. This suggests that at lower P settings, the impact of V on densification is more pronounced, whereas at higher P settings, the effect of V becomes less significant. Consequently, optimizing P and V parameters is crucial for achieving desired densification levels in different samples.

Figure 4 a) Appearance of the LP-DED fabricated samples and b) optical density.

The microstructure of AM materials can be explained by the MP microstructure using Hunt’s columnar-equiaxed transition criteria.[27, 32, 33] As shown in Figure 5a, MPs typically exhibit a bimodal microstructure comprising two types of grains: ED at the top with no preferential crystallographic orientation and CD at the bottom that show a preference for growing from the bottom part to the center along the direction of the thermal gradient.[21, 33-35] This is attributed to the higher G/R ratio at the bottom part of the MP and the lower G/R ratio at the top, as illustrated in Figure 5b, where G/R is the grain morphology factor determining either ED or CD, and G × R is the cooling rate that determines the size of the grain. Typically, the extremely high G and G × R values in the AM process foster directional solidification, and enhance the textures of the microstructures of alloys.[36, 37]

Figure 5 a) Schematic of the MP microstructure and b) columnar-equiaxed transition criteria, adapted from ref. 27 with permission.[27, 32, 33]

The dendrite microstructural features, including the PDAS size and shape of the grains of the samples, were characterized by observing the SEM images of the aqua regia-etched YZ cross-section. PDAS is one of the factors in influencing mechanical properties and it was known that smaller PDAS increases various mechanical properties.[25, 26] As shown in Figure 6a, among the samples, S7 yielded the highest PDAS with a value of 3.7 ± 0.1 μm, while S3 yielded the lowest PDAS with a value of 1.7 ± 0.3 μm; consequently, the PDAS increased as the P increased and V decreased. In contrast, as shown in Figure 6b, all samples exhibited a bimodal grain microstructure consisting of CD and ED regions. Samples S7–S9, fabricated with the highest P of 160 W, exhibited a predominance of CD, while samples S1–S3, fabricated with the lowest P of 100 W, displayed an almost exclusive ED presence, and resulted in a trend that shifted from an ED-dominant to CD-dominant microstructure with increasing P and decreasing V, respectively; namely, high P values increased the dendrite structure, which is consistent with other research.[14]

Figure 6 SEM images of the YZ plane of the samples with a) higher magnitudes containing PDAS and b) lower magnitudes containing CD and ED regions.

The elemental microsegregation of the samples was analyzed using EDS mapping. Figure 7a,b illustrate the distributions of the main elements (Ni, Cr, Fe, Nb, and Mo) in samples S7 (with the highest energy density) and S3, respectively. The Mo and Nb contents in the interdendritic regions were higher than those in the dendritic regions, as indicated by the yellow arrow. Both samples exhibited significant Mo and Nb segregation with no clear differences in their segregation behaviors. Based on the obtained results and previous reports, it can be concluded that the observed phase corresponds to the Laves phase.[7, 16, 19]

Figure 7 EDS maps of samples of a) S7 and b) S3.

XRD analysis was conducted on the polished YZ cross-section of the samples to confirm the phase states. As shown in Figure 8, all the samples exhibited peaks corresponding to the reference Ni (PDF #04-0850) in the XRD analysis. Interestingly, in sample S7, the relative intensities of the (111) and (200) peaks were similar, even though (111) has the highest-intensity peak, indicating that (100) tends to be oriented in the BD (z-direction), which is in agreement with other studies.[3, 7, 38, 39] However, all samples exhibited a minor peak shift to a lower diffraction angle compared with Ni (PDF #04-0850), implying the presence of residual stress in the samples.[3, 38]

Figure 8 XRD patterns of the LP-DED fabricated samples.

One of the key features of AM that influences the mechanical properties is the crystallographic texture,[36] which was investigated using EBSD. As shown in Figure 9a, by increasing P and decreasing V, directional grain growth occurs along the z-direction with a {100} crystallographic orientation, which is an easy growth direction for the FCC crystal structure,[3, 36] which was observed in the samples. The values of the texture strength measure, MUD, increased as P increased and V decreased; however, apart from sample S7, no distinguishable crystallographic textures were observed for the samples, and S7 exhibited the highest texture with most grains aligned in the {100} crystallographic orientation; this finding is consistent with the XRD results shown in Figure 8.

Figure 9 EBSD a) inverse pole figure maps and b) the corresponding {001} pole figures with multiples of uniform distribution (MUD) values of the YZ plane.

3.3 Tensile Properties

A tensile test was performed at RT, and the results showed trends corresponding to the features of the microstructure. As shown in the optical images in Figure 4, the porosity increased with V in the sample fabricated at the lowest P of 100 W, whereas the elongation (El) of these samples decreased, as shown in Figure 10a. However, with an increase in V, the minor decreases in the PDAS and grain size shown in Figure 6 and 9 led to a minor monotonic increase in the ultimate tensile strength (UTS) for the samples produced at P = 120 and 160 W. Consequently, the tensile properties exhibited negligible variations because fewer changes were observed in the microstructure.

Figure 10 Tensile stress–strain curves of the samples.

3.4 Process Window

A process map illustrating the relationship between P, V, ED, and the feasibility of sample fabrication was established based on the experimental data obtained in this study. Figure 11 illustrates that the pink region represents high ED, while the blue region represents low ED. Additionally, samples S2 and S3, located in the low ED area, exhibited higher porosity owing to insufficient fusion. Conversely, sample S7, situated in the high ED area, was not fully produced because of powder adhesion in the nozzle. Consequently, the approximate optimal region is indicated by a yellow line.

Figure 11 P–V process map with ED contour.

4 Discussion

4.1 Pore Formation and Mechanical Property Impact

Pores are one of the major defects that significantly affect the mechanical properties of parts; which can primarily occur owing to both high- or low-energy input, as well as the insufficient overlap of laser tracks.[40]

High-energy input during the melting process can result in the formation of an unstable MP at extremely high temperatures and severe Marangoni convection, which in turn leads to the generation of spherical pores either by trapping the protective gas (Ar) or metallic vapor.[3, 40] As shown in Figure 4b, samples S7 and S1 fabricated with a higher energy density showed spherical pores with a maximum diameter of 40 μm. These pores were primarily formed owing to the trapping of Ar gas and were unlikely attributed to metallic vapor because of the high melting points of all the main elements of the Ni625 alloy. It is known that spherical pores with diameters <130 μm have negligible detrimental effects on the mechanical properties of the material.[3] Moreover, as illustrated in Figure 10a, sample S1 displayed satisfactory tensile properties, despite the presence of spherical pores.

Low-energy input cannot completely melt the metallic powder in the previously deposited layer, thus leading to irregularly shaped lack of fusion pores, as shown in Figure 4b. Samples S2 and S3 produced with lower energy input contained irregularly shaped pores with sizes over 100 μm; these samples exhibited lower elongation tensile properties, as shown in Figure 10a.

Insufficient overlap among laser tracks can also cause a lack of fusion pores, which may be attributed to a large hatch distance and/or layer thickness.[40] However, in this study, the primary cause of the lack of fusion pores was identified as low-energy input, predominantly due to low P.

4.2 Effects of P and V on Grain Size and Morphology

P and V are the primary process parameters used to adjust the energy density to tailor the microstructure, and they significantly affect the MP solidification process parameters G and R.[27, 32, 33] Therefore, a comprehensive understanding of G and R is crucial for predicting or explaining the microstructural features observed in experimental samples, and simulations are an effective tool for their calculation.[27, 41, 42]

As shown in the solidification map in Figure 5b, G × R is the cooling rate that determines the size of the grain, whereas (G/R) is the morphology factor that determines the shapes of the grains. In this study, a maximum cooling rate of 3.5 × 104 K s−1 was achieved for sample S3, which is close to the intrinsic cooling rate of LP-DED, which ranges from 103 to 104 K s−1.[21]

At increasing P and decreasing V values, the PDAS increased while the grain shapes shifted from being predominantly ED-dominant to CD-dominant, as shown in Figure 6b. It is believed that these behaviors can be attributed to the changes in G × R and G/R, as illustrated in Figure 12.

Figure 12 Simulated a) average G × R and a’) G × R contours, and b) average G/R and b’) G/R contours.

As shown in Figure 12a, the impact of P on G × R is minor at low V values but becomes significant at high V. Therefore, the G × R values of the samples are almost the same at V = 5 mm s−1, and the PDASs of these samples do not change significantly, as shown in Figure 6a. Conversely, G × R increased as a function of V as also proven by other researchers,[27, 41, 42] and the highest and lowest G × R values were obtained for S3 and S7, respectively; accordingly, S3 and S7 respectively exhibited the lowest and highest PDAS values equal to 1.7 ± 0.3 and 3.7 ± 0.1 μm, as shown Figure 6a.

As shown in Figure 12b, G/R is less affected by P but is significantly affected by V; additionally, G/R decreases as V increases, thus suggesting that CD increases with decreasing V. Correspondingly, the directional grain growth along the z-direction with the {100} crystallographic orientation is most significant in the samples with the lowest V of 5 mm s−1, as shown in Figure 9.

As shown in Figure 12a’,b’, higher G/R and lower G × R values are observed at the bottom of the MP; in contrast, lower G/R and higher G × R were obtained at the top of the MP[27, 41, 42] and these behaviors are most significant at low V, thus indicating that the morphology of the microstructure is prone to CD. Correspondingly, the texture strength measure MUDs were higher in fabricated samples with the lowest V, as shown in Figure 9.

4.3 Verification of Tensile Properties

Although there were no dramatic differences in the tensile behavior of each sample in this study, the results were still comparable to the tensile results from other existing studies. As illustrated in Figure 13 and as listed in Table 3, the UTS and yield strengths (YS) of samples exhibited minor changes, with UTS changing from 1008 ± 2 to 941 ± 9 MPa and YS changing from 682 ± 11 to 640 ± 7 MPa. However, in the samples fabricated with the lowest P of 100 W, the elongation noticeably decreased as V increased owing to the higher porosity caused by the lack of fusion, as shown in Figure 4. Conversely, according to the reference data in Table 3, it is known that the Ni625 alloy can be fabricated using a broad range of process parameters (for example, P may change from 220 to 1500 W and V from 8.3 to 33.3 mm s−1) yielding higher tensile properties than casting.

Figure 13 Comparison of tensile properties in this study with those obtained in other research studies.
LabelPVQdE D = P/(Vd)UTSYSEl
[W][mm s−1][g min−1][mm][J mm−2][MPa][MPa][%]
S11005.02.00.540.0951 ± 7655 ± 1542 ± 2
S210010.04.00.520.01008 ± 2682 ± 1136 ± 1
S310015.04.00.513.31005 ± 7674 ± 1328 ± 4
S41205.02.00.548.0941 ± 9640 ± 742 ± 2
S512010.04.00.524.0959 ± 3666 ± 741 ± 1
S612015.04.00.516.0989 ± 4669 ± 1237 ± 1
S71605.02.00.564.0–––
S816010.04.00.532.0944 ± 4670 ± 1042 ± 1
S916015.04.00.521.3960 ± 6672 ± 940 ± 1
[7]2208.32.30.466.01020.9675.823.1
[14]33033.37.00.414.11073 ± 5723 ± 2326 ± 2
[15]50012.52.51.233.3882 ± 7480 ± 2036 ± 5
[19]150015.07.5520.0733.7500.429.4
[29]Casting485.0275.025.0
Table 3. Comparison of process parameters and tensile properties in this study with those obtained in references.

In addition, based on the literature data listed in Table 3, the UTS decreases at increasing P. A higher P not only increases the evaporation[21] of Al, Cr, Fe, and Co in the Ni625 alloy by increasing the MP temperature, but also accelerates precipitation growth owing to a lower cooling rate, thus leading to a degradation of mechanical properties. Therefore, using P values as small as possible is advantageous for the microstructure and mechanical properties of the material and machine maintenance. In this study, tensile properties similar to those reported in other research studies[7, 13, 14, 18] were obtained by using a lower P combination with a small hatch space, as shown in Figure 13. A small hatch space increases remelting, which reduces the lack of fusion[43] and increases the ED grains.[3]

This study is believed to be the first report on the optimization of the strength and ductility of Ni625 alloys using a relatively low P value, thus demonstrating that high-performance Ni625 alloys can also be fabricated with lower P.

5 Conclusions

Extensive empirical testing on the Lasermeister was performed with common AM materials, including Fe-, Ni-, and Ti-based alloys. Herein, to develop process maps for the Ni625 alloy specific to this machine, the processability, microstructure, and mechanical properties of the alloy were experimentally and numerically investigated under various fabrication parameters. Key findings include: 1) A simulation model was established to predict the MP thermal history, including the dimensions and G and R rates; 2) The dimensions and highest temperatures of the MP were considerably affected by P but less affected by V, leading to high P values and increased size and maximum temperature of the MP; 3) Fully dense Ni625 alloy parts (>99.5%) were fabricated under conditions where P was >100 W and V was in the range of 5–15 mm s−1; 4) As P increased and V decreased, a corresponding increase in the dendritic structure and texture was observed. Notably, the sample synthesized with the highest P value of 160 W and lowest V value of 5 mm s−1 exhibited the most pronounced dendritic structure and texture; 5) A positive correlation was observed between the microstructure and tensile properties with lower elongations for finer microstructures. In particular, sample S3, which had the finest microstructure and highest porosity, exhibited the lowest elongation; 6) P ranged from 100 to 160 W, V varied between 5 and 15 mm s−1, and a corresponding process map for ED was established; and 7) The samples showed tensile strength values comparable to those in other research studies, with UTS and YS ranging from 1008 ± 2 to 941 ± 9 MPa and from 682 ± 11 to 640 ± 7 MPa, respectively.

This study demonstrated that a combination of lower P values and smaller hatch spacings can effectively strengthen Ni625 alloys. It was also found that there several parameters can be set to achieve similar outcomes. Indeed, these findings pave the way for the formulation of various “recipes” in the future tailored to the shape and complexity of different parts, thus opening new avenues for part development.

References

  1.  P. R. Gradl, T. Teasley, C. Protz, C. Katsarelis, P. Chen, in AIAA Propulsion and Energy Forum 2021.
  2. P. R. Gradl, C. Protz, T. Wammen, in AIAA Propulsion and Energy Forum and Exposition 2019.
  3. Y. Ekubaru, O. Gokcekaya, T. Ishimoto, K. Sato, K. Manabe, P. Wang, T. Nakano, Mater. Des. 2022, 221, 110976.
  4. D. Svetlizky, M. Das, B. Zheng, A. L. Vyatskikh, S. Bose, A. Bandyopadhyay, J. M. Schoenung, E. J. Lavernia, N. Eliaz, Mater. Today 2021, 49, 271.
  5. D. Svetlizky, B. Zheng, A. Vyatskikh, M. Das, S. Bose, A. Bandyopadhyay, J. M. Schoenung, E. J. Lavernia, N. Eliaz, Mater. Sci. Eng. A 2022, 840, 142967.
  6. A. Bandyopadhyay, K. D. Traxel, M. Lang, M. Juhasz, N. Eliaz, S. Bose, Mater. Today 2022, 52, 207.
  7. J. Wang, Y. Wang, Y. Su, J. Shi, Mater. Sci. Eng. A 2022, 830, 142296.
  8. T. Ünal-Saewe, L. Gahn, J. Kittel, A. Gasser, J. H. Schleifenbaum, Procedia Manuf. 2020, 47, 1050.
  9. J. M. Wilson, C. Piya, Y. C. Shin, F. Zhao, K. Ramani, J. Clean. Prod. 2014, 80, 170.
  10. V. K. Balla, S. Banerjee, S. Bose, A. Bandyopadhyay, Acta Biomater. 2010, 6, 2329.
  11. P. R. Gradl, C. S. Protz, Acta Astronaut. 2020, 174, 148.
  12. S. Pratheesh Kumar, S. Elangovan, R. Mohanraj, J. R. Ramakrishna, Mater. Today Proc. 2021, 46, 7892.
  13. A. Poudel, P. R. Gradl, S. Shao, N. Shamsaei, Mater. Sci. Eng. A 2024, 889, 145826.
  14. J. Nguejio, F. Szmytka, S. Hallais, A. Tanguy, S. Nardone, M. Godino Martinez, Mater. Sci. Eng. A 2019, 764, 138214.
  15. M. Rombouts, G. Maes, M. Mertens, W. Hendrix, J. Laser Appl. 2012, 24, 052007.
  16. Y. L. Hu, Y. L. Li, S. Y. Zhang, X. Lin, Z. H. Wang, W. D. Huang, Mater. Sci. Eng. A 2020, 772, 138711.
  17. G. Marchese, X. Garmendia Colera, F. Calignano, M. Lorusso, S. Biamino, P. Minetola, D. Manfredi, Adv. Eng. Mater. 2017, 19, 2.
  18. Y. L. Hu, X. Lin, X. B. Yu, J. J. Xu, M. Lei, W. D. Huang, J. Alloys Compd. 2017, 711, 267.
  19. Y. L. Hu, X. Lin, S. Y. Zhang, Y. M. Jiang, X. F. Lu, H. O. Yang, W. D. Huang, J. Alloys Compd. 2018, 767, 330.
  20. R. Savinov, Y. Wang, J. Shi, Mater. Sci. Eng. A 2023, 884, 145542.
  21. N. Kwabena Adomako, N. Haghdadi, S. Primig, Mater. Des. 2022, 223, 111245.
  22. G. P. Dinda, A. K. Dasgupta, J. Mazumder, Mater. Sci. Eng. A 2009, 509, 98.
  23. Z. Tian, C. Zhang, D. Wang, W. Liu, X. Fang, D. Wellmann, Y. Zhao, Y. Tian, Appl. Sci. 2020, 10, 81.
  24. D. K. Gorai, T. K. Kundu, IOP Conf. Ser. Mater. Sci. Eng. 2018, 338, 012041.
  25. J. M. V. Quaresma, A. Carlos, A. Garcia, Metall. Mater. Trans. A: Phys. Metall. Mater. Sci. 2000, 31, 3167.
  26. K. S. Cruz, E. S. Meza, F. A. P. Fernandes, J. M. V. Quaresma, L. C. Casteletti, A. Garcia, Metall. Mater. Trans. A: Phys. Metall. Mater. Sci. 2010, 41, 972.
  27. J. Shao, G. Yu, X. He, S. Li, R. Chen, Y. Zhao, Opt. Laser Technol. 2019, 119, 105662.
  28. Y. Chen, Y. Yan, B. Li, Automot. Innov. 2020, 3, 328.
  29. B. K. Anil Kumar, M. G. Ananthaprasad, K. Gopalakrishna, IOP Conf. Ser. Mater. Sci. Eng. 2016, 149, 012116.
  30. O. Gokcekaya, T. Ishimoto, T. Todo, R. Suganuma, R. Fukushima, T. Narushima, T. Nakano, Crystals 2021, 11, 9.
  31. Y. Ekubaru, O. Gokcekaya, T. Nakano, Crystals 2022, 12, 1348.
  32. T. DebRoy, H. L. Wei, J. S. Zuback, T. Mukherjee, J. W. Elmer, J. O. Milewski, A. M. Beese, A. Wilson-Heid, A. De, W. Zhang, Prog. Mater. Sci. 2018, 92, 112.
  33. W. Zhao, Y. Sun, P. Che, Z. Ning, H. Fan, H. Yang, J. Sun, P. K. Liaw, A. H. W. Ngan, Y. Huang, Mater. Des. 2024, 237, 112538.
  34. Z. Zhou, L. Huang, Y. Shang, Y. Li, L. Jiang, Q. Lei, Mater. Des. 2018, 160, 1238.
  35. Z. Tong, X. Ren, J. Jiao, W. Zhou, Y. Ren, Y. Ye, E. A. Larson, J. Gu, J. Alloys Compd. 2019, 785, 1144.
  36. O. Gokcekaya, T. Ishimoto, S. Hibino, J. Yasutomi, T. Narushima, T. Nakano, Acta Mater. 2021, 212, 116876.
  37. S. H. Sun, K. Hagihara, T. Ishimoto, R. Suganuma, Y. F. Xue, T. Nakano, Addit. Manuf. 2021, 47, 102329.
  38. Y. L. Hu, X. Lin, Y. L. Li, S. Y. Zhang, X. H. Gao, F. G. Liu, X. Li, W. D. Huang, Mater. Des. 2020, 186, 108359.
  39. R. J. Vikram, A. Singh, S. Suwas, J. Mater. Res. 2020, 35, 1949.
  40. J. N. Zhu, E. Borisov, X. Liang, E. Farber, M. J. M. Hermans, V. A. Popovich, Addit. Manuf. 2021, 38, 101802.
  41. M. S. Pham, B. Dovgyy, P. A. Hooper, C. M. Gourlay, A. Piglione, Nat. Commun. 2020, 11, 749.
  42. Z. Gan, G. Yu, X. He, S. Li, Int. J. Heat Mass Transf. 2017, 104, 28.
  43. L. E. dos Santos Paes, M. Pereira, F. A. Xavier, W. L. Weingaertner, L. O. Vilarinho, J. Manuf. Process. 2022, 73, 67.
논문 페이지로 이동

The Fastest Laptops for 2024

FLOW-3D 수치해석용 노트북 선택 가이드

2024년 가장 빠른 노트북

PCMag이 테스트하는 방법 소개 : 기사 원본 출처: https://www.pcmag.com/picks/the-fastest-laptops

CFD를 수행하기 위한 노트북 선정 기준은 별도로 없지만 아래 일반적인 성능 테스트를 수행한 노트북은 선택이 도움이 됩니다.

PC Labs는 매년 100개 이상의 노트북을 테스트합니다. 심층 벤치마킹에 따르면, 이것들은 오늘날 시중에서 가장 빠른 노트북입니다.

돈으로 살 수 있는 가장 빠른 노트북을 찾으시나요? “빠르다”는 것을 어떻게 정의하느냐에 따라 다르기 때문에 어려운 문제입니다. 노트북 성능에 대해 이야기할 때는 다양한 종류 의 속도가 적용됩니다. 바로 PCMag이 등장하는 부분입니다.

PCMag 분석가는 수십 년 동안 노트북을 테스트한 경험이 있으며 모든 시나리오에서 가장 빠른 기계를 정확히 찾아내는 방법을 알고 있습니다.

PCMag은 매년 100대 이상의 노트북을 검토하고 각각을 엄격한 테스트 모음에 넣어 생산성, 콘텐츠 생성 및 그래픽 워크로드에 대한 속도를 정량화합니다. (또한 디자인, 사용성, 연결성, 번들 소프트웨어 등도 평가합니다.)

현재 테스트한 가장 빠른 노트북으로 선택한 제품은 MSI의 Titan 18 HX로, 타의 추종을 불허하는 원시 처리 및 그래픽 속도를 자랑하는 제품입니다.

PCMag은 보다 구체적인 사용 사례와 다양한 예산에 맞는 추가 고속 노트북을 선택했습니다. 확인해 보시고, 속도에 따라 노트북을 구매하는 방법도 알아보세요. PCMag의 조언은 최적의 제품을 구매하는데 도움을 줄 것입니다.

MSI Titan 18 HX

Fastest Cost-Is-No-Object Laptop : MSI Titan 18 HX

The Lenovo Legion Pro 7i Gen 9 16

Fastest High-End Gaming Laptop: Lenovo Legion Pro 7i Gen 9 16

Acer Nitro V 15 (ANV15-51-59MT)

Fastest Value-Priced Gaming Laptop

Acer Nitro V 15 (ANV15-51-59MT)

Asus ROG Zephyrus G14 (2024)

Fastest Compact Gaming Laptop: Asus ROG Zephyrus G14 (2024)

Asus Zenbook 14 OLED Touch (UM3406) right angle

Fastest Ultraportable Laptop: Asus Zenbook 14 OLED Touch (UM3406)

Apple MacBook Pro 16-Inch (2024, M4 Pro)

Fastest Mac Laptop: Apple MacBook Pro 16-Inch (2024, M4 Pro)

The Dell Precision 5490

Fastest Business Laptop: Dell Precision 5490

Lenovo Yoga Pro 9i 16 Gen 9 left angle

Fastest Big-Screen Productivity Laptop: Lenovo Yoga Pro 9i 16 Gen 9:

The Asus ProArt P16 (H7606)

Fastest Content-Creation Laptop: Asus ProArt P16 (H7606)

HP ZBook Fury 16 G11 right angle

Fastest Workstation Laptop: HP ZBook Fury 16 G11

복잡한 노트북 CPU 모델명 완벽하게 이해하기

출처: 본 자료는 IT WORLD에서 인용한 자료입니다.

https://www.itworld.co.kr/ 2024.12.18

초단간 요약

최신 고성능 윈도우 노트북을 원한다면 다음 세 가지를 살펴보자.

  • 인텔 : 모델명이 ‘2’로 시작하고 ‘V’로 끝나는 코어 울트라 시리즈 2(Core Ultra Series 2). 예를 들면 인텔 코어 울트라 5 226V(시리즈2)가 있다.
  • AMD : 라이젠 AI 300 시리즈. 예시로 AMD 라이젠 AI 7 프로 360.
  • 퀄컴 : 스냅드래곤 X 시리즈의 플러스(Plus) 또는 엘리트(Elite) 제품

이 세 가지 프로세서는 성능과 배터리 수명 면에서 애플 맥북의 M 시리즈와 경쟁하도록 설계됐다. 그러나 노트북을 선택할 때는 프로세서뿐 아니라 다양한 요소를 함께 고려해야 한다.

인텔 프로세서

인텔의 최신 프로세서는 다음 세 가지 범주로 나뉜다.

  • 인텔 코어 울트라(Intel Core Ultra) : 프리미엄 칩으로, AI 전용 프로세서를 탑재했다(예 : 인텔 코어 울트라 7 155U).
  • 인텔 코어(Intel Core) : 주류 노트북에 사용되는 칩으로, 코어 울트라보다 한 단계 아래다(예 : 인텔 코어 7 150U).
  • 인텔 프로세서(Intel Processor) : 과거 펜티엄과 셀러론 브랜드를 대체하는 저가형 PC 칩이다(예 : 인텔 프로세서 N200).

인텔은 프로세서를 성능 등급에 따라 ‘3’, ‘5’, ‘7’, ‘9’로 세분화했다. 숫자가 높을수록 더 많은 코어를 가지고 있다는 의미이며, 이미지 처리 및 비디오 작업 속도가 향상된다. 코어 5와 코어 울트라 5 칩은 웹 브라우징 및 오피스 작업에 적합하다.

Intel Core Ultra 9 processor 185H with different parts of the model name broken down.

Intel

모델명 뒤에 붙는 접미사도 중요하다. 이 글자는 프로세서가 어떻게 최적화되었는지를 나타낸다. 긴 접미사 목록 중에 알아두어야 할 주요 단어는 ‘U’와 ‘H’다. U는 배터리 수명을, H는 성능을 강조한다. 코어 울트라 5 226V의 ‘V’는 코어 울트라 제품 라인에만 적용되는 접미사다.

구형 모델은 12세대 코어 i5 1235U처럼 이름에 ‘i’와 세대 번호가 포함되어 있다. 14세대에 이르러 인텔은 모든 것을 재설정하고 이제 ‘시리즈 1’부터 세기 시작했다(예 : 코어 울트라 155U). 즉, 최신 인텔 칩의 모델명은 구형 모델보다 짧다. 가격이 적당한 경우라면 구형 모델도 여전히 고려해 볼만하다.

AMD 프로세서

AMD는 인텔만큼 브랜딩 개편에 적극적이지는 않다. 애플 및 퀄컴과 경쟁하는 AI 300 시리즈 칩 외에 나머지 프로세서는 2023년 도입된 더 길고 혼란스러운 명명 체계를 따르고 있다.

AMD processor name with various attributes broken down

AMD

예시로 AMD 라이젠 5 8640HS를 살펴본다.

  • 첫 번째 숫자 ‘8’은 세대를 의미하며, 2024년에 출시된 칩을 나타낸다(7735HS는 2023년 제품).
  • ‘5’는 성능 등급을 나타내며, 인텔과 마찬가지로 숫자가 높을수록 성능이 좋다는 의미다. 인텔 코어 5와 코어 7 체계와 유사하게 홀수로 계산된다.
  • 마지막 글자는 프로세서의 최적화 방식이다. ‘U’는 배터리 수명, ‘H’는 성능을 우선시한다.

이 명명 체계를 따르는 칩은 AMD의 구형 젠 4(Zen 4) 아키텍처를 기반으로 하지만, 최신 AI 300 시리즈는 젠 5 아키텍처를 사용한다. AMD가 프로세서 라인 대부분을 최신 아키텍처로 전환함에 따라 이에 맞는 새로운 브랜드가 등장할 것으로 예상된다.

퀄컴 프로세서

퀄컴은 올해 초 전력 효율성에 중점을 두고 PC CPU 경쟁에 합류했다. 퀄컴의 스냅드래곤 X 칩은 휴대폰, 태블릿, 애플의 M 시리즈 프로세서에서 볼 수 있는 것과 동일한 Arm 기반 아키텍처를 사용하며, 우수한 PC 성능과 긴 배터리 수명을 제공한다. 무엇보다 퀄컴의 직관적인 브랜드 전략이 신선하게 다가온다.

  • 스냅드래곤 X 엘리트(Snapdragon X Elite) : 최고급 모델
  • 스냅드래곤 X 플러스(Snapdragon X Plus) : 그보다 한 단계 낮은 모델

마이크로소프트 서피스 노트북에 탑재된 스냅드래곤 X 플러스를 사용해 본 경험에 따르면, 충분한 성능과 하루 종일 지속되는 배터리 수명을 제공했다.

다만, Arm 기반 프로세서가 모든 윈도우 소프트웨어와 호환되는 것은 아니다. 스냅드래곤 PC에서 Arm이 아닌 앱을 실행하는 마이크로소프트의 에뮬레이션 엔진에서도 호환성 문제가 발생할 수 있다. 에뮬레이션 개선과 Arm 버전의 소프트웨어를 출시하는 개발자가 늘어나면서 상황이 점점 개선되고 있지만, 인텔과 AMD 노트북에서는 겪지 않아도 될 골칫거리가 여전히 남아 있다.

CPU 시장의 긍정적인 변화

복잡한 이름을 살펴보는 것이 혼란스러울 수 있고 AI에 대한 강조가 다소 과장된 면이 있지만, PC 프로세서 분야에서 3가지 업체가 경쟁하는 덕분에 상황은 개선되고 있다. 지난 4년간 애플은 전력 효율성 측면에서 독보적인 성과를 보여줬다. 그러나 인텔, AMD, 퀄컴이 새로운 프로세서를 내놓으며 애플의 수준에 도달하고 있다.

물론 복잡한 브랜드와 명명 체계는 단점이지만, 이런 경쟁 덕분에 더 나은 성능과 배터리 수명을 갖춘 제품이 등장하고 있다. 사용자에게 긍정적인 변화다.
dl-itworldkorea@foundryco.com

아래 과거 자료도 선택에 큰 도움이 됩니다.

2023년 01월 11일

본 자료는 IT WORLD에서 인용한 자료입니다.

일반적으로 수치해석을 주 업무로 사용하는 경우 노트북을 사용하는 경우는 그리 많지 않습니다. 그 이유는 CPU 성능을 100%로 사용하는 해석 프로그램의 특성상 발열과 부품의 성능 측면에서 데스크탑이나 HPC의 성능을 따라 가기는 어렵기 때문입니다.

그럼에도 불구하고, 이동 편의성이나 발표,  Demo 등의 업무 필요성이 자주 있는 경우, 또는 계산 시간이 짧은 경량 해석을 주로 하는 경우, 노트북이 주는 이점이 크기 때문에 수치해석용 노트북을 고려하기도 합니다.

보통 수치해석용 컴퓨터를 검토하는 경우 CPU의 Core수나 클럭, 메모리, 그래픽카드 등을 신중하게 검토하게 되는데 모든 것이 예산과 직결되어 있기 때문입니다.  따라서 해석용 컴퓨터 구매 시 어떤 것을 선정 우선순위에 두는지에 따라 사양이 달라지게 됩니다.

해석용으로 노트북을 고려하는 경우, 보통 CPU의 클럭은 비교적 선택 기준이 명확합니다. 메모리 또한 용량에 따라 가격이 정해지기 때문에 이것도 비교적 명확합니다. 나머지 가격에 가장 큰 영향을 주는 것이 그래픽카드인데, 이는 그래픽 카드의 경우 일반적인 게임용이나 포토샵으로 일반적인 이미지 처리 작업을 수행하는 그래픽카드와 3차원 CAD/CAE에 사용되는 업무용 그래픽 카드는 명확하게 분리되어 있고, 이는 가격 측면에서 매우 차이가 많이 납니다.

통상 게임용 그래픽카드는 수치해석의 경우 POST 작업시 문제가 발생하는 경우가 종종 발생하기 때문에 일반적으로 선택 우선 순위에서 충분한 확인을 한 후 구입하는 것이 좋습니다.

FLOW-3D는 OpenGL 드라이버가 만족스럽게 수행되는 최신 그래픽 카드가 적합합니다. 최소한 OpenGL 3.0을 지원하는 것이 좋습니다. FlowSight는 DirectX 11 이상을 지원하는 그래픽 카드에서 가장 잘 작동합니다. 권장 옵션은 NVIDIA의 Quadro K 시리즈와 AMD의 Fire Pro W 시리즈입니다.

특히 엔비디아 쿼드로(NVIDIA Quadro)는 엔비디아가 개발한 전문가 용도(워크스테이션)의 그래픽 카드입니다. 일반적으로 지포스 그래픽 카드가 게이밍에 초점이 맞춰져 있지만, 쿼드로는 다양한 산업 분야의 전문가가 필요로 하는 영역에 광범위한 용도로 사용되고 있습니다. 주로 산업계의 그래픽 디자인 분야, 영상 콘텐츠 제작 분야, 엔지니어링 설계 분야, 과학 분야, 의료 분석 분야 등의 전문가 작업용으로 사용되고 있습니다. 따라서 일반적인 소비자를 대상으로 하는 지포스 그래픽 카드와는 다르계 산업계에 포커스 되어 있으며 가격이 매우 비싸서 도입시 예산을 고려해야 합니다.

MSI, CES 2023서 인텔 코어 i9-13980HX 탑재 노트북 벤치마크 공개

2023.01.11

원문보기

Mark Hachman  | PCWorld

MSI가 새로운 노트북 CPU 벤치마크, 그리고 그 CPU가 내장돼 있는 신제품 노트북 제품군을 모두 CES 2023에서 공개했다. CES에서 인텔은 노트북용 13세대 코어 칩, 코드명 랩터 레이크와 핵심 제품인 코어 i9-13980HX를 발표했다.

ⓒ PCWorld

새로운 노트북용 13세대 코어 칩이 게임 플레이에서 12% 더 빠르다는 정도의 약간의 정보는 이미 알려져 있다. 사용자가 기다리는 것은 실제 CPU가 탑재된 노트북에서의 성능이지만 보통 벤치마크는 제품 출시가 임박해서야 공개되는 것이 보통이다. 올해는 다르다.

CES 2023에서 MSI는 인텔 최고급 제품군인 코어 i9-13980HX 프로세서가 탑재된 타이탄 GT77 HX과 레이더 GE78 HX를 공개했다. 이례적으로 여기에 더해 PCI 익스프레서 5 SSD의 실제 성능을 측정하는 크리스털디스크마크, 모바일 프로세서 실행 속도를 측정하는 시네벤치 벤치마크 점수도 함께 제공했다. 다음 영상의 결과부터 말하자면 인텔 최신 프로세서를 큰 폭으로 따돌릴 만한 수치다.

https://www.youtube.com/embed/3kvrOIEOUlw

ⓒ PCWorld

MSI는 레이더 GE78 HX 외에도 레이더 GE68 HX 그리고 게이밍 노트북 같지 않은 외관의 스텔스 16 스튜디오, 스텔스 14, 사이보그 14 등 2023년에 출시될 다른 노트북도 전시했다. 오래된 PC 애호가라면 MSI 노트북 전면을 장식한 화려한 복고풍의 라이트 브라이트(Lite Brite) LED를 반가워할지도 모른다. 바닥면 섀시가 투명한 플라스틱 소재로 MSI 로고가 새겨져 있는 제품도 있다. 상세한 가격, 출시일, 사양 등은 추후 공개 예정이다.
editor@itworld.co.kr 

원문보기:
https://www.itworld.co.kr/news/272199#csidx870364b15ea6aa28b53a990bc5c0697 

‘코어 i7 vs. 코어 i9’ 나에게 맞는 고성능 노트북 CP

2021.06.14

고성능 노트북을 구매할 때는 코어 i7과 코어 i9 사이에서 선택의 갈림길에 서게 된다. 코어 i7 CPU도 강력하지만 코어 i9는 최고의 성능을 위해 만들어진 CPU이며 보통 그에 상응하는 높은 가격대로 판매된다.

CPU에 초점을 둔다면 관건은 성능이다. 성능을 좌우하는 두 가지 주요소는 CPU의 동작 클록 속도(MHz), 그리고 탑재된 연산 코어의 수다. 그러나 노트북에서 한 가지 중요한 제약 요소는 냉각이다. 냉각이 제대로 되지 않으면 고성능도 쓸모가 없다. 가장 적합한 노트북 CPU를 결정하는 데 도움이 되도록 인텔의 지난 3개 세대 CPU의 코어 i7과 i9에 대한 정보를 모았다. 최신 세대부터 시작해 역순으로 살펴보자.

11세대: 코어 i9 vs. 코어 i7

인텔의 11세대 타이거 레이크(Tiger Lake) H는 한 가지 큰 이정표를 달성했다. 인텔이 2015년부터 H급 CPU에 사용해 온 14nm 공정을 마침내 최신 10nm 슈퍼핀(SuperFin) 공정으로 바꾼 것이다. 오랫동안 기다려온 변화다.

인텔이 자랑할 만한 10nm 고성능 칩을 내놓자 타이거 레이크 H를 장착한 노트북도 속속 발표됐다. 얇고 가볍고 예상외로 가격도 저렴한 에이서 프레데터 트라이톤(Acer Predator Triton) 300 SE를 포함해 일부는 벌써 매장에 출시됐다. 모든 타이거 레이크 H 칩이 8코어 CPU라는 점도 달라진 부분이다. 이전 세대의 경우 같은 제품군 내에서 코어 수에 차이를 둬 성능 기대치를 구분했다.

클록 차이도 크지 않다. 코어 i7-11800H의 최대 클록은 4.6GHz, 코어 i9-11980HK는 5GHz로, 클록 속도 증가폭은 약 8.6% 차이다. 나쁘지 않은 수치지만 둘 다 8코어 CPU임을 고려하면 대부분의 사용자에게 코어 i9는 큰 매력은 없다.

다만 코어 i9에 유리한 부분을 하나 더 꼽자면 코어 i9-11980HK가 65W의 열설계전력(TDP)을 옵션으로 제공한다는 점이다. 높은 TDP는 최상위 코어 i9에만 제공되는데, 이는 전력 및 냉각 요구사항을 충족하는 노트북에서는 코어 i7 버전보다 더 높은 지속 클록 속도를 제공할 수 있음을 의미한다.

대신 이런 노트북은 두껍고 크기도 클 가능성이 높다. 따라서 두 개의 얇은 랩톱 중에서(하나는 코어 i9, 하나는 코어 i7) 고민하는 사람에겐 열 및 전력 측면의 여유분은 두께와 크기를 희생할 만큼의 가치는 없을 것이다.

*11세대의 승자: 대부분의 사용자에게 코어 i7

10세대: 코어 i9 vs. 코어 i7

인텔은 10세대 코멧 레이크(Comet Lake) H 제품군에서 14nm를 고수했다. 그 대신 코어 i9 CPU 외에 코어 i7에도 8코어 CPU를 도입, 사용자가 비싼 최상위 CPU를 사지 않고도 더 뛰어난 성능을 누릴 수 있게 했다.

11세대 노트북이 나오기 시작했지만 10세대 CPU 제품 중에서도 아직 괜찮은 제품이 많다. 예를 들어 MSI GE76 게이밍 노트북은 빠른 CPU와 고성능 155W GPU를 탑재했고, 전면 모서리에는 RGB 라이트가 달려 있다.

11세대 칩과 마찬가지로 코어와 클록 속도의 차이가 크지 않으므로 대부분의 사용자에게 코어 i7과 코어 i9 간의 차이는 미미하다. 코어 i9-10980HK의 최대 부스트 클록은 5.3GHz, 코어 i7-10870H는 5GHz로, 두 칩의 차이는 약 6%다. PC를 최대 한계까지 사용해야 하는 경우가 아니라면 더 비싼 비용을 들여 10세대 코어 i9를 구매할 이유가 없다.

*10세대 승자: 대부분의 사용자에게 코어 i7

9세대: 코어 i9 대 코어 i7

인텔은 9세대 커피 레이크 리프레시(Coffee Lake Refresh) 노트북 H급 CPU에서 14nm 공정을 계속 유지했다. 코어 i9는 더 높은 클록 속도(최대 5GHz)를 제공하며 8개의 CPU 코어를 탑재했다. 물론 이 칩은 2년 전에 출시됐지만 인텔이 설계를 도운 XPG 제니아(Xenia) 15 등 아직 괜찮은 게이밍 노트북이 있다. 얇고 가볍고 빠르며 엔비디아 RTX GPU를 내장했다.

8코어 4.8GHz 코어 i9-9880HK와 4.6GHz 6코어 코어 i7-9850의 클록 속도 차이는 약 4%로, 실제 사용 시 유의미한 차이로 이어지는 경우는 극소수다. 두 CPU 모두 기업용 노트북에 많이 사용됐다. 대부분의 소비자용 노트북에는 8코어 5GHz 코어 i9-9880HK와 6코어 4.5GHz 코어 i7-9750H가 탑재됐다. 이 두 CPU의 클록 차이는 약 11%로, 이 정도면 유의미한 차이지만 마찬가지로 대부분의 경우 실제로 체감하기는 어렵다.

그러나 코어 수의 차이는 멀티 스레드 애플리케이션에서 큰 체감 효과로 이어지는 경우가 많다. 3D 모델링 테스트인 씨네벤치(Cinebench) R20에서 코어 i9-9980HK를 탑재한 구형 XPS 15의 점수는 코어 i7-9750H를 탑재한 게이밍 노트북보다 42% 더 높았다. 8코어 코어 i9의 발열을 심화하는 무거운 부하에서는 성능 차이가 약 7%로 줄어들었다. 여기에는 노트북의 설계가 큰 영향을 미칠 것이다. 어쨌든 일부 상황에서는 8코어가 6코어보다 유리하다.

또한 수치해석의 경우 결과를 분석하는 작업중의 많은 부분이 POST 작업으로 그래픽처리가 필요하다. 따라서 아래 영상편집을 위한 노트북에 대한 자료도 선택에 도움이 될것으로 보인다.

영상 편집을 위한 최고의 노트북 9선

Brad Chacos, Ashley Biancuzzo, Sam Singleton | PCWorld

원문보기

2022.12.29

영상을 편집하다 보면 컴퓨터의 여러 리소스를 집약적으로 사용하기 마련이다. 그래서 영상 편집은 대부분 데스크톱 PC에서 하는 경우가 많지만, 노트북에서 영상을 편집하려 한다면 PC만큼 강력한 사양이 뒷받침되어야 한다. 

ⓒ Gordon Mah Ung / IDG

영상 편집용 노트북을 구매할 때 가장 비싼 제품을 선택할 필요는 없다. 사용 환경에 맞게 프로세서, 디스플레이의 품질, 포트 종류 등을 다양하게 고려해야 한다. 다음은 영상 편집에 최적화된 노트북 제품이다. 추천 제품을 확인한 후 영상 편집용 노트북을 테스트하는 팁도 참고하자. 

1. 영상 편집용 최고의 노트북, 델 XPS 17(2022)

ⓒ  IDG

장점
• 가격 대비 강력한 기능
• 밝고 풍부한 색채의 대형 디스플레이
• 썬더볼트 4 포트 4개 제공
• 긴 배터리 수명 
• 시중에서 가장 빠른 GPU인 RTX 3060

단점
• 무겁고 두꺼움
• 평범한 키보드
• USB-A, HDMI, 이더넷 미지원

델 XPS 17(2022)이야말로 콘텐츠 제작에 최적화된 노트북이다. 인텔 12세대 코어 i7-12700H 프로세서 및 엔비디아 지포스 RTX 3060는 편집을 위한 뛰어난 성능을 제공한다. 1TB SSD도 함께 지원되기에 데이터를 옮길 때도 편하다. 

XPS 17은 SD카드 리더, 여러 썬더볼트 4 포트, 3840×2400 해상도의 17인치 터치스크린 패널, 16:10 화면 비율과 같은 영상 편집자에게 필요한 기능을 포함한다. 무게도 2.5kg 대로 비교적 가볍다. 배터리 지속 시간은 한번 충전 시 11시간인데, 이전 XPS 17 버전보다 1시간 이상 늘어난 수치다. 

2. 영상 편집에 최적화된 스크린, 델 XPS 15 9520

ⓒ  IDG

장점
• 뛰어난 OLED 디스플레이
• 견고하고 멋진 섀시(Chassis)
• 강력한 오디오
• 넓은 키보드 및 터치패드

단점
• 다소 부족한 화면 크기
• 실망스러운 배터리 수명
• 시대에 뒤떨어진 웹캠
• 제한된 포트

델 XPS 15 9520은 놀라운 OLED 디스플레이를 갖추고 있으며, 최신 인텔 코어 i7-12700H CPU 및 지포스 RTX 3050 Ti 그래픽이 탑재되어 있다. 컨텐츠 제작 및 영상 편집용으로 가장 선호하는 제품이다. 시스템도 좋지만 투박하면서 금속 소재로 이루어진 외관이 특히 매력적이다. 

15인치 노트북이지만 매일 갖고 다니기에 다소 무거운 것은 단점이다. XPS 17 모델에서 제공되는 포트도 일부 없다. 그러나 멋진 OLED 디스플레이가 단연 돋보이며, 3456X2160 해상도, 16:10 화면 비율, 그리고 매우 선명하고 정확한 색상을 갖추고 있어 좋다. 

3. 최고의 듀얼 모니터 지원, 에이수스 젠북 프로 14 듀오 올레드

ⓒ IDG

장점
• 놀라운 기본 디스플레이와 보기 쉬운 보조 디스플레이 
• 탁월한 I/O 옵션 및 무선 연결
• 콘텐츠 제작에 알맞은 CPU 및 GPU 성능 

단점
• 생산성 노트북 치고는 부족한 배터리 수명
• 작고 어색하게 배치된 트랙패드
• 닿기 어려운 포트 위치

에이수스 젠북 프로 14 듀오(Asus Zenbook Pro 14 Duo OLED)는 일반적이지 않은 노트북이다. 일단 사양은 코어 i7 프로세서, 지포스 RTX 3050 그래픽, 16GB DDR5 메모리, 빠른 1TB NVMe SSD를 포함해 상당한 성능을 자랑한다. 또한 초광도의 547니트로 빛을 발하는 한편 DCI-P3 색영역의 100%를 커버하는 14.5인치 4K 터치 OLED 패널을 갖추고 있다. 사실상 콘텐츠 제작자를 위해 만들어진 제품이라 볼 수 있다.

가장 흥미로운 부분은 키보드 바로 위에 위치한 12.7인치 2880×864 스크린이다. 윈도우에서는 해당 모니터를 보조 모니터로 간주하며, 사용자는 번들로 제공된 에이수스 소프트웨어를 사용해 트랙패드로 사용하거나 어도비 앱을 위한 터치 제어 패널을 표시할 수 있다. 어떤 작업이든 유용하게 써먹을 수 있다.

젠북 프로 14 듀오 올레드는 기본적으로 휴대용이자 중간급 워크스테이션이다. 단, 배터리 수명은 평균 수준이기 때문에 중요한 작업 수행이 필요한 경우, 반드시 충전 케이블을 가지고 다녀야 한다. 그럼에도 불구하고 젠북 프로 14 듀오 올레드는 3D 렌더링 및 인코딩과 같은 작업에서 탁월한 성능을 보여 콘텐츠 제작자들에게 맞춤화 된 컴퓨터이다. 듀얼 스크린은 역대 최고의 기능이다.

4. 영상 편집하기 좋은 포터블 노트북, 레이저 블레이드 14(2021)

ⓒ IDG

장점
• AAA 게임에서 뛰어난 성능
• 훌륭한 QHD 패널
• 유난히 적은 소음 

단점
• 700g으로 무거운 AC 어댑터
• 비싼 가격
• 썬더볼트 4 미지원

휴대성이 핵심 고려 사항이라면, 레이저 블레이드 14(Razer Blade 14) (2021)를 선택해 보자. 노트북 두께는 1.5cm, 무게는 1.7kg에 불과해 비슷한 수준의 노트북보다 훨씬 가볍다. 사양은 AMD의 8-코어 라이젠 9 5900HX CPU, 엔비디아의 8GB 지포스 RTX 3080, 1TB NVMe SSD, 16GB 메모리를 탑재하고 있어 사양도 매우 좋다. 

그러나 휴대성을 대가로 몇 가지 이점을 포기해야 할 수 있다. 일단 14인치 IPS 등급 스크린은 공장에서 보정된 상태로 제공되지만, 최대 해상도는 2560×1440다. 또 풀 DCI-P3 색영역을 지원하지만 4K 영상 편집은 불가능하다. 거기에 레이저 블레이드 14는 SD 카드 슬롯도 없다. 다만 편집 및 렌더링을 위한 강력한 성능을 갖추고 있고 가방에 쉽게 넣을 수 있는 제품인 것은 분명하다. 

5. 배터리 수명이 긴 노트북, 델 인스피론 16

ⓒ Dell

장점
• 넉넉한 16인치 16:10 디스플레이
• 긴 배터리 수명
• 경쟁력 있는 애플리케이션 성능 
• 편안한 키보드 및 거대한 터치패드 
• 쿼드 스피커(Quad speakers)

단점
• GPU 업그레이드 어려움
• 512GB SSD 초과 불가
• 태블릿 모드에서는 어색하게 느껴질 수 있는 큰 스크린 

긴 배터리 수명을 가장 최우선으로 고려한다면, 델 인스피론 16(Dell Inspiron 16)을 살펴보자. 콘텐츠 제작 작업을 하며테스트해보니, 인스피론 16은 한 번 충전으로 16.5시간 동안 이용할 수 있다. 외부에서 작업을 마음껏 편집할 수 있는 시간이다. 그러나 무거운 배터리로 인해 무게가 2.1 kg에 달하므로 갖고 다니기에 적합한 제품은 아니다. 

가격은 저렴한 편이나 몇 가지 단점이 있다. 일단 인텔 코어 i7-1260P CPU, 인텔 아이리스 Xe 그래픽, 16GB 램, 512GB SSD 스토리지를 탑재하고 있다. 이 정도 사양으로 영상 편집 프로젝트 대부분을 작업할 수 있으나, 스토리지 용량이 부족하기 때문에 영상 파일을 저장할 경우 외장 드라이브가 필요하다. 그러나 델 인스피론 16이 진정으로 빛을 발하는 부분은 단연 배터리 수명이다. 또한 강력한 쿼드 스피커 시스템도 사용해 보면 만족할 것이다. 포트의 경우, USB 타입-C 2개, USB-A 3.2 Gen 1 1개, HDMI 1개, SD 카드 리더 1개, 3.5mm 오디오 잭 1개가 제공된다. 

6. 게이밍과 영상 편집 모두에 적합한 노트북, MSI GE76 레이더

ⓒ MSI

장점
• 뛰어난 성능을 발휘하는 12세대 코어 i9-12900HK
• 팬 소음을 크게 줄이는 AI 성능 모드
• 1080p 웹캠과 훌륭한 마이크 및 오디오로 우수한 화상 회의 경험 제공

단점
• 동일한 유형의 세 번째 버전
• 어수선한 UI
• 비싼 가격 

사양이 제일 좋은 제품을 찾고 있을 경우, 크고 무거운 게이밍 노트북을 선택해 보자. MSI GE76 레이더(Raider)는 강력한 14-코어 인텔 코어 i9-12900HK 칩, 175와트의 엔비디아 RTX 3080 Ti가 탑재됐고, 충분한 내부 냉각 성능 덕분에 UL의 프로시온(Procyon) 벤치마크의 어도비 프리미어 테스트에서 다른 노트북보다 훨씬 뛰어난 성능을 보였다. MSI GE76 레이더는 심지어 고속 카드 전송을 위해 PCle 버스에 연결된 SD 익스프레스(SD Express) 카드 리더도 갖추고 있다.

동일한 제품의 작년 모델은 게이머 중심의 360Hz 1080p 디스플레이를 지원한다. 영상 편집 과정에서는 그닥 이상적이지 않은 사양이다. 그러나 2022년의 12UHS 고급 버전은 4K, 120Hz 패널을 추가했는데, 이 패널은 콘텐츠 생성에 맞춰 튜닝 되지는 않았으나 17.3인치의 넓은 스크린 크기이기에 영상 편집자에게 꽤 유용하다. 

7. 가성비 좋은 노트북, HP 엔비 14t-eb000(2021) 

ⓒ IDG

장점
• 높은 가격 대비 우수한 성능
• 환상적인 배터리 수명
• 성능 조절이 감지되지 않을 정도의 저소음 팬 
• 썬더볼트 4 지원

단점
• 약간 특이한 키보드 레이아웃
• 비효율적인 웹캠의 시그니처 기능

가장 빠른 영상 편집 및 렌더링을 원할 경우 하드웨어에 더 많은 비용을 들여야 하지만, 예산이 넉넉하지 않을 때가 있다. 이때 HP 엔비(Envy) 14 14t-eb000) (2021)를 이용해보면 좋다. 가격은 상대적으로 저렴한 편이고 견고한 기본 컨텐츠 제작에 유용하다. 

엔트리 레벨의 지포스 GTX 1650 Ti GPU 및 코어 i5-1135G7 프로세서는 그 자체로 업계 최고 제품은 아니다. 하지만 일반적인 편집 작업을 충분히 수행할 수 있는 사양이다. 분명 가성비 좋은 제품이다. 14인치 1900×1200 디스플레이는 16:10 화면 비율로 생산성을 향상하고, 공장 색 보정과 DCI-P3는 지원하지 않지만 100% sRGB 지원을 제공한다. 그뿐만 아니라, HP 엔비 14의 경우 중요한 SD 카드 및 썬더볼트 포트가 포함되며, 놀라울 정도로 조용하게 실행된다. 

8. 컨텐츠 제작에 알맞은 또다른 게이밍 노트북, 에이수스 ROG 제피러스 S17

ⓒ

장점
• 뛰어난 CPU 및 GPU 성능
• 강력하고 혁신적인 디자인
• 편안한 맞춤형 키보드

단점
• 약간의 압력이 필요한 트랙패드
• 상당히 높은 가격

에이수스 ROG 제피러스(Zephyrus) S17은 영상 편집자의 궁극적인 꿈이다. 이 노트북은 초고속 GPU 및 CPU 성능과 함께 120Hz 화면 재생률을 갖춘 놀라운 17.3인치 4K 디스플레이를 탑재하고 있다. 견고한 전면 금속 섀시, 6개의 스피커 사운드 시스템 및 맞춤형 키보드는 프리미엄급 경험을 더욱 향상한다. 거기다 SD 카드 슬롯 및 풍부한 썬더볼트 포트가 포함되어 있어 더욱 좋다. 그러나 이를 위해 상당한 비용을 지불해야 한다. 예산이 넉넉하고 최상의 제품을 원한다면 제피루스 S17을 선택하면 된다. 

9. 강력한 휴대성을 가진 노트북, XPG 제니아 15 KC 

ⓒ XPG 

장점
• 가벼운 무게
• 조용함
• 상대적으로 빠른 속도

단점
• 중간 수준 이하의 RGB
• 평범한 오디오 성능
• 느린 SD 카드 리더 

사양이 좋은 노트북의 경우, 대부분 부피가 크고 무거워서 종종 2.2kg 또는 2.7kg를 넘기도 한다. XPG 제니아 15 KC(XPG Xenia 15 KC)만은 예외다. XPG 제니아 15 KC의 무게는 1.8kg가 조금 넘는 수준으로, 타제품에 비해 상당히 가볍다. 또한 소음도 별로 없다. 원래 게이밍 노트북 자체가 소음이 크기에 비교해보면 큰 장점이 될 수 있다. 1440p 디스플레이와 상대적으로 느린 SD 카드 리더 성능으로 인해 일부 콘텐츠 제작자들이 구매를 주저할 수 있으나, 조용하고 휴대하기 좋은 제품을 찾고 있다면 제니아 15 KC가 좋은 선택지다. 

영상 편집 노트북 구매 시 고려 사항

영상 편집 노트북 구매 시 고려해야 할 가장 중요한 사항은 CPU 및 GPU다. 하드웨어가 빨라질수록 편집 속도도 빨라진다. 필자는 UL 프로시온 영상 편집 테스트(UL Procyon Video Editing Test)를 통해 속도를 테스트해보았다. 이 벤치마크는 2개의 서로 다른 영상 프로젝트를 가져와 색상 그레이딩 및 전환과 같은 시각적 효과를 적용한 다음, 1080p와 4K 모두에서 H.264, H.265를 사용해 내보내는 작업을 어도비 프리미어가 수행하도록 한다. 

ⓒ Gordon Mah Ung / IDG

성능은 인텔의 11세대 프로세서를 실행하는 크고 무거운 노트북에서 가장 높았고, AMD의 비피 라이젠 9(beefy Ryzen 9) 프로세서를 탑재한 노트북이 바로 뒤를 이었다. 10세대 인텔 칩은 여전히 상당한 점수를 기록하고 있다. 위의 차트에는 없으나 새로운 인텔 12세대 노트북은 더 빨리 실행된다. 최고 성능의 노트북은 모두 최신 인텔 CPU 및 엔비디아의 RTX 30 시리즈 GPU를 결합했는데, 두 기업 모두 어도비 성능 최적화에 많은 시간 및 리소스를 투자했기 때문에 놀라운 일은 아니다. 

GPU는 어도비 프리미어 프로에서 CPU보다 더 중요하지만, 매우 빠르게 수확체감 지점에 다다른다. 최고급 RTX 3080 그래픽을 사용하는 노트북은 RTX 3060 그래픽을 사용하는 노트북보다 영상 편집 속도가 더 빠르나, 속도 차이가 크지는 않다. 델 XPS 17 9710의 점수를 살펴보면, 지포스 RTX 3060 노트북 GPU는 MSI GE76 레이더의 가장 빠른 RTX 3080보다 14% 더 느릴 수 있다. 특히 GE76 레이더가 델 노트북에 비해 얼마나 더 크고 두꺼운지를 고려할 때 수치가 크지는 않다.

일반적으로 그래픽과 영상 편집을 위해 적어도 RTX 3060을 갖추는 것을 권장한다. 그러나 영상 편집은 워크플로에 크게 의존한다. 특정 작업 및 도구는 CPU 집약적이거나 프리미어보다 GPU에 더 의존할 수 있다. 이 경우 원하는 요소의 우선순위를 조정하길 바란다. 앞서 언급한 목록은 기본적으로 여러 요소를 종합적으로 고려해서 만든 내용이다.

인텔 및 엔비디아는 각각 퀵 싱크(Quick Sync) 및 쿠다(CUDA)와 같은 도구를 구축하는 데 수년을 보냈고, 이로 인해 많은 영상 편집 앱의 속도는 크게 향상될 수 있다. AMD 하드웨어는 영상 편집에 적합하나 특히 워크플로가 공급업체별 소프트웨어 최적화에 의존하는 경우, 특별한 이유가 없는 한 인텔 및 엔비디아를 사용하는 것을 추천한다. 

영상 촬영 ⓒ Gordon Mah Ung/IDG

그러나 내부 기능만 신경 써서는 안된다. PC월드의 영상 디렉터인 아담 패트릭 머레이는 “영상 편집에 이상적인 노트북에는 카메라로 촬영 중 영상 파일을 저장하는 SD 카드 리더가 포함되어 있다”라고 강조한다. 또한 머레이는 영상 편집에 이상적인 게임용 노트북에서 흔히 볼 수 있는 초고속 1080p 패널보다 4k, 60Hz 패널을 갖춘 노트북을 선택할 것을 추천한다.

4K 영상을 잘 편집하려면 4K 패널이 필요하며, 초고속 화면 재생률은 게임에서처럼 영상 편집에는 아무런 의미가 없다. 예를 들어, 개인 유튜브 채널용으로 일상적인 영상만 만드는 경우 색상 정확도가 중요하지 않을 수 있다. 그러나 색상 정확도가 중요할 경우, 델타 E < 2 색상 정확도와 더불어 DCI-P3 색 영역 지원은 필수적이다. 

게임용 노트북은 사양이 좋지만 콘텐츠 제작용으로는 조금 부족해 보일 수 있다. 게임용과 콘텐츠 제작용으로 함께 쓰는 노트북을 원한다면, 게임용으로 노트북 한 대를 구매하고, 색상을 정확히 파악하기 위한 모니터를 추가로 구매하는 것도 방법이다. 
editor@itworld.co.kr

원문보기:
https://www.itworld.co.kr/topnews/269913#csidxa12f167cd9eef5abfb1b6d099fb54ea 

그래픽 카드

AMD FirePro Naver Shopping 검색 결과

2021-12-15 기준

현재 NVIDIA Quadro pro graphic card : 네이버 쇼핑 (naver.com)

코어가 많은 그래픽카드의 경우 가격이 상상 이상으로 높습니다. 빠르면 빠를수록 좋겠지만 어디까지나 예산에 맞춰 구매를 해야 하는 현실을 감안할 수 밖에 없는 것 같습니다.

한가지 유의할 점은 엔비디아의 GTX 게이밍 하드웨어는 모델에 따라 다르기는 하지만, 볼륨 렌더링의 속도가 느리거나 오동작 등 몇 가지 제한 사항이 있습니다. 일반적으로 노트북에 내장된 통합 그래픽 카드보다는 개별 그래픽 카드를 강력하게 추천합니다. 최소한 그래픽 메모리는 512MB 이상이어야 하고 1GB이상을 권장합니다.


2021-12-15 현재 그래픽카드의 성능 순위는 위와 다음과 같습니다.
출처: https://www.videocardbenchmark.net/high_end_gpus.html

주요 Notebook

출시된 모든 그래픽 카드가 노트북용으로 장착되어 출시되지는 않기 때문에, 현재 오픈마켓 검색서비스를 제공하는 네이버에서 Lenovo Quadro 그래픽카드를 사용하는 노트북을 검색하면 아래와 같습니다. 검색 시점에 따라 상위 그래픽카드를 장착한 노트북의 대략적인 가격을 볼 수 있을 것입니다.

<검색 방법>
네이버 쇼핑 검색 키워드 : 컴퓨터 제조사 + 그래픽카드 모델 + NoteBook 형태로 검색
Lenovo quadro notebook or HP quadro notebook 또는 Lenovo firepro notebook or HP firepro notebook


( 2021-12-15기준)

대부분 검색 시점에 따라 최신 CPU와 최신 그래픽카드를 선택하여 검색을 하면 예산에 적당한 노트북을 자신에게 맞는 최상의 노트북을 어렵지 않게 선택할 수 있습니다.

(주)에스티아이씨앤디 솔루션사업부

Melt pool EBSD and X-ray computed tomography analysis results.

High-speed synchrotron X-ray imaging of melt pool dynamics during ultrasonic melt processing of Al6061

알루미늄 6061의 초음파 용융 처리 중 용융 풀 역학에 대한 고속 동기화된 X선 영상 촬영

Lovejoy Mutswatiwa, Lauren Katch, Nathan J Kizer, Judith A Todd, Tao Sun, Samuel J Clark, Kamel Fezzaa, Jordan S Lum, David M Stobbe, Griffin Jones, Kenneth C Meinert Jr., Andrea P Argüelles, Christopher M Kube

Abstract

Ultrasonic processing of solidifying metals in additive manufacturing can provide grain refinement and advantageous mechanical properties. However, the specific physical mechanisms of microstructural refinement relevant to laser-based additive manufacturing have not been directly observed because of sub-millimeter length scales and rapid solidification rates associated with melt pools. Here, high-speed synchrotron X-ray imaging is used to observe the effect of ultrasonic vibration directly on melt pool dynamics and solidification of Al6061 alloy. The high temporal and spatial resolution enabled direct observation of cavitation effects driven by a 20.2 kHz ultrasonic source. We utilized multiphysics simulations to validate the postulated connection between ultrasonic treatment and solidification. The X-ray results show a decrease in melt pool and keyhole depth fluctuations during melting and promotion of pore migration toward the melt pool surface with applied sonication. Additionally, the simulation results reveal increased localized melt pool flow velocity, cooling rates, and thermal gradients with applied sonication. This work shows how ultrasonic treatment can impact melt pools and its potential for improving part quality.

Introduction

Laser-based metal additive manufacturing (AM), a three-dimensional printing technique, can manufacture single components and structures with highly complex geometries, functionally graded alloys1, tailored microstructures2, and enhanced mechanical properties3. However, for most alloys, thermal cracking, porosity, and columnar grains4 reduce mechanical properties and prevent the widespread adoption of AM parts5. Establishing techniques for influencing solidification toward grain refinement could lead to parts with better mechanical properties and, ultimately, improve the reliability and quality of AM components6. The variation of AM process parameters, such as laser power, scan speed, and energy density7 allows control of thermal gradients and cooling rates, resulting in location-specific microstructural refinement2. However, process parameter optimization can be challenging, especially for alloys that are difficult to print. In addition to process parameter adjustment, inoculants can be added to the AM process to promote heterogeneous nucleation in the melt pool, resulting in grain refinement8. However, inoculants unavoidably change the chemical composition of the material, which can impact the mechanical strength of AM components9. In addition, inoculants can cause inclusions due to settlement and agglomeration10.

Other techniques for solidification control can be achieved by applying external fields such as electromagnetic11, mechanical12, or acoustic13 fields. In casting, electromagnetic fields were reported to increase cooling rates14, which resulted in reduced alloying element segregation and a more homogeneous macrostructure. Low-frequency mold vibration also succeeded in solidification manipulation during casting, resulting in a refined as-cast grain structure15. The application of high-intensity ultrasound on solidifying metals for molten metal processing during welding resulted in grain refinement and improved weld joint strength16. Nonetheless, using these techniques in laser-based metal AM is challenging because of the short length and time scales involved in melt pool dynamics and solidification17.

Following the work of Eskin18 and Abramov19, and applying successful grain refinement techniques in welding20, Todaro et al.21 recently demonstrated that high-intensity ultrasound can promote columnar to equiaxed grain transitions (CET) in laser AM fabricated Ti-6Al-4V and Inconel 625. As a result, components built with a fine, equiaxed grain structure exhibited increased yield and tensile strengths. One form of ultrasonic melt processing in AM involves laser metal powder consolidation on a substrate vibrating at ultrasonic frequencies (i.e., sonicated substrates). An applied ultrasonic frequency of 20 kHz on an AM-fabricated 316L stainless steel plate resulted in a noticeable decrease in grain sizes and an increase in random grain orientations22. Similarly, a reduction in mechanical property anisotropy and grain refinement along the build direction in wire arc AM was recently observed after ultrasonic treatment23. Ivanov et al.24 and Yoon et al.25 leveraged high-frequency pulsed laser irradiation to introduce high-intensity ultrasonic waves in the melt pool, resulting in microstructural refinement. Wang et al.26 used ultrasonic vibration-assisted AM to fabricate Inconel 718 parts and investigated the influence of four ultrasonic frequencies (i.e., 0, 25, 33, and 41 kHz) on microstructural refinement and mechanical properties. While ultrasonic melt processing at 25 kHz increased mechanical strength, the use of higher ultrasonic frequencies was observed to increase porosity and hardness. Wang et al.26 elucidated the effects of frequency, yet the effect of other ultrasonic wave parameters, such as vibration amplitude and acoustic intensity, on grain refinement, remained unclear.

The observed microstructural refinement in AM ultrasonic melt processing reported in the literature is hypothesized to result from increased nucleation rates and sites caused by acoustic cavitation and streaming induced in the melt pool. Acoustic cavitation and streaming have been suggested to compete with Marangoni convection, recoil pressure, and surface tension forces in the melt pool27, influencing solidification rates and thermal gradients and promoting columnar to fine equiaxed grain transitions28. Cavitation was observed in high-speed synchrotron X-ray imaging experiments within a controlled casting with ultrasonic treatment by Wang et al.29. They observed acoustic cavitation bubbles imploding in a Bi-8%Zn alloy on the solid-liquid interface, causing fragmentation of the solid phase in the mushy zone. Moreover, acoustic streaming was observed to disperse solid particles in the liquid, which have been reported to later act as solidification nuclei30. In AM, however, the melting and solidification processes occur rapidly, presenting spatial and temporal resolution challenges in direct cavitation observation. In their study focused on observing grain refinement mechanisms in ultrasound-assisted AM, Ji et al.31 stated that because of extremely high temperature, opacity, and short survival time, it is hardly possible to directly observe the process of ultrasound effect on the molten metal pool in AM through experiments. While direct observation of dendrite fracture would be challenging, recent high-speed X-ray imaging of keyhole dynamics in AM32 allows observation of cavitation bubbles directly during ultrasound-assisted AM.

In this work, high-speed synchrotron X-ray imaging at the Advanced Photon Source, Argonne National Laboratory was used to capture acoustic cavitation in high-temperature, viscous, and opaque sub-millimeter scale melt pools within an Al6061 sample. Ultrasonic treatment was observed to alter keyhole morphology, which could potentially reduce or eliminate porosity generated from keyhole tip collapse, in addition to reducing dynamic keyhole instabilities. Ultrasonic treatment influenced bubble dynamics, causing pore migration toward the melt pool surface. The reported results demonstrated the existence and influence of cavitation on laser-generated melt pool dynamics during ultrasonic melt processing, which was previously hypothesized by Todaro et al.21,22, Feilong et al.23, and Wang et al.26. The multiphysics Computational fluid dynamics (CFD) simulations using the Flow-3DⓇ platform showed an increase in melt pool flow velocity, thermal gradients, and cooling rates with applied ultrasonic treatment. This study provides direct evidence that acoustic cavitation effects are present in laser-generated melt pools and can be studied using high-speed X-ray imaging and CFD simulations. Thus, controlling acoustic cavitation, microstructure, and, henceforth, mechanical properties and part quality is now a closer reality33.

Results

In-situ synchrotron X-ray imaging of acoustic cavitation in melt pools

Figure 1 shows the primary features of the experimental setup. The experiment consisted of a continuous-wave ytterbium fiber laser with user set powers ranging from 100 to 560 W, the high-speed X-ray imaging system (see details in29), and an Al6061 sample mounted vertically on top of a Langevin transducer driven at its lowest order extensional resonance frequency of 20.2 kHz. Single-pulse X-ray images were collected at a rate of 50 kHz to observe melt pool dynamics, cavitation bubble dynamics, and solidification. X-ray computed tomography (CT) and electron backscattered diffraction (EBSD) were used to further characterize the pore structure ex-situ.

Fig. 1: Experimental setup.
Schematic diagram illustrating the experimental setup for high-speed X-ray imaging of melt pools on a vibrating substrate.

A representative X-ray image showing annotated melt pool features and vibration direction is shown in Fig. 2. X-ray absorption and phase contrast allowed easy identification of the solid/liquid transition region, vapor depression area, and microscale bubbles from cavitation. Supplementary Movie 1 shows the entire single-point melt pool and solidification process when the 350 W laser is applied for 3.34 ms without sonication. In addition, the video shows highly dynamic features such as bubble motion, melt pool size fluctuation, and keyhole initiation, growth, and fluctuation. The high spatial (i.e., 2 μm/pixel) and temporal (i.e., 50,000 frames per second) resolutions afforded by the high-energy synchrotron facility enabled direct quantifiable observation of the microscale bubble dynamics within the melt pool. The effect of the vibration could then be easily observed by conducting measurements with and without the active ultrasonic transducer. While the vibration was active, the X-ray imaging allowed direct measurement of the vibration amplitude of approximately 8 μm (more details on image processing and measurements are provided in the “Methods” section).

Fig. 2: Melt pool X-ray frame.
An X-ray frame showing the melt pool boundary at the solid/liquid interface, the keyhole or vapor depression morphology, the keyhole rim, hot spatter, a microbubble, and vibration direction. The video from which this frame was extracted is found in Supplementary Movie 1.

Figure 3a, b depict real-time X-ray image sequences of stationary laser-generated molten Al6061 pool dynamics without and with sonication, respectively. Supplementary Movie 2 is the associated high-speed videos containing the frames seen in Fig. 3a, b. In Fig. 3a, a narrow and deep vapor depression or keyhole can be observed in melt pools without sonication. Keyhole melt pools with these characteristics are known to be susceptible to keyhole porosity in AM when the tip of the vapor depression pinches off and forms a bubble32,34. Without sonication, bubbles were observed to settle at the bottom of the melt pool, where the solidification front could quickly freeze them, resulting in porosity. Figure 3a also shows strong fluctuations in keyhole depth, which is a characteristic of keyhole instability35.

Fig. 3: X-ray image sequences showing laser-generated molten Al6061 pools.
Melt pools (a) without and (b) with sonication. The six X-ray frames were taken at 0.02 ms intervals, beginning at 2.96 ms after the laser was turned on. The video from which these frames were extracted is found in Supplementary Movie 2.

The bubble density is shown to increase due to sonication as depicted in Fig. 3b and Supplementary Movie 2, proving the sonication leads to bubble nucleation in the liquid phase separate from the keyhole region. The bubbles in the melt pool with sonication rapidly nucleate, grow, oscillate, and sometimes implode, demonstrating cavitation bubble behavior. In addition, acoustic streaming effects were observed, where the molten metal flows in the vibration direction36,37. Sonication increased the average bubble diameter and promoted bubble migration towards the melt pool surface (Supplementary Movie 2). Bubbles with larger diameters were observed to implode at the melt pool surface, demonstrating degassing characteristics. In conventional AM, the melt flow-induced drag force dominates bubble dynamics38. Based on the observed bubble dynamics in melt pools with sonication, it can be pointed out that bubble growth due to cavitation increases the buoyancy force, overcoming the drag force that usually traps pores38, steering the bubbles toward the melt pool surface, and promoting degassing39. In addition, we speculate that primary and secondary Bjerknes acoustic radiation forces may exist in the melt pool, facilitating bubble translation toward the melt pool surface and causing degassing40. The concentration of porosity toward the melt pool surface induced by sonication might be convenient in metal AM because the remelting between successive layers could eliminate the residual porosity from previous layers.

Figure 3b also shows a reduction in the keyhole depth fluctuations and an increase in the keyhole tip radius with sonication. These phenomena resulted in the elimination of the keyhole tip pinch-off porosity32. However, sonication was observed to eject molten metal from the melt pool, as shown in the X-ray frame at 2.96 ms with sonication in Fig. 3b. Further investigation on the influence of substrate vibration directions (i.e., in-plane or out-of-plane vibration) and vibration amplitudes and frequencies could help minimize potential spatter in laser-based AM with ultrasonic melt processing and will be explored in our future research.

Influence of ultrasonic treatment on melt pool geometry and dynamics

The variations in the keyhole and melt pool depths, with and without sonication, are illustrated in Fig. 4. The melt pool depths, keyhole depths, and melt pool widths were measured from the point where sizable contrast difference between the liquid/solid and gas/liquid phases could be observed in the X-ray images. From Fig. 4a, it can be observed that the keyhole depth without sonication was larger than the sonicated keyhole. Melt pool and keyhole depths were shown to fluctuate at constant laser power41, indicative of instabilities34. The depth fluctuations were quantified as one standard deviation about the mean of the measured depths. With sonication, the melt pool depth standard deviation was 66.3 μm, whereas it was 111.6 μm without. Similarly, the keyhole depth standard deviation was 31.6 μm compared to 57.6 μm with and without sonication, respectively. This indicates ultrasonic treatment reduces fluctuations, leading to more stable dynamics. Without sonication, the melt pool began in conduction mode as shown in Fig. 4c from 2.8 to 4.25 ms, after which the melt pool transitioned into the keyhole mode. Conversely, with sonication, the melt pool started directly in keyhole mode. In both cases, the transition from conduction to keyhole mode occurred rapidly until stabilizing after about 5.5 ms.

Fig. 4: Influence of ultrasonic treatment on melt pool and keyhole geometry.
a Keyhole depth, b Keyhole aspect ratios (keyhole depth divided by fixed laser beam diameter of 80 μm), c Melt pool depths, and d Melt pool aspect ratios (melt pool width divided by depth based on measurements from X-ray images) with and without sonication. Red plain line shows measurements without sonication while black line with circular markers shows measurements with sonication.

Keyhole morphology also plays a role in melt pool dynamics and defect formation during laser-based metal AM processes. Fig. 4b shows the Keyhole aspect ratios calculated from measured depths divided by the 80 μm laser diameter35. These results show lower keyhole aspect ratios in sonicated melt pools. A high aspect ratio represents a deep and narrow keyhole with a needle-like tip, while a low keyhole aspect ratio represents a wide keyhole with an observable tip radius. A deep and narrow keyhole traps laser beam reflections at the bottom, leading to a J-shaped keyhole in moving laser scenarios32, which are susceptible to keyhole tip pinch-off porosity38,42. Therefore, ultrasonic treatment in metal AM can potentially eliminate one of the major keyhole porosity driving mechanisms by decreasing the keyhole aspect ratio and increasing keyhole-tip radius. Figure 4 d depicts the melt pool aspect ratio with and without sonication. In the absence of sonication, a high melt pool aspect ratio was observed when the melt pool was in conduction mode (i.e., from 2.7 to 4.4 ms) compared to the keyhole mode. There was not a significant difference in the melt pool aspect ratio due to sonication.

Laser energy absorptivity is known to be influenced by melt pool and keyhole depths43. Thus, the difference in melt pool geometries in ultrasonically treated melt pools relative to non-ultrasonically treated melt pools could result from the variation in the position of the laser focal point relative to the melt surface caused by the back-and-forth motion of the vibrating sample, promoting multiple laser beam reflections, resulting in improved laser energy absorptivity. This is possible at high vibration amplitudes to laser spot size ratios. However, in our case, a 16 μm peak-to-peak vibration amplitude and a laser spot size of 80 μm will not significantly influence laser energy absorptivity. Therefore, we speculate that the increased absorptivity could be due to the raised melt pool surface above the sample due to ultrasonic vibration causing the keyhole rim to rise while the recoil pressure keeps the bottom of the keyhole stationary. Hence, it results in deeper keyholes that promote multiple laser beam reflections on the vapor/liquid interface and increased absorptivity. In addition, the melt pool temperature could have increased because of bubble implosions, resulting in a larger melt region with applied ultrasound. Improved laser energy absorptivity and large melt pools are advantageous in metal AM to potentially reduce component build time. To investigate these claims further, CFD simulations were conducted to explain the impact of sonication on thermal gradients and cooling rates.

Multiphysics modeling of melt pool dynamics and solidification in ultrasound-assisted AM

High-speed X-ray imaging was able to provide real-time evidence of acoustic cavitation and melt pool dynamics in laser-generated melt pools driven by an external ultrasonic field. Additional insight into pressure distributions, thermal gradients, and cooling rate information is available through bridging the experiments with CFD simulations. In particular, CFD offers the ability to connect thermal properties to microstructural development. To further investigate the influence of ultrasonic treatment on solidification, we conducted multiphysics simulations of single-spot laser-generated melt pools with and without ultrasonic vibration using Flow-3DⓇ. Identical laser and ultrasonic parameters and substrate material used in the X-ray imaging experiments were adopted in the simulations. To reduce the simulation time, the laser duration was set to 0.8 ms compared to 3.4 ms in the experiments. The X-ray images were used to validate the simulations by directly observing melt pool and keyhole morphologies, cavitation bubbles, and solidification structures. Fig. 5a, b compare CFD simulated melt pools to melt pool geometries directly captured in X-ray imaging for the cases of without and with sonication. Deep and narrow keyholes observed with high-speed X-ray imaging in melt pools without sonication were replicated in the simulations. Similarly, an increased keyhole tip radius observed with X-ray imaging in melt pools with sonication was captured in the Flow-3DⓇ simulation. Supplementary Movies 3 and 4 show simulated keyhole dynamics for the two cases. Furthermore, Supplementary Movies 5 and 6 show the results of simulated melt pool dynamics. Similar to the melt pool dynamics undergoing sonication captured by X-ray imaging (i.e., Supplementary Movie 2), the simulated melt pools (i.e., Supplementary Movie 5) showed acoustic cavitation-driven bubble nucleation and implosion caused by pressure variation in the melt pool. Furthermore, the simulated solidification structure with ultrasonic treatment shows frozen cavitation-induced pores like those observed in X-ray imaging and X-ray CT. To further validate the simulations, the measured melt pool aspect ratios (width/depth) from X-ray images were compared with the simulated melt pool aspect ratios. Figs. 5c, d show melt pool aspect ratios, which were found to be closely consistent between simulations and experiments. The close agreement in aspect ratios speaks to the simulations accurately representing the laser energy transfer into the pool

Fig. 5: CFD melt pool simulation comparison with X-ray results.
a Melt pool simulation without and with sonication, b comparable experimental results without and with sonication, c Aspect ratios (depth/width) observed in the simulations, and d corresponding experimental aspect ratios.

Melt pool flow dynamics are primarily driven by surface tension, Marangoni convection, and recoil pressure. The application of ultrasound introduces acoustic streaming as an additional driving force. Simulations allowed us to quantify acoustic streaming by comparing velocity vectors at points in the fluid with and without applied ultrasonic treatment. Fig. 6a shows melt pool speed contours and velocity vectors with and without sonication. Supplementary Movies 7 and 8 show additional melt pool dynamics. The higher melt pool velocities in melt pools with sonication confirm that acoustic streaming is a major factor in fluid flow. Figure 6b shows the pressure distribution. Large pressure fluctuations are observed in the presence of sonication. The frames shown in Fig. 6b were taken from the simulation results during solidification and when the laser was switched off. This was done to decouple the sonication from thermal energy input. Supplementary Movies 9 and 10 show animations of pressure distribution in solidifying melt pools with and without sonication, respectively. It can be seen from Fig. 6b that the pressure variation in the melt pool with sonication promoted bubble nucleation. In addition, the influence of ultrasonic vibration can be observed in Fig. 6b with sonication, as ripples of high and low-pressure regions captured by the solidification. Without sonication, no significant pressure variation was observed during solidification. Acoustic cavitation bubble nucleation occurs when the localized pressure within a liquid drops below the vapor pressure of that liquid. Therefore, in Al6061 laser-generated melt pools, it can be seen that if the localized pressure within the melt pool drops below the vapor pressure of molten Al6061, nucleation of bubbles will occur. To investigate the influence of pressure variation on bubble nucleation during melting, the image sequence in Fig. 6c shows the pressure contours at a bubble nucleation site within the melt pool. A decrease in melt pool pressure was observed to result in bubble nucleation, while an increase in pressure promoted bubble implosion.

Fig. 6: CFD melt pool simulation results with and without sonication.
a Simulation frames showing velocity vectors of points in the liquid, b pressure distributions, c pressure field at the nucleation of a cavitation bubble and after the collapse.

Microstructure development is directly linked to solidification rates and thermal gradients. To investigate the influence of ultrasonic treatment on solidification conditions, we collected time history temperature gradients and cooling rates at a point within the melt pools with and without sonication. Figure 7a shows the point data probing location at which the time history of parameters that can be related to microstructural development was collected. Figure 7b shows the time history of pressure, cooling rate, thermal gradient, and velocity at the data probing point, with and without sonication. It can be observed that high pressure was observed in melt pools without compared to those with sonication. Conversely, higher cooling rates were observed in melt pools with sonication. Similarly, higher thermal gradients and fluid velocities were observed in melt pools with compared to those without sonication. Figure 7c shows the overall cooling rates and thermal gradients at each simulation time frame over the entire simulation. It can be observed that the overall thermal gradient did not respond to ultrasonic treatment. However, the overall melt pool cooling rate increased with the applied ultrasonic treatment.

Fig. 7: Melt pool thermal history from CFD simulation.
a Point data probing location. b The time history of fluid pressure, cooling rates, thermal gradients, and fluid velocities at the data probing point with and without sonication. c Melt pool thermal gradients and cooling rates at each time frame during the entire simulation with (red line plain line) and without sonication (black line with circular markers).

Acoustic cavitation characterization and influence on microstructural development

The primary aim of this article is to unveil the physics associated with ultrasonically driving the melt pool. A secondary aim and a topic of future work is to unveil conditions that lead to refined or tailored microstructures toward improved quality and performance of AM parts. Nevertheless, the solidification microstructures formed in melt pools with and without sonication were characterized using electron backscatter diffraction (EBSD). Fig. 8 a, b show the microstructures and crystallographic orientations of the grains in melt pools without and with sonication, respectively. Since EBSD is destructive, it is noted that the non-sonicated case is a different sample having a single point melt with the same laser power and duration as the sonicated melt pool case. For both samples, the melt pool boundary was traced using standard optical images, in which the melt region was clear (see Supplementary Figs. 6 and 7) and then superimposed on the EBSD grain map. Epitaxial grain growth and cracking along grain boundaries were evident in both cases. A qualitative reduction in grain size is observed in the sonication case but is difficult to ascertain because of the large pore structure as seen by the dark features in Fig. 8b.

Fig. 8: Melt pool EBSD and X-ray computed tomography analysis results.
EBSD grain map showing the solidification microstructure (a) without and (b) with sonication. c High-speed X-ray frame showing the final solidification structure and corresponding X-ray computed tomography visualization showing the porosity features and indications of the sonication-driven vibrations (seen by the red arrows).

Moreover, X-ray computed tomography analysis was performed on the final solidification structure (prior to EBSD) to characterize the influence of cavitation and acoustic streaming in sonicated laser-generated melt pools. An X-ray frame from the high-speed imaging showing the final solidification structure and a 3D isosurface of cavitation-induced porosity in the melt pool is shown in Fig. 8c. The X-ray computed tomography reveals evidence of frozen cavitation bubbles and ultrasonic vibration-induced-ripples in the melt pool (i.e., labeled by arrows in the X-ray computed tomography scan image). The ultrasonic wavelength in Al6061 at a frequency of 20.2 kHz was calculated to be 0.32 m, which is orders of magnitude higher than the melt pool depth and width. Thus, the micron scale ripples observed resulted from the sinusoidal variation in pressure from the ultrasonic vibration, which we have also observed in CFD simulations. This discovery calls attention to the influence of vibration amplitudes on cavitation in laser-based AM with ultrasonic treatment, which has not been previously explored. Figure 8c also shows a higher concentration of pores near the sample surface relative to the bottom of the melt pool. Thus, it is further corroborated that ultrasonic treatment causes bubble migration toward the melt pool surface.

Cavitation in ultrasonic molten metal processing has been explored by several researchers28,39,44,45, who conducted casting experiments on light metallic alloys. High-temperature cavitometry46,47 and high-speed imaging48 were used to establish a cavitation threshold in terms of acoustic intensity49. The first-order linear approximation of ultrasonic intensity, I, in an acoustic field is44

where ρ is the fluid density, c is the speed of sound in the fluid, A is the wave amplitude and f is the ultrasonic frequency. An acoustic intensity cavitation threshold of 100 W/cm2 was established for light metal alloys through casting experiments with ultrasonic melt processing44. In the experiments described in the literature29,45, an ultrasonic transducer horn was immersed in molten metal to introduce a propagating wave directly into the solidifying metal. Hence, the cavitation threshold could be established for sizable molten metal pools, and solidification rates would be significantly lower than those in AM processes. Nevertheless, the 100 W/cm2 cavitation threshold has been proposed for laser-based AM printing of light metallic alloys on sonicated substrates21,22,23,31,37,50,51,52,53,54,55,56. However, laser AM fundamentally differs from casting because of the submillimeter-size melt pools that exist for milliseconds owing to the associated rapid solidification rates. In casting, metal melting and solidification are separate processes, whereas melting, molten metal agitation, and solidification occur simultaneously in laser AM with sonication to generate acoustic cavitation. In addition, ultrasonic melt processing in casting involves wave propagation in a solidifying molten metal, while in AM, it involves local vibration of the molten metal. Such factors indicate different physical environments for cavitation in casting and AM. Therefore, validation of acoustic cavitation thresholds in laser-generated melt pools is needed, underpinning the importance of our technique.

Using a wave speed of 4718 m/s, density of 2586 kg/m3, wave amplitude of 8 μm, and frequency of 20.2 kHz in Equation (1) resulted in an acoustic intensity of 628.9 W/cm2. Our calculated acoustic intensity is above the established 100 W/cm2 cavitation threshold. However, cavitation was observed in the CFD simulations at an average acoustic intensity of 10 W/cm2, which is much lower than the established cavitation intensity threshold and the calculated intensity from Equation (1). Therefore, the established cavitation threshold from casting light metals with sonication overestimates the acoustic intensity required to induce cavitation in laser-generated melt pools on vibrating substrates. In the future, we will explore the influence of acoustic intensity on cavitation, porosity, and microstructure refinement.

Discussion

The application of ultrasound in solidifying melt pools in laser-based AM has been shown to promote columnar to equiaxed grain transition57,58 resulting in improved and homogenized mechanical properties and random crystallographic orientations50. By adopting observed microstructural refinement mechanisms in casting with ultrasonic treatment, acoustic cavitation and streaming28 have been hypothesized as the primary driving mechanisms of microstructural refinement in laser-based AM. Unambiguous evidence of cavitation in sub-millimeter scale and opaque laser-generated melt pools has been elusive until now. Here, the real-time influence of ultrasonic vibration on melt pool, keyhole, and bubble dynamics and the solidification of laser-generated melt pools was revealed. We also elucidated the impact of ultrasonic vibration at 20.2 kHz on melt pool and keyhole morphologies. Furthermore, we explained the potential influence of ultrasonic vibration on laser energy absorptivity and its benefits in AM. EBSD and XCT techniques were used to analyze the microstructures and solidification structures with and without applied sonication. The influence of ultrasonic vibration on melt pool flow velocity, pressure distribution, and solidification conditions with and without sonication was investigated using Flow-3DⓇ multiphysics CFD simulation software.

Melt pool and keyhole dynamics in laser-based AM processes influence porosity formation mechanisms38 and dictate the resulting solidification microstructures59 and mechanical properties60 of AM components. Marangoni flow, recoil pressure, and surface tension are some of the major driving forces governing melt pool and keyhole dynamics27. Generating melt pools on a substrate vibrating at ultrasonic frequencies introduces an additional force that drives melt pool flow in the wave propagation direction (i.e., acoustic streaming)37, which competes with existing forces in the melt pool. We used high-speed synchrotron X-ray imaging and Flow-3DⓇ simulations to show that acoustic streaming dominates the melt pool and keyhole dynamics in the laser-generated melt pool with sonication. Moreover, physical evidence of real-time acoustic cavitation in submillimeter-sized laser-generated melt pools was revealed in situ using high-speed X-ray imaging. Ultrasonic vibration was observed to increase bubble density in the melt pool and promote bubble migration toward the melt pool surface. X-ray computed tomography scan of the final solidification structure further demonstrated that ultrasonic vibration drives pores toward the melt pool surface and that vibration amplitude influences molten metal flow rather than ultrasonic wavelength.

Keyhole morphology analysis from high-speed X-ray images revealed a wide and shallow keyhole with applied sonication. A deep and narrow keyhole was observed in the case without sonication. Deep and narrow keyhole geometries are susceptible to keyhole tip collapse porosity32; therefore, by changing the keyhole morphology, ultrasonic treatment could potentially eliminate one of the major porosity formation mechanisms in laser AM. It is important, however, to note that sonication-induced cavitation resulted in porosity, as revealed by post-process EBSD and X-ray computed tomography scan results Therefore, these observations spark interest in further investigations on ultrasonic wave parameter optimization to leverage cavitation for porosity reduction and location-specific microstructural refinement. Furthermore, cavitation-induced porosity in AM ultrasonic melt processing could be used to manufacture porous structures for biomedical applications. Frequency modulation and the use of multiple ultrasound sources could potentially provide a certain degree of control over cavitation in laser-generated metal pools.

The application of ultrasonic vibration in laser-based AM was considered to increase the laser beam reflection from the liquid/gas interface in the melt pool because of increased keyhole depth caused by the raised keyhole rim. Increased laser beam reflection can potentially improve laser energy absorptivity61, resulting in larger melt volumes. On the other hand, applying ultrasonic treatment through out-of-plane vibration increased hot spattering due to the molten metal droplets pinching off the melt pool at peak positive and negative vibration amplitudes. Further optimizing vibration frequency, amplitudes, and direction can help mitigate hot spattering.

To investigate the influence of ultrasonic treatment on solidification and microstructural development, we utilized Flow-3DⓇ multiphysics simulations validated with real-time high-speed synchrotron X-ray images of melt pool dynamics. Flow-3DⓇ simulation results showed pressure variation-driven acoustic cavitation in melt pools with applied ultrasonic treatment. The pressure variation in melt pools with and without applied ultrasound was analyzed during the solidification phase (i.e., after the laser was switched off) using color maps. Ultrasonic treatment was also observed to promote high melt pool velocities, cooling rates, and thermal gradients. Higher thermal gradients and melt pool velocities create stronger cooling effects and promote heterogeneous nucleation and grain refinement.

In summary, we provided evidence of acoustic cavitation in laser-generated molten metal pools on sonicated substrates using both high-speed X-ray imaging and CFD simulations. We further showed that ultrasonic treatment influenced melt pool and keyhole dynamics and could potentially eliminate some major keyhole porosity driving mechanisms. We also demonstrated through simulations that ultrasonic treatment creates favorable conditions for heterogeneous nucleation and grain refinement. These results facilitate further investigation into the influence of ultrasonic treatment on microstructural refinement and mechanical property improvement in laser-based AM processes.

Methods

Materials and sample preparation

Al6061 alloy was chosen as the material of interest because of its widespread usage in lightweight material industries such as automotive, aerospace, and many others. Unfortunately, Al6061 is extremely challenging to use in welding or AM because of thermal cracking. Thus, this research has a broader goal of investigating techniques to improve the printability of such alloys. Moreover, manufacturing methods, processes, and conditions highly influence Al6061 grain sizes and mechanical properties, as demonstrated by Eskin44 in the ultrasonic treatment of light metallic alloys. Secondly, applications of Al6061 as an additive manufacturing material have been limited because of residual stress build-up62. Lastly, Al6061 has liquidus and solidus temperatures of 660 °C and 595 °C, respectively, enabling sizable mushy zones necessary for effective and efficient ultrasonic treatment. Al6061 samples with a length of 20 mm, a height of 12 mm, and a thickness of 1.5 mm were used in our experiments. A thickness of 1.5 mm allowed adequate X-ray absorption contrast between the solid, liquid, and gaseous phases during laser melting, making it easy to identify melt pool features (i.e., vapor/gas depression, bubbles, solid-liquid interfaces.).

Ultrasonic wave generation system

Al6061 specimens were adhered to an ultrasonic transducer horn using an adhesive, as illustrated in Supplementary Fig. 1. A 20.2 kHz high-power ultrasonic transducer by Hangzhou Altrasonic Technology Co., Ltd., with a maximum power of 2000 W, was used in this study. The ultrasonic system consisted of a horn, piezoelectric elements, and an ultrasonic generator. The ultrasonic generator converts the power source into high-frequency and high-voltage alternating current and transmits it to the piezoelectric elements, which convert the input electrical energy into mechanical energy (i.e., ultrasonic waves). In our experiments, the transducer generated a continuous longitudinal wave and was operated at the horn’s resonant frequency of 20.2 kHz, with a power of 600 W and vibration amplitude of 8 μm. The transducer power and short time intervals of ultrasonic wave application were chosen to prevent the transducer horn overheating, which may influence melt pool solidification rates and thermal gradients. A custom-designed relay apparatus operated from outside the experimental hutch controlled the transducer on/off switching and the duration of ultrasonic vibration.

X-ray imaging and laser melting system

Experiments were conducted using the high-energy ultrafast synchrotron X-ray imaging system available at the Advanced Photon Source, Argonne National Laboratory, USA. The 32-ID-B beamline at the Advanced Photon Source offers a state-of-the-art high-speed X-ray imaging technique. The intense undulator white beam allows ultrafast image acquisition rates of 50 kHz with a spatial resolution of 2 μm/pixel in a field of view of 1.8 × 1 mm. In addition, a continuous-wave ytterbium fiber laser (IPG YLR-500-AC, IPG Photonics, Oxford, USA, wavelength of 1070 nm, maximum output power of 560 W) and a galvanometer scanner (IntelliSCANde 30, SCANLAB GmbH., Germany)38 were integrated to perform stationary laser melting on bare Al6061 samples. A laser power of 350 W was used in the experiments. Experiments were conducted in the following sequence: the X-ray shutter and camera were first opened to initiate image acquisition. Secondly, the ultrasonic transducer was switched on, and lastly, the laser was turned on. The experimental setup and sequence allowed the sample melting, vapor depression development, and melt pool solidification occurring in an acoustic field to be captured via X-ray imaging. The laser was switched on for 3.34 ms for both cases with and without ultrasonic treatment.

EBSD and X-ray computed tomography analysis

Electron backscattered diffraction patterns (EBSPs) were obtained in the Oxford scanning electron microscope (SEM) instrument by focusing an electron beam on the Al6061 sample. The final polishing of the Al6061 sample was conducted using the Final A polishing pad with 0.04-micron colloidal silica suspension for 12 h. The sample was tilted to approximately 70 degrees with respect to the horizontal, and the diffraction patterns were imaged on a phosphor screen. The images were captured using a low-light CMOS camera. A 1.5-micron step size was used for both samples with and without ultrasonic treatment. The X-ray computed tomography scan was conducted with a Zeiss Xradia Versa 620 CT system using a source accelerating voltage of 80 kV. Images were acquired over 2 h at a voxel size of 1.5 μm and reconstructed using Zeiss proprietary software. The dicom image files were then processed using MATLAB to reveal the influence of ultrasonic vibration on the final solidification structure of the melt pools. A 3D view of sonication-induced pores showing the influence of ultrasonic vibration amplitude on the melt pool solidification was captured using the 3D volume viewer tool in MATLAB.

Image processing

MATLAB image processing toolkit and ImageJ were utilized in the X-ray image analysis. MATLAB codes were developed to normalize a sequence of X-ray images with their average pixel values. To create an X-ray image sequence with a uniform gray value, images within a 5% range of gray values were grouped together. A normalization operation was applied to each distinct group, which allowed enhanced visualization of melt pool features, keyhole dynamics, and bubble motion. Measurements of the melt pool and keyhole depth changes and bubble motion characterization were conducted using ImageJ. Maximum depths and widths on each X-ray frame measured in ImageJ were used to characterize melt pool and keyhole dynamics. The peak-to-peak vibration amplitude on the Al6061 sample surface was also measured as 16 μm using ImageJ.

Multiphysics computational fluid dynamic simulations

A 1 mm2 domain with a 4-μm mesh size was used in the CFD simulations on the Flow-3DⓇ platform. The simulation finish time was set at 1.3 ms, and the laser on time was set at 0.8 ms. Similar to our experiments, the laser power used in the simulations was 350 W, with a laser spot size of 80-μm. Ultrasonic vibration was introduced by defining a non-inertial reference frame with harmonic oscillations on the melt volume (i.e., substrate). The oscillation frequency was set at 20.2 kHz and an amplitude of 8-μm. The execution time for each simulation with and without ultrasonic treatment was one day and 16 h, with each model generating a 2.5 TB output data file (More details on the simulation setup, boundary conditions, and governing equations are provided in Supplementary Material Section 2).

References

  1. Zhang, C. et al. Additive manufacturing of functionally graded materials: a review. Mat. Sci. Eng. A-Struct. 764, 138209 (2019).
  2. Dehoff, R. R. et al. Site specific control of crystallographic grain orientation through electron beam additive manufacturing. Mater. Sci. Tech. 31, 931–938 (2015).
  3. Lewandowski, J. J. & Seifi, M. Metal additive manufacturing: a review of mechanical properties. Annu. Rev. Mater. Res. 46, 151–186 (2016).
  4. Arísoy, Y. M., Criales, L. E. & Özel, T. Modeling and simulation of thermal field and solidification in laser powder bed fusion of nickel alloy IN625. Opt. Laser Technol. 109, 278–292 (2019).
  5. Sames, W. J., List, F. A., Pannala, S., Dehoff, R. R. & Babu, S. S. The metallurgy and processing science of metal additive manufacturing. Int. Mater. Rev. 61, 315–360 (2016).
  6. Mohammadpour, P. & Phillion, A. B. Solidification microstructure selection maps for laser powder bed fusion of multicomponent alloys. IOP Conf. Ser.: Mater. Sci. Eng. 861, 012005 (2020).
  7. Okugawa, M., Furushiro, Y. & Koizumi, Y. Effect of rapid heating and cooling conditions on microstructure formation in powder bed fusion of al-si hypoeutectic alloy: a phase-field study. Mater. 12, 17 (2022).
  8. Martin, J. H. et al. 3D printing of high-strength aluminium alloys. Nature 549, 365–369 (2017).
  9. Spierings, A. B., Dawson, K., Voegtlin, M., Palm, F. & Uggowitzer, P. J. Microstructure and mechanical properties of as-processed scandium-modified aluminium using selective laser melting. CIRP Annals 65, 213–216 (2016).
  10. Xu, J., Li, R. & Li, Q. Effect of agglomeration on nucleation potency of inoculant particles in the al-nb-b master alloy: modeling and experiments. Metall. Mater. Trans. A 52, 1077–1094 (2021).
  11. Y, W., Zhang, L., Yang, W., Ji, S. & Ren, Y. Effect of mold electromagnetic stirring and final electromagnetic stirring on the solidification structure and macrosegregation in bloom continuous casting. Steel Res. Int. 92, 1–8 (2021).
  12. Colegrove, P. A. et al. Application of bulk deformation methods for microstructural and material property improvement and residual stress and distortion control in additively manufactured components. Scripta Mater. 135, 111–118 (2017).
  13. Eskin, G. Influence of cavitation treatment of melts on the processes of nucleation and growth of crystals during solidification of ingots and castings from light alloys. Ultrason. Sonochem. 1, S59–S63 (1994).
  14. Wang, X. et al. Experimental investigation of heat transport and solidification during low frequency electromagnetic hot-top casting of 6063 aluminum alloy. Mat. Sci. Eng. A-Struct. 497, 416–420 (2008).
  15. Kisasoz, A., Guler, K. & Karaaslan, A. Influence of orbital shaking on microstructure and mechanical properties of A380 aluminium alloy produced by lost foam casting. Russ. J. Non-ferrous Metals 58, 238–243 (2017).
  16. Krajewski, A., Wlosinski, W., Chmielewski, T. & Kolodziejczak, P. Ultrasonic-vibration assisted arc-welding of aluminum alloys. B. Pol. Acad. Sci-Tech. 60, 841–852 (2012).
  17. Yang, M., Wang, L. & Yan, W. Phase-field modeling of grain evolutions in additive manufacturing from nucleation, growth, to coarsening. npj Comput. Mater. 7, 56 (2021).
  18. Eskin, G. I. Broad prospects for commercial application of the ultrasonic (cavitation) melt treatment of light alloys. Ultrason. Sonochem 8, 319–325 (2001).
  19. Abramov, O. V. Action of high-intensity ultrasound on solidifying metal. Ultrasonics. 25, 987 (1986).
  20. Sui, C., Liu, Z., Ai, X., Liu, C. & Zou, Z. Effect of ultrasonic vibration on grain size and precipitated phase distribution of 6061 aluminum alloy welded joint. Crystals 12, 841–852 (2022).
  21. Todaro, C. et al. Grain structure control during metal 3D printing by high-intensity ultrasound. Nat. Commun. 11, 142 (2020).
  22. Todaro, C. et al. Grain refinement of stainless steel in ultrasound-assisted additive manufacturing. Addit. Manuf. 37, 101632 (2021).
  23. Feilong, J. et al. Improving microstructure and mechanical properties of thin-wall part fabricated by wire arc additive manufacturing assisted with high-intensity ultrasound. J. Mater. Sci. 58, 012005 (2023).
  24. Ivanov, I. A. et al. Effect of laser-induced ultrasound treatment on material structure in laser surface treatment for selective laser melting applications. Sci. Rep. 11, 1–12 (2021).
  25. Yoon, H. et al. Pulsed laser-assisted additive manufacturing of Ti-6Al-4V for in-situ grain refinement. Sci. Rep. 12, 22247 (2022).
  26. Wang, H., Hu, Y., Ning, F. & Cong, W. Ultrasonic vibration-assisted laser engineered net shaping of Inconel 718 parts: Effects of ultrasonic frequency on microstructural and mechanical properties. J. Mater. Process Tech. 276, 116395 (2020).
  27. Leung, C. L. A. et al. In situ X-ray imaging of defect and molten pool dynamics in laser additive manufacturing. Nat. Commun. 9, 1355 (2018).
  28. Eskin, D. G. et al. Fundamental studies of ultrasonic melt processing. Ultrason. Sonochem. 52, 455–467 (2019).
  29. Wang, B. et al. Ultrafast synchrotron X-ray imaging studies of microstructure fragmentation in solidification under ultrasound. Acta Mater. 144, 505–515 (2018).
  30. Wang, G., Dargusch, M. S., Eskin, D. G. & StJohn, D. H. Identifying the stages during ultrasonic processing that reduce the grain size of aluminum with added Al3Ti1B master alloy. Adv. Eng. Mater. 19, 8 (2017).
  31. Ji, F. et al. Grain refinement and mechanism of steel in ultrasound-assisted wire and arc additive manufacturing. Int. Commun. Heat Mass 143, 106724 (2023).
  32. Zhao, C. et al. Critical instability at moving keyhole tip generates porosity in laser melting. Science 370, 1080–1086 (2020).
  33. Zhang, W., Xu, C., Li, W. & Yang, B. The strengthening effect of high-energy ultrasound treatment on the additively manufactured ZL114A aluminum alloy. Mater. Today Commun. 37, 107254 (2023).
  34. Cunningham, R. et al. Keyhole threshold and morphology in laser melting revealed by ultrahigh-speed X-ray imaging. Science 363, 849–852 (2019).
  35. Gan, Z. et al. Universal scaling laws of keyhole stability and porosity in 3D printing of metals. Nat. Commun. 12, 2379 (2021).
  36. Balasubramani, N., StJohn, D., Dargusch, M. & Wang, G. Ultrasonic processing for structure refinement: An overview of mechanisms and application of the interdependence theory. Mater. 12, 3187 (2019).
  37. Yang, Z. et al. Manipulating molten pool dynamics during metal 3D printing by ultrasound. Appl. Phys. Rev. 9, 2 (2020).
  38. Hojjatzadeh, S. et al. Pore elimination mechanisms during 3D printing of metals. Nat. Commun. 10, 3088 (2019).
  39. Eskin, D. G & Tzanakis, I. High-Frequency Vibration and Ultrasonic Processing. (Springer International Publishing: Cham, 2018).
  40. Supponen, O. et al. The effect of size range on ultrasound-induced translations in microbubble populations. J. Acoust. Soc. Am 147, 3236 (2020).
  41. Guo, Q. et al. In-situ characterization and quantification of melt pool variation under constant input energy density in laser powder bed fusion additive manufacturing process. Addit. Manufact. 28, 600–609 (2019).
  42. Huang, Y. et al. Keyhole fluctuation and pore formation mechanisms during laser powder bed fusion additive manufacturing. Nat. Commun. 13, 1170 (2022).
  43. Khairallah, S. A., Anderson, A. T., Rubenchik, A. & King, W. E. Laser powder-bed fusion additive manufacturing: Physics of complex melt flow and formation mechanisms of pores, spatter, and denudation zones. Acta Mater. 108, 36–45 (2016).
  44. Eskin, G. et al. Ultrasonic Treatment of Light Alloy Melts. 1st edn, (CRC Press, 1998).
  45. Tzanakis, I. & Eskin, D. Ultrasonic Cavitation Treatment of Metallic Alloys (Mater, 2020).
  46. Tzanakis, I., Lebon, G., Eskin, D. & Pericleous, K. Characterizing the cavitation development and acoustic spectrum in various liquids. Ultrason. Sonochem. 34, 651–662 (2017).
  47. Xu, N., Yu, Y., Zhai, W., Wang, J. & Wei, B. A high-temperature acoustic field measurement and analysis system for determining cavitation intensity in ultrasonically solidified metallic alloys. Ultrason. Sonochem. 94, 106343 (2023).
  48. Tzanakis, I. et al. In situ synchrotron radiography and spectrum analysis of transient cavitation bubbles in molten aluminium alloy. Phys. Procedia 70, 841–845 (2015).
  49. Atchley, A. & Prosperetti, A. The crevice model of bubble nucleation. J. Acoust. Soc. Am. 86, 1065–1084 (1989).
  50. Yuan, D. et al. Improvement of the grain structure and mechanical properties of austenitic stainless steel fabricated by laser and wire additive manufacturing assisted with ultrasonic vibration. Mat. Sci. Eng A-Struct. 813, 141177 (2021).
  51. Xu, M. et al. Effect of grain refinement on strain hardening behavior of nickel-based superalloy fabricated by wire arc additive manufacturing. Mater. Lett. 324, 132723 (2022).
  52. Ning, F. et al. Ultrasonic vibration-assisted laser engineered net shaping of inconel 718 parts: microstructural and mechanical characterization. ASME. J. Manuf. Sci. Eng. 140, 061012 (2018).
  53. Wang, J., Zhu, R., Liu, Y. & Zhang, L. Understanding melt pool characteristics in laser powder bed fusion: An overview of single- and multi-track melt pools for process optimization. Adv. Powder Mater. 2, 100137 (2023).
  54. Lebon, G. B., Tzanakis, I., Djambazov, G., Pericleous, K. & Eskin, D. Numerical modeling of ultrasonic waves in a bubbly newtonian liquid using a high-order acoustic cavitation model. Ultrason. Sonochem. 37, 660–668 (2017).
  55. Priyadarshi, A. et al. On the governing fragmentation mechanism of primary intermetallics by induced cavitation. Ultrason. Sonochem. 70, 105260 (2021).
  56. Mi, J., Tan, D. & Lee, T. L. In situ synchrotron X-ray study of ultrasound cavitation and its effect on solidification microstructures. Metall. Mater. Trans. B 46, 1615– 1619 (2015).
  57. Wang, Z. et al. Effects of ultrasonic vibration on microstructure and mechanical properties of 1Cr12Ni3MoVN alloy fabricated by directed energy deposition. Ultrasonics 132, 106989 (2023).
  58. Allen, T. R. et al. Energy-coupling mechanisms revealed through simultaneous keyhole depth and absorptance measurements during laser-metal processing. Phys. Rev. Appl. 13, 064070 (2020).
  59. Tan, D. et al. High-speed synchrotron X-ray imaging studies of the ultrasound shockwave and enhanced flow during metal solidification processes. Metall. Mater. Trans. A 46, 2851–2861 (2015).
  60. Chen, Y. et al. Grain refinement and mechanical properties improvement of Inconel 625 alloy fabricated by ultrasonic-assisted wire and arc additive manufacturing. J Alloy Compd. 910, 164957 (2022).
  61. Simonelli, M. et al. A study on the laser spatter and the oxidation reactions during selective laser melting of 316L stainless steel, Al-Si10-Mg, and Ti-6Al-4V. Metall. Mater. Trans. A. 46, 3842–3851 (2015).
  62. Mehta, A. et al. Additive manufacturing and mechanical properties of the dense and crack free Zr-modified aluminum alloy 6061 fabricated by the laser-powder bed fusion. Addit. Manuf. 41, 101966 (2021).

Propagation Velocity of Excitation Waves Caused by Turbidity Currents

혼탁류에 의한 자극파의 전파 속도

Guohui Xu, Shiqing Sun, Yupeng Ren, Meng Li, Zhiyuan Chen

Abstract

Turbidity currents are important carriers for transporting terrestrial sediment into the deep sea, facilitating the transfer of matter and energy between land and the deep sea. Previous studies have suggested that turbidity currents can exhibit high velocities during their movement in submarine canyons. However, the maximum vertical descent velocity of high-concentration turbid water simulating turbidity currents does not exceed 1 m/s, which does not support the understanding that turbidity currents can reach speeds of over twenty meters per second in submarine canyons. During their movement, turbidity currents can compress and push the water ahead, generating propagating waves. These waves, known as excitation waves, exert a force on the seafloor, resuspending bottom sediments and potentially leading to the generation of secondary turbidity currents downstream. Therefore, the propagation distance of excitation waves is not the same as the initial journey of the turbidity currents, and the velocity of excitation waves within this journey has been mistakenly regarded as the velocity of the turbidity currents. Research on the propagation velocity of excitation waves is of great significance for understanding the sediment supply patterns of turbidity currents and the transport patterns of deep-sea sediments. In this study, numerical simulations were conducted to investigate the velocity of excitation waves induced by turbidity currents and to explore the factors that can affect their propagation velocity and amplitude. The relationship between the velocity and amplitude of excitation waves and different influencing factors was determined. The results indicate that the propagation velocity of excitation waves induced by turbidity currents is primarily determined by the water depth, and an expression (v2 = 0.63gh) for the propagation velocity of excitation waves is provided.

Keywords

turbidity current; excitation wave; propagation speed; flume test; FLOW-3D

1. Introduction

Submarine turbidity currents, often referred to as underwater rivers, are important carriers that transport terrestrial sediments to the deep sea [1,2,3,4,5,6,7]. These turbidity currents, carrying a large amount of silt and sand, not only have strong erosive capabilities on the seabed [8,9,10], but also pose a threat to underwater communication cables, resulting in significant economic losses [11,12,13]. For example, the 2006 Pingdong earthquake in Taiwan caused the rupture of 11 submarine cables within the Kaoping Canyon, resulting in a slowdown in network speed in Southeast Asia for 49 days and requiring the deployment of 11 cable ships for repairs [13,14,15]. Investigating the velocity and patterns of turbidity currents in submarine canyons is of great significance for the protection of infrastructure such as pipelines and cables in these canyons.
One of the main methods for quantitatively studying the velocity of turbidity currents in submarine canyons is to infer their speed through cable ruptures. The first confirmed occurrence of cable rupture caused by a turbidity current was in 1929, when the Grand Banks earthquake triggered the continuous rupture of 12 submarine cables. Inferred maximum turbidity current velocities reached 28 m/s [16,17,18]. Subsequently, multiple cable rupture incidents caused by turbidity currents have occurred worldwide. Table 1 summarizes the inferred maximum turbidity current velocities from these cable rupture incidents.

EventMaximum Turbidity VelocityReferences
18 November 1929 Grand Banks earthquake28 m/s[16,19,20,21]
1953 Suva earthquake in the Fiji Islands5.1 m/s[22]
The Orleansville earthquake of 9 September 1954, Algeria20.6 m/s[23]
Earthquake, Solomon Islands, Western Pacific, 23 December 196610.3 m/s[24]
Incident at Nice airport, France, 16 October 19797 m/s[25]
Taitung earthquake, 22 August 20029.8 m/s[26]
21 May 2003 earthquake in Algeria15.8 m/s[27]
The Taitung earthquake of 10 December 200316.5 m/s[26]
The Taitung earthquake of 18 December 200318.6 m/s[26]
Pingtung earthquake on 26 December 200620 m/s[28]
Typhoon Morakot on 7–9 August 200916.6 m/s[29]
The 15 January 2022 eruption of Hunga volcano33.9 m/s[30]
Table 1. Cable breakage events caused by turbidity currents worldwide.

Previous studies have shown that the maximum vertical velocity of high-concentration turbidity currents in water does not exceed 1 m/s, and the maximum downward velocity of spherical particles in water does not exceed 10 m/s [31]. The maximum velocity of professional athlete Usain Bolt in the 100 m sprint on land is 9.58 m/s, while dolphins in the ocean can reach speeds of up to 20 m/s. Deep-sea turbidity currents, characterized by a small density difference compared to water, are primarily driven by the gravitational component along the direction of flow. However, factors such as bed friction also need to be considered. The driving force behind turbidity currents is primarily the density difference between the turbulent flow and the surrounding water, as well as the gravitational downslope component. Previous studies have detected a maximum sediment concentration of 12% in the basal layer of turbidity currents [32]. However, even high concentrations of suspended sediment, such as 1720 g/L, in seawater with a density of 1020 g/L, do not exceed a maximum vertical velocity of 1 m/s [33]. Similarly, spherical particles also have a maximum settling velocity in water of less than 10 m/s [33]. Turbidity currents, being density-driven flows, have relatively low density differences compared to water, and the gentle slope of submarine canyons also contributes to a smaller gravitational downslope force. Additionally, the influence of bed friction and other factors related to sediment deposition needs to be considered. It is incredible to think that turbidity currents can achieve flow velocities as high as 28 m/s [16,18,28,34,35].
When submarine landslides occur on continental slopes, the sliding mass entering the bottom of submarine canyons can cause the destruction of soft sediment beds. The mixing of sliding or flowing sediment with water forms turbidity currents. Turbidity currents exert pressure and propel the water ahead, forming an excitation wave. This aligns with Paull’s hypothesis that in the course of turbidity currents, a high-pressure zone is formed ahead, capable of causing an increase in pore water pressure in the sediment ahead [36]. Similar to surging waves, the excitation waves generated can propagate downstream along the submarine canyon, with a propagation velocity much greater than the velocity of turbidity currents [31]. The rapid propagation of excitation waves can exert a force on the seafloor of the submarine canyon, causing the resuspension of sediment in front of the head of the turbidity currents, which may lead to the formation of secondary turbidity currents at some downstream locations. The distance between the secondary and initial turbidity currents is actually the propagation distance of the excitation waves, rather than the journey of the initial turbidity currents. Therefore, the speed of the excitation waves within this distance is mistakenly considered as the velocity of the turbidity currents (see Figure 1). This may explain why the velocity of the turbidity currents as deduced from cable breakages is so high.

Figure 1. Diagram of excitation wave propagation due to turbidity current (v1 is the velocity of turbidity current. This refers to the ratio of distance to time experienced by a turbidity current mass moving underwater. v2 is the velocity of secondary turbidity current: the rapidly propagating excitation wave applies a force on the submarine canyon floor, leading to the destruction of the soft sediment floor and the secondary turbidity current. v is the propagation velocity of the excitation wave; this refers to the propagation velocity of the turbidity current excitation wave. This speed is not the velocity of the motion of the water mass. At time t0, the initial turbidity current moves underwater, pushing the stationary water in front to generate an excitation wave. At time t1, the excitation wave is propagating. At time t2, the rapidly propagating excitation wave exerts pressure on the soft bottom bed, resulting in the destruction of the bottom bed and secondary turbidity current).

Turbidity currents are mass movements composed of sediment particles, with a high concentration of the dense basal layer near the seabed. Depending on their density and granulometric composition, turbidity currents can move along submarine canyons through mechanisms such as diffusion, collapse, and flow [37], which differ from the downward movement as a single entity of landslide bodies after slope failure (this distinguishes them from surges). Additionally, during the long-distance movement of turbidity currents in canyons, the completion of subsequent water replenishment may generate multiple excitation waves. Furthermore, secondary excitation waves may also occur during the movement of secondary turbidity currents triggered by the initial turbidity current, which differs significantly from the surges caused by submarine landslides. Furthermore, previous studies [38,39,40,41] on sediment supply during turbidity current movements have mostly focused on the scouring action on the seabed, whereas the resuspension of sedimentary deposits in front of the initial turbidity current caused by excitation waves may serve as an effective mode of sediment supply during the long-distance transport of turbidity currents.
In 2023, Ren et al. proposed that the cause of the long-distance high-speed motion of turbidity currents is due to the excitation waves caused by the primary turbidity currents. However, only preliminary research has been conducted on the comparison of excitation wave velocity and solitary wave velocity, and there has been no specific discussion on the reasons for the excitation wave velocity being much greater than that of the turbidity current. In an experiment conducted using an indoor flume, it was observed that the wavelength of the excitation waves was much larger than the water depth, similar to shallow water waves [33]. The amplitude of excitation waves in proportion to their wavelength was small, consistent with the theory of small-amplitude waves. Similar to the velocity model of shallow water waves, it is expected that the propagation speed of excitation waves is also influenced by the water depth. However, since excitation waves are triggered by sediment-laden turbidity currents, the velocity model may differ from that of surface waves induced by gravitational flows.
The purpose of this study is to simulate and investigate the effects of different factors on the propagation velocity and amplitude of excitation waves through a validated numerical model based on laboratory experiments. The study aims to determine the maximum propagation velocity of excitation waves at a field scale and whether there is attenuation in the long-distance propagation after their formation. In recent studies, seafloor sediment flows have been collectively referred to as turbidity currents [42]. Therefore, we simulated the movement of turbidity currents by sediment flow.
This study uses the CFD-based fluid computation software FLOW-3D to simulate the underwater movement process of turbidity currents. The numerical model is validated against indoor experimental results. During the simulation process, a velocity model for surging wave generation triggered by submarine landslides is used as a reference, and multiple factors that may affect the propagation velocity of the excitation wave are considered. By controlling a single variable, the main factors influencing the excitation wave propagation velocity are determined, and the corresponding expression for excitation wave propagation velocity is provided. The results indicate that the propagation velocity of the excitation wave induced by turbidity currents is primarily determined by the water depth. This research provides a new perspective for understanding the high-speed movement of turbidity currents in submarine canyons and enriches the understanding of the movement patterns of turbidity currents in submarine canyons. In addition, studying the propagation speed of excitation waves is highly significant for the resuspension of underwater sediments, as well as the re-circulation of carbon sequestration, nutrients, heavy metals, and microplastics.

2. Experimental Study on Excitation Waves Induced by Turbidity Currents

2.1. Experimental Design and Apparatus

The experimental apparatus used for the turbidity current-induced excitation wave tests is a straight water tank [33]. The water tank is 12.5 m long, 0.5 m wide, and 0.7 m high. A turbidity source area is located on the right side of the tank to generate turbidity currents. The tank is equipped with a terrain with a certain slope.
Turbidity currents are generated underwater using a weir. The mass ratio of silt and clay used in the experimental turbid water solution was 8:2, with a density of 1600 kg/m3. Previous experiments have shown that this turbid mixture can reach a maximum flow velocity of 18.7 cm/s [31]. Three pressure sensors are placed along the straight section of the tank at intervals of 0.4 m. These sensors continuously monitor the bottom shear stress caused by the turbidity current-induced excitation wave, as well as the force exerted by the turbidity current itself on the bed. The monitoring frequency is set at 100 Hz.

2.2. Experimental Phenomenon and Results

In the laboratory water tank experiments, it was observed that as the turbidity current propagates, a wave is generated ahead of the turbidity front, moving in the same direction as the current and with a velocity greater than the turbidity current velocity [33]. By monitoring the pressure changes on the bed during the turbidity current motion [33], the propagation velocity of the excitation wave, the head movement velocity of the turbidity current, and the amplitude of the excitation wave (obtained from the measured surface elevation changes caused by the wave) can be estimated based on the distances between the sensors and the time when the pressure change peaks occur.
The results of indoor experiments on turbidity currents indicate that they can compress and propel the water ahead of them, generating excitation waves similar to pulses. The propagation speed of these excitation waves caused by turbidity currents is found to be much greater than the velocity of the turbidity current movement at its head, as determined by pressure sensors installed on the seabed.

3. Numerical Simulation of Excitation Waves Induced by Turbidity Currents

FLOW-3D is a powerful computational fluid dynamics (CFD) software that excels in making accurate calculations of free surface and six-degrees-of-freedom motions of objects. Similar to other CFD software, FLOW-3D consists of three modules: pre-processing, solver, and post-processing. In recent years, there have been many simulations of turbidity currents using FLOW-3D due to its superior capabilities. For example, Heimsund (2007) simulated turbidity currents in the Monterey Canyon system using FLOW-3D based on high-resolution bathymetry and flow data [43]. Zhou et al. (2017) used FLOW-3D software to simulate turbidity currents in a flume with obstacles, analyzing the impact of the proportion between obstacle height and flume height on the movement of turbidity currents, including their velocity, flow state, and morphological evolution [44]. In this study, using the CFD software FLOW-3D, the underwater motion process of turbidity currents is simulated. The model is validated by comparing it with experimental results, and the motion of the waves induced by turbidity currents is simulated based on this validation.

3.1. Control Equations

FLOW-3D, a mature three-dimensional fluid simulation software, is used in this study. It employs the RNG turbulence model, which is capable of handling high strain rate flows and is suitable for simulating excitation waves. The research focus of this paper is on sediment gravity flows (turbulent flows), and the control equations used in the calculations include the basic continuity equation, the momentum equation, the turbulent kinetic energy k equation, and the turbulent kinetic energy dissipation rate ε equation.

The continuity equation:

The momentum equation:

The turbulence model:

k equation:

ε equation:

where u, v and w is the flow velocity component in x, y and z directions; Ax, Ay and Az represent the area fraction that can flow in x, y and z directions; Gx, Gy and Gz are the gravitational acceleration in x, y and z directions; fx, fy and fz are the viscous forces in the three directions; VF is the fraction of the volume that can flow; ρ is the fluid density; p is the pressure acting on the fluid element; k is the turbulence energy; ε is the turbulence kinetic energy dissipation rate; μ is turbulence viscosity coefficient

where u, v and w is the flow velocity component in x, y and z directions; Ax, Ay and Az represent the area fraction that can flow in x, y and z directions; Gx, Gy and Gz are the gravitational acceleration in x, y and z directions; fx, fy and fz are the viscous forces in the three directions; VF is the fraction of the volume that can flow; ρ is the fluid density; p is the pressure acting on the fluid element; k is the turbulence energy; ε is the turbulence kinetic energy dissipation rate; 

 μ is turbulence viscosity coefficient μ t = ρ C μ k 2 ε where Cμ = 0.0845;

Gk is the turbulent kinetic energy generation term, expressed as G k = μ t ∂ u i ∂ x j + ∂ u j ∂ x i ∂ u i ∂ x j

and σk and σε are the Prandtl numbers corresponding to the turbulent kinetic energy and dissipation rate, respectively, both of which are 1.39.

In addition, C ε 1 * = C ε 1 − η 1 − η / η 0 1 + β η 3 where Cε1 and Cε2 are the empirical constants, 1.42 and 1.68, respectively.

Furthermore, η = 2 E i j E i j 1 / 2 k ε

where E i j = 1 2 ∂ u i ∂ x j + ∂ u j ∂ x i , η0 = 4.377, β = 0.012.

The general mass continuity equation is as follows:

where VF is the fractional volume open to flow, ρ is the fluid density, RDIF is a turbulent diffusion term, and RSOR is the mass source.

3.2. Model Validation

To determine the factors affecting the velocity of the turbidity-induced excitation wave and its velocity expression, first, the indoor flume test was taken as the prototype. Then, a 1:1 geometric solid model was established, and the simulation parameters were set to be consistent with the flume test parameters [33]. Finally, the simulation results were compared with the laboratory test results.

The computational domain employs the method of unstructured grid and is entirely divided into structured orthogonal grids. Nested grids are used for local refinement at the interfaces of straight sections, resulting in a total of 800,000 grid cells after refinement.

The simulation results were compared with the indoor experimental results, with the velocity of the excitation wave and the turbidity current head being represented by changes in surface elevation and water density. The experimental and simulation results are shown in Table 2, and the calculation formula for the error is |Calculated value−Test value|Test value×100%Calculated value-Test valueTest value×100%.

ResultPropagation Velocity of Excitation Wave (m/s)Velocity of Turbidity Current (m/s)Excitation Wave Amplitude (m)
Sensor 1 to 2Sensor 2 to 3Sensor 1 to 2Sensor 2 to 3Sensor 1 to 2Sensor 2 to 3
Test results1.541.480.240.230.0290.03
Computed results1.551.520.250.230.030.03
Error range0.6%2.7%4.2%0%3.4%0%
Table 2. The test results of the propagation velocity of the excitation wave, the turbidity current velocity, and the excitation wave amplitude are compared with the simulation results.

From the above comparison, it can be observed that the simulated velocities of the excitation wave and the head of the turbidity current align well with the experimental results, indicating the rationality of using the numerical model established in this study for simulating the propagation velocity of the excitation wave induced by turbidity currents.

3.3. Analysis of Factors Affecting the Propagation Velocity of Excitation Waves

An analysis of the factors influencing the propagation velocity of excitation waves was conducted using numerical simulation. The reference model for wave velocity was based on the surge velocity model. The main factors affecting the propagation velocity of excitation waves were summarized, including the turbidity current density ρ, the thickness of the turbidity current source area d, the length of the turbidity current source area L, the depth at the initial flow of turbidity currents h, the canyon width l, and the initial velocity of the turbidity current v0 (as shown in Figure 2). The simulations were performed using a controlled variable approach for different parameters, and the velocity changes of the excitation wave were obtained, as shown in Table 3. The slope angle was fixed at 3°, and sensors were placed at intervals of 100 m starting from a distance of 500 m from the turbidity current source area (named Sensors 1, 2, 3). These sensors were used to extract surface elevation, density, and other relevant parameters at their respective locations. We can obtain the propagating velocity of excitation waves by measuring the time difference in surface elevation changes at the monitoring points. Similarly, we can determine the propagation velocity of turbidity currents by measuring the time difference in density changes.

Figure 2. Excitation wave velocity simulation model and parameters.
Group OrderTurbidity Current Density (kg/m3)Length of Turbidity Source Area
(m)		Canyon Width
(m)		Thickness of Turbidity Source Area
(m)		Depth (m)Initial Velocity of Turbidity Current (m/s)Propagation Velocity of Excitation Wave (m/s)Excitation Wave Amplitude (m)Velocity of Turbidity Current (m/s)
11600100020020200033.430.3455.88
21500100020020200033.090.3045.41
31400100020020200033.350.2234.99
41300100020020200033.330.1774.35
51200100020020200033.860.0923.74
61600100020040200033.051.1099.09
71600100020060200033.392.68910.79
81600100020080200033.214.82812.91
916001000200100200036.437.74413.79
10160020020020200032.930.1815.58
11160040020020200033.490.255.71
12160060020020200033.060.2785.79
13160080020020200033.170.315.72
141600100020020100026.670.565.72
151600100020020300039.650.1695.80
161600100020020400045.980.125.80
171600100020020500049.970.085.96
181600100010020200033.600.3545.72
191600100030020200032.980.3385.97
201600100040020200033.270.3565.87
211600100050020200033.310.3655.86
221600100020020200233.500.5324.35
231600100020020200533.121.3896.56
241600100020020200833.522.2718.10
2516001000200202001033.332.8788.99
Table 3. Simulation results under different variables conditions.

The variations in surface elevation at three sensor locations in the simulated results of five different turbidity current density groups are presented in Figure 3.

Figure 3. Simulation of propagating velocity of excitation wave under the sole variable condition of turbulent current density. (Length of turbidity source area: 1000 m; canyon width: 200 m; thickness of turbidity source area: 20 m; depth: 200 m; initial velocity of turbidity current: 0 m/s).

Based on the simulation results described above, while keeping all other conditions constant, the impact of a single variable, namely, the turbidity current density, on the propagation velocity and amplitude of the excitation wave was analyzed. By fitting the data, the relationship between turbidity current density and the propagation velocity of turbidity currents as well as the amplitude of the excitation wave was obtained, as shown in Figure 4.

Figure 4. Relationship between turbidity current density and turbidity current velocity, as well as excitation wave amplitude.

The simulation results indicate that changes in turbidity current density, while keeping the other conditions constant, do not result in a change in the propagation velocity of the excitation waves. However, they do affect the amplitude of the excitation waves and the velocity of the turbidity current itself. The simulation reveals that within the selected density range, both the amplitude of the excitation waves and the velocity of the turbidity current increase with increasing turbidity current density. When the turbidity current density is equal to that of water (ρTurbidity current = ρWater), there is no turbidity current or excitation wave generation. Thus, the relationship between the turbidity current velocity (v) and density (ρ) is expressed as v = −34.80643 + 0.05082•ρ − 1.59286 × 10−5 ρ2 (ρ > 1000, R2 = 0.994). Additionally, the relationship between the amplitude of the excitation waves (A) caused by turbidity currents and density (ρ) is expressed as A = −0.6021 + 5.9729 × 10−4 ρ (ρ > 1000, R2 = 0.991).

3.3.2. The Influence of the Thickness of the Turbidity Source Area on the Propagation Velocity and Amplitude of Excitation Waves

The variations in surface elevation at three sensor locations in the simulated results of five different thickness of turbidity source area groups are presented in Figure 5.

Figure 5. Simulation of propagating velocity of excitation wave under the sole variable condition of thickness of turbidity source area. (Turbidity current density: 1600 kg/m3; length of turbidity source area: 1000 m; canyon width: 200 m; depth: 200 m; initial velocity of turbidity current: 0 m/s).

Based on the simulation results described above, while keeping all other conditions constant, the impact of a single variable, namely, the thickness of the turbidity source area, on the propagation velocity and amplitude of the excitation wave was analyzed. By fitting the data, the relationship between the thickness of the turbidity source area and the propagation velocity of the turbidity current as well as the amplitude of the excitation wave was obtained, as shown in Figure 6.

Figure 6. Relationship between thickness of turbidity source area and turbidity current velocity, as well as excitation wave amplitude.

Based on the simulated results mentioned above, it can be concluded that, while keeping the other conditions constant, changing only the thickness of the turbidity current source area does not affect the propagation velocity of the excitation waves. However, it does impact both the amplitude of the excitation waves and the velocity of the turbidity current itself. The simulation reveals that within the selected range of thickness values for the turbidity current source area, both the amplitude of the excitation waves and the velocity of the turbidity current increase with an increase in the thickness of the source area. Additionally, it is observed that when the length of the turbidity current source area is zero, neither the turbidity current nor the excitation waves are generated (i.e., no turbidity current is produced when hTurbidity current = 0). Therefore, the relationship between the velocity (v) of the turbidity current and its thickness (h) is expressed as v = 0.27983•h − 0.00146•h2 (h ≥ 0, R2 = 0.999). Similarly, the relationship between the amplitude (A) of the excitation waves caused by the turbidity current and its thickness (h) is A = −0.00375•h − 0.0008•h2 (h ≥ 0, R2 = 0.999).

3.3.3. The Influence of the Length of the Turbidity Source Area on the Propagation Velocity and Amplitude of Excitation Waves

The variations in surface elevation at three sensor locations in the simulated results of five different length of turbidity source area groups are presented in Figure 7.

Figure 7. Simulation of propagating velocity of excitation wave under the sole variable condition of length of turbidity source area. (Turbidity current density: 1600 kg/m3; canyon width: 200 m; thickness of turbidity source area: 20 m; depth: 200 m; initial velocity of turbidity current: 0 m/s).

Based on the simulation results described above, while keeping all other conditions constant, the impact of a single variable, namely, the length of the turbidity source area, on the propagation velocity and amplitude of the excitation wave was analyzed. By fitting the data, the relationship between the length of the turbidity source area and the amplitude of the excitation wave was obtained, as shown in Figure 8.

Figure 8. Relationship between length of turbidity source area and excitation wave amplitude.(Amplitude refers to the surface elevation change caused by the excitation wave).

Through simulations, it has been determined that within the chosen range of the length of the turbidity source area, the amplitude of the excitation waves increases with an increase in the length of the turbidity source area. When the length of the turbidity source area is zero, there is no turbidity current and no generation of excitation waves (i.e., when LTurbidity current = 0). Additionally, for large lengths of the turbidity source area, under the condition of sufficient sediment supply, the variations in surface elevation caused by the waves generated by turbidity currents are negligible. Therefore, the relationship between the amplitude of the excitation waves (A) generated by turbidity currents and the length of the turbidity source area (L) is expressed as follows: A = −0.3624 + 0.10305•ln(L − 6.15619) (L ≥ 0, R2 = 0.997).

3.3.4. The Influence of Depth on the Propagation Velocity and Amplitude of Excitation Waves

The variations in surface elevation at three sensor locations in the simulated results of five different depth groups are presented in Figure 9.

Figure 9. Simulation of propagation velocity of excitation wave under the sole variable condition of depth. (Turbidity current density: 1600 kg/m3; length of turbidity source area: 1000 m; canyon width: 200 m; thickness of turbidity source area: 20 m; initial velocity of turbidity current: 0 m/s).

Based on the simulation results described above, while keeping all other conditions constant, the impact of a single variable, namely, depth, on the propagation velocity and amplitude of the excitation wave was analyzed. By fitting the data, the relationship between depth and the propagation velocity of the excitation wave as well as the amplitude of the excitation wave was obtained, as shown in Figure 10.

Figure 10. Relationship between depth and propagating velocity of excitation wave, as well as excitation wave amplitude.

As the water depth approaches infinity, the excitation wave amplitude can only approach zero but cannot reach zero. Therefore, the characteristics of the excitation wave amplitude change with the water depth are similar to those of the velocity propagation of the excitation wave. The relationship between the velocity of the excitation wave induced by turbidity currents (vExcitation wave) and the water depth (H) can be described as vExcitation wave = −287.05446 + 48.59211•ln(H + 535.14863) (R2 = 0.998). The relationship between the excitation wave amplitude (A) and the water depth (H) can be expressed as A = 1.46573 − 0.22816•ln(H − 47.67563) (R2 = 0.985).

3.3.5. The Influence of the Canyon Width on the Propagation Velocity and Amplitude of Excitation Waves

The variations in surface elevation at three sensor locations in the simulated results of five different canyon width groups are presented in Figure 11.

Figure 11. Simulation of propagating velocity of excitation wave under the sole variable condition of canyon width. (Turbidity current density: 1600 kg/m3; length of turbidity source area: 1000 m; thickness of turbidity source area: 20 m; depth: 200 m; initial velocity of turbidity current: 0 m/s).

When the canyon width is taken as the single variable condition, changing the canyon width does not significantly affect the propagation velocity of excitation waves, the amplitude of excitation waves, and the velocity of turbidity currents. Therefore, it can be concluded that, without considering the impact of the differences in the terrain and sediment on the canyon width, the canyon width has no impact on the propagation of excitation waves and the movement of turbidity currents.

3.3.6. The Influence of the Initial Velocity of the Turbidity Current on the Propagation Velocity and Amplitude of Excitation Waves

The variations in surface elevation at three sensor locations in the simulated results of five different initial velocity of turbidity current groups are presented in Figure 12.

Figure 12. Simulation of propagating velocity of excitation wave under the sole variable condition of initial velocity of turbidity current. (Turbidity current density: 1600 kg/m3; length of turbidity source area: 1000 m; canyon width: 200 m; thickness of turbidity source area: 20 m; depth: 200 m).

Based on the simulation results described above, while keeping all other conditions constant, the impact of a single variable, namely, the initial velocity of the turbidity current, on the propagation velocity and amplitude of the excitation wave was analyzed. By fitting the data, the relationship between the initial velocity of the turbidity current and the amplitude of the excitation wave was obtained, as shown in Figure 13.

Figure 13. Relationship between initial velocity of turbidity current and excitation wave amplitude.

Based on the simulation, it is observed that within the selected range of the initial velocity of the turbidity current, the amplitude of the excitation wave increases linearly with the increase in the initial velocity of the turbidity current. Therefore, the relationship between the amplitude (A) of the excitation wave caused by the turbidity current and the initial velocity of the turbidity current (v0) can be expressed as A = 0.34 + 0.24084•v0 (A ≥ 0, R2 = 0.992).

Through controlling the simulation calculation of a single variable, it was found that there are several factors that can affect the amplitude of the excitation wave. These factors include the turbidity current density ρ, the thickness of the turbidity current source area d, the length of the turbidity current source area L, the water depth h, and the initial velocity of the turbidity current v0. In contrast, there are relatively few factors that influence the propagation velocity of the excitation wave. Within the selected parameter range, only the water depth can affect the propagation velocity of the excitation wave. The physical parameters of the turbidity current, including the turbidity current density ρ, the thickness of the turbidity current source area d, the length of the turbidity current source area L, the canyon width l, and the initial velocity of the turbidity current v0, have no direct influence on the propagation velocity of the excitation wave. Therefore, the turbidity current only serves as a triggering factor for the excitation wave and is not directly related to the propagation velocity of the excitation wave.

3.4. Analyze the Changes in Propagation Velocity of Excitation Waves along a Path

In order to further investigate the underlying truth behind the variation in the propagation velocity of the excitation wave, a discussion on whether there is velocity attenuation along the propagation path of the excitation wave is conducted. Since the seventh group of the excitation wave causes significant changes in surface elevation, the seventh group of the excitation wave is selected as the research object in order to study the variations in surface elevation along the propagation path of the excitation wave. The changes in surface elevation are extracted every 200 m along the sediment slope (with the first extraction point located 400 m away from the source area of the turbidity current). A total of six sets of surface elevation data are extracted (ranging from 400 m to 1400 m distance from the source area of the turbidity current), as shown in Figure 14.

Figure 14. Surface elevation changes during excitation wave propagation along sediment slopes.

The amplitudes and propagation velocities of the excitation wave at each point are shown in Table 4.

Distance from Turbidity Current Source Area (m)Propagation Velocity of Excitation Wave (m/s)Excitation Wave Amplitude (m)
40033.342.524
60036.792.596
80037.132.589
100039.992.566
120040.042.542
140040.132.523
Table 4. Excitation wave velocity during the excitation wave propagation along the sediment slope.

From the table above, it can be observed that the amplitude of the excitation wave does not change while traveling along the slope. This indicates that the change in surface elevation caused by the propagation of the excitation wave does not attenuate. Furthermore, the propagation velocity of the excitation wave gradually increases, although the change is not very pronounced. This variation may be attributed to the change in the water depth caused by the sloping bed. To investigate this, a simulation was conducted in a straight channel with a length of 3000 m. Six sampling points were established from 400 m to 1400 m away from the turbidity current source area to extract the amplitude of the excitation wave. The results of the simulation are presented in Figure 15.

Figure 15. Surface elevation changes during wave propagation along a straight channel.

The amplitudes and propagation velocities of the excitation wave at each point are shown in Table 5.

Distance from Turbidity Current Source Area (m)Propagation Velocity of Excitation Wave (m/s)Excitation Wave Amplitude (m)
40033.892.559
60037.662.692
80037.122.712
100036.922.717
120037.092.715
140037.482.718
Table 5. Excitation wave velocity during the propagation along the straight channel.

The data from the table above indicate that during the propagation of the excitation wave along a straight water channel, its velocity remains constant, except for a slight decrease at the initial point. This phenomenon may be attributed to the fact that in the starting phase, the excitation wave is not fully developed, and hence its velocity is relatively smaller. However, once it is fully developed, the propagation velocity of the excitation wave does not decrease in subsequent processes. Therefore, the propagation velocity of the excitation wave is only dependent on the real-time water depth of the wave. In future studies, we aim to explore the relationships between these influencing factors and other physical parameters, such as the speed of wave propagation, using the effective and accurate method of machine learning algorithms [45].

3.5. Expression of the Propagation Velocity of the Excitation Wave

The propagation of the excitation wave along a long distance does not experience an attenuation in velocity, as is the case with the propagation velocity of solitary waves. Referring to the estimated wave propagation velocity (the square of the propagation velocity is directly proportional to the water depth amplitude) [46], the wavelengths under different water depth conditions were extracted, as shown in Table 6.

Depth (m)Propagation Velocity of Excitation Wave (m/s)Excitation Wave Amplitude (m)Excitation Wave Length (m)
10026.670.562580
20033.430.352850
30039.650.173250
40045.980.123600
50049.970.084150
100066.670.046000
200090.910.029500
4000165.840.317600
Table 6. Physical parameters of excitation wave under different water depth conditions.

From the simulation results of a single variable, the water depth, it could be seen that the wavelengths of the excitation waves were much larger than the water depth. Therefore, further simulations were conducted under water depth conditions ranging from 1000 m to 4000 m. Due to the minimal change in wave amplitude when the water depth reached 4000 m, it was not possible to observe a distinct waveform. However, through simulations with the thickness of the turbidity current source area as the single variable, it was found that an increase in the thickness of the source region led to a larger amplitude of the excitation waves, but it did not affect the wavelength of the excitation waves. Therefore, in order to better extract the wavelength of the excitation waves, the thickness of the source region in the simulation with a water depth of 4000 m was set to 200 m.

Through simulations at water depths of 1000 m and 4000 m, it is observed that the wavelengths of the excitation waves are much larger than the water depth, indicating that these waves belong to the category of shallow water waves. The amplitude of the excitation waves is relatively small compared to their wavelength, aligning with the small amplitude wave theory [47]. According to this theory, the wave velocity of shallow water waves is only dependent on the water depth (h) and gravity acceleration (g), regardless of the wave period. In the case of excitation waves induced by turbidity currents in deep water, the amplitudes of these waves are relatively small compared to the water depth. Referring to the expression for shallow water waves (when the relative water depth, which is the ratio of water depth to wavelength, is much smaller than 1/2), the wave velocity is denoted as 𝐶𝑠=√𝑔ℎ. This implies that the propagation velocity of the excitation waves is also solely related to the water depth. Therefore, a fitting of the square of the propagation velocity of the excitation waves (v2) and the water depth (h) was conducted (Figure 16).

Figure 16. The relationship between the propagation velocity of excitation wave and the depth.

Through fitting, the following can be obtained:

Through fitting, it can be discovered that the propagation model of the velocity of excitation waves is different from the shallow water wave theory. This is because turbidity currents, as granular materials, generate excitation waves by pushing the water in front of them with sediment particles underwater, which is different from the surges formed by solid blocks entering the ocean. Additionally, excitation waves formed by turbidity currents occur in an underwater environment, which may be the reason why the propagation velocity equation for the excitation waves behaves as if the velocity squared is equal to half the Earth’s gravity. This equation reveals the variation in the propagation velocity of the excitation wave with depth, explaining why the average velocity between the monitoring points in the field is greater than the instantaneous velocity measured at these points [41]. Further theoretical research on the propagation velocity of excitation waves requires subsequent field monitoring and the deployment of monitoring systems to more thoroughly investigate the fundamental causes.

4. Conclusions

This study aimed to investigate the velocity of turbidity current-induced excitation waves through numerical simulation. By fixing a single variable, different factors that could affect the propagation velocity and amplitude of the excitation waves were analyzed and discussed, leading to the following three conclusions:

  1. Within the selected parameter range, there are several factors that can influence the amplitude of the excitation waves, including the turbidity current density ρ, the thickness of the turbidity current source area d, the length of the turbidity current source area L, the water depth h, and the initial velocity of the turbidity current v0.The amplitude of the excitation waves is positively correlated with the turbidity density, the thickness of the source area, the length of the source area, and the initial velocity, while it is negatively correlated with the water depth.
  2. Within the selected parameter range, only the water depth can affect the propagation velocity of the excitation waves. As the water depth increases, the propagation velocity of the excitation waves also increases, and a relationship of v2 = 0.63gh (R2 = 0.967) is established between the square of the propagation velocity v2 and the water depth h.
  3. During the propagation of the excitation waves, both the propagation velocity and the changes in surface elevation caused by the waves do not attenuate. Considering the relatively calm deep-sea environment, the high-speed propagation of the excitation waves and the resuspension of bottom sediments they cause not only complement the understanding of turbidity current motion patterns in canyons, but also provide new research directions for deep-sea sediment transport.

References

  1. Azpiroz-Zabala, M.; Cartigny, M.J.B.; Talling, P.J.; Parsons, D.R.; Sumner, E.J.; Clare, M.A.; Simmons, S.M.; Cooper, C.; Pope, E.L. Newly recognized turbidity current structure can explain prolonged flushing of submarine canyons. Sci. Adv. 2017, 3, e1700200.
  2. Daly, R.A. Origin of submarine canyons. Am. J. Sci. 1936, 5, 401–420.
  3. Winterwerp, J. Stratification effects by fine suspended sediment at low, medium, and very high concentrations. J. Geophys. Res. Oceans. 2006, 111, C5.
  4. Nilsen, T.H.; Shew, R.D.; Steffens, G.S.; Studlick, J.R.J. Atlas of Deep-Water Outcrops; American Association of Petroleum Geologists: Tulsa, OK, USA, 2008.
  5. Xu, J. Turbidity Current Research in the Past Century: An Overview. J. Ocean Univ. China 2014, 44, 98–105.
  6. Talling, P.J.; Allin, J.; Armitage, D.A.; Arnott, R.W.C.; Cartigny, M.J.B.; Clare, M.A.; Felletti, F.; Covault, J.A.; Girardclos, S.; Hansen, E.; et al. Key future directions for research on turbidity currents and their deposits. J. Sediment. Res. 2015, 85, 153–169.
  7. Maier, K.L.; Gales, J.A.; Paull, C.K.; Rosenberger, K.; Talling, P.J.; Simmons, S.M.; Gwiazda, R.; McGann, M.; Cartigny, M.J.; Lundsten, E. Linking direct measurements of turbidity currents to submarine canyon-floor deposits. Front. Earth Sci. 2019, 7, 144.
  8. Hughes Clarke, J.E. First wide-angle view of channelized turbidity currents links migrating cyclic steps to flow characteristics. Nat. Commun. 2016, 7, 11896.
  9. Normandeau, A.; Bourgault, D.; Neumeier, U.; Lajeunesse, P.; St-Onge, G.; Gostiaux, L.; Chavanne, C. Storm-induced turbidity currents on a sediment-starved shelf: Insight from direct monitoring and repeat seabed mapping of upslope migrating bedforms. Sedimentology 2020, 67, 1045–1068.
  10. Hill, P.R.; Lintern, D.G. Turbidity currents on the open slope of the Fraser Delta. Mar. Geol. 2022, 445, 106738.
  11. Summers, M. Review of deep-water submarine cable design. In Proceedings of the SubOptic 2001, Kyoto, Japan, 20–24 May 2001; p. 4.
  12. Carter, L.; Gavey, R.; Talling, P.J.; Liu, J.T. Insights into Submarine Geohazards from Breaks in Subsea Telecommunication Cables. Oceanography 2014, 27, 58–67.
  13. Gavey, R.; Carter, L.; Liu, J.T.; Talling, P.J.; Hsu, R.; Pope, E.; Evans, G. Frequent sediment density flows during 2006 to 2015, triggered by competing seismic and weather events: Observations from subsea cable breaks off southern Taiwan. Mar. Geol. 2017, 384, 147–158.
  14. Carter, L.; Burnett, D.; Drew, S.; Hagadorn, L.; Marle, G.; Bartlett-Mcneil, D.; Irvine, N. Submarine Cables and the Oceans: Connecting the World; UNEP-WCMC Biodiversity Series 31; UNEP World Conservation Monitoring Centre: Cambridge, UK, 2010.
  15. Qiu, W. Submarine cables cut after Taiwan earthquake in Dec 2006. Submar. Cable Netw. 2011, 19.
  16. Heezen, B.C.; Ewing, W.M. Turbidity currents and submarine slumps, and the 1929 Grand Banks [Newfoundland] earthquake. Am. J. Sci. 1952, 250, 849–873.
  17. Kuenen, P.H. Estimated size of the Grand Banks [Newfoundland] turbidity current. Am. J. Sci. 1952, 250, 874–884.
  18. Heezen, B.C.; Ericson, D.; Ewing, M. Further evidence for a turbidity current following the 1929 Grand Banks earthquake. Deep-Sea Res. 1954, 1, 193–202.
  19. Heezen, B.C. Whales entangled in deep sea cables. Deep-Sea Res. 1957, 4, 105–115.
  20. Piper, D.J.; Shor, A.N.; Farre, J.A.; O’Connell, S.; Jacobi, R. Sediment slides and turbidity currents on the Laurentian Fan: Sidescan sonar investigations near the epicenter of the 1929 Grand Banks earthquake. Geology 1985, 13, 538–541.
  21. Piper, D.J.; Cochonat, P.; Morrison, M.L. The sequence of events around the epicentre of the 1929 Grand Banks earthquake: Initiation of debris flows and turbidity current inferred from sidescan sonar. Sedimentology 1999, 46, 79–97.
  22. Houtz, R.; Wellman, H. Turbidity current at Kadavu Passage, Fiji. Geol. Mag. 1962, 99, 57–62.
  23. Heezen, B.C.; Ewing, M. Orleansville earthquake and turbidity currents. AAPG Bull. 1955, 39, 2505–2514.
  24. Krause, D.C.; White, W.C.; PIPER, D.J.W.; Heezen, B.C. Turbidity currents and cable breaks in the western New Britain Trench. Geol. Soc. Am. Bull. 1970, 81, 2153–2160.
  25. Piper, D.J.; Savoye, B. Processes of late Quaternary turbidity current flow and deposition on the Var deep-sea fan, north-west Mediterranean Sea. Sedimentology 1993, 40, 557–582.
  26. Soh, W.; Machiyama, H.; Shirasaki, Y.; Kasahara, J. Deep-sea floor instability as a cause of deepwater cable fault, off eastern part of Taiwan. AGU Fall Meet. Abstr. 2004, 2, 1–8.
  27. Cattaneo, A.; Babonneau, N.; Ratzov, G.; Dan-Unterseh, G.; Yelles, K.; Bracène, R.; De Lepinay, B.M.; Boudiaf, A.; Déverchère, J. Searching for the seafloor signature of the 21 May 2003 Boumerdès earthquake offshore central Algeria. Nat. Hazards Earth Syst. Sci. 2012, 12, 2159–2172.
  28. Hsu, S.-K.; Kuo, J.; Chung-Liang, L.; Ching-Hui, T.; Doo, W.-B.; Ku, C.-Y.; Sibuet, J.-C. Turbidity currents, submarine landslides and the 2006 Pingtung earthquake off SW Taiwan. Terr. Atmos. Ocean. Sci. 2008, 19, 7.
  29. Carter, L.; Milliman, J.D.; Talling, P.J.; Gavey, R.; Wynn, R.B. Near-synchronous and delayed initiation of long run-out submarine sediment flows from a record-breaking river flood, offshore Taiwan. Geophys. Res. Lett. 2012, 39, L12603.
  30. Clare, M.A.; Yeo, I.A.; Watson, S.; Wysoczanski, R.; Seabrook, S.; Mackay, K.; Hunt, J.E.; Lane, E.; Talling, P.J.; Pope, E.; et al. Fast and destructive density currents created by ocean-entering volcanic eruptions. Science 2023, 381, 1085–1092.
  31. Ren, Y.; Zhang, Y.; Xu, G.; Xu, X.; Wang, H.; Chen, Z. The failure propagation of weakly stable sediment: A reason for the formation of high-velocity turbidity currents in submarine canyons. J. Ocean. Limnol. 2023, 41, 100–117.
  32. Wang, Z.; Xu, J.; Talling, P.J.; Cartigny, M.J.B.; Simmons, S.M.; Gwiazda, R.; Paull, C.K.; Maier, K.L.; Parsons, D.R. Direct evidence of a high-concentration basal layer in a submarine turbidity current. Deep-Sea Res. Part I Oceanogr. Res. Pap. 2020, 161, 103300.
  33. Ren, Y.; Tian, H.; Chen, Z.; Xu, G.; Liu, L.; Li, Y. Two Kinds of Waves Causing the Resuspension of Deep-Sea Sediments: Excitation and Internal Solitary Waves. J. Ocean Univ. China 2023, 22, 429–440.
  34. Lambert, A.M.; Kelts, K.R.; Marshall, N.F. Measurements of density underflows from Walensee, Switzerland. Sedimentology 1976, 23, 87–105.
  35. Piper, D.J.W.; Shor, A.N.; Hughes Clarke, J.E. The 1929 “Grand Banks” earthquake, slump, and turbidity current. In Sedimentologic Consequences of Convulsive Geologic Events; Geological Society of America: Boulder, CO, USA, 1988; pp. 77–92.
  36. Paull, C.K.; Talling, P.J.; Maier, K.L.; Parsons, D.; Xu, J.; Caress, D.W.; Gwiazda, R.; Lundsten, E.M.; Anderson, K.; Barry, J.P. Powerful turbidity currents driven by dense basal layers. Nat. Commun. 2018, 9, 4114.
  37. Ren, Y.; Zhou, H.; Wang, H.; Wu, X.; Xu, G.; Meng, Q. Study on the critical sediment concentration determining the optimal transport capability of submarine sediment flows with different particle size composition. Mar. Geol. 2023, 464, 107142.
  38. Bagnold, R.A. Auto-suspension of transported sediment; turbidity currents. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 1962, 265, 315–319.
  39. Parker, G. Conditions for the ignition of catastrophically erosive turbidity currents. Mar. Geol. 2003, 46, 307–327.
  40. Pantin, H.M. Interaction between velocity and effective density in turbidity flow: Phase-plane analysis, with criteria for autosuspension. Mar. Geol. 1979, 31, 59–99.
  41. Heerema, C.J.; Talling, P.J.; Cartigny, M.J.; Paull, C.K.; Bailey, L.; Simmons, S.M.; Parsons, D.R.; Clare, M.A.; Gwiazda, R.; Lundsten, E.; et al. What determines the downstream evolution of turbidity currents? Earth Planet. Sci. Lett. 2020, 532, 116023.
  42. Talling, P.J.; Cartigny, M.J.B.; Pope, E.; Baker, M.; Clare, M.A.; Heijnen, M.; Hage, S.; Parsons, D.R.; Simmons, S.M.; Paull, C.K.; et al. Detailed monitoring reveals the nature of submarine turbidity currents. Nat. Rev. Earth Environ. 2023, 4, 642–658.
  43. Heimsund, S. Numerical Simulation of Turbidity Currents: A New Perspective for Small-and Large-Scale Sedimentological Experiments; Sedimentology/Petroleum Geology; University of Bergen: Bergen, Norway, 2007.
  44. Zhou, J.; Cenedese, C.; Williams, T.; Ball, M.; Venayagamoorthy, S.K.; Nokes, R.I. On the Propagation of Gravity Currents Over and through a Submerged Array of Circular Cylinders. J. Fluid Mech. 2017, 831, 394–417.
  45. Saha, S.; De, S.; Changdar, S. An Application of Machine Learning Algorithms on the Prediction of the Damage Level of Rubble-Mound Breakwaters. J. Offshore Mech. Arct. Eng. 2024, 146, 011202.
  46. Russell, J.S. Report on Waves: Made to the Meetings of the British Association; Richard and John E Taylor: London, UK, 1845.
  47. Airy, G.B. Tides and Waves; B. Fellowes: London, UK, 1845.
Nozzle Scour

Study on the Sand-Scouring Characteristics of Pulsed Submerged Jets Based on Experiments and Numerical Methods

실험과 수치 해석을 기반으로 한 펄스 잠수 제트의 모래 침식 특성 연구

Hongliang Wang, Xuanwen Jia,Chuan Wang, Bo Hu, Weidong Cao, Shanshan Li, Hui Wang

Abstract

Water-jet-scouring technology finds extensive applications in various fields, including marine engineering. In this study, the pulse characteristics are introduced on the basis of jet-scouring research, and the sand-scouring characteristics of a pulsed jet under different Reynolds numbers and the impact distances are deeply investigated using Flow-3D v11.2. The primary emphasis is on the comprehensive analysis of the unsteady flow structure within the scouring process, the impulse characteristics, and the geometric properties of the resulting scouring pit. The results show that both the radius and depth of the scour pit show a good linear correlation with the jet-flow rate. The concentration of suspended sediment showed an increasing and then decreasing trend with impinging distance. The study not only helps to enrich the traditional theory of jet scouring, but also provides useful guidance for engineering applications, which have certain theoretical and practical significance.

Keywords

pulsed jet; turbulent structure; scouring characteristics

1. Introduction

Water-jet-scouring technology is widely used in marine engineering and its related ancillary fields, such as in the maintenance and repair of marine structures, extraction of deep-sea resources, dredging works, seabed geological research, and cleaning and maintenance of ships. The jet flow establishes a velocity shear layer at its boundary, leading to the destabilization and subsequent generation of vortices. These vortices undergo continuous deformation, rupture, merging, and evolution into turbulence during their movement. Consequently, they entrain surrounding fluid into the jet region, facilitating the transfer of momentum, heat, and mass between the jet and its ambient environment [1,2,3]. Therefore, numerous scholars have carried out detailed studies on the scouring characteristics associated with jets. Chatterjee et al. [4] investigated the local scouring and sediment-transport phenomena due to the formation of horizontal jets during the opening of sluice gates based on experiments, and successfully established empirical expressions for the correlation between the time of reaching the equilibrium stage, the maximum depth of scouring, and the peak of the dune. The important role of jet-diffusion properties in the scouring process was also emphasized. Hoffmans [5] calculated the equilibrium scour process induced using a horizontal jet in the absence of a streambed and used experiments to verify the accuracy of the equations for jet-scour depths in the relevant literature. Luo et al. [6] investigated the induction mechanism of scour in planar jets through particle-image velocimetry (PIV). It was found that the initial stage of scour was dominated by wall shear, while the later stages of the scour process were mainly influenced by the turbulent vortex. Canepa et al. [7] investigated the scour characteristics of gas-doped water jets and found that gas-doped jets significantly reduce the scour depth if the velocity of the mixture is used as a reference.
Pulsed jets introduce pulsation, resulting in a water-hammer effect, as well as increased diffusion and coil suction rates. These factors contribute to a more intricate interaction between the pulsed jet and the adjacent wall. The process of generation, development and evolution of its internal vortex structure as well as the interaction between the vortex structure and the surrounding ambient fluid and solid wall have changed significantly [8,9]. At this juncture, researchers in this domain have undertaken investigations centered on the utilization of pulsed jets. Coussement et al. [10] investigated the flow characteristics of a pulsed jet in a cross-flow environment based on Large Eddy Simulation (LES). A new approach to characterize mixing was introduced, which successfully explains and quantifies the complex mixing process between the pulsating jet and the ambient fluid. Bi et al. [11] investigated the thrust of a deformable body generated through a pulsed jet based on an axisymmetric immersed-boundary model. The numerical results show that in addition to the momentum flux of the jet, the jet acceleration is also an important source of thrust generation. Zhang et al. [12] studied the complex unsteady flow characteristics of a pulsed jet impinging on a rotating wall using numerical methods, and it was found that the impact pressure of the pulsed jet on the wall is greater than that of the continuous jet on the wall for a certain period of time when the water-hammer effect occurs. Rakhsha et al. [13] used experiments and numerical simulations to study the effect of pulsed jets on the flow and heat-transfer characteristics over a heated plane. It was found that the Nussell number increases with increasing pulse frequency and Reynolds number and decreases with increasing impinging distance. It is evident that existing studies predominantly center on the unsteady flow characteristics of pulsed jets and their properties related to heat and mass transfer. Conversely, there is a noticeable dearth of research concerning the scouring attributes of pulsed jets in the available literature.
The pulsed submerged impinging jet represents a complex jet flow with a significant engineering application background and substantial theoretical research value. Exploring the unsteady hydraulic characteristics of pulsed jets can enhance classical impinging jet theory, deepen our comprehension of the jet–wall interaction mechanism, and establish a scientific foundation for addressing engineering-application challenges. Therefore, this paper introduces the pulse characteristics into the impinging jet, and, based on the Flow-3D software, the sand-scouring characteristics of the impinging jet under different Reynolds numbers and impinging distances are deeply investigated. The surface geometry of the scour pit is characterized while obtaining the pulsation characteristics of the unsteady flow structure during sand scouring. This study not only offers a foundation for implementing flow control and enhancing the understanding of unsteady flow characteristics but also furnishes theoretical backing for predicting impact pressure and impact pit formation.

2. Modeling and Numerical Methods

2.1. Model Building

The geometric model consists of a jet pipe, a body of water, a baffle, and a sand bed, as shown in Figure 1. The inner diameter D of the jet pipe is 20 mm, and the length L is set to 50D to ensure that the turbulence inside the pipe is fully developed. H represents the impinging height, and the initial water height (Hw) is 1600 mm. Baffles positioned on both sides serve to maintain a constant water level. The length Ls and thickness Hs of the sand bed are 5000 mm and 160 mm, respectively. It is worth stating that the sand bed is composed of non-cohesive sand. The median grain size dm of the sand is 0.77 mm, the specific gravity Δ is 1.65, and the particle gradation σg is 1.21.

Figure 1. Geometric modeling for sand scouring.

2.2. Numerical Models

In fluid mechanics, the continuity and momentum equations are the basic governing equations [14]:

where u, v, w denote the velocity of the fluid in the x, y, z direction, respectively; Ax, Ay, Az denote the area fraction of the fluid in the x, y, z direction, respectively; VF denotes the volume fraction; P is the pressure exerted on the fluid micrometric elements; Gx, Gy, Gz are the gravitational acceleration in the x, y, z direction, respectively; and fx, fy, fz are the viscous forces in the x, y, z direction, respectively.

In numerical simulations, the selection of a turbulence model significantly influences the accuracy of the calculations. Hence, it is imperative to choose an appropriate turbulence model. Given that this paper primarily deals with fully developed circular tube turbulence, which entails velocity and momentum coupling among fluids and features substantial time and spatial scales in the non-constant flow, the RNG k–ε turbulence model [15,16,17] has been chosen for the conclusive numerical simulation work. The RNG model takes into account the effect of eddies on turbulence and improves the accuracy of vortex-flow prediction [18]. Its equations are as follows:

where vt is the eddy viscosity coefficient; μ is the kinetic viscosity coefficient; the empirical constants cε1 and cε2 have values of 1.42 and 1.68; c3 = 0.012; η0 = 4.38; cμ = 0.085; and the values of Prandtl numbers αk and αε corresponding to the turbulent kinetic energy k and the dissipation rate ε are both 0.7194.

The Flow-3D software realizes an accurate description of the sediment movement with the help of an empirical equation model proposed by Mastbergen and Van den Berg [19]. The critical Shields number first needs to be calculated from the Soulsby–Whitehouse equation [20], which is given below:

where ρi is the sediment density, ρf is the fluid density, di is the sediment diameter, μf is the hydrodynamic viscosity, and ‖g‖ is the magnitude of gravitational acceleration.

Under the action of the jet, part of the deposited sediment will be disturbed to show a suspended state and it will continue to move under the carrying of the fluid. The uplifting velocities of entrained sediment ulift,i and usetting,i are calculated as follows:

where αi is the sediment carryover coefficient with a recommended value of 0.018 [19]; ns is the normal direction of the bed; and vf is the kinematic viscosity of the liquid.

2.3. Grid-Independent Analysis

It is well known that the number of the grid is closely related to the accuracy and cost of the numerical calculation. In order to investigate the optimal number of grids suitable for this numerical simulation, the scour depth Ht of the sand bed at H/D = 2 and inlet flow velocity Vb = 1.485 m/s is chosen as the monitoring parameter for the grid-independent analysis. Five sets of grid schemes with increasing numbers are set, and the results of the independence analysis are shown in Figure 2. From the figure, it can be seen that the depth of the scour pit Ht increases gradually with the encryption of the grid. When the grid is encrypted to Scheme 4, Ht almost no longer increases. It is considered that the number of meshes at this time can already meet the accuracy requirements of numerical calculations. Therefore, the grid number scheme in Scheme 4 is selected for the subsequent numerical simulation study, and the grid number is 43,825.

Figure 2. Grid-independent analysis.

2.4. Grid Delineation and Boundary Conditions

Within the Flow-3D software, a grid block is used that covers the entire 2D computational area as shown in Figure 1. Given the large aspect ratio of the jet pipe and the significant turbulent coupling between the fluid and sediment near the pipe outlet, grid refinement is implemented in the vicinity of the pipe outlet. The grid-encrypted area is mainly the area between the jet outlet and the sand bed, as shown in Figure 3. In addition, a mesh node is provided at the baffle on each side of the computational domain to ensure proper identification of the fluid boundary during numerical simulations. The upper boundary of the computational domain is defined as a velocity inlet, where the velocity magnitude is denoted as Vb, and the direction is oriented vertically downward. The lower boundary is the wall and no fluid or sediment flux is allowed. The two side boundaries are specified as pressure boundaries and the pressure is set to be 0 Pa. Based on the requirement of 2D numerical simulation, the boundaries of the front and rear sides are set as symmetric boundaries, both with one grid node. At the same time, the boundary-layer mesh near the pipe and the sand bed is encrypted accordingly. y+ is set at around 30 to ensure that the first grid nodes are in the turbulence core region, so as to ensure that the RNG k–ε turbulence model is perfectly adapted to the boundary conditions. Considering that the velocity strength and pressure gradient of the fluid around the baffle are small and it is not an observation area, the encryption of the boundary-layer grid is not performed for the time being.

Figure 3. Computational grid.

Numerical simulations are performed using the discrete control equations of the control volume method, with the diffusion term of the equations in the central difference format and the convection term in the second-order upwind format, and the equations are solved using a coupled algorithm. The standard wall equations are used, and the no-slip option in the wall shear boundary conditions is checked. In the non-stationary numerical simulation, the time step is set to 0.05 s. In order to ensure the accuracy of the numerical calculations, each time step is iterated 100 times, and the convergence accuracy is set to 10−5.

In this paper, the continuous jet is periodically truncated to form a blocking pulsed jet. The pulse period of its pulse velocity can be expressed as T = tj + t0 (tj and t0 are the jet time and truncation time, respectively, taking the value of 0.5 s), and the inlet flow rate of the jet pipe is Vb during the jet time period, while the inlet flow rate of the jet pipe is 0 during the truncation time period, as shown in Figure 4.

Figure 4. Velocity characteristics of the blocking pulsed jet.

3. Experimental Validation

To validate the accuracy of the numerical simulations, an experimental investigation of jet impingement on sediment is conducted. The experimental setup is shown in Figure 5. The parameters characterizing the sediment in the experiments are guaranteed to be the same as the settings in the numerical simulations. Specifically, non-cohesive sand is used with a median particle size dm of 0.77 mm, a specific gravity Δ of 1.65, and a particle gradation σg of 1.21. An angle plate is employed to control the impinging angle of the jet pipe, a COMS camera captures images of the pit, and a laser range finder is utilized for precise measurements of pit depth and dune height. In order to quantitatively describe the effect of jet impingement, the depth of the sand pit and the height of the dune are defined as d and h, respectively.

Figure 5. Schematic diagram of the experimental setup.

Figure 6 compares the stabilized morphology of the sand bed formed under the scouring of the jet for an impinging distance H/D of two in the numerical simulation and the experiment. The inlet flow velocities Vb of the jet pipe are 0.424 m/s, 0.955 m/s, and 1.485 m/s, respectively. As depicted in the figure, the ultimate scouring morphology of the sand bed, as obtained through numerical simulation, closely aligns with the experimental results. This alignment underscores the strong agreement between the numerical simulation and the experimental data. Nevertheless, it must be recognized that the final scour depths of the numerical simulations are all slightly smaller than the experimental values under the same conditions. The possible reason for this is the wall effect, i.e., the porosity of the actual sand bed is not homogeneous, with the upper sand layer being slightly more porous [21], whereas the porosity of the sand bed in the numerical simulation strictly follows the set value. Given that the accuracy of numerical calculations is subject to various influencing factors, and considering that the numerical solution inherently involves an approximation process, the numerical methods employed in this study can be deemed both accurate and dependable.

Figure 6. Comparison of sand-scouring experiment and numerical simulation: (a) Vb = 0.424 m/s; (b) Vb = 0.955 m/s; (c) Vb = 1.485 m/s.

4. Results and Discussion

There are many factors that affect the performance of jet scouring, such as the shape of the nozzle, the size of the nozzle, the inlet flow rate of the jet pipe, the impinging distance, and the sediment parameters. Changes in any one of these factors can have a large effect on the parameters that measure the scouring performance of the jet, such as the depth of the scouring pit |ymin|, the height of the dune ymax, the radius of the scouring pit R. In this paper, the effects of the inlet velocity Vb and impinging distance H/D on the scouring performance of the jet pipe are investigated. Seven working conditions with inlet velocity Vb of 0.424 m/s, 0.690 m/s, 0.955 m/s, 1.220 m/s, 1.485 m/s, 1.751 m/s and 2.016 m/s are calculated for different impinging distances H/D (H/D = 2, 4, 6 and 8). The corresponding Reynolds numbers Re are 8404, 13,657, 18,910, 24,162, 29,415, 34,667, and 39,920, respectively.

4.1. Characterization of Pit at Different Impinging Distances

After the jet impinges on the sand bed for a sustained period of time, the shape of the sand bed will no longer change and remain stable. Figure 7 shows the stable bed morphology formed by the jet impinging on the sand bed with different velocities Vb, and at different impinging distances H/D. The x-axis is at the axial position of the jet pipe, and the y-axis is the initial horizontal plane of the sand bed. As can be seen from the figure, under the condition of Vb = 0.424 m/s, the pit depths |ymin| corresponding to impinging distances H/D of two and four are basically equal. However, when H/D is increased to six, |ymin| becomes significantly smaller, and when H/D is eight, |ymin| increases again. Under the Vb = 0.690 m/s condition, the effect of H/D on the scour pit depth |ymin| is small, and its size basically stays around 3.5 cm. Under the Vb = 0.955 m/s condition, the pit depth corresponding to H/D = eight is slightly smaller than the pit depths at other impinging distances, and the magnitude of |ymin| is basically maintained near 4.6 cm. Under the Vb = 1.220 m/s condition, the change of the scouring pit depth |ymin| with the impinging distance H/D starts to be gradually significant, especially the scouring pit depth |ymin| which decreases by about 1.7 cm when the size of H/D increases from two to six. Under the condition of Vb = 1.220 m/s, the larger the H/D, the smaller the pit depth |ymin|, especially when the H/D is eight, the pit depth is obviously larger than the pit depth at other impinging distances. The corresponding pit depths |ymin| for Vb of 1.751 m/s and 2.016 m/s remain basically unchanged. From the above analysis, it can be seen that under the same Reynolds number conditions to some extent the impinging distance has a very limited effect on the depth of the pit |ymin|. When the impinging distance increases, the depth of the pit begins to decrease. This can be attributed to the fact that the increased distance results in the jet encountering the initial static water resistance over a longer duration, leading to a greater dissipation of kinetic energy and a subsequent reduction in the impinging force of the jet.

Figure 7. Pit characteristics at different impinging distances: (a) Vb = 0.424 m/s; (b) Vb = 0.690 m/s; (c) Vb = 0.955 m/s; (d) Vb = 1.220 m/s; (e) Vb = 1.485 m/s; (f) Vb = 1.751 m/s; (g) Vb = 2.016 m/s.

The depth of the scouring pit serves as a critical parameter for assessing the impact of jet impingement on sand beds, just as the height of the dune represents a key indicator for evaluating the effectiveness of this process. In Figure 7a, it can be seen that the dune height ymax increases synchronously with the increase of the impinging distance H/D at Vb = 0.424 m/s. When Vb ≥ 0.955 m/s, the dune height ymax no longer grows significantly with the increase of impinging distance H/D. To further explore the relationship between dune height and impinging distance, Figure 8 is plotted with the impinging distance as the horizontal coordinate and the dune heights on either side as the vertical coordinate. From the figure, it can be seen that when 0.424 m/s ≤ Vb ≤ 1.485 m/s, the dune height ymax increases with the increase of the impinging distance H/D, and the dune height ymax starts to decrease with the increase of the impinging distance H/D when Vb > 1.485 m/s. The reason behind the aforementioned phenomenon is that when the inlet velocity Vb of the jet pipe is low, suspended sediment tends to displace towards the sides of the dune, causing some of the sediment to accumulate on the dune and thereby increase its height. When Vb ≥ 1.485 m/s, due to the enhanced impact force, most of the suspended sediment no longer moves and accumulates near the dunes and sand pits, and it starts to move on the outside of the dunes, causing the dune height to decrease.

Figure 8. Variation in the height of dunes on either side of the scour pit with Vb: (a) left; (b) right.

In order to clarify the relationship between the pit radius R and the impinging distance H/D, the relationship is given in Figure 9. From the figure, it can be seen that when 0.424 ≤ Vb ≤ 0.690, the increase of impinging distance H/D has basically no effect on the radius R of the pit, and its magnitude always stays near 13 cm. As the inlet velocity Vb of the jet pipe increases (1.220 ≤ Vb ≤ 1.485), the impact of the pulsed jet intensifies. Consequently, the suspended sediment is propelled towards the sides of the sand pit; although, it has not reached the dune and the area beyond it. Instead, a substantial amount of suspended sediment settles within the sand pit on both sides. Simultaneously, as the impact distance increases, the reach of jet impact and the turbulence induced by the jet expand, leading to enhanced sediment transport on both sides of the sand pit. This ultimately results in a reduction in the radius of the scouring pit as the impinging distance increases.

Figure 9. Relationship between pit size and impinging distance.

4.2. Characterization of Piting at Different Reynolds Numbers

Figure 10 depicts the stabilized morphology of the sand pit resulting from the influence of jets with varying Reynolds numbers. Under the conditions of H/D = two and four, the inlet velocity Vb of the jet pipe is 0.424 m/s and 0.690 m/s, and the depth of the pit |ymin| is basically equal, which indicates that the impact of the jet on the sand bed at this time is small, and the sediment is only transported and circulated in the sand pit. When Vb ≥ 0.955, the depth of the pit |ymin| increases significantly with the increase of Vb. Under the condition of H/D = 6, the depth of the pit, denoted as |ymin|, ceases to remain constant when Vb is less than or equal to 0.690 m/s. However, the disparity between the two measurements remains relatively small, suggesting that the impact force and turbulence of the jet are already capable of transporting sediment from the bottom of the pit to its flanks when Vb ≤ 0.690 m/s. In the H/D = 8 condition, due to the impinging distance H/D is larger, and when the velocity of the jet pipe is small (Vb ≤ 0.690 m/s), the kinetic energy of the jet is continuously exchanged with the static water body and then reduced, making its impact force reduce, and the sediment can only be transported and circulated at the bottom of the sand pit. To further investigate the effect of the Reynolds number of the jet on the depth of the pit |ymin|, Figure 11 is plotted with the jet velocity Vb as the horizontal coordinate and the depth of the pit |ymin| as the vertical coordinate. From the figure, it is evident that there exists a strong linear relationship between the depth of the scouring pit and the jet velocity. The data points in the figure can be fitted to establish the following relationship between the depth of the scouring pit and the jet velocity:

Figure 10. Pit characteristics at different Reynolds numbers: (a) H/D = 2; (b) H/D = 4; (c) H/D = 6; (d) H/D = 8.
Figure 11. Linear relationship between scouring-pit depth and jet velocity.

4.3. Characterization of Pits with Different Impinging Times

Figure 12 illustrates the deformation of the sand bed caused by the impact of the pulsed jet over a time range from 0.75 s to 3.5 s (with intervals of 0.25 s). When the jet velocity Vb is 0.424 m/s, within the initial 0.75 s of jet initiation, the impact of the pulsed jet leads to noticeable deformation of the sand pit and dune, with their fundamental shapes taking form. The depth of the pit, denoted as |ymin|, continuously increases from 0.75 s to 2 s, eventually stabilizing around 2.75 s. By the onset of the pulsed jet, the dune has already assumed a fundamental profile, and its maximum height, represented as ymax, exhibits minimal variation over time, remaining relatively constant.

Figure 12. Changes in time scales of pits: (a) Vb = 0.424 m/s; (b) Vb = 0.690 m/s; (c) Vb = 0.955 m/s; (d) Vb = 1.220 m/s; (e) Vb = 1.485 m/s; (f) Vb = 1.751 m/s; (g) Vb = 2.016 m/s.

5. Conclusions

In this paper, a numerical computational study is conducted to examine the characteristics of sand-bed impingement using obstructing pulsed jets. A comprehensive analysis is undertaken, encompassing impingement-pit depth, dune height, and impingement-pit radius. The following conclusions are drawn:

  1. Under consistent jet-velocity conditions, the impingement distance (H/D) has minimal impact on the depth of the scouring pit within the range of 2 ≤ H/D ≤ 6. However, beyond this range (H/D > 6), increased impingement distance leads to heightened jet-energy dissipation, resulting in a weakened impact force and a subsequent reduction in pit depth. Additionally, for lower jet velocities, impinging-distance variations have negligible effects on pit radius, while higher jet velocities induce a decrease in pit radius with an increase in impinging distance.
  2. The study establishes strong linear relationships between both the radius and depth of the scouring pit and the jet velocity. However, the relationship between dune height and pulsed-jet velocity is characterized by randomness and uncertainty. The dynamics of sediment transport contribute to the lack of symmetry in the stable configuration of the sand pit concerning the jet-pipe axis. Furthermore, the relationship between dune height and pulsed-jet velocity exhibits transient characteristics, highlighting the complex nature of these interactions.
  3. The numerical computational analysis emphasizes the transient characteristics of the sand-pit configuration due to sediment-transport dynamics. The stable state of the pit does not assume symmetry with the jet pipe as the axis, introducing a level of asymmetry in the system. This asymmetry is crucial in understanding the complex behavior of the sand-bed impingement. The findings underscore the need to consider dynamic and transient factors when studying the impact of obstructing pulsed jets on sand-bed characteristics.

References

  1. Wang, C.; Wang, X.; Shi, W.; Lu, W.; Tan, S.K.; Zhou, L. Experimental investigation on impingement of a submerged circular water jet at varying impinging angles and Reynolds numbers. Exp. Therm. Fluid Sci. 2017, 89, 189–198.
  2. Hu, B.; Yao, Y.; Wang, M.; Wang, C.; Liu, Y. Flow and Performance of the Disk Cavity of a Marine Gas Turbine at Varying Nozzle Pressure and Low Rotation Speeds: A Numerical Investigation. Machines 2023, 11, 68.
  3. Yu, H.; Wang, C.; Li, G.; Wang, H.; Yang, Y.; Wu, S.; Cao, W.; Li, S. Steady and Unsteady Flow Characteristics inside Short Jet Self-Priming Pump. Sustainability 2023, 15, 13643.
  4. Chatterjee, S.S.; Ghosh, S.N.; Chatterjee, M. Local scour due to submerged horizontal jet. J. Hydraul. Eng. 1994, 120, 973–992.
  5. Hoffmans, G.J. Jet scour in equilibrium phase. J. Hydraul. Eng. 1998, 124, 430–437.
  6. Luo, A.; Cheng, N.-S.; Lu, Y.; Wei, M. Characteristics of Initial Development of Plane Jet Scour. J. Hydraul. Eng. 2023, 149, 06023004.
  7. Canepa, S.; Hager, W.H. Effect of jet air content on plunge pool scour. J. Hydraul. Eng. 2003, 129, 358–365.
  8. Krueger, P.S. Vortex ring velocity and minimum separation in an infinite train of vortex rings generated by a fully pulsed jet. Theor. Comput. Fluid Dyn. 2010, 24, 291–297.
  9. Zhou, Z.; Ge, Z.; Lu, Y.; Zhang, X. Experimental study on characteristics of self-excited oscillation pulsed water jet. J. Vibroeng. 2017, 19, 1345–1357.
  10. Coussement, A.; Gicquel, O.; Degrez, G. Large eddy simulation of a pulsed jet in cross-flow. J. Fluid Mech. 2012, 695, 1–34.
  11. Bi, X.; Zhu, Q. Pulsed-jet propulsion via shape deformation of an axisymmetric swimmer. Phys. Fluids 2020, 32, 081902.
  12. Zhang, L.; Wang, C.; Zhang, Y.; Xiang, W.; He, Z.; Shi, W. Numerical study of coupled flow in blocking pulsed jet impinging on a rotating wall. J. Braz. Soc. Mech. Sci. Eng. 2021, 43, 508.
  13. Rakhsha, S.; Zargarabadi, M.R.; Saedodin, S. Experimental and numerical study of flow and heat transfer from a pulsed jet impinging on a pinned surface. Exp. Heat Transf. 2021, 34, 376–391.
  14. Idowu, I.A.; Adewuyi, J.B. Relationship between continuity and momentum equation in two dimensional flow. Afr. J. Math. Comput. Sci. Res. 2010, 3, 031–035.
  15. Kim, B.J.; Hwang, J.H.; Kim, B. FLOW-3D Model Development for the Analysis of the Flow Characteristics of Downstream Hydraulic Structures. Sustainability 2022, 14, 10493.
  16. Jalal, H.K.; Hassan, W.H. Three-Dimensional Numerical Simulation of Local Scour around Circular Bridge Pier Using Flow-3D Software. In Proceedings of the Fourth Scientific Conference for Engineering and Postgraduate Research, Baghdad, Iraq, 16–17 December 2019; IOP Publishing: Bristol, UK, 2020; Volume 745, p. 012150.
  17. Nazari-Sharabian, M.; Nazari-Sharabian, A.; Karakouzian, M.; Karami, M. Sacrificial piles as scour countermeasures in river bridges a numerical study using flow-3D. Civ. Eng. J. 2020, 6, 1091–1103.
  18. Abraham, J.; Magi, V. Computations of transient jets: RNG ke model versus standard ke model. SAE Trans. 1997, 106, 1442–1452.
  19. Mastbergen, D.R.; Van Den Berg, J.H. Breaching in fine sands and the generation of sustained turbidity currents in submarine canyons. Sedimentology 2003, 50, 625–637.
  20. Soulsby, R. Dynamics of Marine Sands; Thomas Telford Ltd.: London, UK, 1997; ISBN 9780727725844.
  21. Atkins, J.E.; Mcbride, E.F. Porosity and packing of holocene river, dune, and beach sands (1). AAPG Bull. 1992, 76, 339–355.
See Text

EVGA 지포스 RTX 2060 KO 같은 현대적인 그래픽카드는 여러 디스플레이를 동시에 연결할 수 있다. ⓒ BRAD CHACOS/IDG

FLOW-3D POST용 그래픽 카드, 모니터 선택 가이드

High End Graphic Card 안내

원본 출처: https://www.videocardbenchmark.net/high_end_gpus.html

Update: 2024-11-28

PCI-Express(또는 PCI-E) 표준을 사용하는 최근 출시된 AMD 비디오 카드(예: AMD RX 6950 XT)와 nVidia 그래픽 카드(예: nVidia GeForce RTX 3090)는 하이엔드 비디오 카드 차트에서 흔히 볼 수 있습니다.

PassMark - G3D Mark High End Videocards
PassMark - G3D Mark High End Videocards / Price
PassMark – G3D Mark High End Videocards / Price

FLOW-3D POST 성능과 밀접한 그래픽카드의 이해

FLOW Science, inc의 최첨단 POST Processor인 FLOW-3D POST를 최대한 활용하려면 좋은 하드웨어가 있어야 합니다. 이 블로그에서 소프트웨어 엔지니어링의 GUI 개발자/관리자인 Stephen Sanchez는 이러한 하드웨어 권장 사항에 따라 최적의 FLOW-3D POST 경험을 얻을 수 있는 방법에 대해 정보를 제공 합니다.

고품질 그래픽 하드웨어

최소 3GB의 VRAM 이 있는 그래픽 카드로 시작하는 것이 좋습니다 . 이것은 많은 볼륨 렌더링을 수행할 경우 특히 중요합니다. 볼륨 렌더링은 FLOW-3D POST 의 고급 기능으로 iso-surface가 아닌 유체 도메인 전체에서 변수의 세부 사항을 시각화합니다. 이 기능은 매우 통찰력 있지만 후 처리 중에 효과적으로 사용하려면 좋은 하드웨어가 필요합니다.

다음으로 Intel 통합 그래픽을 기본 그래픽 하드웨어로 사용해서는 안됩니다. 인텔 통합 그래픽은 전용 그래픽 하드웨어가 있는 랩톱에서도 대부분의 랩톱에서 일반적입니다(자세한 내용은 아래 참조). 

대부분의 FLOW-3D POST 기능은 이 구성에서 작동하지 않으므로 Intel 통합 그래픽을 지원하지 않습니다. 

FLOW-3D POST 는 NVIDIA 그래픽 카드 와 함께 사용할 때 가장 잘 수행됩니다. FLOW-3D POST 가 잘 작동하는 것으로 확인되었으므로 Maxwell 아키텍처 제품군 이상의 NVIDIA 그래픽 하드웨어를 적극 권장 합니다. 

NVIDIA Quadro 카드는 가장 안정적인 것으로 입증되었습니다. 고급 AMD 카드도 작동해야 하지만 NVIDIA 하드웨어 및 드라이버만큼 안정적이지 않다는 사실을 발견 했으므로 항상 AMD보다 NVIDIA를 권장합니다.

Nvidia 그래픽 카드

노트북의 듀얼 그래픽 카드 – 간단하지만 숨겨진 솔루션

이제 많은 노트북에 NVIDIA 그래픽 카드와 Intel 통합 그래픽 간에 전환 할 수 있는 기능이 있습니다. NVIDIA 카드로 FLOW-3D POST 가 실행되고 있는지 확인하는 것이 중요합니다 . NVIDIA 제어판을 통해 NVIDIA 카드로 노트북을 강제로 실행할 수 있습니다.

그래픽 카드를 Nvidia로 전환

비디오 드라이버 업데이트

비디오 드라이버가 업데이트 되었는지 확인하는 것이 좋습니다. FLOW-3D POST 에서 비디오 드라이버를 업데이트하여 쉽게 해결할 수 있는 아티팩트 및 디스플레이 문제에 대한 보고가 있었습니다 . 비디오 드라이버를 최신 상태로 유지하는 것은 이러한 문제를 방지하는 좋은 방법입니다.

RAM, RAM, RAM!

메모리가 충분하지 않으면 시뮬레이션 후 처리가 불가능할뿐만 아니라 메모리 요구 사항을 인식하는 것이 중요합니다. 최대 10 배의 성능 저하로 이어질 수 있습니다! FLOW-3D POST 에 필요한 RAM 양은 여러 요소, 특히 시뮬레이션 크기에 따라 다릅니다. 사용자에게 최대한의 유연성을 제공하기 위해 메시의 셀 수에 따라 다음과 같은 RAM 권장 사항이 있습니다.

  • 초대형 (2 억 개 이상의 셀) : 최소 128GB
  • 대용량 (6 천 ~ 1 억 5 천만 셀) : 64-128GB
  • 중간 (3 천만 ~ 6 천만 셀) : 32-64GB
  • 소형 (3,000 만 셀 이하) : 최소 32GB

FLOW-3D POST 는 메모리 집약적 일 수 있습니다. 실행할 시뮬레이션 크기에 대한 대략적인 아이디어가 있는 경우, 이 지침을 가능한 한 잘 따르는 것이 좋습니다. 즉, 유연성을 극대화하고 가장 원활한 FLOW-3D POST 경험을 보장하기 위해 문제 크기에 관계없이 가능한 한 많은 RAM을 확보하는 것이 좋습니다.

그래픽 카드를 업그레이드 교체 설치하는 방법

그래픽 카드를 업그레이드하는 것은 성능 향상을 위한 좋은 방법이다. 그래픽 카드 업그레이드를 통해 시각적으로 고사양을 요구하는 POST 작업을 쉽게 소화할 수 있는 컴퓨터로 진화할 수 있다. 

업그레이드를 위한 그래픽 카드 구매시 고려 사항, 기존 PC에 적합한가? 

원하는 그래픽 카드를 결정하는 것은 복잡하고 미묘한 문제다. AMD와 엔비디아는 200달러 미만에서부터 최대 1,500달러에 이르는 지포스(GeForce) RTX 3090에 이르기까지 거의 모든 예산에 대한 선택지를 제공하기 때문이다.

카드의 소음, 발열, 전력 소비 등과 같은 사항을 고려할 수 있겠지만, 일반적으로는 비용 대비 가장 큰 효과를 제공하는 그래픽 카드를 원한다.

컴퓨터가 새 그래픽 카드를 지원하는 적절한 하드웨어인지 확인한다. 

사용자가 겪는 가장 일반적인 문제는 부적절한 파워 서플라이(power supply)다. 충분한 전력을 공급할 수 없거나 사용 가능한 PCI-E 전원 커넥터가 충분하지 않을 수 있다. 필자의 경험상 파워 서플라이는 적어도 제조업체에서 권장하는 파워 서플라이의 요구 사항을 충족해야 한다. 예를 들어, 350W를 소비하는 지포스 GTX 3090을 구입했다면 8핀 전원 커넥터 한 쌍과 함께 엔비디아에서 제안한 최소 750W의 전력 공급 장치를 갖춰야 한다. 

현재 파워 서플라이가 얼마나 많은 전력을 제공하는지 알아보려면 PC 본체를 열고 모든 파워 서플라이에 기본 정보가 나열된 표준 식별 스티커를 확인하면 된다. 또한 사용 가능한 6핀 및 8핀 PCI-E 커넥터의 수를 확인할 수 있다. 

ⓒ Thomas Ryan 파워서플라이
ⓒ Thomas Ryan 파워서플라이

마지막으로 본체 내부에 새 그래픽 카드를 넣을 충분한 공간이 있는지 확인한다. 일부 고급 그래픽 카드는 길이가 상당히 길어 30Cm 이상일 수 있으며, 확장 슬롯이 2개 또는 3개가 될 수 있다. 해당 그래픽 카드의 실제 크기는 제조업체 웹사이트에서 찾을 수 있다. 

여기까지 해결했다면 이제 본격적으로 설치 작업에 착수한다. 


생각보다 간단한 그래픽 카드 설치 작업

그래픽 카드 설치에는 새 그래픽 카드, 컴퓨터, 그리고 십자 드라이버 3가지만 있으면 된다. 설치하기 전 PC를 끄고 전원 플러그를 뽑는다. 

기존 GPU를 제거해야 하는 경우가 아니면, 먼저 프로세서의 방열판에 가장 가까운 긴 PCI-E x16 슬롯을 찾아야 한다. 이 슬롯은 메인보드의 첫 번째 또는 두 번째 확장 슬롯이다. 

이 슬롯에 접근을 차단하는 느슨한 전선이 없는지 확인한다. 기존 그래픽 카드를 교체하는 경우, 연결된 케이블을 모두 분리하고, PC 본체 후면 내부에 고정 브래킷에서 나사를 제거한 다음, 카드를 제거한다. 대부분의 메인보드에는 그래픽 카드를 제자리에 고정하는 PCI-E 슬롯 끝에 작은 플라스틱 걸쇠(latch)가 있다. 이 걸쇠를 눌러 이전 그래픽 카드의 잠금을 해제하고 분리한다.

ⓒ Thomas Ryan PCI-E x16 슬롯에 설치
ⓒ Thomas Ryan PCI-E x16 슬롯에 설치

이제 새 그래픽 카드를 개방형 PCI-E x16 슬롯에 설치할 수 있다. 카드를 슬롯에 완전히 삽입한 다음, PCI-E 슬롯 끝에 있는 플라스틱 걸쇠를 눌러 제자리에 고정한다. 그런 다음 나사를 사용해 그래픽 카드의 금속 고정 브래킷을 PC 본체에 고정한다. 덮개 브래킷 또는 이전 그래픽 카드를 고정했던 나사를 재사용할 수 있다. 

ⓒ Thomas Ryan 그래픽 카드에는 추가 전원 커넥터 연결
ⓒ Thomas Ryan 그래픽 카드에는 추가 전원 커넥터 연결

대부분의 게임용 그래픽 카드에는 추가 전원 커넥터가 필요하다. 추가 전원이 필요한 경우, 해당 PCI-E 전원 케이블을 연결했는지 확인한다. 전원이 제대로 공급되지 않으면 그래픽 카드가 제대로 작동하지 않는다. 이 PCI-E 전원 케이블을 연결하지 않으면 PC 자체가 부팅되지 않을 수 있다.  

그래픽 카드를 고정하고 난 후, 전원을 켠 상태에서 본체 측면 패널을 제자리로 밀어넣고 디스플레이 케이블을 새 그래픽 카드에 연결해 작업을 완료한다. 이제 컴퓨터를 켠다. 

이제 그래픽 카드의 소프트웨어를 업그레이드할 단계가 왔다. 

새 그래픽 카드가 이전 카드와 동일한 브랜드일 경우에는 절차가 간단하다. 제조업체의 웹사이트로 이동해 운영체제에 맞는 최신 드라이버 패키지를 다운로드한다. 그래픽 드라이버는 일반적으로 약 500MB로, 상당히 크다. 인터넷 연결 속도에 따라 다운로드하는 데 시간이 걸릴 수도 있다. 드라이버를 설치하고 컴퓨터를 다시 시작하면 이제 새 그래픽 카드가 제공하는 부드럽고 매끄러운 프레임 속도를 즐길 수 있다.
  
그래픽 카드 제조업체가 바뀐 경우(인털에서 AMD로, 혹은 AMD에서 인텔로), 새 그래픽 카드용 드라이버를 설치하기 전에 이전 그래픽 드라이버를 제거하고 컴퓨터를 다시 시작해야 한다. 이전 드라이버를 제거하지 않으면 새 드라이버와 충돌할 수 있다. 

editor@itworld.co.kr 기사 일부 발췌 인용

그래픽 카드 GPU 온도 확인하는 방법

그래픽 카드 온도 확인은 아주 쉽다. 윈도우에서 바로 온도를 확인할 수 있는 내장 도구도 추가됐다. 또한, 무료 GPU 모니터링 도구가 많이 있고 그중 대다수가 온도를 측정해준다. 조금 더 자세히 알아보자.

ⓒ MARK HACHMAN / IDG 그래픽카드 온도 확인
ⓒ MARK HACHMAN / IDG 그래픽카드 온도 확인

마이크로소프트가 윈도우 10 2020년 5월 업데이트에서 GPU 온도 모니터링 툴을 작업 관리자에 추가했다. 무려 24년이나 걸렸다.

Ctrl+Shift+Esc를 열어 작업 관리자 대화창을 열거나 Ctrl+Alt+Delete에서 ‘작업 관리자’를 선택하거나 윈도우 시작 메뉴 아이콘을 오른쪽 클릭해서 ‘작업 관리자’를 선택한다. 여기에서 ‘성능’ 탭으로 들어가면 왼쪽에 GPU를 확인할 수 있을 것이다. 윈도우 10 2020년 5월 업데이트 혹은 그 이후 버전의 윈도우가 설치되어 있을 때만 사용할 수 있는 기능이다.

하지만 이 기능은 매우 단순하다. 시간 흐름에 따른 온도 변화를 추적하지 않고, 현재의 온도만을 보여준다. 그리고 업무를 하거나 오버클럭 조정 중에 작업 관리자를 여는 것도 귀찮을 수 있다. 마침내 윈도우에 GPU 온도를 확인할 수 있는 기능이 들어간 것은 환영하지만, 뒤이어 설명할 서드파티 도구가 훨씬 더 나은 GPU 온도 확인 옵션을 제공한다.

AMD 라데온 그래픽 카드 사용자가 라데온 세팅(Radeon Setting) 앱을 최신 버전으로 유지하고 있다면 방법은 쉽다. 2017년 AMD는 시각 설정을 변경할 수 있는 라데온 오버레이(Radeon Overlay)를 출시했다. 여기에도 GPU 온도와 다른 중요한 정보를 확인할 수 있는 성능 모니터 기능이 있다.

프로그램을 활성화하려면 Alt+R 키를 눌러 라데온 오버레이를 불러온다. 성능 모니터링 섹션에서 원하는 탭을 선택한다. Ctrl+Shift + 0을 눌러서 성능 모니터링 도구 설정을 단독으로 불러올 수 있다.

라데온 세팅 앱에서 오버클럭 도구인 와트맨(Wattman)으로 이동해 GPU 온도를 확인할 수 있다. 윈도우 바탕 화면을 우클릭하고, 라데온 설정을 선택한 후 게이밍(Gaming) > 글로벌 세팅(Global Setting) > 글로벌 와트맨(Global Wattman) 항목으로 이동한다. 도구를 사용해 지나친 오버클럭으로 그래픽 카드를 날려버리지 않겠다고 서약한 후에는 와트맨에 액세스하고 GPU 온도, 그리고 그래프 형태로 된 핵심적 통계 수치를 볼 수 있다. 여기까지가 전부다.

라데온 사용자가 아닌 사람도 많을 것이다. 스팀의 하드웨어 설문 조사는 전체 응답자 PC 중 75%가 엔비디아 지포스 그래픽 카드를 탑재했다는 결과를 발표했다. 그리고 지포스 익스피리언스 소프트웨어는 GPU 온도 확인 기능을 제공하지 않아서 서드파티 소프트웨어의 손을 빌려야 한다.

그래픽 카드 제조 업체는 보통 GPU 오버 클럭을 위한 특수한 소프트웨어를 제공한다. 이 도구에는 라데온 오버레이처럼 가장 중요한 측정을 실행할 때 OSD(On-Screen Display)를 지속하는 옵션 등이 있다. 여러 종류 중에서 가장 추천하는 것은 다재다능함을 갖춘 MSI의 애프터버너(Afterburner) 도구다. 이 제품은 오랫동안 인기를 얻었는데 엔비디아 지포스, AMD 라데온 그래픽 카드 두 제품 모두에서 잘 작동하고, 반길 만한 다른 기능도 더했다.

IDG HWInfo는 언제나 누구에게나 적합한 모니터링 프로그램
IDG HWInfo는 언제나 누구에게나 적합한 모니터링 프로그램

GPU 온도에 전혀 관심이 없다면? 그렇다면 시스템의 온도 센서를 보여주는 모니터링 소프트웨어를 설치하면 편리할 것이다. HWInfo는 언제나 누구에게나 적합한 모니터링 프로그램으로, PC의 모든 부품의 가상 스냅샷을 보여준다. 스피드팬(SpeedFan) 과 오픈 하드웨어 모니터(Open Hardware Monitor)도 신뢰할 만한 서드파티 앱이다.

‘착한’ GPU 온도는 몇 도?

이제 그래픽 카드를 모니터링하는 소프트웨어를 갖췄다. 하지만 화면을 채우는 숫자는 맥락이 없이는 아무것도 아니다. 그래픽 카드 온도는 어디까지 괜찮은 것일까?

쉬운 대답은 없다. 제품마다 다르다. 이럴 때는 구글이 친구가 된다. 대다수 칩은 섭씨 90도 중반에도 작동하고, 게이밍 노트북에서도 90도까지 온도가 올라가는 경우가 흔히 있다. 그러나 일반 데스크톱 PC 온도가 90도 이상으로 올라간다면 구조 신호나 다름없다. 공기 흐름이 원활한 GPU 1대 시스템에서는 80도 이상 올라가면 위험하다. 팬이 여러 개 달린 커스텀 그래픽 카드는 무거운 워크로드 하에서도 60~70도가 적당하고, 수냉쿨러가 달린 GPU라면 온도가 더 낮아야 할 것이다.

그래픽 카드가 최근 5년 안에 생산된 제품이고 90도 이상으로 뜨거워진다면, 또는 최근 몇 주간 온도가 급격히 상승했다면 다음의 냉각 방법을 고려해보자.


그래픽 카드 온도 낮추는 법

그래픽 카드 온도가 높아졌을 때 하드웨어 업그레이드에 돈을 들이지 않고 개선하지 않기란 어렵다. 그러나 돈을 쏟아붓기 전에 정말 그래야 하는지 필요성을 점검해 보자. 다시 한번 강조하지만 그래픽 카드는 뜨거운 온도를 버틸 수 있도록 설계되어 있다. PC가 무거운 게임이나 영상 편집 중에 강제 종료되는 경우가 아니라면 아마도 걱정할 필요가 없을 것이다.

우선, 시스템의 케이블을 깨끗하게 정리해 GPU 주변의 공기가 원활하게 순환되는지 확인하라. 케이블이 깔끔하게 정리됐다면 케이스에 팬을 추가하는 것도 고려한다. 모든 PC는 최적의 성능을 위해 공기를 빨아들이고 내보내는 팬이 여럿 달려 있는데, POST PC라면 팬은 더 많아야 한다. 저렴한 팬은 10달러부터 구입할 수 있고, RGB 조명이 붙은 화려한 제품은 조금 더 가격이 높다.

마지막으로, GPU와 히트싱크의 써멀 페이스트가 오래되어 말라 있다면 효율이 떨어질 수 있다. 특히 오래된 그래픽 카드라면 더더욱 그렇다. 그리고 아주 드문 경우지만 품질이 좋지 않은 써멀 페이스트가 발라져서 출시되는 경우도 있다. 다른 방법이 모두 효과가 없다면 써멀 페이스트를 다시 바르는 것을 시도해보자. 그러나 과정이 매우 어려울 수 있고 카드마다 조금씩 다르고, 잘못 손댈 경우 사용자 보증 기한의 보호를 받을 수 없게 된다. 

온도를 확실하게 낮추려면 수랭 쿨러를 위한 쿨링 시스템을 고려한다. 대다수 사용자에게는 지나친 모험이지만 대부분 수냉쿨러는 발열과 노이즈 감소 효과가 확실하고 공기 냉각에 있어 병목 현상도 없다.

“업무 효율 향상의 기본” 멀티 모니터 구축 가이드

듀얼 모니터를 사용하면 업무 생산성이 높아진다는 연구 결과가 있지만, 모니터가 많을수록 생산성이 높아지는지 여부에 대해서는 아직 이렇다 할 근거는 없다. 그러나 업무 생산성을 생각하지 않더라도 모니터를 여러 대(3대~6대까지) 사용하는 것은 멋진 일이며, 많은 화면을 봐야 하는 엔지니어는 정말 필요할지도 모른다.

모니터를 세로로 세워두면 긴 문서를 볼 때 스크롤을 적게 해도 된다는 장점이 있다. 멀티 디스플레이 환경을 구축하기 위해 고려해야 할 모든 것들을 살펴보겠다.

멀티 모니터 구축 가이드(www.itworld.co.kr)
멀티 모니터 구축 가이드(www.itworld.co.kr)

1단계 : 그래픽 카드 확인하기

보조 모니터를 구입하기 전에 컴퓨터가 물리적으로 이 모든 모니터들을 감당할 수 있을지 점검해 봐야 한다. 가장 쉬운 방법은 PC의 뒷면을 보고, 그래픽 포트(DVI, HDMI, 디스플레이포트, VGA 등)가 몇 개나 있는지 확인하는 것이다.

별도의 그래픽 카드가 없다면 포트를 2개밖에 발견하지 못할 것이다. 그래픽이 통합된 대부분의 마더보드는 모니터 2개 밖에 설치하지 못한다. 별도의 그래픽 카드가 있다면, 마더보드의 포트를 제외하고 최소 3개의 포트를 발견할 수 있을 것이다.

팁 : 마더보드와 별도 그래픽 카드의 포트를 모두 이용해서 멀티 모니터를 설치할 수도 있지만, 이 경우 성능 저하와 모니터끼리의 속도 차이가 발생할 것이다. 그래도 이렇게 하고 싶다면, PC의 BIOS에서 Configuration > Video > Integrated graphics 로 진입한 다음, ‘always enable’로 설정한다.

그러나 별도의 그래픽 카드에 3개 이상의 포트가 있다고 해서 이것을 모두 동시에 사용할 수 있다는 의미는 아니다. 예를 들어서 구형 엔비디아 카드는 포트가 2개 이상이어도 하나의 카드에 모니터를 2개 이상 연결할 수 없다. 자신의 그래픽 카드가 멀티 모니터를 지원하는지 판단하는 가장 좋은 방법은 그래픽 카드 모델명을 찾아서 원하는 모니터 개수와 함께 검색하는 것이다. 예를 들어, ‘엔비디아 GTX 1660 모니터 4대’라고 검색하면 된다.

EVGA 지포스 RTX 2060 KO 같은 현대적인 그래픽카드는 여러 디스플레이를 동시에 연결할 수 있다. ⓒ BRAD CHACOS/IDG
EVGA 지포스 RTX 2060 KO 같은 현대적인 그래픽카드는 여러 디스플레이를 동시에 연결할 수 있다. ⓒ BRAD CHACOS/IDG

그래픽 카드가 원하는 만큼 충분히 모니터를 지원할 수 있으면 좋지만, 그렇지 않다면 추가 그래픽 카드를 구입해야 한다. 그래픽 카드를 추가로 구입하기 전 타워 안에 충분한 공간(PCI 슬롯)이 있는지, 전원 공급은 충분한지 확인해야 한다.

멀티 모니터용으로만 그래픽 카드를 구입한다면 최신 그래픽 카드 중에서도 저렴한 옵션을 선택하는 것이 좋다. 

아니면 멀티 스트리밍이 지원되는 디스플레이포트를 탑재한 신형 모니터를 사용하는 방법도 있다. 그래픽 카드의 디스플레이포트 1.2에 연결하고, 디스플레이포트 케이블을 사용해 다음 모니터로 연결하는 것이다. 모니터의 크기나 해상도가 같지 않아도 된다. 뷰소닉(ViewSonic)의 VP2468이 이런 제품 중 하나다. 아마존에서 약 210달러에 판매되는 이 24인치 모니터는 디스플레이포트 아웃 외에도 프리미엄 IPS 스크린, 아주 얇은 베젤 등 멀티 모니터 설정에 이상적인 특징을 제공한다.

2단계 : 모니터 선택하기 

그래픽 카드에 대해서 파악했다면 이제 추가 모니터를 구입할 차례다. 사용자에 따라서 기존에 사용하고 있는 모니터, 책상 크기, 추가 모니터 용도 등에 따라서 완벽한 모니터가 달라질 것이다.

필자의 경우, 이미 24인치 모니터 2대를 가지고 있었기 때문에 중앙에 설치할 더 큰 모니터가 필요해서 27인치 모니터를 선택했다. 게임을 하지 않기 때문에 모니터 크기 차이는 상관없었다. 하지만 사용자에 따라서 멀티 모니터로 POST를 하거나 동영상을 보기 위해서는 이러한 구성보다 같은 모니터를 연결하는 것이 더 좋을 것이다.

모니터를 구입하기 전에 PC와 모니터의 포트 호환성을 설펴야 한다. DVI-HDMI 혹은 디스플레이포트-DVI 등 전환해주는 케이블을 이용할 수도 있지만 다소 귀찮다. 그러나 PC나 모니터에 VGA 포트가 있다면, 교체를 권한다. VGA는 아날로그 커넥터이기 때문에 선명도가 떨어진다.

3단계 : PC설정

모니터를 구입하고 나면 PC에 연결하고 PC의 전원을 켠다. 이것으로 모니터 설치가 끝났다. 하지만 완전히 끝난 것은 아니다.

윈도우가 멀티 모니터 환경에서 잘 동작하게 만들어야 하는데, 윈도우 7이나 윈도우 8 사용자라면 바탕화면에서 오른쪽 클릭하고 ‘화면 해상도’를 선택한다. 윈도우 10 사용자라면 ‘디스플레이 설정’을 클릭한다. 그러면 디스플레이를 정렬할 수 있는 창이 나타난다.

ⓒ ITWorld 디스플레이 설정
ⓒ ITWorld 디스플레이 설정

여기서 모니터들이 모두 탐지되는지 확인할 수 있다. ‘식별’을 클릭하면 각 디스플레이에 큰 숫자가 나타난다. 주 모니터(작업 표시줄과 시작 버튼이 나타나는 모니터)로 사용할 모니터에 1번이 나타나야 하는데, 원하는 것을 선택한 다음 아래 여러 디스플레이 설정에서 ‘이 디스플레이를 주 모니터로 만들기’를 클릭한다. 그 다음 ‘다중 디스플레이’ 드롭다운 메뉴에서 복제할 것인지 확장할 것인지를 선택하면 되는데, 대부분의 경우 ‘디스플레이 확장’이 적합하다.

GPU 제어판에서도 다중 모니터를 설정할 수 있다. 바탕화면에서 오른쪽 클릭을 하고 엔비디아, AMD, 인텔 등 그래픽 제조사의 제어판 메뉴를 열어 윈도우와 유사한 방식으로 디스플레이를 설정할 수 있다.

멀티 디스플레이를 구축할 경우에는 같은 모델을 이용하는 것이 해상도나 선명도, 색보정 등의 문제가 발생하지 않아 ‘끊김 없는’ 경험을 할 수 있다.

Intel CPU i9

FLOW-3D 수치해석용 컴퓨터 CPU에 대한 이해 및 선택 방법

구매전 주요 CPU 비교 내용 알아보기

우리는 해석용 컴퓨터를 구매하기 전에 수많은 선택지를 고민하게 됩니다. 성능과 가격, 컴퓨터 최신 CPU, Memory, Chipset, HDD/SSD, Power Supply 등, 그 중에서도 당연코 선택 고민은 CPU 입니다.

이는 수 많은 검토 요인중에 해석 속도와 매우 밀접한 관계를 가지고 있기 때문입니다. 하지만 우리가 직접 테스트를 해볼 수 없지만, 다행히 아래와 같이 전문적으로 테스트를 수행하여 그 결과를 알려주는 보고서를 참고할 수 있습니다.

<샘플 비교자료>

AMD Ryzen AI 9 HX 370 대 Intel i9-14900HX

아래 두 CPU 모두 작년에 출시(또는 첫 벤치마크)되었고, Intel Core i9-14900HX는 멀티스레드(CPU 마크) 테스트에서 약 22% 더 빠르고, 싱글스레드 테스트에서는 약 7% 더 빠릅니다. 그러나 AMD Ryzen AI 9 HX 370은 훨씬 적은 전력을 사용합니다. 이 비교에서 선택된 CPU는 데스크톱, 노트북과 같은 다른 CPU 클래스에 속합니다. 더 적절한 비교를 위해 유사한 CPU 클래스에서 CPU를 선택하는 것을 고려하세요. 아래 값은 PerformanceTest 소프트웨어와 결과에서 제출된 1202개의 벤치마크를 합친 결과이며, 새로운 제출을 포함하도록 매일 업데이트됩니다.

  • 첫 번째 섹션에서는 선택한 각 CPU에 대한 기본 정보가 표시됩니다.
  • 추가 그래프는 선택된 각 CPU의 CPU 마크 및 단일 스레드 값을 보여줍니다.
  • 가격 데이터가 있는 경우 그래프를 통해 달러당 CPU 마크/스레드 등급을 기준으로 비용 대비 가치를 확인할 수 있습니다.
  • 마지막 섹션에서는 CPU의 대략적인 연간 운영 비용을 보여줍니다.
Item×AMD Ryzen AI 9 HX 370×Intel Core i9-14900HX
PriceSearch Online Search Online 
Socket TypeFP8FCBGA1964
CPU ClassDesktop, LaptopLaptop
Clockspeed2.0 GHz2.2 GHz
Turbo SpeedUp to 5.1 GHzUp to 5.8 GHz
# of Physical Cores12 (Threads: 24)24 (Threads: 32)
CacheL1: 960KB, L2: 12.0MB, L3: 8MBL1: 2,176KB, L2: 32.0MB, L3: 36MB
TDP28W55W
Yearly Running Cost$5.11$10.04
Otherw/ Radeon 890MIntel UHD Graphics for 14th Gen Intel Processors
First Seen on ChartQ3 2024Q1 2024
# of Samples1441058
CPU Value0.067.2
Single Thread Rating(% diff. to max in group)4007(-6.8%)4301(0.0%)
CPU Mark(% diff. to max in group)35487(-22.3%)45647(0.0%)

1 – Last seen price from our affiliates NewEgg.com & Amazon.com.

AMD Ryzen AI 9 HX 37035,487
Intel Core i9-14900HX45,647
PassMark Software © 2008-2024
AMD Ryzen AI 9 HX 370NA
Intel Core i9-14900HX67.2
PassMark Software © 2008-2024
AMD Ryzen AI 9 HX 3704,007
Intel Core i9-14900HX4,301
PassMark Software © 2008-2024

Estimated Energy Usage Cost

Estimated Energy Adjustable Values
Average hours of use per dayAverage CPU Utilization (0-100%)1Power cost, $ per kWh2
825

1Average user usage is typically low and can vary from task to task. An estimate load 25% is nominal.
2Typical power costs vary around the world. Check your last power bill for details. Values of $0.15 to $0.45 per kWh are typical.

AMD Ryzen AI 9 HX 370Intel Core i9-14900HX
Max TDP28W55W
Power consumption per day (kWh)0.060.11
Running cost per day$0.014$0.028
Power consumption per year (kWh)20.440.1
Running cost per year$5.11$10.04

Shown CPU power usage is based on linear interpolation of Max TDP (i.e. max load). Actual CPU power profile may vary.

CPU 성능비교 방법

아래 사이트를 방문하여 구입을 원하는 CPU에 대한 성능을 비교해 볼 수 있습니다. 비교 방법은 아래 그림에서 처럼 “Add other CPU:” 검색창에 원하는 CPU 모델명을 입력한 후 “Compare” 버튼을 클릭하면 아래와 같이 여러개의 CPU 비교 내용을 볼 수 있습니다.

https://www.cpubenchmark.net/singleCompare.php

CPU 성능비교 방법

Item×AMD Ryzen 7 7435HS×Intel Core i7-13620H×Intel Core i5-1235U×Intel Core i9-14900HX
PriceSearch Online Search Online Search Online Search Online 
Socket TypeFP7r2FCBGA1744FCBGA1744FCBGA1964
CPU ClassDesktop, LaptopLaptopLaptop, Mobile/EmbeddedLaptop
Clockspeed3.1 GHz2.4 GHz1.3 GHz2.2 GHz
Turbo SpeedUp to 4.5 GHzUp to 4.9 GHzUp to 4.4 GHzUp to 5.8 GHz
# of Physical Cores8 (Threads: 16)10 (Threads: 16)10 (Threads: 12)24 (Threads: 32)
CacheL1: 512KB, L2: 4.0MB, L3: 16MBL1: 864KB, L2: 9.5MB, L3: 24MBL1: 928KB, L2: 6.5MB, L3: 12MBL1: 2,176KB, L2: 32.0MB, L3: 36MB
TDP45W45W15W55W
Yearly Running Cost$8.21$8.21$2.74$10.04
OtherIntel UHD Graphics for 13th Gen Intel ProcessorsIntel Iris Xe GraphicsIntel UHD Graphics for 14th Gen Intel Processors
First Seen on ChartQ2 2024Q1 2023Q1 2022Q1 2024
# of Samples87104123241058
CPU Value0.049.543.367.2
Single Thread Rating(% diff. to max in group)3228(-25.0%)3689(-14.2%)3218(-25.2%)4301(0.0%)
CPU Mark(% diff. to max in group)23985(-47.5%)24844(-45.6%)13388(-70.7%)45647(0.0%)

CPU에 대한 이해 및 선택 방법

last update : 2021-12-15

자료출처 : 본 기사는 PCWorld Australia의 내용과 www.itworld.co.kr의 기사를 기반으로 일부 가필하여 게재한 내용입니다.

해석용 컴퓨터를 선정하기 위해서는 가장 먼저 선택해야 하는 것이 있다. AMD인가, 인텔인가? 두 업체는 CPU 시장의 양대산맥과도 같다. 인텔이 새롭게 출시한 12세대 앨더 레이크 CPU 시리즈가 벤치마크 기록을 깼지만, 지난해 출시된 AMD의 라이젠 5000 아키텍처를 고수하거나, 다른 신제품을 기다릴만한 이유도 있다. 인텔과 AMD CPU를 자세히 살펴보자.

ⓒ Gordon Mah Ung


비교 대상 제품 

2021.11.09

PC 조립 부품을 예산 기준으로 결정하고, 반도체 수급난에서 CPU를 정가에 구매할 수 있다고 가정했을 때, 인텔과 AMD 제품 선택지를 몇 가지로 압축할 수 있다.

인텔성능/효율 코어쓰레드가격
Core i9 12900K/KF8/824590달러/570달러
Core i7 12700K/KF8/420410달러/390달러
Core i5 12600K/KF6/416290달러/270달러
AMD  성능 코어 쓰레드    가격   
Ryzen 9 5950X1632800달러
Ryzen 9 5900X1224550달러
Ryzen 7 5800X816450달러
Ryzen 5 5600X612300달러

비교적 저렴한 인텔 CPU인 F 시리즈는 통합 그래픽카드가 없어 별도의 GPU가 필요하다. 라이젠 프로세서는 외장 그래픽카드와 짝을 이루어야 한다. 인텔이 ‘한 방’을 노리고 있기 때문에 이 비교에서는 최상급인 16코어 라이젠 9 5950X도 함께 살펴볼 예정이다. 12900KF가 최대 8코어이기 때문에 라이젠 9 5950X와 직접적인 비교 대상은 아니지만, 인텔은 AMD와 꽤 대등하게 싸우고 있다. CPU에만 80만원을 지출할 계획이라면 더 큰 파워 서플라이가 필요하다.

인텔 코어 CPU 에 대한 이해

인텔 코어 CPU에 대한 자료를 찾아보면 쿼드(Quad) 코어, 하이퍼-스레딩(Hyper-Threading), 터보-부스팅(Turbo-Boosting), 캐시(Cache) 크기 같은 용어를 많이 볼 수 있다.
인텔 코어 i3, i5, i7, i9는 각각 어떻게 다를까?
칩셋에는 세대가 있는데, 세대의 의미와 차이는 무엇일까?
하이퍼-스레딩은 무엇이고 클럭 속도는 어느 정도가 적합할까?

새 프로세서를 구입하기 전에 먼저 현재 사용하고 있는 인텔 CPU를 이해해보자.
지금 내 PC 성능이 어느 정도인지 알기 위해서이다.
가장 빠른 방법은 제어판 > 시스템 및 보안 항목에서 시스템을 선택하는 것이다.

여기에서 현재 PC에 설치된 CPU, RAM, 운영체제 정보를 확인할 수 있다.
프로세서 아래에 현재 설치된 인텔 CPU가 무엇인지, 인텔 코어 i7-4790, 인텔 코어 i7-8500U 같은 모델명을 확인할 수 있을 것이다. 또 Ghz가 단위인 CPU 클럭 속도를 알 수 있다. 나중에 이와 관련해 더 자세히 설명을 하겠다.

일단 CPU부터 알아보자.
CPU 모델명에는 숫자가 많아 어려워 보이지만, 이 숫자가 무슨 의미인지 이해하는 것은 어려운 일이 아니다.

모델명의 앞 부분인 “인텔 코어”는 인텔이 만든 코어 시리즈 프로세스 중 하나라는 의미다. 코어는 인텔에서 가장 크고, 인기있는 제품군이다. 따라서 많은 인텔 제품 데스크톱과 노트북 컴퓨터에서 인텔 코어라는 표기를 발견할 수 있다.

참고 : 인텔은 셀룰론(Celeron), 펜티엄(Pentium), 제온(Xeon) 등 다양한 프로세스 제품군을 판매하고 있지만, 이 기사는 인텔 코어 프로세스에 초점을 맞춘다.

그 다음 “i7”은 CPU 내부 마이크로 아키텍처 디자인의 종류이다.
자동차가 클래스와 엔진 종류로 나눠지는 것과 비슷하다. 이들 ‘엔진’이 하는 일은 동일하다. 그러나 차량 브랜드에 따라 일을 하는 방법이 다르다.
인텔의 경우 코어 브랜드 CPU의 클래스인 i3, i5, i7이 각각 사양이 다르다. 여기서 사양이란 코어의 수, 클럭 속도, 캐시 크기, 터보 부스트 2.0과 하이퍼스레딩 같은 고급 기능 지원 여부를 말한다.
코어 i5와 i7 데스크톱 프로세서는 통상 쿼드 코어(코어가 4개)이고, 로우엔드(저가) 코어 i3 데스크톱 프로세스는 듀얼 코어(코어가 2개)다.

이제 SKU와 세대에 대해 알아보자. 앞서 예로 들은 “4790”으로 설명하겠다.
첫 번째 숫자인 “4”는 CPU의 세대이고, “790”는 일종의 일련번호, 또는 ID 번호이다. 즉 인텔 코어 i7이 4세대 CPU라는 이야기이다.

그런데 ‘접미사’가 붙는 경우가 있다. 위에서 예로 든 모델에는 접미사가 없지만 “Intel Core i7-8650U” 같이 끝에 접미사가 붙은 모델이 있다. 여기에서 “U”는 “Ultra Low Power(초저전력)”를 의미한다.
인텔은 모델명에 다양한 접미사를 사용하는데 세대에 따라 의미가 바뀌는 경우가 있다. 따라서 현재 사용하고 있는 CPU 모델을 정확히 해석하려면 링크된 인텔의 ‘접미사 목록’ 페이지를 참고하자.

CPU의 세대는 중요할까?

꽤 중요하다. 간단히 말해, 그리고 일반적으로 세대가 높을 수록, 즉 새로울 수록 더 좋다. 하지만 세대별로 개선된 정도는 각기 다르다.

인텔에 따르면, 최신 8세대 인텔 코어 프로세스는 7세대보다 최대 40%까지 성능이 향상됐다. 물론 비교 대상에 따라 성능 향상치가 크게 다르다. SKU가 세대별로 다를 수 있기 때문이다. 예를 들어, 인텔 코어 i7-8850U는 있지만 인텔 코어 i7-7850U는 없다.

세대가 높을 수록 최신 프로세서라는 것이 기본 원칙이다. 더 발전한 기술과 설계의 이점을 누릴 수 있다는 의미이며, PC 성능도 따라서 향상될 것이다.

코어가 많을 수록 좋을까?
간단히 대답하면, 일반적으로 코어 수가 적은 것보다 많은 것이 좋다. 코어가 1개인 프로세서는 한 번에 스레드 1개만 처리할 수 있다. 그리고 코어가 2개인 프로세서는 2개를, 코어가 4개인 쿼드 코어 프로세서는 4개를 처리할 수 있다.

그렇다면 스레드(Thread)는 무엇일까? 아주 간단히 설명하면, 스레드는 특정 프로그램에서 나와 프로세서를 통과하는 연속된 데이터 데이터 흐름을 말한다. PC의 모든 것은 프로세서를 통과하는 스레드로 귀결된다.

즉, 논리적으로 코어가 많을 수록 한 번에 처리할 수 있는 스레드가 많다. PC가 더 빠르고 효율적으로 데이터를 처리하고 명령을 실행할 수 있다는 이야기이다. 그러나 새 CPU를 조사하면서 코어 수에만 초점을 맞추면 자칫 코어 수만큼 중요한 수치인 클럭 속도를 무시할 위험이 있다.

CPU의 각 코어에는 Ghz가 단위인 클럭 속도가 있다. 클럭 속도는 CPU 실행 속도다. 클럭 속도가 빠를 수록, CPU가 한 번에 처리 및 실행할 수 있는 명령이 많다.

클럭 속도는 통상 높을 수록 더 좋다. 그러나 발열과 관련된 제약 때문에 프로세서의 코어 수가 많을 수록 클럭 속도가 낮은 경향이 있다. 이런 이유로 코어 수가 많은 PC가 최고의 성능을 발휘하지 못하는 경우도 있다.
그렇다면 가장 알맞은 클럭 속도는 어느 정도일까?


클럭 속도는 PC로 하려는 일에 따라 달라진다. 일부 애플리케이션은 싱글스레드로 실행된다. 반면, 여러 스레드를 활용하도록 만들어진 애플리케이션도 있다. 비디오 렌더링이나 일부 게임 환경이 여기에 해당된다. 이 경우, 코어 수가 많은 프로세서가 클럭 속도가 높지만 코어가 하나인 프로세스보다 성능이 훨씬 더 높다.
수치해석의 경우는 계산량이 많은 큰 해석의 경우 멀티코어가 훨씬 유리하다.

웹 브라우징 같은 일상적인 작업에서는 클럭 속도가 높은 i5 프로세서가 i7보다 가격 대비 성능이 훨씬 더 높다는 의미이다. 즉, 코어 수가 많은 프로세서보다 클럭 속도는 높고 코어 수가 적은 프로세서를 구입하는 것이 훨씬 경제적인 대안이 될 수도 있다.

하이퍼-스레딩이란?

앞서 언급했듯, 일반적으로 프로세서 코어 하나가 한 번에 하나의 스레드만 처리할 수 있다. 즉, CPU가 듀얼 코어라면 동시에 처리할 수 있는 스레드가 2개다. 그러나 인텔은 하이퍼-스레딩이라는 기술을 개발해 도입했다. 가상으로 운영체제가 인식하는 코어를 2배 증가시키는 방법으로 하나의 코어가 동시에 여러 스레드를 처리할 수 있는 기술이다.

즉 i5의 물리적 코어 수는 4개이지만, 여러 스레드를 지원하는 애플리케이션을 실행시키면 하이퍼-스레딩이 코어 수를 가상으로 2배 늘려서 성능을 크게 향상하는 방법이다.

터보 부스트(Turbo Boost)란?

인텔의 터보 부스트는 프로세서가 필요한 경우 동적으로 클럭 속도를 높이는 기능이다. 터부 부스트로 높을 수 있는 최대 클럭 속도는 활성 코어의 수, 추정되는 전류 및 전력 소모량, 프로세서 온도에 따라 달라진다.

알기 쉽게 설명하면, 인텔 터보 부스트 기술은 사용자의 프로세서 사용 현황을 모니터링, 프로세서가 ‘열 설계 전력’의 최대치에 얼마나 가까이 도달했는지 판단한 후 적절한 수준으로 클럭 속도를 높인다. 기본적으로 가장 적절하고 우수한 클럭 속도와 코어 수를 제공한다.

현재 터보 부스트 테크놀로지 2.0 버전이 사용되고 있으며, 여러 다양한 7세대 및 8세대 인텔 코어 i7과 i5 CPU에서 이를 지원한다.

i3, i5, i7, i9 프로세서 중 하나를 선택하기 전에 클럭 속도, 코어 수와 함께 기억해야 할 한 가지가 또 있다.

캐시 크기

CPU가 동일한 데이터를 계속 사용하는 경우, CPU는 이 데이터를 프로세서의 일부분인 캐시라는 곳에 저장된다. 캐시는 RAM과 비슷하다. 그러나 메인보드가 아닌 CPU에 구축되어 있어 훨씬 더 빠르다.
캐시 크기가 크면 더 빨리 더 많은 데이터에 액세스 할 수 있다. 클럭 속도 및 코어 수와 다르게, 캐시 크기는 무조건 클 수록 더 좋다. 메모리가 많을 수록 CPU 성능이 향상된다.

7세대 코어 i3 및 코어 i5 프로세서 U 및 Y 시리즈 캐시 크기는 3MB, 4MB이다. 코어 i7의 캐시 크기는 4MB이다. 현재 8세대 프로세서의 캐시 메모리는 6MB, 8MB, 9MB, 12MB이다.

코어 i3, i5, i7, i9의 차이점은 무엇일까?
일반적으로 코어 i7은 코어 i5, 코어 i5는 코어 i3보다 나은 프로세서이다. 코어 i7의 코어 수는 7개가 아니다. 코어 i3 역시 코어 수가 3개가 아니다. 코어 수나 클럭 속도가 아닌 상대적인 연산력의 차이를 알려주는 수치다.

2017년 출시된 코어 i9 시리즈는 고가의 고성능 프로세서이다. 최상급인 코어 i9-7980X의 코어 수와 클럭 속도는 18개와 2.6GHz, 한 번에 처리할 수 있는 스레드는 32개이다. 가장 저렴한 코어 i9-7900X의 경우 각각 10코어, 3.3GHz(기본 클럭 속도), 20 스레드이다.

수치해석 측면에서 구입해야 할 컴퓨터를 고려한다면 CPU 성능은 현재 최신코어인 i7과 i9을 구입하는 것이 원하는 성능을 정확히 제공하는 CPU를 선택하는 방법이지만 예산과 성능이라는 선택의 문제가 존재한다.

editor@itworld.co.kr

AMD CPU 에 대한 이해

썸네일
썸네일

AMD CPU 이름 규칙 및 코드명, 종류, 세대, 소켓 알아보기

AMD 1600, AMD 2400G, Athlon 240GE, AMD 3990X 등 AMD에 다양한 종류의, 다양한 모델명을 가진 cpu들이 있습니다. AMD cpu, apu의 종류와 세대, 소켓에 대해서 알아보도록 하며 이 글에서는 2017년 3월 3일 이후 나온 ‘라이젠’ 시리즈의 cpu, apu에 대해서만 다루도록 하겠습니다.

AMD 라이젠 시리즈는 현재 3세대까지 출시되었으며, 크게 일반 cpu, 하이엔드 cpu(스레드리퍼), 일반 APU, 모바일 APU으로 나뉩니다. 또한 소켓은 현재까지 나온 cpu 중 하이엔드 cpu를 제외한 cpu는 모두 am4소켓입니다.

AMD CPU 이름 규칙

이름 규칙

 

이름 규칙

AMD 라이젠 시리즈는 ‘AMD 라이젠 7 1700X’를 예로 들면, 앞의 ‘AMD’는 회사 이름을 나타내며

뒤에 ‘라이젠 7’은 성능을 나타냅니다.
‘라이젠 3’은 메인스트림,
‘라이젠 5’는 고성능,
‘라이젠 7’은 최고 성능입니다.

그리고 뒤에 ‘1’은 세대를 나타냅니다.
‘1700’은 Zen 1세대이며,
‘AMD 라이젠 5 2400G’와 같이 APU는 기존 세대에 비해 조금 개선되긴 했지만, 다음 세대 정도까지에 개선은 아니라서 세대는 같지만, ‘400G’앞에 붙는 숫자는 1이 더해져서 나옵니다.

그리고 두번째 자리 ‘7’은 성능을 나타냅니다.
‘2,3’은 메인스트림,
‘4,5,6’은 고성능,
‘7,8’은 최고 성능입니다.

그리고 세네번째 자리는 세세한 기능의, 세세한 성능의 변화 정도로 생각하시면 됩니다.

출처: https://minikupa.com/52 [미니쿠파]

 

인텔 코어 i9-12900K 리뷰 | 왕좌 탈환 노리는 ‘인텔의 귀환’

2021.11.09

Gordon Mah Ung | PCWorld구원 서사를 좋아하지 않는 사람은 없다. 인텔 12세대 코어 i9-12900K는 오랫동안 회자될 귀환 이야기의 주인공이다. 한때 강력하고 득의양양했던 챔피언은 수 년 전 부활한 AMD 라이젠 프로세서의 손에 굴욕적인 패배를 겪었고 어떻게 해서든 다시 한번 싸울 방법을 찾아 마침내 승리를 외치려고 한다. 이제 카메라가 페이드아웃 되면서 엔딩 크레딧으로 넘어간 셈이다.

인생이나 기술은 그런 헐리우드식 결말을 맺기 어렵지만, 인텔 코어 i9-12900K는 그런 드라마의 주인공 역할을 상당히 잘 해낸 것 같다. 지난 몇 년 동안 AMD 프로세서에 두들겨 맞은 후 태어난 12900K는 경쟁 제품인 라이젠 9 5950X보다 훨씬 더 나은 CPU로 더 많은 사용자에게 활용 가능성을 안겼다. 화끈한 KO 승리를 거둔 것은 전혀 아니지만, 인텔 12세대 앨더 레이크 프로세서의 뛰어난 장점과 기능을 고려할 때 바로 오늘 구입할 수 있는 하이엔드 데스크톱 프로세서다. 

ⓒ Gordon Mah Ung


12세대 앨더 레이크는 어떤 CPU?

인텔 12세대 앨더 레이크는 근본적으로 인텔 7 공정을 기반으로 만들어진 하이브리드 CPU 설계다. 사실 이것만으로도 엄청난 일이다. 14나노 트랜지스터 기술에 5년 이상을 허비한 끝에, 앨더 레이크는 마침내 하나의 노드를 뛰어넘었다. (기존 10나노 공정이 리브랜드된 후 인텔 7이라는 이름으로 불린다.)

새롭게 설계된 고성능 CPU 코어와 더 작아진 효율 코어를 혼합하여 성능 대 전력 비율의 균형을 최적화했다. 완전히 재설계된 큰 코어를 가진 인텔의 첫 번째 인텔 7 프로세스 데스크톱 CPU라고 이해하는 것이 가장 쉽다. 그리고 여기에 더해 여러 개의 나머지 효율성 코어 성능이 이전 10세대 코어만큼 우수하다. 또한, 12세대 앨더 레이크는 PCIe 5.0, DDR5 메모리, LGA1700 소켓을 비롯해 새로운 표준을 다수 지원한다.

ⓒ Intel

CPU 렌더링 성능

인텔의 전통점 강점이 아니었던 3D 렌더링과 모델링부터 시작하자. 지금까지는 PC에서 3D 모델링 애플리케이션 실사용자가 많지 않아서, 이들 전문 애플리케이션의 실행 성능에 큰 의미를 두지 않았다는 것이 인텔의 주장이었다. 라이젠 CPU의 눈부신 성능에 뒤지는 경우에만 렌더링 성능에서 피벗을 뺐다는 점에 주목하는 사람도 많다.

맥슨 시네벤치 R23부터 시작한다. 맥슨 시네마4D 애플리케이션에 사용되는 렌더링 엔진 테스트이며, 같은 렌더링 엔진이 일부 어도비 애플리케이션에도 내장되어 있다.

최신 버전은 10분 쓰로틀링 테스트를 기본값으로 제안한다. 인텔 10세대, 11세대 칩과 윈도우 11 환경을 테스트한 결과는 없지만, 윈도우 10과 10코어 코어 i9-10900K가 1만 4,336점을 받았고 8코어 코어 i9-11900K는 1만 6,264점을 받았다. 사실 둘 다 2만 2,168점을 받은 AMD 12코어 라이젠 9 5900X과는 상대가 되지 않는다. 그래서 굳이 16코어 라이젠 9 5950X와 비교할 필요가 없었다.

눈길을 끄는 것은 코어 i9-12900K의 긴 파란 막대다. 인텔이 앨더 레이크에서 추구한 하이브리드 설계를 추구하는 것에 여러 가지 말이 많았지만, 12900K는 오랫동안 라이젠의 홈그라운드였던 렌더링 벤치마크에서 AMD의 1, 2위 CPU를 아주 약간이나마 능가해 호사가의 입을 단속한다.

ⓒ IDG

하지만 인텔이 옳다. 모든 CPU 코어와 쓰레드를 다 쓰는 애플리케이션을 사용하는 사람은 그다지 많지 않다. 따라서 시네벤치로 단일 쓰레드 성능을 살펴보는 것도 중요하다. 시네벤치 멀티코어 성능은 라이트룸 클래식 올코어 영상 인코딩이나 사진 내보내기 성능을 알려주고, 시네벤치 R23 단일 쓰레드 성능은 그보다는 오피스나 포토샵 실행에 조금 더 가깝다. 다시 한번 강조하지만, 코어 i9-10900K와 윈도우 11 결과는 없지만, 10세대 제품의 기존 점수는 1,325점, 11세대 제품은 1,640점을 기록한 AMD 라이젠과 비슷한 수준이다.

그러나 인텔 최신 성능 코어는 라이젠 9 5950X보다 성능이 19% 높고, 구형 10세대 칩보다 31%나 나아져 당혹스러울 정도였다. 맥북 프로 M1 맥스와 앨더 레이크를 비교하면 어떨지를 궁금해 하는 이에게 알려주자면, 앨더 레이크가 우세하다. 모바일 칩과 데스크톱 칩을 비교하는 단일 쓰레드 성능 테스트에서 12세대 앨더 레이크 CPU는 애플 최신 M1 칩보다 약 20%나 더 빨랐다. 물론 인텔 제품은 노트북용 칩이 아니었지만, 인텔 12세대 CPU를 탑재한 노트북이 출시되면 충분히 맥북 프로의 경쟁자가 될 것이다.

ⓒ IDG
ⓒ IDG
ⓒ IDG
ⓒ IDG
ⓒ IDG
ⓒ IDG

압축 성능

CPU의 압축 성능은 인기있고 무료인 7-Zip 내부 벤치마크로 측정했다. 벤치마크는 CPU 쓰레드 수를 살펴보고 테스트하면서 자체적으로 여러 번 스풀링을 반복한다. 압축 테스트에서는 코어를 전부 사용하는 경우 압축 성능에서 24%, 압축 해제 성능에서 35% 더 높은 수치를 보여준 라이젠이 가장 큰 승자다.

7-cpu.com에 따르면, 압축 측면에서는 메모리 지연 시간, 데이터 캐시의 크기 및 TLB(translation look ahead buffer)가 중요한 반면, 압축을 풀 때는 정수 및 분기 예측 실패 패널티(branch misprediction penalties)가 중요하다. 결국, 실제 애플리케이션으로 파일 압축하거나 압축을 푸는 것은 보통 단일 쓰레드에 의존하기 때문에 멀티 쓰레드 성능과의 상관 관계는 이론에 그친다고 할 수 있다.

12세대 코어 i9의 문제는 심지어 압축 성능도 화려하지 않다는 것이다. 실제로 11세대 코어 i9은 윈도우 10 단일 쓰레드 성능에서 7,916으로 약간 더 빠르다. 간단히 요약하면 라이젠 9이 7-zip 테스트에서 압축 성능 우위를 유지했다. 이견은 있을 수 없다. 일부는 초기 DDR5 메모리의 지연 시간과 7-Zip이 특별한 명령을 사용하지 않는 이유도 있겠지만, 어쨌든 압축 테스트에서는 라이젠이 승리했다.

ⓒ IDG

인코딩 성능

CPU 인코딩 테스트는 무료이자 오픈소스인 핸드브레이크 트랜스코더/인코더를 사용하여 무료이자 오픈소스인 4K 티어스 오브 스틸(Tears of Steel) 영상을 H.265 코덱과 1080p 해상도로 변환하는 작업을 수행한다. 라이젠 9은 인코딩을 약 6% 더 빨리 끝내면서 다시 1위를 차지했다. 압도적인 승리는 아니지만 어쨌거나 1등이다. 

ⓒ IDG

합성 테스트

이제 긱벤치 5로 옮겨간다. 이 테스트는 21개의 작은 개별 루프로 구성된 합성 벤치마크인데, 개발자인 프라이메이트 랩스(Primate Labs)는 텍스트 렌더링에서 HDR, 기계 언어 및 암호화 성능에 이르기까지 모든 분야에서 인기있는 애플리케이션을 모델링했다고 한다. 긱벤치는 과거 논란의 중심에 있었지만, 여전히 인기가 높은 벤치마크다. 3D 렌더링과 압축, 인코딩 등에서 순위가 오르내렸던 코어 i9-12900K는 라이젠 9 5950X보다 8%가량 

긱벤치 벤치마크는 과거에 논란의 대상이 되었지만, 오늘날에는 비난받지 않고서 어떤 테스트를 유지하는 것이 어렵다. 하지만 이 제품은 어리석게도 인기가 있고, 당신이 긱벤치 5에 대해 어떻게 생각하든 간에, 사람들은 CPU가 거기에서 어떻게 작동하는지 보고 싶어한다. 3D 렌더링, 압축 및 인코딩을 어느 정도 반복한 결과, 인텔 코어 i9-12900K가 라이젠 9 5950X보다 약 8% 앞서는 것으로 나타났다.

ⓒ IDG
ⓒ IDG

콘텐츠 제작 성능 

전체 점수는 코어 i9-12900K가 라이젠 9 59050X에 비해 4% 더 앞선다. 프로시언 2.0은 이미지 보정(retouch)와 일괄 내보내기라는 2가지 방식으로 결과를 나눈다. 프로시언에 따르면, 이미지 보정에서는 기본적으로 12세대 코어 i9과 라이젠 9이 동점이었다. 주로 라이트룸 클래식 사진 내보내기 성능을 시험한 일괄 처리에서는 코어 i9가 최대 5%까지 앞섰다. 라이트룸 사진 내보내기가 멀티코어 성능에 의존하는 경향이 크기 때문에 마지막 결과에 놀랐다. 라이젠 9의 승리를 예상했기 때문이다. 결과는 그렇지 않았다. 

ⓒ IDG
ⓒ IDG
ⓒ IDG
ⓒ IDG
ⓒ IDG

AI 성능

ⓒ IDG
ⓒ IDG

실생활 성능

비싼 컴퓨터로 인디 영화를 위한 특수 효과를 만들거나 이국적인 여행에서 찍은 사진을 편집하는 것을 상상하기 쉽지만, 세상 일의 대다수는 청구서를 지불하는 지루한 작업과 더 연관이 깊다. 따라서 마이크로소프트 오피스 성능을 UL의 프로시언 2.0 오피스 생산성 테스트를로 측정했다. 어도비와 마찬가지로, 다루는 마이크로소프트 워드, 엑셀, 파워포인트 및 아웃룩에서 고품질 미디어를 많이 다루는 작업을 대상으로 한다. 현실이 지루한 것처럼, 이런 작업이 가장 현실적이라고 할 수 있을 것이다.

오피스나 사무적이고 딱딱한 아웃룩 성능에 열광하는 사람에게는 라이젠보다 16% 빠른 코어 i9-12900K가 유리한 것으로 나타났다. 개별 애플리케이션을 결과에 따르면 12세대 코어 i9는 워드에서 14%, 엑셀에서 19%, 파워포인트에서 10%, 아웃룩에서 19% 더 빠르다. 

ⓒ IDG
ⓒ IDG

게이밍 성능

첫 번째 차트의 수직 축 눈금은 60와트에서 340와트까지를 표시하며, 0은 시간 수평 축을 의미한다. 먼저 모든 코어를 사용하여 시네벤치 R20을 실행했는데, 12900K(빨간색) 막대가 320와트의 총소비량까지 올라간 것을 볼 수 있다. 이것은 거의 라이젠 9 5950X(보라색)의 최대치보다 거의 100와트 더 많다. 약 45% 더 많은 양이다. 일단 모든 코어에 대해 두 칩 모두 시네벤치를 완료하면, 단일 코어나 쓰레드를 사용하여 칩을 실행한다. 이제 115와트 범위의 12세대 코어 i9의 총 시스템 전력을 볼 수 있는데, 라이젠 9가 약 10와트를 더 소비한다. 코어 i9가 테스트를 더 빨리 끝내고 라이젠 9 시스템보다 더 적은 전력을 사용한 것도 확인할 수 있다. 

ⓒ IDG

전력 소비

ⓒ IDG
ⓒ IDG

쓰레드 스케일링

인텔의 11세대부터 12세대까지의 세대별 성능 변화는 경이롭다. 단일 쓰레드를 사용함으로써 코어 i9-12900K는 이전 제품보다 42% 더 빠르며 그 속도에서 조금 올라간다. 8개 쓰레드에서 최신 세대의 코어 i9 최대치를 기록할 때 12세대 코어 i9은 놀랍게도 82% 더 빠르다. 지난 3월 출시된 11세대 칩과 비교하면 완전히 놀라운 변화다. 직접 전력 양을 추적해보지는 않았지만, 이전 11세대 코어 i9-11900K는 시네벤치 R20 실행에 거의 380와트 가까이를 사용한 반면, 12세대 코어 i9는 약 320와트를 사용했다. 따라서, 12세대 코어는 훨씬 적은 전력을 사용하면서도 훨씬 더 빠르다.

ⓒ IDG
ⓒ IDG

인텔 코어 i9-12900K, 결론

조금 의외일지도 모르겠다. 최고의 CPU라는 것은 존재하지 않는다는 것이 결론이다.

그보다는 특정 요구에 가장 적합한 CPU가 곧 최고의 CPU다. 이 긴 벤치마크는 각 요구사항을 6개 부문으로 나눠 각 분야에서 어떤 칩이 승리했는지를 확인했다. 인텔에 좋은 소식은 거의 모든 부문에서 좋은 위치를 차지하고 있다는 것이다.

렌더링 / 하이쓰레드 카운트 
하이 쓰레드 카운트 애플리케이션 및 렌더링에서 코어 i9-12900K는 시네벤치 R23 테스트에서 가까스로 승리라는 결과를 냈지만, 다른 CPU 렌더링 테스트에서는 훨씬 미묘한 결과가 나왔다. 솔직히 90% 렌더링 PC용 칩을 선택한다면, 라이젠 9 5950X가 아마 더 나은 선택일 것이다. 
승리 : 라이젠 9 5950X.

콘텐츠 제작
앞서 살펴본 바와 같이, 콘텐츠 제작은 단순히 쓰레드가 제일 많기만 하면 되는 작업이 아니고, 12세대 코어 i9은 라이젠 9 5950X보다 더 많은 역량을 증명했다. 포토샵, 라이트룸 클래식, 프리미어 프로를 주로 다룬다면 인텔이 더 나은 선택이 될 것이다. 
승리 : 코어 i9-12900K.

실생활
오피스 생산성과 크롬의 벤치마크를 통해 반응성이 더 높은 것이 인텔 CPU라는 점을 확인했다. 물론 결과에 동의하지만 동시에 라이젠 9 5950X도 두 사용례를 모두 잘 처리할 수 있다고도 믿는다. 아웃룩, 워드 실행이나 인터넷 검색이 주 작업인 하이엔드 데스크톱을 조립할 경우 약간 등급을 낮춰도 될 것 같다.
승리: 코어 i9-12900K.

게이밍
실제 게임 플레이에서 차이를 보려면 CPU보다 GPU에 더 집중해야 한다. 그렇지만 게임 테스트에서 인텔 12세대 코어 i9은 분명히 라이젠보다 점수가 높거나 거의 동점이었다. 의심의 여지없이 최고의 게임용 CPU다. 하지만 어느 쪽을 택해도 좋은 선택이다.
승리 : 코어 i9-12900K.

기능
인텔 12세대 플랫폼은 PCIe 5.0 및 DDR5 메모리라는 새로운 세계를 열었다. 또한, 필요한 경우 썬더볼트를 사용할 수 있고 와이파이 6E까지도 통합되어 있다. 물론, DDR5의 가치가 없다고 말하는 이들도 있고 그런 주장에도 이유가 있겠지만, 인텔로서는 충분히 새로운 점이 있다. 
승리 : 코어 i9-12900K.

가치
아직도 AMD 라이젠 9 5950X가 그리 대단한 가치가 없다고 생각하는 사람도 있고, 그 전 해에 2,000달러나 했던 CPU와 성능이 동등한데도 가격이 750달러에 불과한 것을 칭찬하는 사람도 있다. 만약 라이젠 9의 가격이 터무니없이 저렴하다고 생각하는 쪽이라면, 589달러라는 코어 i9-12900K의 공격적인 가격표를 보고 당장 구매하겠다고 소리칠 것이다. 하지만 이 가격은 대량 구매시 적용되는 값이다. 그렇지만 전통적으로 대량구매 가격은 초기 수요가 확정되면 시중가와 몇 달러 차이 나지 않는다. 그렇다. 여기서 가격 대비 가치가 높은 제품은 인텔이다. 그야말로 해가 서쪽에서 뜰 기세다.
승리 : 코어 i9-12900K.

코어 i9-12900K는 위대한 과거 명성을 회복하고 다시 왕좌를 탈환하려고 나섰다. 앨더 레이크는 기다릴 가치가 충분했다. 인텔에게 박수를 보낸다, 브라보. editor@itworld.co.kr 

ⓒ ROB SCHULZ / IDG

FLOW-3D 해석용 HDD, SSD 선택 가이드

SSD 성능 평가 안내

아래 차트는 200만 개가 넘는 PerformanceTest 벤치마크 결과를 사용하여 만들어졌으며 매일 업데이트됩니다. 이러한 전체 점수는 하드 디스크 드라이브의 읽기 속도, 쓰기 속도 및 탐색 시간을 측정하는 세 가지 다른 테스트에서 계산됩니다. 이 차트에는 Western Digital(WD), Samsung 및 Crucial과 같은 많은 주요 제조업체의 드라이브가 포함되어 있습니다. 결과에 따르면, 최고 성능의 SSD(솔리드 스테이트 드라이브)는 Gen4 및 Gen5 인터페이스를 사용하는 M.2 NVMe 드라이브입니다.

Highend Drive

원문 출처: https://www.harddrivebenchmark.net/high_end_drives.html

PassMark - Disk Rating High End Drives

Top 100 Solid State Drive

SSD Drive에 대한 이해

원문출처 : 본 자료는 ITWORLD 에서 작성된 자료로 수치해석 엔지니어에게 도움이 될 수 있어 인용 제공하였습니다.
https://www.itworld.co.kr/news/185628

“폼팩터와 속도로 구분한” SSD 선택 가이드

Alaina Yee | PCWorldSSD(Solid State Drive)는 분명 구식 하드 디스크 드라이브보다 이점이 있다. SSD가 더 빠르고 조용하며 전력도 덜 소비한다. 문제는 사양에 일련의 약어가 포함되어 있기 때문에 자신에게 필요한 것이 무엇인지 파악하기가 어려울 수 있다는 점이다. 

방법은 간단하다. 폼 팩터와 속도만 선택하면 된다. 이 가이드에서 그 방법을 설명하고자 한다.

SSD 폼팩터 : M.2 드라이브 vs 2.5인치 드라이브

폼팩터부터 시작해 보자. SSD는 모양과 크기가 다양하지만 M.2와 2.5가 가장 보편적인 유형이다. 각 유형은 저마다 장점이 있다. 껌처럼 생긴 M.2 드라이브는 마더보드에 직접 연결되고(그래서 데스크톱 PC의 선정리가 깔끔해지며) 일부 유형은 2.5인치 드라이브보다 빠르다. 일반적인 저장장치처럼 PC에 삽입되는 사각형의 2.5인치 드라이브가 더 저렴한 경우가 많다.

기타 덜 보편적인 폼팩터로는 PCIe 추가 카드와 U.2 드라이브가 있으며, 둘 다 데스크톱 PC에 사용된다. PCIe 추가 카드는 사운드 카드나 그래픽 카드와 비슷해 보이며 같은 PCIe 슬롯을 사용하여 마더보드에 연결된다. U.2 SSD는 2.5인치 드라이브와 비슷해 보이지만 제공업체가 마더보드에 U.2 커넥터를 추가한 경우에만(또는 M.2 슬롯에 사용하기 위해 어댑터를 구매한 경우에만) 작동한다. 또한 구형 노트북이나 미니 PC에 사용되는 mSATA 드라이브도 있지만 최신 하드웨어에서 M.2 드라이브로 대체되었으며 mSATA와 M.2 SSD는 서로 호환되지 않는다.

그렇다면 어떤 유형을 선택할까? 데스크톱이나 노트북이 지원할 수 있는 것과 성능 요구사항, 예산 규모, 제작 선호도에 따라 달라진다. 대부분의 사람들은 2.5인치와 M.2 폼팩터 중에서 선택하는 데 집중할 수 있다. PCIe 추가 카드와 U.2는 더 틈새시장이며, mSATA는 기존 드라이브를 교체하거나 구형 호환 하드웨어에 추가할 때나 사용된다.

ⓒ ROB SCHULZ / IDG

최신 하드웨어나 약간 오래된 고급 하드웨어가 적용된 데스크톱 시스템의 경우 M.2와 2.5인치 드라이브를 모두 사용할 수 있을 것이다. 많은 사람이 둘 중에 선택하지 않고, 조합하여 사용한다. M.2를 부팅 드라이브로 사용하고 2.5인치 드라이브는 추가 저장장치로 사용하는 식이다. 이 조합은 케이블 관리 문제와 일반적인 케이블 복잡성을 줄이면서 제작자가 단일 PC에서 빠르고 합리적인 고용량 SSD를 활용하는 데 도움이 된다.

구형 데스크톱 시스템의 경우 2.5인치 드라이브만 선택할 가능성이 높다. 일부 M.2 드라이브로 더 빠른 속도를 원한다면, 마더보드에 PCIe 3.0 슬롯이 있는 경우 PCIe 추가 어댑터를 고려할 수 있다. 이 확장 카드는 M.2 드라이브를 넣을 수 있어서 PCIe 슬롯에 사용할 수 있다.

노트북의 경우, 신형 노트북을 구성하면서 SSD 폼팩터를 선택할 수 있는 경우 최고의 가성비를 제공하는 것을 선택한다. 하지만 대부분의 노트북은 선택권이 없을 것이다.

M.2 슬롯이 없는 구형 마더보드인가, PCIe 3.0 x4, x8, x16 슬롯이 있으면 M.2 NVMe – PCI 3.0 어댑터 카드를 사용할 수 있다. ⓒ MHQJRH / AMAZON

구형 노트북을 업그레이드할 때도 선택권이 없을 수 있다. 노트북의 구성으로 인해 1가지 폼팩터로 제한될 수 있다. 자신의 모델에 M.2 슬롯, 2.5인치 드라이브 베이 등이 있는지 확인하려면 온라인 사용 설명서를 찾거나 포럼과 레딧(Reddit)에서 검색해야 한다. 또한 고객 지원 부서로 문의할 수 있다. 노트북과 호환되는 드라이브를 구매하되, 인터페이스 유형(다음 섹션에서 다룸)과 오리지널 2.5인치 드라이브의 Z 높이 등의 세부사항에 주의하자. 또한 배터리 사용 시간에 영향을 미칠 수 있기 때문에 리뷰를 찾아보고 고려 중인 특정 SSD의 소비전력도 확인하자.

시스템에 적합한 것을 선택한 후 우리의 노트북에 SSD 설치하기 단계별 설명에 따라 더 쉽고 빠르게 업그레이드할 수 있다.

SSD 속도 : SATA vs NVMe

이제 속도로 넘어가 보자. SSD를 SATA 또는 NVMe 드라이브라고 지칭할 때 기대할 수 있는 속도 범위를 알 수 있다. 모든 SSD가 동일한 디지털 인터페이스로 데이터를 전송하지 않는다. 일부는 여전히 SATA(Serial ATA)를 사용하며 신형 모델은 PCIe(PCI Express)를 통한 NVMe(Non-Volatile Memory Express) 프로토콜을 사용한다.

SATA는 구형이며, 예상했듯이 SATA 드라이브는 NVMe보다 느리다. 이 인터페이스는 SSD와의 데이터 전송 속도를 제한한다. 하지만 SATA SSD는 하드 디스크 드라이브(HDD)보다 훨씬 빠르다. 평균 읽기 및 쓰기 속도가 초당 500MB 수준이며, 이는 HDD보다 3~6배 정도 빠른 수치이다. 여기에 가격까지 합리적이기 때문에 가성비 좋은 PC 조립 및 업그레이드를 할 수 있다. 우리는 새 PC를 구매하는 모든 사람에게 SATA SSD를 추천하고 있으며, 구형 PC를 업그레이드하는 경우에는 더욱 그렇다. HDD 대비 성능 개선이 상당하며, 웹 사이트 로딩 같은 일상적인 상황에서도 대부분의 사람들은 완전히 다른 컴퓨터를 사용하고 있는 느낌을 받게 될 것이다.

ⓒ GORDON MAH UNG

NVMe는 SATA 같은 한계가 없다. NVMe SSD는 매우 빠르다. 현재, SATA 드라이브보다 5~6배 정도 빠르며, 최신 제품은 현재 약 10배 정도 더 빠르다. 제조사들이 디자인을 다듬고 더 빠른 모델을 더 많이 출시하면서 NVMe 드라이브의 속도도 지속적으로 높아질 것이다.

NVMe SSD의 속도를 고려할 때 주의해야 할 용어는 PCIe Gen 3(PCIe 3.0)과 PCIe Gen 4(PCIe 4.0)이다. ‘x2’ 또는 ‘x4’(‘2배속’ 또는 ‘4배속’이라고 읽음)로 표기되어 있는 경우 드라이브가 사용할 수 있는 PCIe 레인 수를 나타낸다. 레인이 많으면 드라이브가 한 번에 전송할 수 있는 데이터도 많아진다. 최신 PCIe Gen3 x4 SSD의 읽기 및 쓰기 속도는 평균 초당 2,500~3,200MB이며 PCIe Gen4 x4 드라이브는 평균 초당 5,000MB이다.

그렇다면 어떻게 선택할까? 폼팩터와 마찬가지로 모든 상황에서 똑같이 결정할 수는 없다. 2.5인치 SSD는 모두 SATA 드라이브이며 M.2 SSD는 SATA와 NVMe로 제공되기 때문에 마더보드가 지원하는 것을 구매해야 한다. M.2 슬롯은 SATA만 지원하거나, NVMe만 지원하거나, 둘 다 지원할 수 있다. 데스크톱 PC 마더보드에서는 보드에서 최소 1개의 슬롯이 둘 다 지원하며, 두 번째 슬롯이 둘 다 또는 SATA만 지원하는 경우가 있다. 노트북에서는 그때그때 다를 수 있기 때문에 특정 모델의 사양을 살펴보자.

일부 노트북은 다른 노트북보다 업그레이드가 편할 수 있다. 위 이미지의 노트북의 경우 MVNe를 지원하는 2개의 M.2 슬롯이 있다. ⓒ IDG

인터페이스 유형의 경우 SATA 드라이브는 일상 작업 및 게이밍에도 충분히 빠르며, NVMe는 대용량 파일 전송 시간을 절약해야 하는 고성능 PC에 좋다. 전체적으로 예산과 PC가 얼마나 오래되었는지에 따라 결정하게 된다. 

NAND 유형과 DRAM이 없는 드라이브

인터페이스 유형은 SSD의 속도를 나타내는 주요 지표가 되지만, SSD에 사용되는 NAND(플래시 메모리)의 구체적인 유형과 DRAM 캐시 포함 여부도 영향을 미친다.

하지만 대부분의 사람은 이런 측면을 심층적으로 고려할 필요가 없으며, 다양한 유형의 파일 전송 시 드라이브의 성능이 더욱 중요하고 이런 결과는 각 리뷰에서 확인할 수 있다. 

SLC(Single-Level Cell), MLC(Multi-Level Cell), TLC(Triple-Level Cell), QLC(Quad-Level Cell) NAND는 각각 장단점이 있지만, 매장에 재고가 있는지가 더욱 중요하기 때문이다. 요즘 제조사들이 이용을 낮추고 드라이브 용량을 늘리면서 대부분의 소비자용 SSD는 TLC와 QLC로 제작된다.

SAMSUNG 삼성의 980 프로는 TLC NAND를 사용한다. MLC NAND를 사용하는 970 프로와 달라진 점이다. 최근에는 MLC NAND를 사용한 일반 소비자용 SSD를 찾기가 쉽지 않다.

마찬가지로 DRAM이 없는 드라이브는 일부 벤치마크에서 DRAM 캐시가 있는 동급 SSD와 비교하여 상대적으로 뒤처지지만(무작위 쓰기 등) 인터페이스 성능이 떨어지는 SSD와 비교한 성능이 여전히 중요하다. DRAM이 없는 NVMe SSD는 여전히 SATA SSD보다 빠르며, DRAM이 없는 SATA SSD는 여전히 HDD보다 빠르다. 이런 기대치를 충족하지 못하는 DRAM이 없는 SSD나 DRAM 캐시가 있는 모델과 가격이 같은 SSD는 피하자. 또한 전반적인 성능이 필요한 경우에도 피하자. 하지만 모든 D램리스 SSD를 피하고자 예산을 늘릴 필요는 없다.

요약

이 모든 정보를 파악하고도 아직 어떻게 해야 할지 모르겠다면 걱정하지 말자. 아래의 두 가지 질문에만 답해보면 구매할 SSD의 유형을 파악할 수 있다.
1. 자신의 PC나 노트북에 장착되는 유형은 무엇인가? (2.5인치 SSD, M.2 SSD, 둘 다?)
2. 자신의 PC나 노트북이 지원하는 인터페이스 유형은 무엇인가? (SATA, NVMe, 둘 다?)

데스크톱 PC의 마더보드 사양을 보거나 노트북의 사용 설명서, 제조사 포럼, 레딧 등만 살펴보아도 이런 질문에 쉽게 대답할 수 있다. 

노트북의 경우 (해당하는) 2.5인치 드라이브의 최대 Z 높이를 확인하여 장착 여부를 판단하고, 고려 중인 SSD의 소비전력도 파악한다. 후자는 배터리 사용 시간에 영향을 미칠 수 있다. 성능을 고려하되 자신의 요구사항도 평가하자. 중간급 또는 가성비 제품으로 충분한 데도 최고의 품질을 위해 비용을 지불할 필요는 없다. 다르게 이야기하는 인터넷 댓글들은 무시하자. editor@itworld.co.kr

수치해석에서 SSD가 필요한가?

본 자료는 ITWORLD 기사에서 2021년 3월과 05일 자료와 2021년 12월 14일 자료에서 발췌 인용된 자료입니다. (출처 : www.itworld.co.kr)

수치해석을 하는 경우 계산과정에서 생성되는 결과 파일 사이즈는 매우 크기 때문에, 빠른 디스크 속도는 사용자의 총 해석시간을 줄이는데 큰 도움이 됩니다.

수치해석 업무를 담당하는 사용자에게 SSD가 필요한가? 한마디로 말하면 수치해석을 하는 모든 사람은 보유하고 있는 수치해석 장비의 디스크를 SSD로 업그레이드하는 것이 좋다. 가장 빠른 기계식 하드 드라이브도 SSD 속도에는 미치지 못한다.

기존 노트북, 또는 데스크톱의 하드 드라이브를 SSD로 교체하면 완전히 새로운 시스템처럼 느낄 수 있다. 수치해석을 하는 사용자는 SSD를 구입하는 것은 컴퓨터를 업그레이드하는데 가장 적합한 옵션이다.

SSD는 기계식 하드 드라이브보다 기가바이트 당 비용이 더 많이 들기 때문에 초 고용량으로 제공되지 않는 경우가 많다. 속도와 저장 공간이 필요한 경우, 128GB 나 256GB의 SSD를 구입해 부팅 드라이브로 사용하고, 기존 하드 드라이브를 PC의 보조 저장 장치로 사용하면 최선의 선택이 된다.

하드 드라이브는 가격 대비 용량 측면에서 여전히 큰 이점을 제공하며, 자주 사용되지 않는 데이터를 저장하는 용도로 적합하다. 그러나 운영체제, 프로그램, 자주 사용하는 데이터에는 보유하고 있는 시스템이 지원한다면 NVMe SSD, 지원하지 않는다면 SATA SSD를 사용하는 것이 좋다.

아래 그래프를 보면 SSD를 왜 사용해야 하는지 명확해진다.

SSD Speed compare
SSD Speed compare

NVMe/M.2/SATA SSD 비교 정리

 NVMe SSDM.2 SSDSATA SSD
속도PCIe 3.0
최대 3,500MBps

PCIe 4.0
최대 7,500MBps


 		SATA
최대 550MBps

NVMe PCIe 3.0
최대 3,500MBps

NVMe PCIe 4.0
최대 7,500MBps		최대 550MBps






 
폼팩터 종류M.2
U.2*
PCIe 카드*
*일반적이지 않은 종류		N/A


 		2.5인치 드라이브
M.2

 
인터페이스 종류N/A
 		SATA
NVMe		N/A
 
장점속도가 빠름공간을 덜 차지함속도와 가격의 균형
단점가격이 비쌈

 		SATA M.2가
2.5인치 SATA보다
비싼 경우가 있음		속도가 느리고
공간을 많이 차지함
 

SATA SSD vs. NVMe SSD

시장에 SATA SSD와 NVMe SSD가 아직 공존하는 데는 이유가 있다. 메모리 기반 SSD의 잠재력을 감안할 때 결국 새로운 버스와 프로토콜이 필요할 수밖에 없으리란 점은 초기부터 명확했다. 그러나 초창기 SSD는 비교적 속도가 느렸으므로 기존 SATA 스토리지 인프라를 사용하는 편이 훨씬 더 편리했다.

SATA 버스는 버전 3.3에 이르러 16Gbps까지 발전했지만 거의 모든 상용 제품은 여전히 6Gbps에 머물러 있다(오버헤드를 더해 대략 550MBps). 버전 3.3이라 해도 현재 SSD 기술, 특히 RAID 구성으로 낼 수 있는 속도에 비하면 한참 느리다.

그 다음으로 등장한 방법은 역시 기존 기술이지만 대역폭이 훨씬 더 높은 버스 기술인 PCI 익스프레스, 즉 PCIe 활용이다. PCIe는 그래픽 및 기타 애드온 카드를 위한 기본 데이터 전송 계층이다. 3.x 세대 PCIe는 복수의 레인(대부분의 PC에서 최대 16개)을 제공하며, 각 레인은 1GBps(985MBps)에 가까운 속도로 작동한다.

PCIe는 썬더볼트 인터페이스의 기반이기도 하다. 썬더볼트는 게임용 외장 그래픽 카드, 그리고 내장 NVMe와 거의 대등한 속도를 내는 외장형 NVMe 스토리지에서 진가를 발휘하기 시작했다. 많은 사용자들이 이제 느끼고 있지만, 인텔이 썬더볼트를 버리지 않은 것은 현명한 판단이었다.

물론 PCIe 스토리지는 NVMe보다 몇 년 전에 나왔다. 그러나 이전 솔루션은 SATA, SCSI, AHCI와 같은 하드 드라이브가 스토리지 기술의 정점이었던 시절에 개발된 오래된 데이터 전송 프로토콜에 발목을 잡혔다. NVMe는 저지연 명령과 다수의 큐(최대 6만 4,000개)를 제공함으로써 스토리지의 발목을 잡았던 제약을 없앤다. 지속적인 원을 그리며 데이터가 기록되는 하드 드라이브와 달리 SSD에서는 마치 산탄처럼 데이터가 흩어져 저장되므로 특히 후자, 즉 다수의 큐가 큰 효과를 발휘한다.

가격 : NVMe > SATA

예상했겠지만, SSD는 속도가 빠를수록 가격이 비싸다. 시중에 판매되는 1TB SATA SSD의 가격은 10만 원 초반대이며, 1TB NVMe PCIe 3.0 드라이브의 가격은 10만 원 중후반대다. 1TB PCIe 4.0 드라이브 가격은 10만 원 초반대부터 20만 원대까지 다양하다. 조금 저렴한 1TB PCIe 4.0 드라이브는 최대 속도가 5,000MBps 정도다.

폼팩터 종류에 따라 가격 차이가 나지는 않는다. 2.5인치 SATA SSD와 M.2 모델의 가격이 동일한 경우가 대부분이다. 가끔 2.5인치 모델이 M.2 모델보다 저렴한 경우가 있는데, 일반적이지는 않다.

SSD 선택 시 유의해서 봐야할 것

물론 저장 용량과 가격이 중요하다. 또한 긴 보증기간은 조기 데이터 사망에 대한 우려를 완화시킬 수 있다. 대부분의 SSD 제조업체는 3년 보증을 제공하며 일부 더 좋은 모델은 5년을 보증한다. 그러나 이전 세대의 SSD와는 달리, 몇 년 전에 혹독한 내구성 테스트로 입증한 것처럼 최신 SSD는 일반 소비자가 어지간히 사용해서는 마모되지 않는다.

SSD는 NVMe 혹은 SATA를 사용해 PC의 나머지 부분과 통신한다. 일반적으로 SATA는 NVMe보다 속도가 느리다. 반면 M.2는 사실상 폼팩터에 가까우므로 시중에는 NVMe M.2 SSD와 SATA M.2 SSD가 모두 출시되어 있다. 

다만 제품 광고나 설명서에서 가끔 NVMe 드라이브임을 나타내기 위해 ‘M.2 SSD’라는 표현을 사용하고, 2.5인치 폼팩터 SSD임을 나타내기 위해 ‘SATA SSD’라는 표현을 사용한다. 따라서 ‘M.2 SSD’나 ‘SATA SSD’라는 표현을 액면 그대로 받아들이면 안 된다. 반드시 기술 사양을 확인하고 노트북 또는 데스크톱 PC의 스토리지 드라이브의 대략적인 속도를 확인해야 한다.

유의해야 할 것은 SSD를 PC에 연결하는 데 사용되는 기술이다.

  • SATA: 연결 유형과 전송 프로토콜을 나타내며, 대부분의 2.5인치 및 3.5인치 하드 드라이브와 SSD를 PC에 연결한다. SATA III 속도는 약 600MBps에 달할 수 있으며, 대부분의 현대 드라이브는 최대 속도를 제공한다.
  • PCIe: 이 인터페이스는 컴퓨터의 4개의 PCIe 레인을 활용해 SATA 속도를 훨씬 능가해 거의 4GBps를 제공한다(PCIe 3세대). 이런 파괴적인 속도는 강력한 NVMe 드라이브와 잘 어울린다. 메인보드의 PCIe 레인과 M.2 슬롯 모두 PCIe 인터페이스를 지원하도록 유선으로 연결할 수 있으며, “검정” M.2 드라이브를 PCIe 레인에 슬롯화할 수 있는 어댑터를 구입할 수 있다.
  • NVMe: 비휘발성 메모리 익스프레스(Non-Volatile Memory Express) 기술은 PCIe의 풍부한 대역폭을 활용해 SATA 기반 드라이브를 비교조차 못할 정도로 매우 빠른 SSD를 만든다. NVMe에 대해 더 자세히 알고 싶다면 여기를 클릭하라.
  • M.2: 설명이 쉽지 않다. 많은 사람이 M.2 드라이브가 모두 NVMe 기술과 PCIe 속도를 사용한다고 생각하지만 사실이 아니다. M.2는 단순히 폼 팩터에 불과하다. 물론 대부분의 M.2 SSD는 NVMe를 사용하지만 일부는 여전히 SATA를 사용한다. 많은 최신 울트라북이 저장을 위해 M.2를 사용한다.
  • U.2 및 mSATA: mSATA 및 U.2 SSD에서도 문제가 발생할 수 있지만, 이 형식을 지원하는 메인보드와 제품 가용성은 드물다. M.2가 대중화되기 전에 일부 구형 울트라북에 mSATA가 포함되어 있으며, 필요할 경우 드라이브를 사용할 수 있다.  

물론 속도도 중요하지만, 대부분의 최신 SSD는 SATA III 인터페이스를 지원한다. 그러나 전부 다 그런 것은 아니다.

구입전 사용자가 알아야 할 NVMe SSD

NVMe 드라이브는 구입하기 전에 어떤 특징을 갖고 있는지 알고 있어야 한다. 표준 SATA SSD는 이미 PC 부팅 시간과 로딩 시간을 대폭 단축하고 훨씬 저렴하다. NVMe 드라이브는 특히 대량으로 데이터를 정기적으로 전송하는 경우, 삼성 960 프로와 같은 M.2 폼 팩터나 또는 PCIe 드라이브가 가장 많은 효과를 누릴 수 있다. 그렇지 않으면 NVMe 드라이브는 가격만 비쌀뿐 가치도 없다.  

NVMe SSD를 구입하기로 결정한 경우, PC에서 SSD를 처리할 수 있는지 확인해야 한다. 이는 비교적 새로운 기술이므로, 지난 몇 년 내에 제작한 메인보드만이 M.2 연결이 가능하다. 스카이레이크 시대의 AMD 라이젠과 주류 인텔 칩을 고려하라. PCIe 어댑터에 탑재된 NVMe SSD는 M.2 채택이 확산되기 전인 초기에 널리 사용됐지만 지금은 매우 드물다. NVMe SSD를 구입하기 전에 실제로 NVMe를 사용할 수 있는지 확인하고 최대한 활용하기 위해서는 4개의 PCIe 레인이 필요하다는 점에 유의해야 한다. 

NVMe 드라이브를 최대한 활용하려면 운영체제를 실행해야 하기 때문에 드라이브를 인식하고 부팅할 수 있는 시스템이 있어야 한다. 지난 1~2년 전에 구입한 PC는 NVMe 드라이브에서 부팅하는데 아무런 문제가 없지만, 좀 더 오래된 메인보드는 지원하지 않을 수 있다. 구글에서 자신의 메인보드를 검색하고 NVMe 부팅을 지원하는지 확인하라. 보드의 BIOS 업데이트를 설치해야 할 수도 있다. 하드웨어가 NVMe SSD에서 부팅할 수 없는 경우에도 보조 드라이브로 사용할 수 있어야 한다.  

2021 최고의 SSD 선택 가이드

Brad Chacos | PCWorldSSD(Solid-State Drive)로 전환하는 것은 PC를 위한 최상의 업그레이드다. SSD는 긴 부팅 시간을 없애고, 프로그램과 게임 로드 속도를 높이는 등 일반적으로 컴퓨터를 빠르게 한다. 그러나 모든 SSD가 동일한 것은 아니다. 최고의 SSD는 합리적인 가격으로 훌륭한 성능을 제공한다. 가격에 고민하지 않을 경우, 놀라울 정도의 빠른 읽기 및 쓰기 속도를 제공하는 제품도 있다. 

대부분 사용자를 위한 최고의 SSD: SK 하이닉스 골드 S31 SATA SSD  
가성비 최고의 SSD: 애드링크 S22 QLC SATA 2.5인치 SSD 
최고의 NVME SSD: SK 하이닉스 골드 P31 M.2 NVMe SSD(1TB) 
최고의 PCIe 4.0 SSD: 삼성 980 프로 PCIe 4.0 NVMe SSD(1TB)

많은 SSD가 2.5인치 폼 팩터로 제공되며 기존 하드 드라이브에서 사용하는 것과 동일한 SATA 포트를 통해 PC와 통신한다. 그러나 최첨단 NVMe(Non-Volatile Memory Express) 드라이브는 메인보드의 M.2에 직접 연결하는 작은 스틱 형태의 SSD다. PCIe 어댑터에 장착되는 이 드라이브는 구입하기 전에 메인보드에 슬롯이 있는지 확인해야 한다. 그래픽 카드나 사운드 카드처럼 메인보드에 꽂을 수 있는 SSD와 미래형 3D 크로스포인트(3D XPoint) 드라이브 등이 등장함에 따라 완벽한 SSD를 선택하는 것은 예전처럼 간단하지 않다. 

그래서 이 가이드가 필요하다. 본지는 사용자 상황에 적합한 SSD를 찾기 위해 수많은 SSD를 테스트했다. 본지가 선정한 최고 인기 제품과 SSD 선택 시 무엇을 고려해야 하는지 알아보자. 참고로, 이번 가이드는 내장형 SSD만 적용한 것이다. 


최신 SSD 뉴스

  • 구입해야 하는 SSD에 대한 가이드를 확인하고, 각 시스템에서 가장 적합한 SSD의 종류에 대해 알아보자. 
  • 인텔은 모든 데스크톱 소비자 버전의 옵테인(Optane) 드라이브를 단종시켰지만, 이 기술은 노트북과 서버에 그대로 남아있다. 옵테인 SSD는 엄청난 랜덤 액세스 성능과 놀라운 내구성을 제공했지만, 용량이 제한적이면서도 가격은 매우 높았다. 향후 노트북에서 느린 NAND SSD 속도를 높이기 위한 캐싱 형태의 기능으로 사용될 것이다. 
  • 스토리지 제조업체는 공급망 문제로 인해 출시 후 구성 요소를 조정하는 경우가 많지만, 한 PC하드웨어 전문매체는 최근 에이데이타(Adata)가 훨씬 느린 버전으로 XPG 8200 프로의 컨트롤러를 교체한 것을 포착했다.  


대부분 사용자를 위한 최고의 SSD, SK 하이닉스 골드 S31 SATA SSD 

ⓒ SK Hynix

삼성의 주력인 EVO SSD 제품군은 2014년 이래로 줄곧 본지의 권장 목록에서 1위를 차지했으며, 현재 삼성 860 EVO는 여전히 속도, 가격, 호환성 및 5년 보증 및 뛰어난 마법사 관리 소프트웨어의 안정성 등 조화를 원하는 사람들에게 좋은 선택지다. 그러나 대부분의 사람들은 SK 하이닉스 골드 S31을 사는 것이 낫다. 

골드 S31은 지금까지 본지가 테스트 한 가장 빠른 SATA SSD 가운데 하나일뿐만 아니라 동급 최강의 870 EVO와 견줄 수 있을만한 거리에 있다. 하지만 이 드라이브의 가격은 놀랍다. 250GB 드라이브의 경우 44달러, 500GB 드라이브의 경우 57달러, 1TB의 경우 105달러인 골드 S31은 500GB 모델에 70달러를 청구하는 삼성 제품보다 훨씬 저렴하다(국내에서는 1T 13만 5,000원, 500G 7만 5,000원, 250G 4만 8,000원에 판매하고 있다. 편집자 주). .

리뷰 당시 본지는 “실제 48GB 사본 테스트 수행시 골드 S31은 지속적인 읽기 및 쓰기 작업에서 테스트한 제품 가운데 가장 빠른 드라이브임을 입증했다”라고 평가했다. 이 제품은 이 평가로 충분하다.

SK 하이닉스는 정확히 제품 이름이 아니기 때문에 브랜드 자체에 대해 조금 딴지를 걸 수도 있다. 그럼에도 불구하고 SK 하이닉스는 지구상에서 가장 큰 반도체 제조업체 가운데 하나다. SK 하이닉스는 시작부터 NAND 및 컨트롤러 기술을 개발해왔으며, 수많은 컴퓨터 업체의 SSD 제조업체였지만 판매선상에는 자리하지 못했다. 이제 그 선상에 섰고, 결과는 훌륭했다. 

더 큰 용량이 필요하거나 단순히 검증된 브랜드를 고수하고 싶다면, 250GB, 500GB, 1TB 및 2TB 모델로 제공하는 삼성 870 EVO를 선택하면 된다. 이 제품은 SK 하이닉스보다 조금 더 빠르지만, 그 대가로 비용이 더 많이 든다. 삼성 870 EVO는 대부분의 SSD에 비해 매우 매력적이고 저렴한 패키지를 제공하고 있기 때문에 골드 S31이 얼마나 더 좋은 것인지 알 수 있다. 삼성 870 QVO는 1TB에서 무려 8TB에 이르는 용량을 가진 또 다른 강력한 경쟁 제품이지만 다음 세션에서 논의할 것이다.


가성비 최고의 SSD: 애드링크(AddLink) S22 QLC SATA 2.5인치 SSD

ⓒ Addlink

매우 저렴한 가격에 훌륭한 성능을 제공하는 SK하이닉스 골드 S31은 최고의 가성비 SSD로, 대부분의 사용자에게 최고의 SSD다. 하지만 어떤 이유로든 골드 S31에 관심이 없는 이들에겐 더 많은 선택지가 있다. 

이제 기존의 MLC(Multi-Level Cell)와 TLC(Triple-Level Cell) SSD 가격이 급락함에 따라 제조업체는 SSD 가격을 더욱 낮출 수 있는 새로운 QLC(Quad-Level Cell) 드라이브를 출시했다. 

이 새로운 기술을 통해 제조업체는 매우 빠른 SSD에 버금가는 속도와 함께 하드 드라이브와 같은 수준의 용량을 가진 SSD를 출시할 수 있었다. 다만 삼성 860 QVO를 포함한 1차 QLC 드라이브는 수십 기가바이트의 데이터를 한번에 전송할 때 쓰기 속도가 하드 드라이브 수준으로 떨어졌다. 

애드링크(Addlink) S22 QLC SSD는 이 같은 어려움을 겪지 않는다. 기존 TLC SSD는 여전히 QLC 드라이브에 비해 속도 우위를 유지하고 있지만, 애드링크 S22는 512GB에 59달러, 1TB에 99달러의 저렴한 가격에 판매하고 있다. 하지만 SK 하이닉스 골드 S31이 거의 같은 금액으로 판매되고 있다는 사실에 주목할 필요가 있다. 

대량의 데이터를 한번에 이동할 계획이 없고, 더 많은 저장공간이 필요하다면 삼성의 2세대 QLC 제품인 삼성 870 QVO가 좋은 선택이다. 실제로 애드링크의 SSD보다 조금 더 빠르다. 그러나 아마존에서 1TB가 110달러, 2TB의 경우 205달러, 4TB 450달러, 8TB 900달러로 더 비싸다. 1TB보다 적은 용량은 판매하지 않는다. 구형 삼성 860 QVO도 여전히 좋은 선택이긴 하지만 최신 870 QVO는 모든 면에서 최고다.

하지만 메인보드가 더 빠르고 새로운 NVMe M.2 드라이브를 지원한다면 선택지는 달라진다. 


최고의 NVMe SSD: SK 하이닉스 골드 P31 M.2 NVMe SSD(1TB) 

ⓒ SK Hynix

성능이 가장 중요하다면 삼성 970 프로 또는 씨게이트 파이어쿠다(Seagate FireCuda) 510이 가장 빠른 NVMe SSD이지만, 대부분의 사람은 SK 하이닉스 골드 P31을 구입하는 것이 좋다. SK 하이닉스는 가성비 범주에서 전체 SSD를 장악하고 있다. 

SK 하이닉스 골드 P31은 128비트 TLC NAND를 탑재한 최초의 NVMe SSD이며, 96 NAND 레이어를 사용하는 다른 제품들을 뛰어넘었다. 본지가 테스트한 모델은 크리스탈디스크마크(CrystalDiskMark) 6와 AS SSD의 종합 벤치마크에서도 완전히 인정받았으며, 보도자료에서 주장했던 3.5Gbps 읽기 및 쓰기 속도에 거의 도달했다.

또한 실제 48GB 및 450GB 파일 전송 테스트에서 더 비싼 SSD에 비교했을 때도 뒤지지 않았다. SK 하이닉스 골드 P31은 최상급 드라이브처럼 작동하지만, 저렴한 드라이브보다 조금 더 비쌀 뿐이다. 500G 제품은 75달러에, 1TB 제품은 125달러에 구입할 수 있다(국내에서는 1T 19만 8,000원, 500G 9만 8,000원에 판매하고 있다. 편집자 주). 

마이크론 크루셜(Crucial) P5는 비용 효율적인 NVMe SSD로, 만약 SK 하이닉스 골드 P31이 없었다면, 최고의 선택지가 될 수 있었다. 하지만 골드 P31가 조금 더 빠르고, 조금 더 저렴하다. 그래도 크루셜 P5는 대안 제품이 될 수 있다.

하지만 예산이 빠듯하다면, 약간 더 적은 비용으로 매력적인 선택지를 찾을 수 있다. 웨스턴 디지털 블루(Western Digital Blue) SN550 NVMe SSD는 앞서 언급한 제품처럼 빠르거나 화려한 성능을 갖고 있진 않다. 하지만 가격이 훨씬 저렴하다. 250GB의 경우 45달러, 500GB의 경우 65달러, 1TB의 경우 130달러와 같은 보급형 가격에도 불구하고 WD 블루 SN550은 고가의 제품 성능을 충분히 발휘할 수 있다. 신뢰성에 대한 좋은 이력을 가진 기존 브랜드를 이은 제품이며, 평균보다 긴 5년 보증을 제공한다. 


또 다른 훌륭한 NVMe SSD 

– 애드링크 S70 NVMe SSD: 좀 더 높은 성능을 원한다면 애드링크(Addlink) S70 NVMe SSD 또한 탁월한 선택지가 될 수 있다. 이 제품은 WD 드라이브보다 성능이 약간 우수하다. 하지만 본지는 이 제품의 가격이 인상된 후부터는 일상적인 컴퓨터 사용자에게 WD 블루 SN550을 추천한다. 애드링크는 WD만큼 잘 알려져 있지 않지만, S70 NVMe SSD에 대해 5년 보증을 제공한다.  

– PNY XLR8 CS 3030: 이 제품은 좋은 가격에 빠른 성능을 제공하는 또 다른 선택지다. 하지만 일상적인 사용에는 탁월하지만, 긴 쓰기 작업에서는 수렁에 빠질 수 있다.

– 에이데이타의 XPG SX8200 프로와 킹스톤(Kingston) KC2500: 더 빠른 속도를 위해 좀더 많은 비용을 써도 괜찮다면 삼성 970 프로 수준의 성능을 지닌 에이데이타의 XPG SX8200 프로와 킹스톤 KC2500도 있다. 킹스톤 KC2500은 한번의 테스트에서 최고 등급에 도달하지 못했지만, 항상 선두권을 유지하고 있었다. 경쟁 제품과 거의 동일한 가격으로 구입할 수 있으며, 고성능 NVMe SSD를 구입하는 경우 고려해볼 만한 제품이다. 

새로운 유형의 대용량 SSD 덕분에 충분한 저장용량과 함께 엄청난 NVMe 속도를 얻을 수 있게 됐지만, 이에 대한 비용은 감수해야 한다. OWC 아우라 P12는 NVMe 평균 이상의 쓰기 성능과 4TB 제품을 929달러에 제공한다. 최고의 세이브런트 로켓(Sabrent Rocket) Q는 최고의 성능과 놀라운 8TB 용량으로 모든 것을 만족시키지만, 1,500달러라는 놀라운 가격이 기다리고 있다. 최첨단은 저렴하지 않다.


최고의 PCIe 4.0 SSD: 삼성 980 프로 PCIe 4.0 NVMe SSD(1TB)

ⓒ samsung

대부분의 NVMe SSD는 표준 PCIe 3.0 인터페이스를 사용하지만, 최첨단 기술을 지원하는 일부 제품에는 훨씬 더 빠른 PCIe 4.0 드라이브가 있다. 현재 AMD의 라이젠 3000 프로세서만 PCIe 4.0을 지원하며 X570 또는 B550 메인보드에 장착하는 경우에만 지원한다. 하지만 이 기준을 충족하면 PCIe 4.0 SSD는 가장 빠른 PCIe 3.0 NVMe SSD가 따라오지 못할 성능을 보여준다. 

커세어(Corsair), 기가바이트(Gigabyte), 세이브런트는 최초의 PCIe 4.0 SSD를 출시했으며, 모두 약 200달러에 1TB 용량과 유사한 성능을 제공했다. 하지만 본지가 선정한 최고의 PCIe 4.0 SSD는 조금 더 비싸다. 

본지는 최근에서야 PCIe 4.0 SSD 테스트를 추가했지만, 지금까지 테스트한 제품 가운데 최고는 삼성 980 프로였다. 이 제품은 테스트에서 삼성이 주장한 7Gbps 읽기 속도와 5Gbps 쓰기 속도를 초과했다. 이 제품은 실제 파일 전송 테스트를 통과했지만, 450GB 전송 테스트에서 발견한 것처럼 막대한 양의 데이터를 전송하는 경우 속도가 약간 느려질 수 있다. 하지만 대부분의 사용자가 SSD를 이렇게 힘들게 다루진 않는다.

하지만 모든 성능은 프리미엄급이다. 그럼에도 불구하고 250GB 90달러, 500GB 150달러, 1TB 용량은 230달러이다. 

WD 블랙 SN850은 삼성 980 프로의 성능에 뒤처져 있지만, 거의 같은 가격으로 판매한다. 본지는 리뷰에서 “최강의 단일 SSD PCIe4 스토리지 성능을 찾는다면 어느 쪽도 문제가 되지 않을 것”이라고 평가했다. 

 

PCIe 4.0 속도가 빠른 SSD를 원하지만 삼성의 동급 최고의 성능을 위해 많은 비용을 소비하고 싶지 않다면 XPG 겜믹스 S50 라이트를 고려한다. 본지는 “XPG 겜믹스 S50 라이트는 우리가 테스트한 최초의  PCIe 4 SSD로, 차세대라는 추가 비용이 들지 않는다. 실제로 시스템을 실행하는 시스템에서는 삼성 980 프로와 차이를 구분하기 어려울 것이다”라고 설명했다.  

겜믹스 S50 라이트는 1TB의 경우 140달러, 2TB의 경우 260달러다.


NVMe SSD 설정시 알아야 할 사항

NVMe 드라이브는 구입하기 전에 어떤 특징을 갖고 있는지 알고 있어야 한다. 표준 SATA SSD는 이미 PC 부팅 시간과 로딩 시간을 대폭 단축하고 훨씬 저렴하다. NVMe 드라이브는 특히 대량으로 데이터를 정기적으로 전송하는 경우, 삼성 960 프로와 같은 M.2 폼 팩터나 또는 PCIe 드라이브를 가장 많은 효과를 누릴 수 있다. 그렇지 않으면 NVMe 드라이브는 가격만 비쌀뿐 가치도 없다.  

NVMe SSD를 구입하기로 결정한 경우, PC에서 SSD를 처리할 수 있는지 확인해야 한다. 이는 비교적 새로운 기술이므로, 지난 몇 년 내에 제작한 메인보드만 M.2 연결이 가능하다. 스카이레이크 시대의 AMD 라이젠과 주류 인텔 칩을 고려한다. PCIe 어댑터에 탑재된 NVMe SSD는 M.2 채택이 확산되기 전인 초기에 널리 사용됐지만 지금은 매우 드물다. NVMe SSD를 구입하기 전에 실제로 NVMe를 사용할 수 있는지 확인하고 최대한 활용하기 위해서는 4개의 PCIe 레인이 필요하다는 점에 유의해야 한다. 

NVMe 드라이브를 최대한 활용하려면 운영체제를 실행해야 하므로 드라이브를 인식하고 부팅할 수 있는 시스템이 있어야 한다. 지난 1~2년동안 구입한 PC라면 NVMe 드라이브를 부팅하는 데 문제가 없어야하지만, 이전 메인보드에서는 지원이 어려울 수 있다. 구글에서 메인보드를 검색하고 NVMe에서 부팅을 지원하는지 확인한다. 보드에서 BIOS 업데이트를 설치해야 할 수도 있다. 하드웨어가 NVMe SSD에서 부팅할 수 없는 경우에도 시스템은 이를 보조 드라이브로 사용할 수 있어야 한다. 


SSD 선택에서 고려해야 할 것

물론 저장 용량과 가격이 중요하다. 또한 긴 보증기간은 조기 데이터 사망에 대한 우려를 완화시킬 수 있다. 대부분의 SSD 제조업체는 3년 보증을 제공하며 일부 더 좋은 모델은 5년을 보증한다. 그러나 이전 세대의 SSD와는 달리, 몇 년 전에 혹독한 내구성 테스트로 입증한 것처럼 최신 SSD는 일반 소비자가 어지간히 사용해서는 마모되지 않는다.

가장 유의해야 할 것은 SSD를 PC에 연결하는 데 사용되는 기술이다.
– SATA: 연결 유형과 전송 프로토콜을 나타내며, 대부분의 2.5인치 및 3.5인치 하드 드라이브와 SSD를 PC에 연결한다. SATA III 속도는 약 600MBps에 달할 수 있으며, 대부분의 현대 드라이브는 최대 속도를 제공한다. 

– PCIe: 이 인터페이스는 컴퓨터의 4개의 PCIe 레인을 활용해 SATA 속도를 훨씬 능가해 거의 4GBps를 제공한다(PCIe 3세대). 이런 파괴적인 속도는 강력한 NVMe 드라이브와 잘 어울린다. 메인보드의 PCIe 레인과 M.2 슬롯 모두 PCIe 인터페이스를 지원하도록 유선으로 연결할 수 있으며, M.2 드라이브를 PCIe 레인에 슬롯화할 수 있는 어댑터를 구입할 수 있다. 

– NVMe: 비휘발성 메모리 익스프레스(Non-Volatile Memory Express) 기술은 PCIe의 풍부한 대역폭을 활용해 SATA 기반 드라이브와는 비교조차 못할 정도로 매우 빠른 SSD를 만든다. NVMe에 대해 더 자세히 알고 싶다면 여기를 클릭하라.  

– M.2: 설명이 쉽지 않다. 많은 사람이 M.2 드라이브가 모두 NVMe 기술과 PCIe 속도를 사용한다고 생각하지만 사실이 아니다. M.2는 단순히 폼 팩터에 불과하다. 물론 대부분의 M.2 SSD는 NVMe를 사용하지만 일부는 여전히 SATA를 사용한다. 많은 최신 울트라북이 저장을 위해 M.2를 사용한다. 

– U.2 및 mSATA: mSATA 및 U.2 SSD에서도 문제가 발생할 수 있지만, 이 형식을 지원하는 메인보드와 제품 가용성은 드물다. M.2가 대중화되기 전에 일부 구형 울트라북에 mSATA가 포함되어 있으며, 필요할 경우 드라이브를 사용할 수 있다.  

물론 속도도 중요하지만, 대부분의 최신 SSD는 SATA 3 인터페이스를 지원한다. 그러나 전부 다 그런 것은 아니다.


SSD vs. 하드 드라이브 

SSD가 필요한가? “필요하다.” 본지는 모든 사람이 SSD로 업그레이드할 것으로 진심으로 권장한다. 가장 빠른 기계식 하드드라이브도 SSD 속도에는 미치지 못한다. 기존 노트북, 데스크톱의 하드드라이브를 SSD로 교체하면 완전히 새로운 시스템처럼 느낄 수 있다. SSD를 구입하는 것은 컴퓨터를 업그레이드하는 데 가장 적합한 선택이다. 

SSD는 기계식 하드드라이브보다 기가바이트 당 저장 비용이 많이 들기 때문에 대용량으로 제공하지 않는 경우가 많다. 속도와 저장 공간이 동시에 필요한 경우, 128GB 크루셜 BX300과 같은 제한된 용량의 SSD를 구입해 부팅 드라이브로 사용하고, 기존 하드드라이브를 PC의 보조 저장장치로 설정한다. 프로그램을 부팅 드라이브에 넣고 미디어 및 기타 파일을 하드드라이브에 저장하면 준비가 다 된 것이다. editor@itworld.co.kr 

FLOW-3D 수치해석용 컴퓨터 선택 가이드

Top 20 Fastest Desktops for 2024

본 자료는 Computer에 대한 전문적인 지식보다는 수치해석을 주 목적으로 FLOW-3D 를 이용하기 위한 해석용 컴퓨터를 선택할 때 도움을 주기 위한 자료입니다.

흔히 고성능 컴퓨터는 표준 데스크톱 컴퓨터와 어떻게 다른지 궁금하게 생각하는데, 보통 HPC(high performance computing)는 더욱 강력한 프로세서, 더 큰 메모리, 뛰어난 그래픽 성능을 갖추고 있어 일반적인 표준 데스크톱보다 훨씬 빠르게 여러 가지 복잡한 작업을 동시에 처리할 수 있습니다. 따라서 시중에서 판매하는 고사양의 컴퓨터에 CPU, Memory, Graphic Card 등을 보완하거나 고사양으로 만들어진 컴퓨터를 구매하게 되면, 단일 노드의 HPC(high performance computing)와 유사한 성능을 확보할 수 있습니다.

하지만 개인이 여러 컴퓨터를 대상으로 테스트를 수행하기 어렵기 때문에, 전문가들이 테스트를 수행하여 공개하는 보고서를 참조하여 도움을 얻는 것이 효율적입니다.

아래 전문 성능비교 테스트 보고서가 시스템 선택에 도움이 될 것으로 생각합니다. 참고로, 당사는 기사를 제공하는 기관과 전혀 관련이 없음을 알려드립니다.

Top 20 Fastest Desktops for 2024

Edit: 2024-11-28

원문 출처: https://www.pcbenchmarks.net/fastest-desktop.html

PositionScoreBL#CPU TypeCPU speed (MHz)#Phys. CPUsOSMotherboardRAMVideo cardDate uploaded
126054.32223537Intel Core i9-14900KS31881Windows 11 Pro for Workstations build 26100 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 APEX ENCORE49.0 GBGeForce RTX 40902024-10-19 05:20:40
225140.32102766Intel Core i9-14900KS31881Windows 11 Pro for Workstations build 26100 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 APEX ENCORE49.0 GBGeForce RTX 40902024-05-16 19:37:40
325130.72229143Intel Core i9-14900KS31881Windows 11 Pro for Workstations build 26100 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 FORMULA32.5 GBGeForce RTX 40902024-10-25 16:08:42
425022.62096097Intel Core i9-14900KF31881Windows 11 Pro for Workstations build 26100 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 APEX ENCORE49.0 GBGeForce RTX 40902024-05-08 01:22:49
524977.12093965Intel Core i9-14900KF31871Windows 11 Pro for Workstations build 22631 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 APEX ENCORE49.0 GBGeForce RTX 40902024-05-04 21:23:54
624550.71756060Intel Core i9-13900KS31881Windows 10 Home build 19045 (64-bit)Micro-Star International Co., Ltd. MAG Z790 TOMAHAWK WIFI DDR4(MS-7D91)32.5 GBGeForce RTX 40902023-02-27 01:36:21
724124.92010540Intel Core i9-14900KF31881Windows 11 Pro for Workstations build 22631 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 APEX ENCORE32.6 GBGeForce RTX 40902024-01-30 06:25:31
823924.41989560Intel Core i9-13900KS31881Windows 11 Pro for Workstations build 22631 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 APEX ENCORE32.6 GBGeForce RTX 40902024-01-06 11:51:42
923117.01986111Intel Core i9-14900K31871Windows 11 Pro for Workstations build 22631 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 APEX ENCORE32.6 GBGeForce RTX 40902024-01-02 23:37:24
1023035.82196479Intel Core i9-14900K31881Windows 11 Professional Edition build 26120 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 FORMULA32.5 GBGeForce RTX 40902024-09-16 06:54:48
1123011.32219063AMD Ryzen 9 9950X43011Windows 11 Pro for Workstations build 26100 (64-bit)ASUSTeK COMPUTER INC. ROG CROSSHAIR X870E HERO48.8 GBGeForce RTX 40902024-10-14 01:33:56
1223002.92219004AMD Ryzen 9 9950X43011Windows 11 Pro for Workstations build 26100 (64-bit)ASUSTeK COMPUTER INC. ROG CROSSHAIR X870E HERO48.8 GBGeForce RTX 40902024-10-13 22:45:27
1322696.62216075Intel Core i9-14900KS31881Windows 11 Professional Edition build 26100 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 APEX ENCORE49.0 GBGeForce RTX 40902024-10-10 10:13:14
1422676.21936617Intel Core i9-14900K31871Windows 11 Professional Edition build 22631 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 APEX ENCORE32.6 GBGeForce RTX 40902023-10-31 18:47:25
1522626.02214448AMD Ryzen 9 9950X43001Windows 11 Pro for Workstations build 26100 (64-bit)ASUSTeK COMPUTER INC. ROG CROSSHAIR X870E HERO32.4 GBGeForce RTX 40902024-10-08 12:43:52
1622561.71947982Intel Core i9-14900K31881Windows 11 Professional Edition build 22631 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 FORMULA32.5 GBGeForce RTX 40902023-11-16 12:20:10
1722561.52214771AMD Ryzen 9 9950X43001Windows 11 Pro for Workstations build 26100 (64-bit)ASUSTeK COMPUTER INC. ROG CROSSHAIR X870E HERO32.4 GBGeForce RTX 40902024-10-08 21:38:56
1822423.62014883Intel Core i9-14900K31881Windows 11 Professional Edition build 22635 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 FORMULA32.5 GBGeForce RTX 40902024-02-03 17:43:54
1922378.52079225Intel Core i9-14900K31881Windows 11 Professional Edition build 26100 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 FORMULA32.5 GBGeForce RTX 40902024-04-16 04:53:25
2022368.41947167Intel Core i9-14900K31871Windows 11 Professional Edition build 22631 (64-bit)ASUSTeK COMPUTER INC. ROG MAXIMUS Z790 FORMULA32.5 GBGeForce RTX 40902023-11-15 11:19:39

CPU 벤치마크

아래는 차트에 나타나는 모든 단일 및 다중 소켓 CPU 유형의 목록입니다. 열특정 프로세서 이름을 클릭하면 해당 프로세서가 나타나는 차트로 이동하여 강조 표시됩니다.

https://www.cpubenchmark.net/CPU_mega_page.html

CPU NameCoresCPU MarkThread MarkTDP (W)SocketCategory
AMD Ryzen Threadripper PRO 7995WX96153,5983,964350sTR5Desktop
AMD Ryzen Threadripper 7980X64133,9023,956350sTR5Desktop
AMD Ryzen Threadripper PRO 7985WX64133,1943,890350sTR5Desktop
[Dual CPU] AMD Ryzen Threadripper PRO 3995WX64113,6932,559280sWRX8Desktop, Server
[Dual CPU] AMD Ryzen Threadripper PRO 3975WX3298,8112,676280sWRX8Desktop, Server
AMD Ryzen Threadripper 7970X3298,6854,137350sTR5Desktop
AMD Ryzen Threadripper PRO 7975WX3295,6234,065350sTR5Desktop
AMD Ryzen Threadripper PRO 5995WX6493,1923,207280sWRX8Desktop, Server
AMD Ryzen Threadripper PRO 3995WX6483,6972,598280sWRX8Desktop, Server
AMD Ryzen Threadripper 7960X2483,6244,123350sTR5Desktop
AMD Ryzen Threadripper PRO 7965WX2480,9203,945350sTR5Desktop
AMD Ryzen Threadripper 3990X6480,6592,565280sTRX4Desktop
AMD Ryzen Threadripper PRO 5975WX3275,6543,315280sWRX8Desktop, Server
Intel Core Ultra 9 285K2468,7685,087125FCLGA1851Desktop
AMD Ryzen Threadripper PRO 5965WX2466,6803,359280sWRX8Desktop, Server
AMD Ryzen 9 9950X1666,3584,731170AM5Desktop
[Dual CPU] AMD Ryzen Threadripper PRO 3955WX1663,8852,439280sWRX8Desktop, Server
AMD Ryzen Threadripper 3970X3263,1152,665280sTRX4Desktop
AMD Ryzen 9 7950X1662,7044,275170AM5Desktop
AMD Ryzen 9 7950X3D1662,5114,149120AM5Desktop
AMD Ryzen Threadripper PRO 3975WX3262,4772,656280sWRX8Desktop, Server
Intel Core i9-14900KS2462,3744,871150FCLGA1700Desktop
Intel Core Ultra 7 265KF2061,9644,956125FCLGA1851Desktop
Intel Core i9-13900KS2461,5364,746150FCLGA1700Desktop
Intel Core i9-14900K2460,1164,735125FCLGA1700Desktop
AMD Ryzen Threadripper PRO 7955WX1659,9684,096350sTR5Desktop
Intel Core i9-14900KF2459,5634,710125FCLGA1700Desktop
Intel Core Ultra 7 265K2059,1624,784125FCLGA1851Desktop
Intel Core i9-13900K2458,9964,620125FCLGA1700Desktop
Intel Core i9-13900KF2458,3044,609125FCLGA1700Desktop
AMD Ryzen Threadripper 3960X2454,8912,682280sTRX4Desktop
AMD Ryzen 9 9900X1254,6954,684120AM5Desktop

Hardware Selection for FLOW-3D Products – FLOW-3D

부분 업데이트 / ㈜에스티아이씨앤디 솔루션사업부

In this blog, Flow Science’s IT Manager Matthew Taylor breaks down the different hardware components and suggests some ideal configurations for getting the most out of your FLOW-3D products.

개요

본 자료는 Flow Science의 IT 매니저 Matthew Taylor가 작성한 자료를 기반으로 STI C&D에서 일부 자료를 보완한 자료입니다. 본 자료를 통해 FLOW-3D 사용자는 최상의 해석용 컴퓨터를 선택할 때 도움을 받을 수 있을 것으로 기대합니다.

수치해석을 하는 엔지니어들은 사용하는 컴퓨터의 성능에 무척 민감합니다. 그 이유는 수치해석을 하기 위해 여러 준비단계와 분석 시간들이 필요하지만 당연히 압도적으로 시간을 소모하는 것이 계산 시간이기 때문일 것입니다.

따라서 수치해석용 컴퓨터의 선정을 위해서 단위 시간당 시스템이 처리하는 작업의 수나 처리량, 응답시간, 평균 대기 시간 등의 요소를 복합적으로 검토하여 결정하게 됩니다.

또한 수치해석에 적합한 성능을 가진 컴퓨터를 선별하는 방법으로 CPU 계산 처리속도인 Flops/sec 성능도 중요하지만 수치해석을 수행할 때 방대한 계산 결과를 디스크에 저장하고, 해석결과를 분석할 때는 그래픽 성능도 크게 좌우하기 때문에 SSD 디스크와 그래픽카드에도 관심을 가져야 합니다.

FLOW SCIENCE, INC. 에서는 일반적인 FLOW-3D를 지원하는 최소 컴퓨터 사양과 O/S 플랫폼 가이드를 제시하지만, 도입 담당자의 경우, 최상의 조건에서 해석 업무를 수행해야 하기 때문에 가능하면 최고의 성능을 제공하는 해석용 장비 도입이 필요합니다. 이 자료는 2022년 현재 FLOW-3D 제품을 효과적으로 사용하기 위한 하드웨어 선택에 대해 사전에 검토되어야 할 내용들에 대해 자세히 설명합니다. 그리고 실행 중인 시뮬레이션 유형에 따라 다양한 구성에 대한 몇 가지 아이디어를 제공합니다.

CPU 최신 뉴스

2024년 04월 01일 기준

CPU Benchmarks
이미지 출처 : https://www.cpubenchmark.net/high_end_cpus.html

CPU의 선택

CPU는 전반적인 성능에 큰 영향을 미치며, 대부분의 경우 컴퓨터의 가장 중요한 구성 요소입니다. 그러나 데스크탑 프로세서를 구입할 때가 되면 Intel 과 AMD의 모델 번호와 사양을 이해하는 것이 어려워 보일 것입니다.
그리고, CPU 성능을 평가하는 방법에 의해 가장 좋은 CPU를 고른다고 해도 보드와, 메모리, 주변 Chip 등 여러가지 조건에 의해 성능이 달라질 수 있기 때문에 성능평가 결과를 기준으로 시스템을 구입할 경우, 단일 CPU나 부품으로 순위가 정해진 자료보다는 시스템 전체를 대상으로 평가한 순위표를 보고 선정하는 지혜가 필요합니다.

PassMark - CPU Mark High End CPUs Updated 31st of March 2024
PassMark – CPU Mark High End CPUs Updated 31st of March 2024

<출처>https://www.cpubenchmark.net/high_end_cpus.html

수치해석을 수행하는 CPU의 경우 예산에 따라 Core가 많지 않은 CPU를 구매해야 하는 경우도 있을 수 있습니다. 보통 Core가 많다고 해석 속도가 선형으로 증가하지는 않으며, 해석 케이스에 따라 적정 Core수가 있습니다. 이 경우 예산에 맞는 성능 대비 최상의 코어 수가 있을 수 있기 때문에 Single thread Performance 도 매우 중요합니다. 아래 성능 도표를 참조하여 예산에 맞는 최적 CPU를 찾는데 도움을 받을 수 있습니다.

CPU 성능 분석 방법

부동소수점 계산을 하는 수치해석과 밀접한 Computer의 연산 성능 벤치마크 방법은 대표적으로 널리 사용되는 아래와 같은 방법이 있습니다.

FLOW-3D의 CFD 솔버 성능은 CPU의 부동 소수점 성능에 전적으로 좌우되기 때문에 계산 집약적인 프로그램입니다. 현재 출시된 사용 가능한 모든 CPU를 벤치마킹할 수는 없지만 상대적인 성능을 합리적으로 비교할 수는 있습니다.

특히, 수치해석 분야에서 주어진 CPU에 대해 FLOW-3D 성능을 추정하거나 여러 CPU 옵션 간의 성능을 비교하기 위한 최상의 옵션은 Standard Performance Evaluation Corporation의 SPEC CPU2017 벤치마크(현재까지 개발된 가장 최신 평가기준임)이며, 특히 SPECspeed 2017 Floating Point 결과가 CFD Solver 성능을 매우 잘 예측합니다.

이는 유료 벤치마크이므로 제공된 결과는 모든 CPU 테스트 결과를 제공하지 않습니다. 보통 제조사가 ASUS, Dell, Lenovo, HP, Huawei 정도의 제품에 대해 RAM이 많은 멀티 소켓 Intel Xeon 기계와 같은 값비싼 구성으로 된 장비 결과들을 제공합니다.

CPU 비교를 위한 또 다른 옵션은 Passmark Software의 CPU 벤치마크입니다. PerformanceTest 제품군은 유료 소프트웨어이지만 무료 평가판을 사용할 수 있습니다. 대부분의 CPU는 저렴한 옵션을 포함하여 나열됩니다. 부동 소수점 성능은 전체 벤치마크의 한 측면에 불과하지만 다양한 워크로드에서 전반적인 성능을 제대로 테스트합니다.

예산을 결정하고 해당 예산에 해당하는 CPU를 선택한 후에는 벤치마크를 사용하여 가격에 가장 적합한 성능을 결정할 수 있습니다.

<참고>

SPEC의 벤치 마크 ( https://www.spec.org/benchmarks.html#cpu )

SPEC CPU 2017 (현재까지 가장 최근에 개발된 CPU 성능측정 기준)

다른 컴퓨터 시스템에서 컴퓨팅 계산에 대한 집약적인 워크로드를 비교하는데 사용할 수 있는 성능 측정을 제공하도록 설계된 SPEC CPU 2017에는 SPECspeed 2017 정수, SPECspeed 2017 부동 소수점, SPECrate 2017 정수 및 SPECrate 2017 부동 소수점의 4 가지 제품군으로 구성된 43 개의 벤치 마크가 포함되어 있습니다. SPEC CPU 2017에는 에너지 소비 측정을 위한 선택적 메트릭도 포함되어 있습니다.

<SPEC CPU 벤치마크 보고서>

벤치마크 결과보고서는 제조사별, 모델별로 테스트한 결과를 아래 사이트에 가면 볼 수 있습니다.

https://www.spec.org/cgi-bin/osgresults

<보고서 샘플>

  • SPEC CPU 2017

Designed to provide performance measurements that can be used to compare compute-intensive workloads on different computer systems, SPEC CPU 2017 contains 43 benchmarks organized into four suites: SPECspeed 2017 Integer, SPECspeed 2017 Floating Point, SPECrate 2017 Integer, and SPECrate 2017 Floating Point. SPEC CPU 2017 also includes an optional metric for measuring energy consumption.

클럭 대 코어

일반적으로 클럭 속도가 높은 칩은 CPU 코어를 더 적게 포함합니다. FLOW-3D는 병렬화가 잘되어 있지만, 디스크 쓰기와 같이 일부 작업은 기본적으로 단일 스레드 방식으로 수행됩니다. 따라서 데이터 출력이 빈번하거나 큰 시뮬레이션은 종종 더 많은 코어가 아닌, 더 높은 클럭 속도를 활용합니다. 마찬가지로 코어 및 소켓의 다중 스레딩은 오버헤드를 발생시키므로 작은 문제의 해석일 경우 사용되는 코어 수를 제한하면 성능이 향상될 수 있습니다.

CPU 아키텍처

CPU 아키텍처는 중요합니다. 최신 CPU는 일반적으로 사이클당 더 많은 기능을 제공합니다. 즉, 현재 세대의 CPU는 일반적으로 동일한 클럭 속도에서 이전 CPU보다 성능이 우수합니다. 또한 전력 효율이 높아져 와트당 성능이 향상될 수 있습니다. Flow Science에는 구형 멀티 소켓 12, 16, 24 코어 Xeon보다 성능이 뛰어난 최근 세대 10~12 Core i9 CPU 시스템을 보유하고 있습니다.

오버클럭

해석용 장비에서는 CPU를 오버클럭 하지 않는 것이 좋습니다. 하드웨어를 다년간의 투자라고 생각한다면, 오버클럭화는 발열을 증가시켜 수명을 단축시킵니다. CPU에 따라 안정성도 저하될 수 있습니다. CPU를 오버클럭 할 때는 세심한 열 관리가 권장됩니다.

하이퍼스레딩

<이미지출처:https://gameabout.com/krum3/4586040>

하이퍼스레딩은 물리적으로 1개의 CPU를 가상으로 2개의 CPU처럼 작동하게 하는 기술로 파이프라인의 단계수가 많고 각 단계의 길이가 짧을때 유리합니다. 다만 수치해석 처럼 모든 코어의 CPU를 100% 사용중인 장시간 수행 시뮬레이션은 일반적으로 Hyper Threading이 비활성화 된 상태에서 더 잘 수행됩니다. FLOW-3D는 100% CPU 사용률이 일반적이므로 새 하드웨어를 구성할 때 Hyper Threading을 비활성화하는 것이 좋습니다. 설정은 시스템의 BIOS 설정에서 수행합니다.

몇 가지 워크로드의 경우에는 Hyper Threading을 사용하여 약간 더 나은 성능을 보이는 경우가 있습니다. 따라서, 최상의 런타임을 위해서는 두 가지 구성중에서 어느 구성이 더 적합한지 시뮬레이션 유형을 테스트하는 것이 좋습니다.

스케일링

여러 코어를 사용할 때 성능은 선형적이지 않습니다. 예를 들어 12 코어 CPU에서 24 코어 CPU로 업그레이드해도 시뮬레이션 런타임이 절반으로 줄어들지 않습니다. 시뮬레이션 유형에 따라 16~32개 이상의 CPU 코어를 선택할 때는 FLOW-3D 및 FLOW-3D CAST의 HPC 버전을 사용하거나 FLOW-3D CLOUD로 이동하는 것을 고려하여야 합니다.

AMD Ryzen 또는 Epyc CPU

AMD는 일부 CPU로 벤치마크 차트를 석권하고 있으며 그 가격은 매우 경쟁력이 있습니다. FLOW SCIENCE, INC. 에서는 소수의 AMD CPU로 FLOW-3D를 테스트했습니다. 현재 Epyc CPU는 이상적이지 않고 Ryzen은 성능이 상당히 우수합니다. 발열은 여전히 신중하게 다뤄져야 할 문제입니다.

<관련 기사>

https://www.techspot.com/news/78122-report-software-fix-can-double-threadripper-2990wx-performance.html

Graphics 고려 사항

FLOW-3D는 OpenGL 드라이버가 만족스럽게 수행되는 최신 그래픽 카드가 필요합니다. 최소한 OpenGL 3.0을 지원하는 것이 좋습니다. 권장 옵션은 엔비디아의 쿼드로 K 시리즈와 AMD의 파이어 프로 W 시리즈입니다.

특히 엔비디아 쿼드로(NVIDIA Quadro)는 엔비디아가 개발한 전문가 용도(워크스테이션)의 그래픽 카드입니다. 일반적으로 지포스 그래픽 카드가 게이밍에 초점이 맞춰져 있지만, 쿼드로는 다양한 산업 분야의 전문가가 필요로 하는 영역에 광범위한 용도로 사용되고 있습니다. 주로 산업계의 그래픽 디자인 분야, 영상 콘텐츠 제작 분야, 엔지니어링 설계 분야, 과학 분야, 의료 분석 분야 등의 전문가 작업용으로 사용되고 있습니다. 따라서 일반적인 소비자를 대상으로 하는 지포스 그래픽 카드와는 다르계 산업계에 포커스 되어 있으며 가격이 매우 비싸서 도입시 예산을 고려해야 합니다.

유의할 점은 엔비디아의 GTX 게이밍 하드웨어는 볼륨 렌더링의 속도가 느리거나 오동작 등 몇 가지 제한 사항이 있습니다. 일반적으로 노트북에 내장된 통합 그래픽 카드보다는 개별 그래픽 카드를 강력하게 추천합니다. 최소한 그래픽 메모리는 512MB 이상을 권장합니다.

PassMark - G3D Mark High End Videocards
PassMark – G3D Mark High End Videocards

출처 : https://www.videocardbenchmark.net/high_end_gpus.html

원격데스크탑 사용시 고려 사항

Flow Science는 nVidia 드라이버 버전이 341.05 이상인 nVidia Quadro K, M 또는 P 시리즈 그래픽 하드웨어를 권장합니다. 이 카드와 드라이버 조합을 사용하면 원격 데스크톱 연결이 완전한 3D 가속 기능을 갖춘 기본 하드웨어에서 자동으로 실행됩니다.

원격 데스크톱 세션에 연결할 때 nVidia Quadro 그래픽 카드가 설치되어 있지 않으면 Windows는 소프트웨어 렌더링을 사용합니다. FLOW-3D 가 소프트웨어 렌더링을 사용하고 있는지 확인하려면 FLOW-3D 도움말 메뉴에서 정보를 선택하십시오. GDI Generic을 소프트웨어 렌더링으로 사용하는 경우 GL_RENDERER 항목에 표시됩니다.

하드웨어 렌더링을 활성화하는 몇 가지 옵션이 있습니다. 쉬운 방법 중 하나는 실제 콘솔에서 FLOW-3D를 시작한 다음 원격 데스크톱 세션을 연결하는 것입니다. Nice Software DCV 와 같은 일부 VNC 소프트웨어는 기본적으로 하드웨어 렌더링을 사용합니다.

RAM 고려 사항

프로세서 코어당 최소 4GB의 RAM은 FLOW-3D의 좋은 출발입니다. POST Processor를 사용하여 후처리 작업을 할 경우 충분한 양의 RAM을 사용하는 것이 좋습니다.

현재 주력제품인 DDR4보다 2배 빠른 DDR5가 곧 출시된다는 소식도 있습니다.

일반적으로 FLOW-3D를 이용하여 해석을 할 경우 격자(Mesh)수에 따라 소요되는 적정 메모리 크기는 아래와 같습니다.페이지 보기

  • 초대형 (2억개 이상의 셀) : 최소 128GB
  • 대형 (60 ~ 1억 5천만 셀) : 64 ~ 128GB
  • 중간 (30-60백만 셀) : 32-64GB
  • 작음 (3 천만 셀 이하) : 최소 32GB

HDD 고려 사항

수치해석은 해석결과 파일의 데이터 양이 매우 크기 때문에 읽고 쓰는데, 속도면에서 매우 빠른 SSD를 적용하면 성능면에서 큰 도움이 됩니다. 다만 SSD 가격이 비싸서 가성비 측면을 고려하여 적정수준에서 결정이 필요합니다.

CPU와 저장장치 간 데이터가 오고 가는 통로가 그림과 같이 3가지 방식이 있습니다. 이를 인터페이스라 부르며 SSD는 흔히 PCI-Express 와 SATA 통로를 이용합니다.

흔히 말하는 NVMe는 PCI-Express3.0 지원 SSD의 경우 SSD에 최적화된 NVMe (NonVolatile Memory Express) 전송 프로토콜을 사용합니다. 주의할 점은 MVMe중에서 SATA3 방식도 있기 때문에 잘 구별하여 구입하시기 바랍니다.

그리고 SSD를 선택할 경우에도 SSD 종류 중에서 PCI Express 타입은 매우 빠르고 가격이 고가였지만 최근에는 많이 저렴해졌습니다. 따라서 예산 범위내에서 NVMe SSD등 가장 효과적인 선택을 하는 것이 좋습니다.
( 참고 : 해석용 컴퓨터 SSD 고르기 참조 )

기존의 물리적인 하드 디스크의 경우, 디스크에 기록된 데이터를 읽기 위해서는 데이터를 읽어내는 헤드(바늘)가 물리적으로 데이터가 기록된 위치까지 이동해야 하므로 이동에 일정한 시간이 소요됩니다. (이러한 시간을 지연시간, 혹은 레이턴시 등으로 부름) 따라서 하드 디스크의 경우 데이터를 읽기 위한 요청이 주어진 뒤에 데이터를 실제로 읽기까지 일정한 시간이 소요되는데, 이 시간을 일정한 한계(약 10ms)이하로 줄이는 것이 불가능에 가까우며, 데이터가 플래터에 실제 기록된 위치에 따라서 이러한 데이터에의 접근시간 역시 차이가 나게 됩니다.

하지만 HDD의 최대 강점은 가격대비 용량입니다. 현재 상용화되어 판매하는 대용량 HDD는 12TB ~ 15TB가 공급되고 있으며, 이는 데이터 저장이나 백업용으로 가장 좋은 선택이 됩니다.
결론적으로 데이터를 직접 읽고 쓰는 드라이브는 SSD를 사용하고 보관하는 용도의 드라이브는 기존의 HDD를 사용하는 방법이 효과적인 선택이 될 수 있습니다.

PassMark – Disk Rating High End Drives

PassMark - Disk Rating High End Drives
PassMark – Disk Rating High End Drives

출처 : https://www.harddrivebenchmark.net/high_end_drives.html

상기 벤치마크 테스트는 테스트 조건에 따라 그 성능 곡선이 달라질 수 있기 때문에 조건을 확인할 필요가 있습니다. 예를 들어 Windows7, windows8, windows10 , windows11 모두에서 테스트한 결과를 평균한 점수와 자신이 사용할 컴퓨터 O/S에서 테스트한 결과는 다를 수 있습니다. 상기 결과에 대한 테스트 환경에 대한 내용은 아래 사이트를 참고하시기 바랍니다.

참고 : 테스트 환경

페이지 보기

river depth

Ecological inferences on invasive carp survival using hydrodynamics and egg drift models

수리역학 및 알 이동 모델을 활용한 외래종 잉어 생존에 대한 생태적
추론

Ruichen Xu, Duane C. Chapman, Caroline M. Elliott, Bruce C. Call, Robert B. Jacobson, Binbin Wang

Abstract

Bighead carp (Hypophthalmichthys nobilis), silver carp (H. molitrix), black carp (Mylopharyngodon piceus), and grass carp (Ctenopharyngodon idella), are invasive species in North America. However, they hold significant economic importance as food sources in China. The drifting stage of carp eggs has received great attention because egg survival rate is strongly affected by river hydrodynamics. In this study, we explored egg-drift dynamics using computational fluid dynamics (CFD) models to infer potential egg settling zones based on mechanistic criteria from simulated turbulence in the Lower Missouri River. Using an 8-km reach, we simulated flow characteristics with four different discharges, representing 45–3% daily flow exceedance. The CFD results elucidate the highly heterogeneous spatial distribution of flow velocity, flow depth, turbulence kinetic energy (TKE), and the dissipation rate of TKE. The river hydrodynamics were used to determine potential egg settling zones using criteria based on shear velocity, vertical turbulence intensity, and Rouse number. Importantly, we examined the difference between hydrodynamic-inferred settling zones and settling zones predicted using an egg-drift transport model. The results indicate that hydrodynamic inference is useful in determining the ‘potential’ of egg settling, however, egg drifting paths should be taken into account to improve prediction. Our simulation results also indicate that the river turbulence does not surpass the laboratory-identified threshold to pose a threat to carp eggs.

Introduction

Bighead carp (Hypophthalmichthys nobilis), silver carp (H. molitrix), black carp (Mylopharyngodon piceus), and grass carp (Ctenopharyngodon idella), are considered invasive in North America. These species were imported into North America in the 1970’s to support aquaculture and escaped into the wild where they alter aquatic environments and food webs, resulting in undesirable ecological consequences1,2,3. On the other hand, these carp species are important food sources in China, yet their populations in their native environment have been declining due to over-fishing and the negative effects on fish habitats resulting from dam construction4,5. As either native or invasive species, it is of great importance to understand their life cycles in order to identify potential intervention strategies to control their populations6.

These rheophilic, broadcast-spawning carps exhibit prolific reproduction, with a single female carp capable of producing between 100,000 and one million eggs annually7. Carps typically engage in spawning during the spring and summer months when the temperature is within a range favorable for successful reproduction (peaking at roughly 20–24 ∘C) and during periods of high flows8,9. They select specific locations for spawning characterized by high turbulence, including rocky rapids, riffles, islands, river confluences, and bends. This choice helps prevent the settling of eggs onto the riverbed, as sediment burial causes high mortality10. Within 3–5 h after spawning, eggs absorb a large amount of water in a process known as water hardening, leading to an increase in egg size and decrease in egg density. The water-hardening process leads to a decrease in settling velocity by approximately 70%, making eggs more likely to suspension in the water column10,11.

After spawning and fertilization, the drift stage of carp eggs begins, a critical early-life stage in carp recruitment. Eggs hatch in approximately 30 h at optimal temperatures10,12. During the drift stage before hatching, eggs are susceptible to predation, relying entirely on river currents and turbulence to remain suspended until hatch. After hatching, larval carp remain in the drift for a period, but they can behaviorally avoid settling10,12. Because hydrodynamics plays a critical role in the suspension, dispersion, and transport of carp eggs across various scales in rivers, numerous studies have been conducted to explore river hydraulics and turbulence in relation to suitable carp spawning grounds, survival potential, and hatch locations13,14,15,16. A key survival condition is the necessity for eggs to remain suspended in the water column throughout the entire egg drift stage, or at the very least, to avoid settling and being buried by sediment. Consequently, assessing whether river hydrodynamics can support this condition is a fundamental step in gauging recruitment success.

Flow velocity has been used as a simple indicator for assessing the suspension of eggs in rivers. For instance, Kocovsky et al.17 used a threshold velocity of 0.7 m/s as suitable for the spawn-to-hatch environment. Selection of 0.7 m/s is based on early literature with limited mechanistic studies9,18. Lower critical flow velocities were also reported in the literature. Tang et al.19 suggested a value of 0.25 m/s based on a flume experiment, which agreed with some early field observations in the Yangtze River. Murphy and Jackson20 found that mean velocities of 0.15–0.25 m/s allowed for egg suspension in four tributary rivers of the Great Lakes. Guo et al.21 suggested a critical flow velocity of 0.3 m/s in a flume experiment. Because rivers are largely non-uniform and vary in size and morphology, selecting a specific flow velocity as the sole empirical indicator for assessing suitability of carp recruitment is rather challenging.

While using flow velocity as an indicator for examining egg suspension or settling might be practical, it does not fully represent the underlying physics, especially in areas where turbulence is not well correlated with mean flow velocity. To account for the mechanism of egg suspension, Garcia et al.22 proposed three different criteria involving the ratio of shear velocity and egg settling velocity, the ratio of vertical turbulence intensity and egg settling velocity, and the Rouse number to predict the suspension and settling of carp eggs. In their laboratory experiment, they observed that 65% of eggs remained in suspension with a mean flow velocity of 0.07 m/s, corresponding to a Rouse number of 1.32 and shear velocity of 0.004 m/s. At higher flow velocities of 0.2 and 0.4 m/s, with Rouse numbers of 0.57 and 0.58 and shear velocity of 0.008 and 0.016 m/s, respectively, all eggs were in suspension. These observations agree well with the empirical values of Rouse number classification for sediment transport for bedload, partial suspension, full suspension, and washload23. Therefore, using these parameters is better supported by the mechanism of particle suspension compared to velocity alone.

Given the above simple criteria of using shear velocity or Rouse number, hydraulic models or measurements can be used to infer whether a stream or a river reach can support a favorable environment for egg suspension in the egg-drift stage17. In addition, three dimensional hydrodynamic models can provide additional insights into the spatial distributions of potential egg settling zones, given the strong spatial heterogeneity of river turbulence24,25,26. In this paper, we use an 8-km reach in the Lower Missouri River as representative of channelized segments of the Upper Mississippi River basin where carps are established. We used computational fluid dynamics (CFD) modeling to explore the overall suitability for egg drift and to infer potential egg settling zones, with an emphasis on understanding the spatial distributions of hydrodynamics associated with in-stream hydraulic structures, river morphology, and strong topographic gradients on the riverbed. Specifically, we examine the criteria of egg suspension and evaluate the locations where the hydrodynamics are unfavorable for suspending eggs. Our objective is to evaluate whether the potential egg settling zones based on hydrodynamic inference would agree with entrapment locations that can be estimated using drift models. We additionally evaluate whether turbulence conditions indicated in the model approach criteria for turbulence-induced damage to carp eggs as determined in laboratory studies.

Methods

Study site

The study site is a selected reach in the Lower Missouri River near Lexington, Missouri (Fig. 1). The reach is approximately 8 km long with a sinuosity index of 1.12. The mean bankful width is 331.4 m. The bed is mostly covered by medium and coarse sand (D50 = 0.55 mm) with fine muddy materials (< 0.125 mm) near the banks and close to the dike fields27,28. The mean annual discharge is approximately 1700 m3/s measured at a U.S. Geological Survey (USGS) gaging station approximately 24 km downstream (station no. 06895500, Waverly, Missouri, USGS). The reach is representative of rivers that have been highly engineered to support navigation and bank stability, with complex hydraulic conditions where water flows around and over the rock channel-training structures29,30. This reach has been used as the main site for model development stage of SDrift31,32, an egg drift model used in this study. The previous studies have accumulated substantial data for the bathymetric-topographic digital elevation model (DEM), water surface elevations, and cross-channel velocity profiles33, which have been used for calibration and validation of our CFD model.

Figure 1. Bathymetry map of the study site in the Lower Missouri River. Black line represents the measurement of water surface elevation. Black triangles represent the river miles measured from the confluence with the Mississippi River near St. Louis, Missouri. Twelve red lines represent the cross sectional transects of velocity measurement at Q=2282 m3/s. Ten blue lines represent the cross sectional transects of velocity measurement at Q=3060 m3/s. Map was generated with ArcGIS Pro v. 3.2 https://www.esri.com/en-us/home. Basemap is U.S. Army Corps of Engineers Imagery, 2012. River miles are from the U.S. Army Corps of Engineers, 1960, https://www.nwk.usace.army.mil/Missions/Civil-Works/Navigation/.

Hydrodynamic model

The flow was simulated using FLOW-3D HYDRO with a Reynolds-averaged Navier-Stokes (RANS) solver and a Re-Normalization Group (RNG) modified k−ε turbulence sub-model. The model was set up for solving the steady-state flows under four discharge conditions ( Q = 1342, 2282, 3060 and 4219 m3/s, referred to as Q1 to Q4 conditions), which correspond to approximately 45–3% daily flow exceedance during spawning season. A Cartesian mesh with a final size of 4×4×0.4 m in the east-north-up coordinate system was used after a mesh independence study to evaluate optimal mesh dimensions31.

The upstream and downstream boundary conditions were set to the measured flow discharge and calculated hydrostatic pressure from the measured water-surface elevation, respectively. The model was calibrated by adjusting the roughness coefficient until the simulated water-surface elevations agree with the measured data, where the water-surface elevations were measured using a ship-mounted, real-time corrected kinematic global navigation satellite system (RTK-GNSS). The measured cross-channel velocities at 22 locations at two flow conditions (Q=2282 and 3060 m3/s) were used to evaluate model performance, where the velocities were measured using a ship-board acoustic Doppler current profiler (ADCP, Workhorse Rio Grande, Teledyne, Inc) at each cross section with four repeated transects. The ADCP had a vertical resolution of 0.5 m and horizontal resolution of 1 m. The velocities within 1 m below the water surface and within 1 m above the river bed were not measured due to instrument blanking distance and measurement noise. Additional details on model calibration and evaluation are in Li et al.31.

Egg drift model

The egg drift model SDrift was used for egg transport modeling in this study31. This model uses Lagrangian particle tracking to simulate the transport of carp eggs, where turbulent fluctuations are modeled using an explicit solution for the Langevin equation, i.e., the Markov-chain continuous random walk (CRW) algorithm34,35,36. The density and diameter of carp eggs were determined as a function of post-fertilization time and water temperature based on the regression equation to the laboratory measured data11. The details of regression can be found in31. The time-varying characteristics of eggs result in evolving egg settling velocity in the water, which is determined based on the drag law for spherical particles37.

SDrift was incorporated with the CFD model outputs to predict transport of silver carp eggs in the selected reach. A broad surface-spawning event across the entire cross section at an upstream location in the model (x= 427,130 m, near River Mile 314) was simulated by releasing 6600 model eggs on the water surface at 33 locations31. All eggs were tracked until they were transported outside the downstream boundary or ‘entrapped’ in the model domain determined by the model criterion.

Criterion of egg entrapment from the egg drift model

SDrift allows the simulated eggs to be ‘entrapped’ if they are stationary for a pre-defined duration. The entrapment would occur if a simulated egg is transported into a low velocity zone and eventually loses its momentum. From the model evaluation, entrapment primarily occurs in the region with high topographic gradients, e.g., near the bank and hydraulic structures. A duration of 30 s was used here to determine the entrapment, i.e., if a simulated egg does not move for 30 s, it would be considered entrapped and would no longer be tracked. Although the entrapment does not necessarily provide a certain prediction of egg settling, it offers insight into locations where the eggs may be stopped and eventually buried by bed sediment. The selection of a 30-s duration is somewhat arbitrary. From a physics standpoint, this duration should ideally exceed the largest turbulent time scale. However, due to the extensive spatial scale of the modeled reach and the river-training structures, the turbulent time scale varies significantly across space. Furthermore, both the spatial resolution in the CFD simulation and the temporal resolution in particle tracking have the potential to influence particle movements and their entrapment. Therefore, determining the optimal duration requires further investigation in future studies.

Criterion of egg suspension and settling from the hydrodynamic model

Suspension of carp eggs depends on whether the flow can provide adequate upward motions that overcome their settling. Analogous to sediment suspension and transport38, several means have been used to quantify the settling and suspension of carp eggs in turbulent flows. Here we analyze three parameters following Garcia et al.22: the ratio between shear velocity and settling velocity, the ratio between vertical turbulence intensity and settling velocity, and the Rouse number.

Shear velocity

Shear velocity (u∗) is a velocity scale defined from the bed shear stress. The ratio of shear velocity and particle terminal velocity (wt), a so-called movability number (M∗=u∗/wt), has been used to classify sediment transport39. Different critical values have been proposed to define particle suspension38,39. Here, the critical value of 1.0 is used following the studies of carp eggs20,22: locations with u∗/wt<1 are the potential settling zones of carp eggs, where particle terminal velocity is the egg settling velocity (wt=Vegg).

Because shear velocity only represents the bed shear but does not provide the vertical variability in the water column, we applied a scaling method so that potential egg suspension and settling can be evaluated in the entire water column. Using the relationship between bed shear and turbulence kinetic energy (TKE)40,41, i.e., τb=C1ρk with C1=0.1940, the movability number can be estimated at every grid point using the TKE determined from the CFD simulation:

The potential egg settling zones were then determined based on M∗<1.

Vertical turbulence intensity

The vertical turbulence intensity (wrms′) is a direct parameter to quantify the turbulent velocity scale in the vertical direction, which can be used to define the initiation of particle suspension38. Therefore, we also calculated the ratio between wrms′ and V{egg} as the second indicator for egg settling: locations with wrms′/Vegg<1 are the potential settling zones of carp eggs. Here, we estimated w′ based on anisotropy of turbulent fluctuations in open channel flows:

with Du=2.30, Dv=1.27, and Dw=1.6342. This gives wrms′/Vegg=0.75TKE/Vegg where TKE was obtained from the CFD simulations.

Rouse number

In sediment transport, the Rouse number has been used to describe the suspended load38. The Rouse number is defined as Ro=wt/(βκu∗) with wt=Vegg for carp eggs, where κ is von Kárman constant and β is a coefficient related to diffusion of particles22,23:

The Rouse number (Ro, also used as Z or P in the literature), can be used to classify the sediment transport similar to the movability number. Hearn23 suggested that sediment particles are in 100% suspension or wash load when Ro<1.2; particles are partially suspended when 1.2<Ro<2.5; particles are predominantly transported by bedload if Ro>2.5. Here, we use 1.2 as the criterion, such that the potential egg settling zones were determined based on Ro>1.2.

Results and discussion

Model calibration and evaluation

The model calibration results for water-surface elevation are shown in Fig. 2 for four flow conditions31. The elevation of river bed in the main channel is also plotted for reference. The root-mean-square-error (RMSE) in the water surface elevation between the measurement and modeling is 0.07, 0.03, 0.04, and 0.03 m, for Q1 to Q4, respectively. The RMSE is considered to be small compared to the length of the reach and the water depths.

Figure 2. Result of model calibration using the measured water surface elevation for four discharge conditions from Li et al.31 and Elliott et al.33. Black solid lines are measured data. Red dashed lines are modeled results.

The measurement-modeling comparison of double-averaged velocities over the flow depth and the cross section in both streamwise (Us) and transverse (Ut) directions is given in Fig. 3 for two measured conditions (Q2 and Q3). The RMSE of Us and Ut is 0.055 and 0.028 m/s, much smaller than the mean flow of 1.29 and 1.38 m/s in the measured cross sections for Q2 and Q3, respectively. The direct measurement-modeling comparison in all 22 cross sections is given in the supplementary file (Figs. S1 and S2).

Figure 3. Comparison between computational fluid dynamics (CFD) modeled and acoustic Doppler current profiler (ADCP) measured velocities in the streamwise direction (Us) and transverse direction (Ut) at 22 cross sections under the two surveyed conditions Q2 and Q333. The 1:1 dashed line represents perfect agreement.

Mean flow characteristics

The CFD simulated flow depth and depth-averaged flow velocity for two out of four conditions are shown in Figures 4 and 5. Greater depths are located downstream from the dikes (i.e., in scour holes) and near the right bank at the upstream bend (i.e., Easting 431,000–432,000 m, downstream of river mile 311). Shallower depths are located upstream from the dikes and along the left bank in the downstream bend (i.e., Easting 432,000–433,500 m, in the vicinity of river mile 310).

Flow velocities are greater at a higher discharge, and are strongly related to the in-stream hydraulic structures: high velocities are located within the main channel and low velocities are located close to the dike areas and both sides of the bank. For Q1, the L-head dikes on the left bank around Easting 430,500–431,000 m (upstream of river mile 311) block the flow into the left bank, resulting in channel narrowing and an area of localized higher velocity. Relatively faster velocities are also located close to the right bank from Easting 432,000–433,500 m (in the vicinity of river mile 310) and then shaped by the L-head dike at Easting 433,500–434,500 m (between river miles 309 and 310). When water enters the L-head dike area at Easting 430,500–431,000 m (between river miles 311 and 312) in high discharge conditions (e.g., Q4), the localized fast flow is not observed.

Figure 4. Flow depth in the reach: (a) Q1; (b) Q4. River miles 309–313 are indicated in the plot by black triangles.
Figure 5. Depth-averaged flow velocity in the reach: (a) Q1; (b) Q
4. River miles 309–313 are indicated in the plot by black triangles.

Turbulence quantities

Two turbulence quantities were selected to elucidate the turbulence in the reach: the depth-averaged TKE (Fig. 6) and the depth-averaged dissipation rate of TKE (Fig. 7). For Q1, TKE shows a similar spatial pattern as the flow velocity, indicating that the high TKE is usually associated with high velocities. For Q4, additional high TKE regions are located within the low velocity zones near the dikes. These high turbulence regions are caused by the interaction of flow with the hydraulic structures. For instance, enhanced turbulence may occur within wakes downstream from the flows over the dikes. Strong shear-induced turbulence may also occur at the water surface near the edge of the dikes close to the main channel. Similar to TKE, the locations of high TKE dissipation rate are coincident with high velocity in the main channel and near the dikes where strong flow-structure interactions occur.

Figure 6. Depth-averaged turbulence kinetic energy (TKE): (a) Q1; (b) Q4. River miles 309–313 are indicated in the plot by black triangles.
Figure 7. Depth-averaged turbulence dissipation rate: (a) Q1; (b) Q4. River miles
309–313 are indicated in the plot by black triangles.

To examine the correlation between turbulence and the mean flow in the reach, Fig. 8 elucidates the ratio between TKE and the mean kinetic energy (MKE) where MKE is defined based on mean velocity values, MKE = 0.5(U2+V2+W2). The data show that the TKE/MKE ratio is much smaller than 1 in the main channel, a typical open-channel feature. However, near the river bank and in the dike fields, greater TKE than MKE is common, with the spatial distribution of TKE/MKE>1 being dependent on discharge. This result documents strong interactions between water flow and the solid boundaries, which generate substantial turbulence comparing to the reduced mean velocity in these regions. Within these regions, particles would be expected to have longer residence times32.

Figure 8. The ratio between turbulent kinetic energy (TKE) and mean kinetic energy (MKE) in the reach: (a) Q1; (b) Q4. River miles 309–313 are indicated in the plot by black triangles.

Egg suspension and settling

The CFD modeling results allow for analysis of potential egg settling zones based on the criteria of particle suspension outlined in section “Criterion of egg suspension and settling from the hydrodynamic model”. In Fig. 9, the potential egg settling locations are plotted based on the Rouse number criterion for all four discharge conditions. The plot shows that potential settling zones are located near the river banks, in dike fields, and even in the channel at locations with strong gradients in the bed morphology. We note that the criterion was applied to all data points simulated in the CFD. Therefore, the settling zones represent the x–y locations where turbulence is inadequate to suspend eggs. Not surprisingly, the estimated potential settling zones become smaller with increasing discharge. Results using shear velocity and vertical turbulence intensity criteria show similar results, which are plotted in the supplementary file (Figs. S3 and S4).

Figure 9. Predicted egg settling locations using the criterion of Rouse number. Black dots show the locations where the turbulence is inadequate to keep eggs suspended, i.e., inferring egg settling. Note that the egg settling is evaluated at all nodes in the three-dimensional computational fluid dynamics (CFD) simulation results. River miles 309–313 are indicated in the plot by red triangles.
Figure 10. Predicted egg settling location using the egg drift model, SDrift31. River miles 309–313 are indicated in the plot by red triangles.

Figure 10 shows the predicted locations of entrapped eggs using the egg drift model, SDrift31. Comparing Fig. 10 with Fig. 9, we found that both hydrodynamic-inferred potential settling locations and drift-model predicted locations include the regions near the dike fields and the sparse areas in the channel where strong topographic gradients are present. However, careful examination of the wing dike areas (Fig. 11 under Q1 condition and Fig. 12 under Q4 condition), shows that the predicted egg settling zones using two methods are located in different regions near the dike areas. SDrift results indicate that egg entrapment is mainly located adjacent to the dikes, whereas the hydrodynamic inference indicates strong egg settling potential downstream from the dikes under low-flow conditions, such as the discharge condition Q1 (Fig. 11). The potential egg settling zones are substantially decreased by increasing discharge (Fig. 12). SDrift results indicate that egg entrapment is primarily due to interception of egg movement due to strong topographic gradients near the dikes while being tracked in the model under these hydrodynamic conditions. Although this does not directly imply that the eggs would settle in these areas, higher probability of egg-dike interaction would occur that could potentially affect egg survival. In contrast, the hydrodynamic inference only suggests hydrodynamic conditions that are favorable for egg settling, which differs from the drift models.

Figure 11. Zoom-in view of estimated egg settling zone under discharge condition Q1 using (a) SDrift model and (b) hydrodynamic inference based on Rouse number criterion. River miles 312 and 313 are indicated in the plot by red triangles.
Figure 12. Zoom-in view of estimated egg settling zone under discharge condition Q4 using (a) SDrift model and (b) hydrodynamic inference based on Rouse number criterion. River miles 312 and 313 are indicated in the plot by red triangles.

In addition, the drift model predicts substantial egg entrapment near the left bank upstream of the bend located around x=43,100 m (upstream of river mile 311), where these regions were not inferred from hydrodynamic data. The differences indicate that eggs can be entrapped within locations where hydrodynamics would indicate suspension. The potential entrapment in the drift model is likely due to the reduction in egg-drift speed close to the left bank, which increases the probability of egg settling. In curved rivers reaches, the unevenly distributed flow in the cross section and secondary flow may push eggs towards the outer side of the channel, which can increase the probability of the particle-bank interaction.

Figure 13. Trajectories of 200 SDrift simulated eggs near the left bank at the release point at two discharges: (a) Q1, (b) Q4. River miles 309–313 are indicated in the plot by red triangles.

The drift trajectories of 200 simulated eggs released near the left bank for discharge Q1 and Q4 can be used to visualize drift dynamics simulated in SDrift (Fig. 13). The modeling results show that, under Q1, there is minimal egg drift into the low-flow region between the L-head dikes and the left bank in Area 1, as well as into the high-riverbed region close to the left bank in Area 2. This restriction occurs because the elevation of the dikes in Area 1 are higher than the water surface elevation during low-flow conditions, preventing eggs from entering these areas. As a result, the drift model predicts minimal entrapment of eggs in these areas. However, the hydrodynamic inference only takes into account favorable conditions for egg settling, implying significant settling in these regions even when trajectories would fail to transport eggs into the areas. Nevertheless, under higher-flow conditions that permit eggs to enter these areas (see Fig. 13b), particularly in Area 1, entrapment of eggs can occur (see Fig. 10), even though the hydrodynamic inference does not indicate significant settling compared to other low-velocity areas.

Vertical distribution of potential egg settling zones

To examine the likelihood of egg settling based on vertical position in the water column, the number of cells were counted that satisfy the criterion of egg settling based on hydrodynamic inference at the same vertical height above the riverbed (z) under the four simulated discharges. Figure 14 illustrates an example based on Rouse number criterion. The results show that the flow condition of Q1 has substantially more counts (about one order of magnitude) due to weaker turbulence compared to the other three flow conditions (Fig. 14a and b). We interpret this large change between Q1 and higher discharges as a threshold resulting when flows begin to overtop the wing dikes. Overtopping flows substantially decrease low-turbulence areas downstream and landward of wing dikes.

The modeling data also indicate that egg settling is more likely to occur in the lower part of water column but not near the riverbed. Taking Q1 as an example, the peak of the number of counts are located about 2 m above the riverbed, with the number of counts decreasing both towards surface and towards the riverbed (Fig. 14a). In the normalized water column profile (Fig. 14b), substantial counts are located within the bottom 20% of the water column. We note that various water depths occur across the river reach, and hence the number of counts on the x-axis of the plots (Fig. 14a and b) are different before and after the water column normalization.

Examining the probability distribution function (PDF), we found that four discharge conditions show similar vertical profiles: egg settling has more than 10% probability within approximately the bottom 5 m (Fig. 14c), corresponding to approximately the bottom 20% of water depth (Fig. 14d). This result suggests that when eggs are transported to the bottom 20% layer, the hydrodynamic condition is less favorable for them to be re-suspended compared to higher-up in the water column. Similar results of profiles were found for the criterion using shear velocity and the vertical turbulence intensity, albeit the number of counts and the PDF values are different due to different criteria (see supplementary file, Figs. S5 and S6).

Figure 14. Vertical distribution of hydrodynamic-inferred egg settling locations using the criterion of Rouse number. (a) Number of counts as a function of different heights (z) above the riverbed; (b) number of counts as a function of the normalized heights which are normalized using flow depth (H); (c) probability distribution function (PDF) of the occurrence as a function of z; (d) PDF of the occurrence as a function of z/H.

Discussion on the egg survival

Examining river hydrodynamics in three dimensions through well-calibrated models yields valuable insights into the spatial distribution of flow velocity, water depth, and associated turbulence. These parameters can be used to identify potential locations where carp eggs may settle. However, using and interpreting results based on hydrodynamic criteria must be exercised with careful consideration. For instance, the Rouse number classification for particle suspension involves a broad range of values. In this study, we adopted Ro>1.2 as an indicator of egg settling, with Ro=1.2 representing the lower Rouse number bound for partial suspension. Conservatively, a critical value of Ro=2.523 is recommended for assessing predominantly bedload particle transport, indicating minimal to no suspension in the water column. Hence, at Rouse numbers between 1.2 and 2.5, partial suspension would be expected. In addition, the analysis using three-dimensional drift model results indicates that carp eggs would not drift into the egg settling zones within the L-head dikes and left bank (Area 1 in Fig. 13), for example, which would have predicted settling using hydrodynamic inference under the low-flow condition. This is because the actual egg drift pathway is governed by various parameters including egg spawning locations, streamlines of water flows, and interactions of flow and hydraulic structures. Consequently, predictions relevant to invasive carp management would improve when using the hydrodynamic-inferred egg settling zones if these additional parameters were taken into account.

Although egg settling zones based on hydrodynamic inference may not represent the actual conditions for egg settling, those predictions provide valuable information about the local hydrodynamics and suitability for egg settling at lower computational cost compared to drift modeling (for example SDrift). Therefore, this information could be useful for managers in determining the desirability of implementing hydraulic controls for egg settling. For example, if flow patterns can be adjusted to guide eggs into low-turbulence zones with adequate residence time, the hydrodynamics would facilitate the desired settling of eggs, aligning with management objectives for controlling aquatic invasive species. However we noted that solely using hydrodynamic inference may be misleading in invasive carp management without knowledge of drift pathways.

While high turbulence zones are the necessary environment for carp eggs to be suspended, eggs can be damaged or killed if turbulence exceeds a certain threshold. Prada et al.43 found an increased mortality in drifting grass carp eggs when exposed to turbulence with TKE greater than 2 m2/s2 for 1 minute in a grid-stirred turbulence tank. When TKE reaches 2.7 m2/s2, the mortality rate increased by nearly 30%. The corresponding maximal shear stresses were found to be 20 and 30 N/m2 near the grid for these two TKE values respectively. From our hydrodynamic model, mean TKE in the simulated reach under discharges Q1 to Q4 ranges from 0.01 to 0.02 m2/s2, with maximal depth-averaged TKE ranging from 0.16 to 0.21 m2/s2. The maximal TKE in the water column is found within 0.31–0.38 m2/s2 under four discharge conditions. These values are much smaller than the reported values that are harmful for carp eggs. Therefore, in a typical egg drift process, it is unlikely for eggs to experience persistent, extreme turbulence that could cause direct damage or mortality.

However, strong turbulence often generates high suspension and transport of sediment in the river. The abrasion between carp eggs and the suspended sediment may affect the egg survival rate. In the laboratory experiment conducted by Prada et al.15, carp eggs were found to drift within the lower 75% of the water column with lower flow velocity in the flume (0.08 m/s). When the flow velocity was increased to 0.22 m/s, the egg distribution in the water column was uniform, indicating a well-suspended condition for carp eggs. With further increasing flow velocity, Prada et al.15 observed that eggs were drifting more towards the bottom where they collided with the sediment particles. This indicates that the suspension of sediment could affect the vertical distribution of suspended eggs. They also observed reduced survival rate in medium and high flows compared to the control, while the survival rate was almost the same in low flow compared to the control. They also observed different larvae behaviors in different flow velocities, which may also contribute to the survival of carps. In our simulated Missouri River reach, the river turbulence may not pose a threat to carp eggs, but the suspended sediment could have negative effects. There has been limited study on the quantitative effects of sediment abrasion on egg mortality, indicating a fruitful subject for future studies.

Conclusions

In this study, we analyzed the simulated hydrodynamics of an 8-km reach in the Lower Missouri River, a site characterized by extensive channelization and river training. Four discharges representing 45–3% daily flow exceedance were examined. Calibration and validation of the simulations were conducted based on field observations. Flow depth, mean flow velocity, and turbulence quantities were investigated through computational fluid dynamics modeling. Simulated results show highly varied spatial distributions of mean flow and turbulence characteristics, primarily attributed to the curvature of the channel, variation in bed morphology, and the presence of river-training hydraulic structures, including wing dikes and L-head dikes.

To investigate the use of hydrodynamics for inferring the settling and suspension of carp eggs, we applied three criteria established in previous carp egg studies to analyze the spatial distribution of potential settling zones. The simulation results enabled the identification of low turbulence zones where insufficient suspension may hinder carp egg development. When comparing these hydrodynamic-inferred egg settling zones with the entrapment predicted by a Lagrangian egg-drift model, we observed that egg drift paths significantly influenced the locations where eggs may settle or be intercepted by in-stream hydraulic structures. Therefore, it is crucial to consider additional factors, such as spawning locations and drift paths, when using hydrodynamic inference to identify potential egg settling zones and larval nursery locations for invasive carp management.

Lastly, river turbulence may also influence carp egg survival through shear stresses and interactions with suspended sediment. Our data indicate that turbulence kinetic energy in the river does not surpass the laboratory-identified threshold associated with direct egg damage. However, abrasion from suspended sediment and the complex interactions between eggs and hydraulic structures, riverbed, and banks, accentuated by high morphological variations as demonstrated in the entrapment areas in the egg drift model, could affect the overall survival rate of carp eggs.

Data availibility

The data of field measurements and modeling are available in the online repository doi:10.5066/P9X5M3WH33.

References

  1. Irons, K. S., Sass, G. G., Mcclelland, M. A. & Stafford, J. D. Reduced condition factor of two native fish species coincident with invasion of non-native Asian carps in the Illinois River, USA—is this evidence for competition and reduced fitness?. J. Fish Biol. 71, 258–273. https://doi.org/10.1111/j.1095-8649.2007.01670.x (2007).
  2. Cudmore, B., Mandrak, N. E., Dettmers, J. M., Chapman, D. C., & Kolar, C. S. Binational ecological risk assessment of bigheaded carps (Hypophthalmichthys spp.) for the Great Lakes Basin. Technical Report 2011/114 (2012).
  3. Chick, J. H., Gibson-Reinemer, D. K., Soeken-Gittinger, L. & Casper, A. F. Invasive silver carp is empirically linked to declines of native sport fish in the Upper Mississippi River system. Biol. Invasions 22(2), 723–734. https://doi.org/10.1007/s10530-019-02124-4 (2020).
  4. Chapman, D. C. et al. Bigheaded carps of the Yangtze and Mississippi Rivers. In Fishery Resources, Environment, and Conservation in the Mississippi and Yangtze (Changjiang) River Basins (eds. Chen, Y. et al.) 113–127 (American Fisheries Society, 2016). https://doi.org/10.47886/9781934874448.
  5. Tang, C., Yan, Q., Li, W., Yang, X. & Zhang, S. Impact of dam construction on the spawning grounds of the four major Chinese carps in the three gorges reservoir. J. Hydrol. 609, 127694. https://doi.org/10.1016/j.jhydrol.2022.127694 (2022).
  6. Chapman, D. C. et al. Status of the major aquaculture carps of China in the Laurentian Great Lakes Basin. J. Great Lakes Res. 47(1), 3–13. https://doi.org/10.1016/j.jglr.2020.07.018 (2021).
  7. Garcia, T., Jackson, P. R., Murphy, E. A., Valocchi, A. J. & Garcia, M. H. Development of a fluvial egg drift simulator to evaluate the transport and dispersion of Asian carp eggs in rivers. Ecol. Model. 263, 211–222. https://doi.org/10.1016/j.ecolmodel.2013.05.005 (2013).
  8. Deters, J. E., Chapman, D. C. & McElroy, B. Location and timing of Asian carp spawning in the Lower Missouri River. Environ. Biol. Fishes 96(5), 617–629. https://doi.org/10.1007/s10641-012-0052-z (2013).
  9. Yih, P. & Liang, T. Natural conditions of the spawning grounds of the domestic fishes in Yangtze River and essential external factor for spawning. Act Hydrobiol. Sin. 5, 1–15 (1964).
  10. George, A. E. & Chapman, D. C. Embryonic and larval development and early behavior in grass carp, Ctenopharyngodon idella: Implications for recruitment in rivers. PLoS ONE 10, 3. https://doi.org/10.1371/journal.pone.0119023 (2015).
  11. George, A. E., Garcia, T. & Chapman, D. C. Comparison of size, terminal fall velocity, and density of bighead carp, silver carp, and grass carp eggs for use in drift modeling. Trans. Am. Fish. Soc. 146(5), 834–843. https://doi.org/10.1080/00028487.2017.1310136 (2017).
  12. George, A. E. & Chapman, D. C. Aspects of embryonic and larval development in bighead carp Hypophthalmichthys nobilis and silver carp Hypophthalmichthys molitrix. PLoS ONE 8(8), 1932–6203. https://doi.org/10.1371/journal.pone.0073829 (2013).
  13. Kasprak, A., Jackson, P. R., Lindroth, E. M., Lund, J. W. & Ziegeweid, J. R. The role of hydraulic and geomorphic complexity in predicting invasive carp spawning potential: St Croix River, Minnesota and Wisconsin, United States. PLoS ONE 17(2), e0263052. https://doi.org/10.1371/journal.pone.0263052 (2022).
  14. Zhu, Z. et al. Using reverse-time egg transport analysis for predicting Asian carp spawning grounds in the Illinois River. Ecol. Model. 384, 53–62. https://doi.org/10.1016/j.ecolmodel.2018.06.003 (2018).
  15. Prada, A. F., George, A. E., Stahlschmidt, B. H., Chapman, D. C. & Tinoco, R. O. Survival and drifting patterns of grass carp eggs and larvae in response to interactions with flow and sediment in a laboratory flume. PLoS ONE 13(12), 1932–6203. https://doi.org/10.1371/journal.pone.0208326 (2018).
  16. Heer, T., Wells, M. G. & Mandrak, N. E. Asian carp spawning success: Predictions from a 3-d hydrodynamic model for a Laurentian Great Lake tributary. J. Great Lakes Res. 47(1), 37–47. https://doi.org/10.1016/j.jglr.2020.07.007 (2021).
  17. Kocovsky, P. M., Chapman, D. C. & McKenna, J. E. Thermal and hydrologic suitability of Lake Erie and its major tributaries for spawning of Asian carps. J. Great Lakes Res. 38(1), 159–166. https://doi.org/10.1016/j.jglr.2011.11.015 (2012).
  18. Abdusamadov, A. S. Biology of white amur, Ctenopharyngodon idella, silver carp, Hypophthalmichthys molitrix, and bighead, Aristichthys nobilis, acclimatized in the Terek region of the Caspian basin. Vopr. Ikhtiologii 3, 425–433 (1987).
  19. Tang, M., Huang, D., Huang, L., Xiang, F. & Yin, W. Preliminary forecast of hydraulic characteristic test of grass, green, silver carp, bighead carp egg incubation conditions in the three gorges reservoir area. Reserv. Fisher. 4, 26–30 (1989).
  20. Murphy, E. A. & Jackson, P. R. Hydraulic and water-quality data collection for the investigation of Great Lakes Tributaries for Asian carp spawning and egg-transport suitability. Report 2013-5106 (2013).
  21. Guo, H. et al. Settling and transport properties of grass carp and silver carp eggs in the water-hardened phase: Implications for resource protection and invasion control during early life period. Ecol. Ind. 148, 110064. https://doi.org/10.1016/j.ecolind.2023.110064 (2023).
  22. Garcia, T. et al. A laboratory investigation of the suspension, transport, and settling of silver carp eggs using synthetic surrogates. PLoS ONE 10(12), 1–19. https://doi.org/10.1371/journal.pone.0145775 (2016).
  23. Hearn, C. J. The Dynamics of Coastal Models (Cambridge University Press, 2008).
  24. Sukhodolov, A. N. et al. Turbulent flow structure at a discordant river confluence: Asymmetric jet dynamics with implications for channel morphology. J. Geophys. Res. Earth Surf. 122(6), 1278–1293. https://doi.org/10.1002/2016JF004126 (2017).
  25. Le, T. B. et al. Large-eddy simulation of the Mississippi River under base-flow condition: Hydrodynamics of a natural diffluence-confluence region. J. Hydraul. Res. 57(6), 836–851. https://doi.org/10.1080/00221686.2018.1534282 (2019).
  26. Li, G. et al. Turbulence near a sandbar island in the lower Missouri River. River Res. Appl. 39(9), 1857–1874. https://doi.org/10.1002/rra.4180 (2023).
  27. Gaeuman, D. & Jacobson, R. B. Acoustic bed velocity and bed load dynamics in a large sand bed river. J. Geophys. Res.-Earth Surface 111, 2. https://doi.org/10.1029/2005jf000411 (2006)
  28. .Poulton, B. C. & Allert, A. L. An evaluation of the relative quality of dike pools for benthic macroinvertebrates in the Lower Missouri River, USA. River Res. Appl. 28(10), 1658–1679. https://doi.org/10.1002/rra.1558 (2012).
  29. Galat, D. L. & Lipkin, R. Restoring ecological integrity of great rivers: Historical hydrographs aid in defining reference conditions for the Missouri River. Hydrobiologia 422, 29–48. https://doi.org/10.1023/A:1017052319056 (2000).
  30. Jacobson, R. B. & Galat, D. L. Flow and form in rehabilitation of large-river ecosystems: An example from the Lower Missouri River. Geomorphology 77(3–4), 249–269. https://doi.org/10.1016/j.geomorph.2006.01.014 (2006).
  31. Li, G. et al. A three-dimensional Lagrangian particle tracking model for predicting transport of eggs of rheophilic-spawning carps in turbulent rivers. Ecol. Model. 470, 110035 (2022).
  32. Li, G. et al. Evaluations of lagrangian egg drift models: From a laboratory flume to large channelized rivers. Ecol. Model. 475, 110200 (2023).
  33. Elliott, C. M., Call, B. C., Li, G., & Wang, B. Field data and models of the Missouri River at Sheepnose Bend, near Lexington, Missouri, 2019–2021. In U.S. Geological Survey data release. https://doi.org/10.5066/P9X5M3WH (2022).
  34. Bocksell, T. L. & Loth, E. Random walk models for particle diffusion in free-shear flows. AIAA J. 39(6), 1086–1096. https://doi.org/10.2514/2.1421 (2001).
  35. Wang, B., Huijie, W. & Wan, X.-F. Transport and fate of human expiratory droplets-a modeling approach. Phys. Fluids 32(8), 083307. https://doi.org/10.1063/5.0021280 (2020).
  36. Wang, B., Sullivan, L. L. & Wood, J. D. Modeling wind-driven seed dispersal using a coupled Lagrangian particle tracking and 1-D k-ε turbulence model. Ecol. Model.486, 110503. https://doi.org/10.1016/j.ecolmodel.2023.110503 (2023).
  37. Goossens-Walter, R. A. Review of the empirical correlations for the drag coefficient of rigid spheres. Powder Technol. 352, 350–359. https://doi.org/10.1016/j.powtec.2019.04.075 (2019).
  38. van Rijn, L. C. Sediment transport, part ii: Suspended load transport. J. Hydraul. Eng. 110(11), 1613–1641. https://doi.org/10.1061/(ASCE)0733-9429(1984)110:11(1613) (1984).
  39. Dey, S. A., Zeeshan, S. K. & Padhi, E. Terminal fall velocity: the legacy of stokes from the perspective of fluvial hydraulics. Proc. R. Soc. A: Math. Phys. Eng. Sci. 475(2228), 20190277. https://doi.org/10.1098/rspa.2019.0277 (2019).
  40. Kim, S.-C., Friedrichs, C. T., Maa, J.P.-Y. & Wright, L. D. Estimating bottom stress in tidal boundary layer from acoustic doppler velocimeter data. J. Hydraul. Eng. 126(6), 399–406. https://doi.org/10.1061/(ASCE)0733-9429(2000)126:6(399) (2000).
  41. Liao, Q., Wang, B. & Wang, P.-F. In situ measurement of sediment resuspension caused by propeller wash with an underwater particle image velocimetry and an acoustic doppler velocimeter. Flow Meas. Instrum. 41, 1–9. https://doi.org/10.1016/j.flowmeasinst.2014.10.008 (2015).
  42. Nezu, I. & Nakagawa, H. Turbulence in Open Channel Flows (Routledge, 1993).
  43. Prada, A. F. et al. Influence of turbulence and in-stream structures on the transport and survival of grass carp eggs and larvae at various developmental stages. Aquat. Sci. 82, 1. https://doi.org/10.1007/s00027-019-0689-1 (2020).
View Page
Velocity of pipe

Dynamic Performance of Suspended Pipelines with Permeable Wrappers under Solitary Waves

단일 파동 하에서 투과성 포장지가 있는 현수 파이프라인의 동적 성능

Youkou Dong, Enjin Zhao, Lan Cui, Yizhe Li, Yang Wang

Abstract

Submarine pipelines are widely adopted around the world for transporting oil and gas from offshore fields. They tend to be severely ruined by the extreme waves induced by the natural disaster, such as hurricanes and tsunamis. To maintain the safety and function integrity of the pipelines, porous media have been used to wrap them from the external loads by the submarine environment. The functions of the porous wrappers under the hydrodynamic impact remain to be uncovered before they are widely accepted by the industry. In this study, a numerical wave tank is established with the immersed boundary method as one of the computational fluid dynamics. The submarine pipelines and their porous wrappers are two-way-coupled in terms of displacement and pressure at their interfaces. The impact from the solitary waves, which approximately represent the extreme waves in the reality, on the pipelines with different configurations of the porous wrapper is investigated. The results present significant protective functions of the wrappers on the internal pipelines, transferring the impact forces from the pipelines to the wrappers. The protective effects tend to be enhanced by the porosity and thickness of the wrappers. The influence of the pipeline configurations and the marine environment are then analysed. As for the front pipeline, an increase in the gap leads to a slight increase in the horizontal forces on both the wrapper and the pipeline, but a significant increase in the vertical forces. As for the rear pipeline, because of the shield function of the front pipeline, the velocity within the gap space and the forces on the pipes are decreased with the decrease in the gap size. The complex flow fields around the pipelines with wrappers are also illuminated, implying that the protection function of the wrapper is enhanced by the wave height reduction.

Keywords

extreme wave; submarine pipeline; external wrapper; coupling analysis; computational fluid dynamics

1. Introduction

Pipelines that are laid on or below the seabed and continuously transport large amounts of oil (or gas) are collectively referred to as submarine pipelines. They constitute the main transporting structures and currently they are the most economical and reliable selections in the design of transportation tools. Pipelines are usually installed within the seabed sediments under the protection of rock berms [1]. However, the sediments around the pipelines may be scoured by contour currents and internal waves, which expose the pipelines to the threat of complex marine environments [2]. The scour mechanism and its evolution process around the in-position pipelines were investigated by many scholars, such as Reference [3]. Occasionally, segments of a pipeline may be suspended between high points through continental slopes due to an uneven seabed profile. For example, suspended pipelines were widely used in the Ormen Lange projects, with massive depressions and landslide blocks scattered along the 120-km-long route [4].
Natural disaster, such as hurricanes and tsunamis, may induce extreme waves that generate enormous impact loads on the pipelines and may cause serious ruins to the whole production and transportation system [5,6,7]. Tsunamis, one of the major marine disasters caused by earthquakes and submarine landslides [8,9], send surges of water with extremely long waves that are not especially steep [10]. The tsunami triggered by a 9.0-Mw earthquake in 2011 extensively destroyed 70% of the total 200,000 structures along the Miyagi coastline, including submarine pipelines, seawalls, and coastal bridges. A tsunami is typically composed of several transient waves with varying amplitudes, wave-lengths, and wave periods during propagation. Solitary waves were proposed to simulate the tsunami waves by decomposing them into N-waves through the Korteweg-de Vries equation [11,12,13,14]. Since then, the run-up process of the tsunami waves along the shoreline was investigated with the depth-averaged smooth particle hydrodynamics method [15,16]. References [17,18] quantified the impact loads over cylinders from a tsunami wave.
To protect the marine structures from potential damages due to extreme marine conditions, engineers have developed outer protections in terms of wrappers made of porous media. A porous medium enhances the buffering performance of the structures and dissipates part of the incoming wave energy [19]. For example, the turbulent intensities on a permeable breakwater were significantly attenuated in the numerical analysis by References [20,21,22]. Naturally, porous media are expected to be protective to submarine pipelines under extreme marine conditions, although thermal insulation and erosion prevention were mainly considered in designing pipeline coatings in the industry [23,24]. Reference [25] quantified the wave forces on pipelines buried in an impermeable bed with coverings of porous media. References [26,27] evaluated the protective performance of a porous polymer coating on subsea pipelines under sudden impacts. The drag reduction function of the porous coatings over cylinders were then quantified by Reference [28]. Two factors were considered to influence the stabilization effect of the porous coatings on pipelines: the production of an entrainment layer through the coating and the triggering of turbulent transition of the detaching shear layers. In engineering practice, applications of porous coatings on submarine pipelines are limited. Concrete wrappers, mainly designed to counteract the buoyancy forces of pipelines, can be considered as one kind of porous wrapper with medium permeability. In addition, porous wrappers made with woven carbon-fiber materials or polyurethane foam may be designed in future for pipeline protection.
The above literature review revealed that few studies were performed to examine the protective effect by the porous media on submarine pipelines, which is the main aim of this study. The porous wrapper and the submarine pipeline modules are simulated in a numerical wave tank (NWT) with the immersed boundary (IB) method. The numerical methods and equations will be provided in Section 2. Verification of the numerical model is provided in Section 3. The parametric simulations are in Section 4, in which the effects of different waves on various pipelines with porous wrappers are analysed. The conclusions are given in Section 5.

2. Numerical Methods

For simulating the interactions between pipelines and waves, the finite volume methods have been widely used. In this study, the commercial finite volume package FLOW-3D® (version 11.1.0; 2014; https://www.flow3d.com (accessed on 10 December 2022); Flow Science, Inc., Santa Fe, NM, USA). Flow-3D aims to solve the transient response of fluids under interactions with structures, internal and external loads and multi-physical processes. It features some advantages in terms of a high level of accuracy in solving the Navier-Stokes equation with the volume of fluid (VOF) method, efficient meshing techniques for complex geometries, and high efficiency level for large-scale problems. Also, Flow-3D provides the flexibility and utility for flowing through porous media. A two-dimensional numerical wave tank was constructed by using the immersed boundary (IB) method and an in-house subroutine termed as IFS_IB. A submarine pipeline and porous medium were two-way coupled at the interface described by the individual volume fractions [29]. The pipeline was wrapped with a layer of a porous medium. A solitary wave was generated at the inlet boundary of the tank to simulate an approaching tsunami. Non-slip wall conditions were assigned at the bottom of the tank and the pipe surface, which was also specified with a roughness coefficient. The top boundary was defined as a free boundary and configured with the atmospheric pressure. A Neumann-type absorbing boundary condition, a stable, local, and absorbing numerical boundary condition for discretized transport equations [30], was imposed on the outlet boundary to attenuate the reflections of the outgoing waves. A transition zone is set within a certain range from the boundary to reduce the horizontal gradient force of the elements near the boundary and suppress the calculation wave caused by this boundary condition. Through the relaxation coefficient, the predicted value on the inner boundary of the transition zone and the initial value on the outer boundary are continuously transitioned to achieve the purpose of reducing the reflection of propagating waves. The CUSTOMIZATION function of the software FLOW-3D was utilised to impose the Neumann-type absorbing boundary condition. The FLOW-3D distribution includes a variety of FORTRAN source subroutines that allow the user to customize FLOW-3D to meet their requirements. The FORTRAN subroutines provided allow the user to customize boundary conditions, include their own material property correlations, specify custom fluid forces (i.e., electromagnetic forces), add physical models to FLOW-3D, and have additional benefits. Several “dummy” variables have been provided in the input file namelists that users may use for custom options. A user definable namelist has also been provided for customization. Makefiles are provided for Linux and Windows distributions and Visual Studio solution files are provided for Windows distributions to allow users to recompile the FLOW-3D code with their customizations.

2.1. Governing Equations

The governing equations involved include the continuity equations and Reynolds-averaged Navier-Stokes equations. The mass and momentum are conserved in a two-dimensional zone [31]:

where U is the velocity vector, X is the Cartesian position vector, g denotes the gravitational acceleration vector, and ρ represents the weighted averaged density. The term μ is the viscosity. σκ∇α identifies the surface tension effects with σ as the surface tension and α as the fluid volume fraction. Each cell in the fluid domain has a water volume fraction (α) ranging between 0 and 1, where 1 represents cells that are fully occupied with water, while 0 represents cells that fully occupied with air. Values between 1 and 0 represent free surface between air and water. The free surface elevation is defined by using the volume of fluid (VOF) function:

where VF is the volume of fluid fraction, FSOR is the source function, FDIF is the diffusion function; Ax, Ay, and Az represent the fractional areas; and u, v, and w are the velocity components in the x, y, and z directions.

2.2. Porous Media Module

In FLOW-3D, the porous medium’s flow resistance is modelled by the inclusion of a drag term in the momentum equations (Equation (2)). Coarse granular material is used in most coastal engineering applications, in which case the Forchheimer model is suitable. Using this model, a drag term Fdui is added to the righthand-side of Equation (2):

where |U| is the norm of the velocity vector, n the porosity, and a and b are the factors.

2.3. Solitary Wave Boundary

The solitary wave is generated in terms of variations of the surface elevation η and velocities u and v by following McCowan’s theory [32]:

where h is the still water depth; Q is the reference value

where X = x − c0t; 𝑐0=√𝑔𝐻+ℎ; H is the wave height; and t is the elapsed time.

3. Validation

3.1. Propagation over a Porous Breakwater

An experimental test on the propagation process of a solitary wave over a permeable breakwater was performed by Reference [20], which was simulated in this study to validate the adopted two-way coupling model (Figure 1a). The length, width, and depth of the flume tank were 25, 0.5, and 0.6 m, respectively. A permeable breakwater was mounted at the bottom of the flume, which had dimensions of 13 cm and 6.5 cm in the length and height, respectively. The porous breakwater with an average porosity of 0.52 was configured by glass beads with a constant diameter of 1.5 cm. Two wave gauges were fixed before (WG1) and behind (WG2) the breakwater, respectively. The initial still water depth h was assumed to be 10.6 cm. Height of the solitary wave H was considered to be 4.77 cm. In the numerical model, the calculation zone had dimensions of 5 m in length and 0.25 m in height. The second order quadrilateral mesh elements were adopted. The grid around the breakwater was the finest of 0.001 m. The adopted time step size was 0.05 s. The numerical predictions of the water elevations at the locations WG1 and WG2 by the adopted numerical tool FLOW-3D are close to both the experimental measurements and the numerical predictions from another CFD FLUENT version 14.0.1 [33] (Figure 1). Figure 1b,c show the comparison of monitored water levels at the two water level monitoring points in Figure 1a. It can be seen that the experimental results of the two monitoring points are consistent with the numerical simulation results, indicating that the propagating solitary wave energy is basically completely dissipated and then flows out. If the propagating wave energy is not dissipated, the phenomenon of wave reflection will occur. The waves monitored at the two monitoring points will appear superposition of propagating waves and reflected waves. The numerical simulation results do not agree with the physical experiment results. The fluctuations of the water surface elevation after the bypass of the incoming wave are due to its residual reflection at the right absorbing boundary condition, which arrives at WG2 at an earlier time than WG1. Evolution of the wave surfaces was also compared between the experimental and the numerical models (Figure 2), which demonstrates that the numerical tool is sufficiently reliable. The velocity of the wave is reduced by the porous medium as it partially infiltrates into the breakwater, which is shown as in Figure 3 by comparing the horizontal velocity distributions between the experimental and numerical results at times of 1.5 s and 2 s. The numerical predictions of the flow velocities have slight discrepancies with the experimental measurements, which are attributed to the material assumptions made in the numerical model for the glass beads in the experimental setup.

Jmse 11 01872 g001

Figure 1. The diagrammatic sketch of the numerical setup (non–scaled) (a) and the temporal evolution comparison of water surface between experimental and numerical results (b,c).

Jmse 11 01872 g002

Figure 2. Water surface comparison between experimental and numerical results.

Jmse 11 01872 g003

Figure 3. Comparison of horizontal velocity distribution between experimental and numerical results.

3.2. Forces on Pipeline

Another experimental test of a solitary wave impacting a pipeline was performed by Reference [34], which was also reproduced in this study for validation purposes. The calculation zone had dimensions of 40 m in length and 0.6 m in height. The solitary wave had a height of 0.0555 m with the initial water depth of 0.192 m. The pipe had a diameter of 0.048 m, which had a distance of 0.136 m over the bottom boundary of the model. A dense mesh consisting of 413,411 cells was employed with a mesh size of 0.1 mm around the pipe, which proved to be sufficiently fine through convergence studies. History of the horizontal and vertical forces, normalized by ρgL(πD2/4) with L as the unit length of 1 m, is compared between the experimental and numerical results (Figure 4). Both the peak values and the transient variations of the forces predicted by the numerical analysis converge to the measured values in the experimental test. The slight discrepancy between the numerical and experimental results at 2.5 s and 3.1 s, which may be induced by the error of the numerical model simulating the complicated turbulence behaviour, is acceptable in relation to the requirements of this study as our concern is mainly the peak values of forces.

Jmse 11 01872 g004

Figure 4. Force comparison between the experimental and numerical results.

Therefore, the adopted numerical tool is sufficiently reliable to simulate the interactions between solitary waves and the permeable structure through the above validation cases.