Schematic diagram of HP-LPBF melting process.

Modeling and numerical studies of high-precision laser powder bed fusion

Yi Wei ;Genyu Chen;Nengru Tao;Wei Zhou
https://doi.org/10.1063/5.0191504

In order to comprehensively reveal the evolutionary dynamics of the molten pool and the state of motion of the fluid during the high-precision laser powder bed fusion (HP-LPBF) process, this study aims to deeply investigate the specific manifestations of the multiphase flow, solidification phenomena, and heat transfer during the process by means of numerical simulation methods. Numerical simulation models of SS316L single-layer HP-LPBF formation with single and double tracks were constructed using the discrete element method and the computational fluid dynamics method. The effects of various factors such as Marangoni convection, surface tension, vapor recoil, gravity, thermal convection, thermal radiation, and evaporative heat dissipation on the heat and mass transfer in the molten pool have been paid attention to during the model construction process. The results show that the molten pool exhibits a “comet” shape, in which the temperature gradient at the front end of the pool is significantly larger than that at the tail end, with the highest temperature gradient up to 1.69 × 108 K/s. It is also found that the depth of the second track is larger than that of the first one, and the process parameter window has been determined preliminarily. In addition, the application of HP-LPBF technology helps to reduce the surface roughness and minimize the forming size.

Topics

Heat transferNonequilibrium thermodynamicsSolidification processComputer simulationDiscrete element methodLasersMass transferFluid mechanicsComputational fluid dynamicsMultiphase flows

I. INTRODUCTION

Laser powder bed fusion (LPBF) has become a research hotspot in the field of additive manufacturing of metals due to its advantages of high-dimensional accuracy, good surface quality, high density, and high material utilization.1,2 With the rapid development of electronics, medical, automotive, biotechnology, energy, communication, and optics, the demand for microfabrication technology is increasing day by day.3 High-precision laser powder bed fusion (HP-LPBF) is one of the key manufacturing technologies for tiny parts in the fields of electronics, medical, automotive, biotechnology, energy, communication, and optics because of its process characteristics such as small focal spot diameter, small powder particle size, and thin powder layup layer thickness.4–13 Compared with LPBF, HP-LPBF has the significant advantages of smaller focal spot diameter, smaller powder particle size, and thinner layer thickness. These advantages make HP-LPBF perform better in producing micro-fine parts, high surface quality, and parts with excellent mechanical properties.

HP-LPBF is in the exploratory stage, and researchers have already done some exploratory studies on the focal spot diameter, the amount of defocusing, and the powder particle size. In order to explore the influence of changing the laser focal spot diameter on the LPBF process characteristics of the law, Wildman et al.14 studied five groups of different focal spot diameter LPBF forming 316L stainless steel (SS316L) processing effect, the smallest focal spot diameter of 26 μm, and the results confirm that changing the focal spot diameter can be achieved to achieve the energy control, so as to control the quality of forming. Subsequently, Mclouth et al.15 proposed the laser out-of-focus amount (focal spot diameter) parameter, which characterizes the distance between the forming plane and the laser focal plane. The laser energy density was controlled by varying the defocusing amount while keeping the laser parameters constant. Sample preparation at different focal positions was investigated, and their microstructures were characterized. The results show that the samples at the focal plane have finer microstructure than those away from the focal plane, which is the effect of higher power density and smaller focal spot diameter. In order to explore the influence of changing the powder particle size on the characteristics of the LPBF process, Qian et al.16 carried out single-track scanning simulations on powder beds with average powder particle sizes of 70 and 40 μm, respectively, and the results showed that the melt tracks sizes were close to each other under the same process parameters for the two particle-size distributions and that the molten pool of powder beds with small particles was more elongated and the edges of the melt tracks were relatively flat. In order to explore the superiority of HP-LPBF technology, Xu et al.17 conducted a comparative analysis of HP-LPBF and conventional LPBF of SS316L. The results showed that the average surface roughness of the top surface after forming by HP-LPBF could reach 3.40 μm. Once again, it was verified that HP-LPBF had higher forming quality than conventional LPBF. On this basis, Wei et al.6 comparatively analyzed the effects of different laser focal spot diameters on different powder particle sizes formed by LPBF. The results showed that the smaller the laser focal spot diameter, the fewer the defects on the top and side surfaces. The above research results confirm that reducing the laser focal spot diameter can obtain higher energy density and thus better forming quality.

LPBF involves a variety of complex systems and mechanisms, and the final quality of the part is influenced by a large number of process parameters.18–24 Some research results have shown that there are more than 50 factors affecting the quality of the specimen. The influencing factors are mainly categorized into three main groups: (1) laser parameters, (2) powder parameters, and (3) equipment parameters, which interact with each other to determine the final specimen quality. With the continuous development of technologies such as computational materials science and computational fluid dynamics (CFD), the method of studying the influence of different factors on the forming quality of LPBF forming process has been shifted from time-consuming and laborious experimental characterization to the use of numerical simulation methods. As a result, more and more researchers are adopting this approach for their studies. Currently, numerical simulation studies on LPBF are mainly focused on the exploration of molten pool, temperature distribution, and residual stresses.

  1. Finite element simulation based on continuum mechanics and free surface fluid flow modeling based on fluid dynamics are two common approaches to study the behavior of LPBF molten pool.25–28 Finite element simulation focuses on the temperature and thermal stress fields, treats the powder bed as a continuum, and determines the molten pool size by plotting the elemental temperature above the melting point. In contrast, fluid dynamics modeling can simulate the 2D or 3D morphology of the metal powder pile and obtain the powder size and distribution by certain algorithms.29 The flow in the molten pool is mainly affected by recoil pressure and the Marangoni effect. By simulating the molten pool formation, it is possible to predict defects, molten pool shape, and flow characteristics, as well as the effect of process parameters on the molten pool geometry.30–34 In addition, other researchers have been conducted to optimize the laser processing parameters through different simulation methods and experimental data.35–46 Crystal growth during solidification is studied to further understand the effect of laser parameters on dendritic morphology and solute segregation.47–54 A multi-scale system has been developed to describe the fused deposition process during 3D printing, which is combined with the conductive heat transfer model and the dendritic solidification model.55,56
  2. Relevant scholars have adopted various different methods for simulation, such as sequential coupling theory,57 Lagrangian and Eulerian thermal models,58 birth–death element method,25 and finite element method,59 in order to reveal the physical phenomena of the laser melting process and optimize the process parameters. Luo et al.60 compared the LPBF temperature field and molten pool under double ellipsoidal and Gaussian heat sources by ANSYS APDL and found that the diffusion of the laser energy in the powder significantly affects the molten pool size and the temperature field.
  3. The thermal stresses obtained from the simulation correlate with the actual cracks,61 and local preheating can effectively reduce the residual stresses.62 A three-dimensional thermodynamic finite element model investigated the temperature and stress variations during laser-assisted fabrication and found that powder-to-solid conversion increases the temperature gradient, stresses, and warpage.63 Other scholars have predicted residual stresses and part deflection for LPBF specimens and investigated the effects of deposition pattern, heat, laser power, and scanning strategy on residual stresses, noting that high-temperature gradients lead to higher residual stresses.64–67 

In short, the process of LPBF forming SS316L is extremely complex and usually involves drastic multi-scale physicochemical changes that will only take place on a very small scale. Existing literature employs DEM-based mesoscopic-scale numerical simulations to investigate the effects of process parameters on the molten pool dynamics of LPBF-formed SS316L. However, a few studies have been reported on the key mechanisms of heating and solidification, spatter, and convective behavior of the molten pool of HP-LPBF-formed SS316L with small laser focal spot diameters. In this paper, the geometrical properties of coarse and fine powder particles under three-dimensional conditions were first calculated using DEM. Then, numerical simulation models for single-track and double-track cases in the single-layer HP-LPBF forming SS316L process were developed at mesoscopic scale using the CFD method. The flow genesis of the melt in the single-track and double-track molten pools is discussed, and their 3D morphology and dimensional characteristics are discussed. In addition, the effects of laser process parameters, powder particle size, and laser focal spot diameter on the temperature field, characterization information, and defects in the molten pool are discussed.

II. MODELING

A. 3D powder bed modeling

HP-LPBF is an advanced processing technique for preparing target parts layer by layer stacking, the process of which involves repetitive spreading and melting of powders. In this process, both the powder spreading and the morphology of the powder bed are closely related to the results of the subsequent melting process, while the melted surface also affects the uniform distribution of the next layer of powder. For this reason, this chapter focuses on the modeling of the physical action during the powder spreading process and the theory of DEM to establish the numerical model of the powder bed, so as to lay a solid foundation for the accuracy of volume of fluid (VOF) and CFD.

1. DEM

DEM is a numerical technique for calculating the interaction of a large number of particles, which calculates the forces and motions of the spheres by considering each powder sphere as an independent unit. The motion of the powder particles follows the laws of classical Newtonian mechanics, including translational and rotational,38,68–70 which are expressed as follows:����¨=���+∑��ij,

(1)����¨=∑�(�ij×�ij),

(2)

where �� is the mass of unit particle i in kg, ��¨ is the advective acceleration in m/s2, And g is the gravitational acceleration in m/s2. �ij is the force in contact with the neighboring particle � in N. �� is the rotational inertia of the unit particle � in kg · m2. ��¨ is the unit particle � angular acceleration in rad/s2. �ij is the vector pointing from unit particle � to the contact point of neighboring particle �⁠.

Equations (1) and (2) can be used to calculate the velocity and angular velocity variations of powder particles to determine their positions and velocities. A three-dimensional powder bed model of SS316L was developed using DEM. The powder particles are assumed to be perfect spheres, and the substrate and walls are assumed to be rigid. To describe the contact between the powder particles and between the particles and the substrate, a non-slip Hertz–Mindlin nonlinear spring-damping model71 was used with the following expression:�hz=��������+��[(�����ij−�eff����)−(�����+�eff����)],

(3)

where �hz is the force calculated using the Hertzian in M. �� and �� are the radius of unit particles � and � in m, respectively. �� is the overlap size of the two powder particles in m. ��⁠, �� are the elastic constants in the normal and tangential directions, respectively. �ij is the unit vector connecting the centerlines of the two powder particles. �eff is the effective mass of the two powder particles in kg. �� and �� are the viscoelastic damping constants in the normal and tangential directions, respectively. �� and �� are the components of the relative velocities of the two powder particles. ��� is the displacement vector between two spherical particles. The schematic diagram of overlapping powder particles is shown in Fig. 1.

FIG. 1.

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Schematic diagram of overlapping powder particles.

Because the particle size of the powder used for HP-LPBF is much smaller than 100 μm, the effect of van der Waals forces must be considered. Therefore, the cohesive force �jkr of the Hertz–Mindlin model was used instead of van der Waals forces,72 with the following expression:�jkr=−4��0�*�1.5+4�*3�*�3,

(4)1�*=(1−��2)��+(1−��2)��,

(5)1�*=1��+1��,

(6)

where �* is the equivalent Young’s modulus in GPa; �* is the equivalent particle radius in m; �0 is the surface energy of the powder particles in J/m2; α is the contact radius in m; �� and �� are the Young’s modulus of the unit particles � and �⁠, respectively, in GPa; and �� and �� are the Poisson’s ratio of the unit particles � and �⁠, respectively.

2. Model building

Figure 2 shows a 3D powder bed model generated using DEM with a coarse powder geometry of 1000 × 400 × 30 μm3. The powder layer thickness is 30 μm, and the powder bed porosity is 40%. The average particle size of this spherical powder is 31.7 μm and is normally distributed in the range of 15–53 μm. The geometry of the fine powder was 1000 × 400 × 20 μm3, with a layer thickness of 20 μm, and the powder bed porosity of 40%. The average particle size of this spherical powder is 11.5 μm and is normally distributed in the range of 5–25 μm. After the 3D powder bed model is generated, it needs to be imported into the CFD simulation software for calculation, and the imported geometric model is shown in Fig. 3. This geometric model is mainly composed of three parts: protective gas, powder bed, and substrate. Under the premise of ensuring the accuracy of the calculation, the mesh size is set to 3 μm, and the total number of coarse powder meshes is 1 704 940. The total number of fine powder meshes is 3 982 250.

FIG. 2.

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Three-dimensional powder bed model: (a) coarse powder, (b) fine powder.

FIG. 3.

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Geometric modeling of the powder bed computational domain: (a) coarse powder, (b) fine powder.

B. Modeling of fluid mechanics simulation

In order to solve the flow, melting, and solidification problems involved in HP-LPBF molten pool, the study must follow the three governing equations of conservation of mass, conservation of energy, and conservation of momentum.73 The VOF method, which is the most widely used in fluid dynamics, is used to solve the molten pool dynamics model.

1. VOF

VOF is a method for tracking the free interface between the gas and liquid phases on the molten pool surface. The core idea of the method is to define a volume fraction function F within each grid, indicating the proportion of the grid space occupied by the material, 0 ≤ F ≤ 1 in Fig. 4. Specifically, when F = 0, the grid is empty and belongs to the gas-phase region; when F = 1, the grid is completely filled with material and belongs to the liquid-phase region; and when 0 < F < 1, the grid contains free surfaces and belongs to the mixed region. The direction normal to the free surface is the direction of the fastest change in the volume fraction F (the direction of the gradient of the volume fraction), and the direction of the gradient of the volume fraction can be calculated from the values of the volume fractions in the neighboring grids.74 The equations controlling the VOF are expressed as follows:𝛻����+�⋅(��→)=0,

(7)

where t is the time in s and �→ is the liquid velocity in m/s.

FIG. 4.

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Schematic diagram of VOF.

The material parameters of the mixing zone are altered due to the inclusion of both the gas and liquid phases. Therefore, in order to represent the density of the mixing zone, the average density �¯ is used, which is expressed as follows:72�¯=(1−�1)�gas+�1�metal,

(8)

where �1 is the proportion of liquid phase, �gas is the density of protective gas in kg/m3, and �metal is the density of metal in kg/m3.

2. Control equations and boundary conditions

Figure 5 is a schematic diagram of the HP-LPBF melting process. First, the laser light strikes a localized area of the material and rapidly heats up the area. Next, the energy absorbed in the region is diffused through a variety of pathways (heat conduction, heat convection, and surface radiation), and this process triggers complex phase transition phenomena (melting, evaporation, and solidification). In metals undergoing melting, the driving forces include surface tension and the Marangoni effect, recoil due to evaporation, and buoyancy due to gravity and uneven density. The above physical phenomena interact with each other and do not occur independently.

FIG. 5.

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Schematic diagram of HP-LPBF melting process.

  1. Laser heat sourceThe Gaussian surface heat source model is used as the laser heat source model with the following expression:�=2�0����2exp(−2�12��2),(9)where � is the heat flow density in W/m2, �0 is the absorption rate of SS316L, �� is the radius of the laser focal spot in m, and �1 is the radial distance from the center of the laser focal spot in m. The laser focal spot can be used for a wide range of applications.
  2. Energy absorptionThe formula for calculating the laser absorption �0 of SS316L is as follows:�0=0.365(�0[1+�0(�−20)]/�)0.5,(10)where �0 is the direct current resistivity of SS316L at 20 °C in Ω m, �0 is the resistance temperature coefficient in ppm/°C, � is the temperature in °C, and � is the laser wavelength in m.
  3. Heat transferThe basic principle of heat transfer is conservation of energy, which is expressed as follows:𝛻𝛻𝛻�(��)��+�·(��→�)=�·(�0����)+��,(11)where � is the density of liquid phase SS316L in kg/m3, �� is the specific heat capacity of SS316L in J/(kg K), 𝛻� is the gradient operator, t is the time in s, T is the temperature in K, 𝛻�� is the temperature gradient, �→ is the velocity vector, �0 is the coefficient of thermal conduction of SS316L in W/(m K), and  �� is the thermal energy dissipation term in the molten pool.
  4. Molten pool flowThe following three conditions need to be satisfied for the molten pool to flow:
    • Conservation of mass with the following expression:𝛻�·(��→)=0.(12)
    • Conservation of momentum (Navier–Stokes equation) with the following expression:𝛻𝛻𝛻𝛻���→��+�(�→·�)�→=�·[−pI+�(��→+(��→)�)]+�,(13)where � is the pressure in Pa exerted on the liquid phase SS316L microelement, � is the unit matrix, � is the fluid viscosity in N s/m2, and � is the volumetric force (gravity, atmospheric pressure, surface tension, vapor recoil, and the Marangoni effect).
    • Conservation of energy, see Eq. (11)
  5. Surface tension and the Marangoni effectThe effect of temperature on the surface tension coefficient is considered and set as a linear relationship with the following expression:�=�0−��dT(�−��),(14)where � is the surface tension of the molten pool at temperature T in N/m, �� is the melting temperature of SS316L in K, �0 is the surface tension of the molten pool at temperature �� in Pa, and σdσ/ dT is the surface tension temperature coefficient in N/(m K).In general, surface tension decreases with increasing temperature. A temperature gradient causes a gradient in surface tension that drives the liquid to flow, known as the Marangoni effect.
  6. Metal vapor recoilAt higher input energy densities, the maximum temperature of the molten pool surface reaches the evaporation temperature of the material, and a gasification recoil pressure occurs vertically downward toward the molten pool surface, which will be the dominant driving force for the molten pool flow.75 The expression is as follows:��=0.54�� exp ���−���0���,(15)where �� is the gasification recoil pressure in Pa, �� is the ambient pressure in kPa, �� is the latent heat of evaporation in J/kg, �0 is the gas constant in J/(mol K), T is the surface temperature of the molten pool in K, and Te is the evaporation temperature in K.
  7. Solid–liquid–gas phase transitionWhen the laser hits the powder layer, the powder goes through three stages: heating, melting, and solidification. During the solidification phase, mutual transformations between solid, liquid, and gaseous states occur. At this point, the latent heat of phase transition absorbed or released during the phase transition needs to be considered.68 The phase transition is represented based on the relationship between energy and temperature with the following expression:�=�����,(�<��),�(��)+�−����−����,(��<�<��)�(��)+(�−��)����,(��<�),,(16)where �� and �� are solid and liquid phase density, respectively, of SS316L in kg/m3. �� and �� unit volume of solid and liquid phase-specific heat capacity, respectively, of SS316L in J/(kg K). �� and ��⁠, respectively, are the solidification temperature and melting temperature of SS316L in K. �� is the latent heat of the phase transition of SS316L melting in J/kg.

3. Assumptions

The CFD model was computed using the commercial software package FLOW-3D.76 In order to simplify the calculation and solution process while ensuring the accuracy of the results, the model makes the following assumptions:

  1. It is assumed that the effects of thermal stress and material solid-phase thermal expansion on the calculation results are negligible.
  2. The molten pool flow is assumed to be a Newtonian incompressible laminar flow, while the effects of liquid thermal expansion and density on the results are neglected.
  3. It is assumed that the surface tension can be simplified to an equivalent pressure acting on the free surface of the molten pool, and the effect of chemical composition on the results is negligible.
  4. Neglecting the effect of the gas flow field on the molten pool.
  5. The mass loss due to evaporation of the liquid metal is not considered.
  6. The influence of the plasma effect of the molten metal on the calculation results is neglected.

It is worth noting that the formulation of assumptions requires a trade-off between accuracy and computational efficiency. In the above models, some physical phenomena that have a small effect or high difficulty on the calculation results are simplified or ignored. Such simplifications make numerical simulations more efficient and computationally tractable, while still yielding accurate results.

4. Initial conditions

The preheating temperature of the substrate was set to 393 K, at which time all materials were in the solid state and the flow rate was zero.

5. Material parameters

The material used is SS316L and the relevant parameters required for numerical simulations are shown in Table I.46,77,78

TABLE I.

SS316L-related parameters.

PropertySymbolValue
Density of solid metal (kg/m3�metal 7980 
Solid phase line temperature (K) �� 1658 
Liquid phase line temperature (K) �� 1723 
Vaporization temperature (K) �� 3090 
Latent heat of melting (⁠ J/kg⁠) �� 2.60×105 
Latent heat of evaporation (⁠ J/kg⁠) �� 7.45×106 
Surface tension of liquid phase (N /m⁠) � 1.60 
Liquid metal viscosity (kg/m s) �� 6×10−3 
Gaseous metal viscosity (kg/m s) �gas 1.85×10−5 
Temperature coefficient of surface tension (N/m K) ��/�T 0.80×10−3 
Molar mass (⁠ kg/mol⁠) 0.05 593 
Emissivity � 0.26 
Laser absorption �0 0.35 
Ambient pressure (kPa) �� 101 325 
Ambient temperature (K) �0 300 
Stefan–Boltzmann constant (W/m2 K4� 5.67×10−8 
Thermal conductivity of metals (⁠ W/m K⁠) � 24.55 
Density of protective gas (kg/m3�gas 1.25 
Coefficient of thermal expansion (/K) �� 16×10−6 
Generalized gas constant (⁠ J/mol K⁠) 8.314 

III. RESULTS AND DISCUSSION

With the objective of studying in depth the evolutionary patterns of single-track and double-track molten pool development, detailed observations were made for certain specific locations in the model, as shown in Fig. 6. In this figure, P1 and P2 represent the longitudinal tangents to the centers of the two melt tracks in the XZ plane, while L1 is the transverse profile in the YZ plane. The scanning direction is positive and negative along the X axis. Points A and B are the locations of the centers of the molten pool of the first and second melt tracks, respectively (x = 1.995 × 10−4, y = 5 × 10−7, and z = −4.85 × 10−5).

FIG. 6.

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Schematic diagram of observation position.

A. Single-track simulation

A series of single-track molten pool simulation experiments were carried out in order to investigate the influence law of laser power as well as scanning speed on the HP-LPBF process. Figure 7 demonstrates the evolution of the 3D morphology and temperature field of the single-track molten pool in the time period of 50–500 μs under a laser power of 100 W and a scanning speed of 800 mm/s. The powder bed is in the natural cooling state. When t = 50 μs, the powder is heated by the laser heat and rapidly melts and settles to form the initial molten pool. This process is accompanied by partial melting of the substrate and solidification together with the melted powder. The molten pool rapidly expands with increasing width, depth, length, and temperature, as shown in Fig. 7(a). When t = 150 μs, the molten pool expands more obviously, and the temperature starts to transfer to the surrounding area, forming a heat-affected zone. At this point, the width of the molten pool tends to stabilize, and the temperature in the center of the molten pool has reached its peak and remains largely stable. However, the phenomenon of molten pool spatter was also observed in this process, as shown in Fig. 7(b). As time advances, when t = 300 μs, solidification begins to occur at the tail of the molten pool, and tiny ripples are produced on the solidified surface. This is due to the fact that the melt flows toward the region with large temperature gradient under the influence of Marangoni convection and solidifies together with the melt at the end of the bath. At this point, the temperature gradient at the front of the bath is significantly larger than at the end. While the width of the molten pool was gradually reduced, the shape of the molten pool was gradually changed to a “comet” shape. In addition, a slight depression was observed at the top of the bath because the peak temperature at the surface of the bath reached the evaporation temperature, which resulted in a recoil pressure perpendicular to the surface of the bath downward, creating a depressed region. As the laser focal spot moves and is paired with the Marangoni convection of the melt, these recessed areas will be filled in as shown in Fig. 7(c). It has been shown that the depressed regions are the result of the coupled effect of Marangoni convection, recoil pressure, and surface tension.79 By t = 500 μs, the width and height of the molten pool stabilize and show a “comet” shape in Fig. 7(d).

FIG. 7.

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Single-track molten pool process: (a) t = 50  ��⁠, (b) t = 150  ��⁠, (c) t = 300  ��⁠, (d) t = 500  ��⁠.

Figure 8 depicts the velocity vector diagram of the P1 profile in a single-track molten pool, the length of the arrows represents the magnitude of the velocity, and the maximum velocity is about 2.36 m/s. When t = 50 μs, the molten pool takes shape, and the velocities at the two ends of the pool are the largest. The variation of the velocities at the front end is especially more significant in Fig. 8(a). As the time advances to t = 150 μs, the molten pool expands rapidly, in which the velocity at the tail increases and changes more significantly, while the velocity at the front is relatively small. At this stage, the melt moves backward from the center of the molten pool, which in turn expands the molten pool area. The melt at the back end of the molten pool center flows backward along the edge of the molten pool surface and then converges along the edge of the molten pool to the bottom center, rising to form a closed loop. Similarly, a similar closed loop is formed at the front end of the center of the bath, but with a shorter path. However, a large portion of the melt in the center of the closed loop formed at the front end of the bath is in a nearly stationary state. The main cause of this melt flow phenomenon is the effect of temperature gradient and surface tension (the Marangoni effect), as shown in Figs. 8(b) and 8(e). This dynamic behavior of the melt tends to form an “elliptical” pool. At t = 300 μs, the tendency of the above two melt flows to close the loop is more prominent and faster in Fig. 8(c). When t = 500 μs, the velocity vector of the molten pool shows a stable trend, and the closed loop of melt flow also remains stable. With the gradual laser focal spot movement, the melt is gradually solidified at its tail, and finally, a continuous and stable single track is formed in Fig. 8(d).

FIG. 8.

VIEW LARGEDOWNLOAD SLIDE

Vector plot of single-track molten pool velocity in XZ longitudinal section: (a) t = 50  ��⁠, (b) t = 150  ��⁠, (c) t = 300  ��⁠, (d) t = 500  ��⁠, (e) molten pool flow.

In order to explore in depth the transient evolution of the molten pool, the evolution of the single-track temperature field and the melt flow was monitored in the YZ cross section. Figure 9(a) shows the state of the powder bed at the initial moment. When t = 250 μs, the laser focal spot acts on the powder bed and the powder starts to melt and gradually collects in the molten pool. At this time, the substrate will also start to melt, and the melt flow mainly moves in the downward and outward directions and the velocity is maximum at the edges in Fig. 9(b). When t = 300 μs, the width and depth of the molten pool increase due to the recoil pressure. At this time, the melt flows more slowly at the center, but the direction of motion is still downward in Fig. 9(c). When t = 350 μs, the width and depth of the molten pool further increase, at which time the intensity of the melt flow reaches its peak and the direction of motion remains the same in Fig. 9(d). When t = 400 μs, the melt starts to move upward, and the surrounding powder or molten material gradually fills up, causing the surface of the molten pool to begin to flatten. At this time, the maximum velocity of the melt is at the center of the bath, while the velocity at the edge is close to zero, and the edge of the melt starts to solidify in Fig. 9(e). When t = 450 μs, the melt continues to move upward, forming a convex surface of the melt track. However, the melt movement slows down, as shown in Fig. 9(f). When t = 500 μs, the melt further moves upward and its speed gradually becomes smaller. At the same time, the melt solidifies further, as shown in Fig. 9(g). When t = 550 μs, the melt track is basically formed into a single track with a similar “mountain” shape. At this stage, the velocity is close to zero only at the center of the molten pool, and the flow behavior of the melt is poor in Fig. 9(h). At t = 600 μs, the melt stops moving and solidification is rapidly completed. Up to this point, a single track is formed in Fig. 9(i). During the laser action on the powder bed, the substrate melts and combines with the molten state powder. The powder-to-powder fusion is like the convergence of water droplets, which are rapidly fused by surface tension. However, the fusion between the molten state powder and the substrate occurs driven by surface tension, and the molten powder around the molten pool is pulled toward the substrate (a wetting effect occurs), which ultimately results in the formation of a monolithic whole.38,80,81

FIG. 9.

VIEW LARGEDOWNLOAD SLIDE

Evolution of single-track molten pool temperature and melt flow in the YZ cross section: (a) t = 0  ��⁠, (b) t = 250  ��⁠, (c) t = 300  ��⁠, (d) t = 350  ��⁠, (e) t = 400  ��⁠, (f) t = 450  ��⁠, (g) t = 500  ��⁠, (h) t = 550  ��⁠, (i) t = 600  ��⁠.

The wetting ability between the liquid metal and the solid substrate in the molten pool directly affects the degree of balling of the melt,82,83 and the wetting ability can be measured by the contact angle of a single track in Fig. 10. A smaller value of contact angle represents better wettability. The contact angle α can be calculated by�=�1−�22,

(17)

where �1 and �2 are the contact angles of the left and right regions, respectively.

FIG. 10.

VIEW LARGEDOWNLOAD SLIDE

Schematic of contact angle.

Relevant studies have confirmed that the wettability is better at a contact angle α around or below 40°.84 After measurement, a single-track contact angle α of about 33° was obtained under this process parameter, which further confirms the good wettability.

B. Double-track simulation

In order to deeply investigate the influence of hatch spacing on the characteristics of the HP-LPBF process, a series of double-track molten pool simulation experiments were systematically carried out. Figure 11 shows in detail the dynamic changes of the 3D morphology and temperature field of the double-track molten pool in the time period of 2050–2500 μs under the conditions of laser power of 100 W, scanning speed of 800 mm/s, and hatch spacing of 0.06 mm. By comparing the study with Fig. 7, it is observed that the basic characteristics of the 3D morphology and temperature field of the second track are similar to those of the first track. However, there are subtle differences between them. The first track exhibits a basically symmetric shape, but the second track morphology shows a slight deviation influenced by the difference in thermal diffusion rate between the solidified metal and the powder. Otherwise, the other characteristic information is almost the same as that of the first track. Figure 12 shows the velocity vector plot of the P2 profile in the double-track molten pool, with a maximum velocity of about 2.63 m/s. The melt dynamics at both ends of the pool are more stable at t = 2050 μs, where the maximum rate of the second track is only 1/3 of that of the first one. Other than that, the rest of the information is almost no significant difference from the characteristic information of the first track. Figure 13 demonstrates a detailed observation of the double-track temperature field and melts flow in the YZ cross section, and a comparative study with Fig. 9 reveals that the width of the second track is slightly wider. In addition, after the melt direction shifts from bottom to top, the first track undergoes four time periods (50 μs) to reach full solidification, while the second track takes five time periods. This is due to the presence of significant heat buildup in the powder bed after the forming of the first track, resulting in a longer dynamic time of the melt and an increased molten pool lifetime. In conclusion, the level of specimen forming can be significantly optimized by adjusting the laser power and hatch spacing.

FIG. 11.

VIEW LARGEDOWNLOAD SLIDE

Double-track molten pool process: (a) t = 2050  ��⁠, (b) t = 2150  ��⁠, (c) t = 2300  ��⁠, (d) t = 2500  ��⁠.

FIG. 12.

VIEW LARGEDOWNLOAD SLIDE

Vector plot of double-track molten pool velocity in XZ longitudinal section: (a) t = 2050  ��⁠, (b) t = 2150  ��⁠, (c) t = 2300  ��⁠, (d) t = 2500  ��⁠.

FIG. 13.

VIEW LARGEDOWNLOAD SLIDE

Evolution of double-track molten pool temperature and melt flow in the YZ cross section: (a) t = 2250  ��⁠, (b) t = 2300  ��⁠, (c) t = 2350  ��⁠, (d) t = 2400  ��⁠, (e) t = 2450  ��⁠, (f) t = 2500  ��⁠, (g) t = 2550  ��⁠, (h) t = 2600  ��⁠, (i) t = 2650  ��⁠.

In order to quantitatively detect the molten pool dimensions as well as the remolten region dimensions, the molten pool characterization information in Fig. 14 is constructed by drawing the boundary on the YZ cross section based on the isothermal surface of the liquid phase line. It can be observed that the heights of the first track and second track are basically the same, but the depth of the second track increases relative to the first track. The molten pool width is mainly positively correlated with the laser power as well as the scanning speed (the laser line energy density �⁠). However, the remelted zone width is negatively correlated with the hatch spacing (the overlapping ratio). Overall, the forming quality of the specimens can be directly influenced by adjusting the laser power, scanning speed, and hatch spacing.

FIG. 14.

VIEW LARGEDOWNLOAD SLIDE

Double-track molten pool characterization information on YZ cross section.

In order to study the variation rule of the temperature in the center of the molten pool with time, Fig. 15 demonstrates the temperature variation curves with time for two reference points, A and B. Among them, the red dotted line indicates the liquid phase line temperature of SS316L. From the figure, it can be seen that the maximum temperature at the center of the molten pool in the first track is lower than that in the second track, which is mainly due to the heat accumulation generated after passing through the first track. The maximum temperature gradient was calculated to be 1.69 × 108 K/s. When the laser scanned the first track, the temperature in the center of the molten pool of the second track increased slightly. Similarly, when the laser scanned the second track, a similar situation existed in the first track. Since the temperature gradient in the second track is larger than that in the first track, the residence time of the liquid phase in the molten pool of the first track is longer than that of the second track.

FIG. 15.

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Temperature profiles as a function of time for two reference points A and B.

C. Simulation analysis of molten pool under different process parameters

In order to deeply investigate the effects of various process parameters on the mesoscopic-scale temperature field, molten pool characteristic information and defects of HP-LPBF, numerical simulation experiments on mesoscopic-scale laser power, scanning speed, and hatch spacing of double-track molten pools were carried out.

1. Laser power

Figure 16 shows the effects of different laser power on the morphology and temperature field of the double-track molten pool at a scanning speed of 800 mm/s and a hatch spacing of 0.06 mm. When P = 50 W, a smaller molten pool is formed due to the lower heat generated by the Gaussian light source per unit time. This leads to a smaller track width, which results in adjacent track not lapping properly and the presence of a large number of unmelted powder particles, resulting in an increase in the number of defects, such as pores in the specimen. The surface of the track is relatively flat, and the depth is small. In addition, the temperature gradient before and after the molten pool was large, and the depression location appeared at the biased front end in Fig. 16(a). When P = 100 W, the surface of the track is flat and smooth with excellent lap. Due to the Marangoni effect, the velocity field of the molten pool is in the form of “vortex,” and the melt has good fluidity, and the maximum velocity reaches 2.15 m/s in Fig. 16(b). When P = 200 W, the heat generated by the Gaussian light source per unit time is too large, resulting in the melt rapidly reaching the evaporation temperature, generating a huge recoil pressure, forming a large molten pool, and the surface of the track is obviously raised. The melt movement is intense, especially the closed loop at the center end of the molten pool. At this time, the depth and width of the molten pool are large, leading to the expansion of the remolten region and the increased chance of the appearance of porosity defects in Fig. 16(c). The results show that at low laser power, the surface tension in the molten pool is dominant. At high laser power, recoil pressure is its main role.

FIG. 16.

VIEW LARGEDOWNLOAD SLIDE

Simulation results of double-track molten pool under different laser powers: (a) P = 50 W, (b) P = 100 W, (c) P = 200 W.

Table II shows the effect of different laser powers on the characteristic information of the double-track molten pool at a scanning speed of 800 mm/s and a hatch spacing of 0.06 mm. The negative overlapping ratio in the table indicates that the melt tracks are not lapped, and 26/29 indicates the melt depth of the first track/second track. It can be seen that with the increase in laser power, the melt depth, melt width, melt height, and remelted zone show a gradual increase. At the same time, the overlapping ratio also increases. Especially in the process of laser power from 50 to 200 W, the melting depth and melting width increased the most, which increased nearly 2 and 1.5 times, respectively. Meanwhile, the overlapping ratio also increases with the increase in laser power, which indicates that the melting and fusion of materials are better at high laser power. On the other hand, the dimensions of the molten pool did not change uniformly with the change of laser power. Specifically, the depth-to-width ratio of the molten pool increased from about 0.30 to 0.39 during the increase from 50 to 120 W, which further indicates that the effective heat transfer in the vertical direction is greater than that in the horizontal direction with the increase in laser power. This dimensional response to laser power is mainly affected by the recoil pressure and also by the difference in the densification degree between the powder layer and the metal substrate. In addition, according to the experimental results, the contact angle shows a tendency to increase and then decrease during the process of laser power increase, and always stays within the range of less than 33°. Therefore, in practical applications, it is necessary to select the appropriate laser power according to the specific needs in order to achieve the best processing results.

TABLE II.

Double-track molten pool characterization information at different laser powers.

Laser power (W)Depth (μm)Width (μm)Height (μm)Remolten region (μm)Overlapping ratio (%)Contact angle (°)
50 16 54 11 −10 23 
100 26/29 74 14 18 23.33 33 
200 37/45 116 21 52 93.33 28 

2. Scanning speed

Figure 17 demonstrates the effect of different scanning speeds on the morphology and temperature field of the double-track molten pool at a laser power of 100 W and a hatch spacing of 0.06 mm. With the gradual increase in scanning speed, the surface morphology of the molten pool evolves from circular to elliptical. When � = 200 mm/s, the slow scanning speed causes the material to absorb too much heat, which is very easy to trigger the overburning phenomenon. At this point, the molten pool is larger and the surface morphology is uneven. This situation is consistent with the previously discussed scenario with high laser power in Fig. 17(a). However, when � = 1600 mm/s, the scanning speed is too fast, resulting in the material not being able to absorb sufficient heat, which triggers the powder particles that fail to melt completely to have a direct effect on the bonding of the melt to the substrate. At this time, the molten pool volume is relatively small and the neighboring melt track cannot lap properly. This result is consistent with the previously discussed case of low laser power in Fig. 17(b). Overall, the ratio of the laser power to the scanning speed (the line energy density �⁠) has a direct effect on the temperature field and surface morphology of the molten pool.

FIG. 17.

VIEW LARGEDOWNLOAD SLIDE

Simulation results of double-track molten pool under different scanning speed: (a)  � = 200 mm/s, (b)  � = 1600 mm/s.

Table III shows the effects of different scanning speed on the characteristic information of the double-track molten pool under the condition of laser power of 100 W and hatch spacing of 0.06 mm. It can be seen that the scanning speed has a significant effect on the melt depth, melt width, melt height, remolten region, and overlapping ratio. With the increase in scanning speed, the melt depth, melt width, melt height, remelted zone, and overlapping ratio show a gradual decreasing trend. Among them, the melt depth and melt width decreased faster, while the melt height and remolten region decreased relatively slowly. In addition, when the scanning speed was increased from 200 to 800 mm/s, the decreasing speeds of melt depth and melt width were significantly accelerated, while the decreasing speeds of overlapping ratio were relatively slow. When the scanning speed was further increased to 1600 mm/s, the decreasing speeds of melt depth and melt width were further accelerated, and the un-lapped condition of the melt channel also appeared. In addition, the contact angle increases and then decreases with the scanning speed, and both are lower than 33°. Therefore, when selecting the scanning speed, it is necessary to make reasonable trade-offs according to the specific situation, and take into account the factors of melt depth, melt width, melt height, remolten region, and overlapping ratio, in order to achieve the best processing results.

TABLE III.

Double-track molten pool characterization information at different scanning speeds.

Scanning speed (mm/s)Depth (μm)Width (μm)Height (μm)Remolten region (μm)Overlapping ratio (%)Contact angle (°)
200 55/68 182 19/32 124 203.33 22 
1600 13 50 11 −16.67 31 

3. Hatch spacing

Figure 18 shows the effect of different hatch spacing on the morphology and temperature field of the double-track molten pool under the condition of laser power of 100 W and scanning speed of 800 mm/s. The surface morphology and temperature field of the first track and second track are basically the same, but slightly different. The first track shows a basically symmetric morphology along the scanning direction, while the second track shows a slight offset due to the difference in the heat transfer rate between the solidified material and the powder particles. When the hatch spacing is too small, the overlapping ratio increases and the probability of defects caused by remelting phenomenon grows. When the hatch spacing is too large, the neighboring melt track cannot overlap properly, and the powder particles are not completely melted, leading to an increase in the number of holes. In conclusion, the ratio of the line energy density � to the hatch spacing (the volume energy density E) has a significant effect on the temperature field and surface morphology of the molten pool.

FIG. 18.

VIEW LARGEDOWNLOAD SLIDE

Simulation results of double-track molten pool under different hatch spacings: (a) H = 0.03 mm, (b) H = 0.12 mm.

Table IV shows the effects of different hatch spacing on the characteristic information of the double-track molten pool under the condition of laser power of 100 W and scanning speed of 800 mm/s. It can be seen that the hatch spacing has little effect on the melt depth, melt width, and melt height, but has some effect on the remolten region. With the gradual expansion of hatch spacing, the remolten region shows a gradual decrease. At the same time, the overlapping ratio also decreased with the increase in hatch spacing. In addition, it is observed that the contact angle shows a tendency to increase and then remain stable when the hatch spacing increases, which has a more limited effect on it. Therefore, trade-offs and decisions need to be made on a case-by-case basis when selecting the hatch spacing.

TABLE IV.

Double-track molten pool characterization information at different hatch spacings.

Hatch spacing (mm)Depth (μm)Width (μm)Height (μm)Remolten region (μm)Overlapping ratio (%)Contact angle (°)
0.03 25/27 82 14 59 173.33 30 
0.12 26 78 14 −35 33 

In summary, the laser power, scanning speed, and hatch spacing have a significant effect on the formation of the molten pool, and the correct selection of these three process parameters is crucial to ensure the forming quality. In addition, the melt depth of the second track is slightly larger than that of the first track at higher line energy density � and volume energy density E. This is mainly due to the fact that a large amount of heat accumulation is generated after the first track, forming a larger molten pool volume, which leads to an increase in the melt depth.

D. Simulation analysis of molten pool with powder particle size and laser focal spot diameter

Figure 19 demonstrates the effect of different powder particle sizes and laser focal spot diameters on the morphology and temperature field of the double-track molten pool under a laser power of 100 W, a scanning speed of 800 mm/s, and a hatch spacing of 0.06 mm. In the process of melting coarse powder with small laser focal spot diameter, the laser energy cannot completely melt the larger powder particles, resulting in their partial melting and further generating excessive pore defects. The larger powder particles tend to generate zigzag molten pool edges, which cause an increase in the roughness of the melt track surface. In addition, the molten pool is also prone to generate the present spatter phenomenon, which can directly affect the quality of forming. The volume of the formed molten pool is relatively small, while the melt depth, melt width, and melt height are all smaller relative to the fine powder in Fig. 19(a). In the process of melting fine powders with a large laser focal spot diameter, the laser energy is able to melt the fine powder particles sufficiently, even to the point of overmelting. This results in a large number of fine spatters being generated at the edge of the molten pool, which causes porosity defects in the melt track in Fig. 19(b). In addition, the maximum velocity of the molten pool is larger for large powder particle sizes compared to small powder particle sizes, which indicates that the temperature gradient in the molten pool is larger for large powder particle sizes and the melt motion is more intense. However, the size of the laser focal spot diameter has a relatively small effect on the melt motion. However, a larger focal spot diameter induces a larger melt volume with greater depth, width, and height. In conclusion, a small powder size helps to reduce the surface roughness of the specimen, and a small laser spot diameter reduces the minimum forming size of a single track.

FIG. 19.

VIEW LARGEDOWNLOAD SLIDE

Simulation results of double-track molten pool with different powder particle size and laser focal spot diameter: (a) focal spot = 25 μm, coarse powder, (b) focal spot = 80 μm, fine powder.

Table V shows the maximum temperature gradient at the reference point for different powder sizes and laser focal spot diameters. As can be seen from the table, the maximum temperature gradient is lower than that of HP-LPBF for both coarse powders with a small laser spot diameter and fine powders with a large spot diameter, a phenomenon that leads to an increase in the heat transfer rate of HP-LPBF, which in turn leads to a corresponding increase in the cooling rate and, ultimately, to the formation of finer microstructures.

TABLE V.

Maximum temperature gradient at the reference point for different powder particle sizes and laser focal spot diameters.

Laser power (W)Scanning speed (mm/s)Hatch spacing (mm)Average powder size (μm)Laser focal spot diameter (μm)Maximum temperature gradient (×107 K/s)
100 800 0.06 31.7 25 7.89 
11.5 80 7.11 

IV. CONCLUSIONS

In this study, the geometrical characteristics of 3D coarse and fine powder particles were first calculated using DEM and then numerical simulations of single track and double track in the process of forming SS316L from monolayer HP-LPBF at mesoscopic scale were developed using CFD method. The effects of Marangoni convection, surface tension, recoil pressure, gravity, thermal convection, thermal radiation, and evaporative heat dissipation on the heat and mass transfer in the molten pool were considered in this model. The effects of laser power, scanning speed, and hatch spacing on the dynamics of the single-track and double-track molten pools, as well as on other characteristic information, were investigated. The effects of the powder particle size on the molten pool were investigated comparatively with the laser focal spot diameter. The main conclusions are as follows:

  1. The results show that the temperature gradient at the front of the molten pool is significantly larger than that at the tail, and the molten pool exhibits a “comet” morphology. At the top of the molten pool, there is a slightly concave region, which is the result of the coupling of Marangoni convection, recoil pressure, and surface tension. The melt flow forms two closed loops, which are mainly influenced by temperature gradients and surface tension. This special dynamic behavior of the melt tends to form an “elliptical” molten pool and an almost “mountain” shape in single-track forming.
  2. The basic characteristics of the three-dimensional morphology and temperature field of the second track are similar to those of the first track, but there are subtle differences. The first track exhibits a basically symmetrical shape; however, due to the difference in thermal diffusion rates between the solidified metal and the powder, a slight asymmetry in the molten pool morphology of the second track occurs. After forming through the first track, there is a significant heat buildup in the powder bed, resulting in a longer dynamic time of the melt, which increases the life of the molten pool. The heights of the first track and second track remained essentially the same, but the depth of the second track was greater relative to the first track. In addition, the maximum temperature gradient was 1.69 × 108 K/s during HP-LPBF forming.
  3. At low laser power, the surface tension in the molten pool plays a dominant role. At high laser power, recoil pressure becomes the main influencing factor. With the increase of laser power, the effective heat transfer in the vertical direction is superior to that in the horizontal direction. With the gradual increase of scanning speed, the surface morphology of the molten pool evolves from circular to elliptical. In addition, the scanning speed has a significant effect on the melt depth, melt width, melt height, remolten region, and overlapping ratio. Too large or too small hatch spacing will lead to remelting or non-lap phenomenon, which in turn causes the formation of defects.
  4. When using a small laser focal spot diameter, it is difficult to completely melt large powder particle sizes, resulting in partial melting and excessive porosity generation. At the same time, large powder particles produce curved edges of the molten pool, resulting in increased surface roughness of the melt track. In addition, spatter occurs, which directly affects the forming quality. At small focal spot diameters, the molten pool volume is relatively small, and the melt depth, the melt width, and the melt height are correspondingly small. Taken together, the small powder particle size helps to reduce surface roughness, while the small spot diameter reduces the forming size.

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Figure 5 A schematic of the water model of reactor URO 200.

Physical and Numerical Modeling of the Impeller Construction Impact on the Aluminum Degassing Process

알루미늄 탈기 공정에 미치는 임펠러 구성의 물리적 및 수치적 모델링

Kamil Kuglin,1 Michał Szucki,2 Jacek Pieprzyca,3 Simon Genthe,2 Tomasz Merder,3 and Dorota Kalisz1,*

Mikael Ersson, Academic Editor

Author information Article notes Copyright and License information Disclaimer

Associated Data

Data Availability Statement

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Abstract

This paper presents the results of tests on the suitability of designed heads (impellers) for aluminum refining. The research was carried out on a physical model of the URO-200, followed by numerical simulations in the FLOW 3D program. Four design variants of impellers were used in the study. The degree of dispersion of the gas phase in the model liquid was used as a criterion for evaluating the performance of each solution using different process parameters, i.e., gas flow rate and impeller speed. Afterward, numerical simulations in Flow 3D software were conducted for the best solution. These simulations confirmed the results obtained with the water model and verified them.

Keywords: aluminum, impeller construction, degassing process, numerical modeling, physical modeling

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1. Introduction

Constantly increasing requirements concerning metallurgical purity in terms of hydrogen content and nonmetallic inclusions make casting manufacturers use effective refining techniques. The answer to this demand is the implementation of the aluminum refining technique making use of a rotor with an original design guaranteeing efficient refining [1,2,3,4]. The main task of the impeller (rotor) is to reduce the contamination of liquid metal (primary and recycled aluminum) with hydrogen and nonmetallic inclusions. An inert gas, mainly argon or a mixture of gases, is introduced through the rotor into the liquid metal to bring both hydrogen and nonmetallic inclusions to the metal surface through the flotation process. Appropriately and uniformly distributed gas bubbles in the liquid metal guarantee achieving the assumed level of contaminant removal economically. A very important factor in deciding about the obtained degassing effect is the optimal rotor design [5,6,7,8]. Thanks to the appropriate geometry of the rotor, gas bubbles introduced into the liquid metal are split into smaller ones, and the spinning movement of the rotor distributes them throughout the volume of the liquid metal bath. In this solution impurities in the liquid metal are removed both in the volume and from the upper surface of the metal. With a well-designed impeller, the costs of refining aluminum and its alloys can be lowered thanks to the reduced inert gas and energy consumption (optimal selection of rotor rotational speed). Shorter processing time and a high degree of dehydrogenation decrease the formation of dross on the metal surface (waste). A bigger produced dross leads to bigger process losses. Consequently, this means that the choice of rotor geometry has an indirect impact on the degree to which the generated waste is reduced [9,10].

Another equally important factor is the selection of process parameters such as gas flow rate and rotor speed [11,12]. A well-designed gas injection system for liquid metal meets two key requirements; it causes rapid mixing of the liquid metal to maintain a uniform temperature throughout the volume and during the entire process, to produce a chemically homogeneous metal composition. This solution ensures effective degassing of the metal bath. Therefore, the shape of the rotor, the arrangement of the nozzles, and their number are significant design parameters that guarantee the optimum course of the refining process. It is equally important to complete the mixing of the metal bath in a relatively short time, as this considerably shortens the refining process and, consequently, reduces the process costs. Another important criterion conditioning the implementation of the developed rotor is the generation of fine diffused gas bubbles which are distributed throughout the metal volume, and whose residence time will be sufficient for the bubbles to collide and adsorb the contaminants. The process of bubble formation by the spinning rotors differs from that in the nozzles or porous molders. In the case of a spinning rotor, the shear force generated by the rotor motion splits the bubbles into smaller ones. Here, the rotational speed, mixing force, surface tension, and fluid density have a key effect on the bubble size. The velocity of the bubbles, which depends mainly on their size and shape, determines their residence time in the reactor and is, therefore, very important for the refining process, especially since gas bubbles in liquid aluminum may remain steady only below a certain size [13,14,15].

The impeller designs presented in the article were developed to improve the efficiency of the process and reduce its costs. The impellers used so far have a complicated structure and are very pricey. The success of the conducted research will allow small companies to become independent of external supplies through the possibility of making simple and effective impellers on their own. The developed structures were tested on the water model. The results of this study can be considered as pilot.

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2. Materials and Methods

Rotors were realized with the SolidWorks computer design technique and a 3D printer. The developed designs were tested on a water model. Afterward, the solution with the most advantageous refining parameters was selected and subjected to calculations with the Flow3D package. As a result, an impeller was designed for aluminum refining. Its principal lies in an even distribution of gas bubbles in the entire volume of liquid metal, with the largest possible participation of the bubble surface, without disturbing the metal surface. This procedure guarantees the removal of gaseous, as well as metallic and nonmetallic, impurities.

2.1. Rotor Designs

The developed impeller constructions, shown in Figure 1Figure 2Figure 3 and Figure 4, were printed on a 3D printer using the PLA (polylactide) material. The impeller design models differ in their shape and the number of holes through which the inert gas flows. Figure 1Figure 2 and Figure 3 show the same impeller model but with a different number of gas outlets. The arrangement of four, eight, and 12 outlet holes was adopted in the developed design. A triangle-shaped structure equipped with three gas outlet holes is presented in Figure 4.

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Figure 1

A 3D model—impeller with four holes—variant B4.

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Figure 2

A 3D model—impeller with eight holes—variant B8.

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Figure 3

A 3D model—impeller with twelve holes—variant B12.

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Figure 4

A 3D model—‘red triangle’ impeller with three holes—variant RT3.

2.2. Physical Models

Investigations were carried out on a water model of the URO 200 reactor of the barbotage refining process (see Figure 5).

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Figure 5

A schematic of the water model of reactor URO 200.

The URO 200 reactor can be classified as a cyclic reactor. The main element of the device is a rotor, which ends the impeller. The whole system is attached to a shaft via which the refining gas is supplied. Then, the shaft with the rotor is immersed in the liquid metal in the melting pot or the furnace chamber. In URO 200 reactors, the refining process lasts 600 s (10 min), the gas flow rate that can be obtained ranges from 5 to 20 dm3·min−1, and the speed at which the rotor can move is 0 to 400 rpm. The permissible quantity of liquid metal for barbotage refining is 300 kg or 700 kg [8,16,17]. The URO 200 has several design solutions which improve operation and can be adapted to the existing equipment in the foundry. These solutions include the following [8,16]:

  • URO-200XR—used for small crucible furnaces, the capacity of which does not exceed 250 kg, with no control system and no control of the refining process.
  • URO-200SA—used to service several crucible furnaces of capacity from 250 kg to 700 kg, fully automated and equipped with a mechanical rotor lift.
  • URO-200KA—used for refining processes in crucible furnaces and allows refining in a ladle. The process is fully automated, with a hydraulic rotor lift.
  • URO-200KX—a combination of the XR and KA models, designed for the ladle refining process. Additionally, refining in heated crucibles is possible. The unit is equipped with a manual hydraulic rotor lift.
  • URO-200PA—designed to cooperate with induction or crucible furnaces or intermediate chambers, the capacity of which does not exceed one ton. This unit is an integral part of the furnace. The rotor lift is equipped with a screw drive.

Studies making use of a physical model can be associated with the observation of the flow and circulation of gas bubbles. They require meeting several criteria regarding the similarity of the process and the object characteristics. The similarity conditions mainly include geometric, mechanical, chemical, thermal, and kinetic parameters. During simulation of aluminum refining with inert gas, it is necessary to maintain the geometric similarity between the model and the real object, as well as the similarity related to the flow of liquid metal and gas (hydrodynamic similarity). These quantities are characterized by the Reynolds, Weber, and Froude numbers. The Froude number is the most important parameter characterizing the process, its magnitude is the same for the physical model and the real object. Water was used as the medium in the physical modeling. The factors influencing the choice of water are its availability, relatively low cost, and kinematic viscosity at room temperature, which is very close to that of liquid aluminum.

The physical model studies focused on the flow of inert gas in the form of gas bubbles with varying degrees of dispersion, particularly with respect to some flow patterns such as flow in columns and geysers, as well as disturbance of the metal surface. The most important refining parameters are gas flow rate and rotor speed. The barbotage refining studies for the developed impeller (variants B4, B8, B12, and RT3) designs were conducted for the following process parameters:

  • Rotor speed: 200, 300, 400, and 500 rpm,
  • Ideal gas flow: 10, 20, and 30 dm3·min−1,
  • Temperature: 293 K (20 °C).

These studies were aimed at determining the most favorable variants of impellers, which were then verified using the numerical modeling methods in the Flow-3D program.

2.3. Numerical Simulations with Flow-3D Program

Testing different rotor impellers using a physical model allows for observing the phenomena taking place while refining. This is a very important step when testing new design solutions without using expensive industrial trials. Another solution is modeling by means of commercial simulation programs such as ANSYS Fluent or Flow-3D [18,19]. Unlike studies on a physical model, in a computer program, the parameters of the refining process and the object itself, including the impeller design, can be easily modified. The simulations were performed with the Flow-3D program version 12.03.02. A three-dimensional system with the same dimensions as in the physical modeling was used in the calculations. The isothermal flow of liquid–gas bubbles was analyzed. As in the physical model, three speeds were adopted in the numerical tests: 200, 300, and 500 rpm. During the initial phase of the simulations, the velocity field around the rotor generated an appropriate direction of motion for the newly produced bubbles. When the required speed was reached, the generation of randomly distributed bubbles around the rotor was started at a rate of 2000 per second. Table 1 lists the most important simulation parameters.

Table 1

Values of parameters used in the calculations.

ParameterValueUnit
Maximum number of gas particles1,000,000
Rate of particle generation20001·s−1
Specific gas constant287.058J·kg−1·K−1
Atmospheric pressure1.013 × 105Pa
Water density1000kg·m−3
Water viscosity0.001kg·m−1·s−1
Boundary condition on the wallsNo-slip
Size of computational cell0.0034m

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In the case of the CFD analysis, the numerical solutions require great care when generating the computational mesh. Therefore, computational mesh tests were performed prior to the CFD calculations. The effect of mesh density was evaluated by taking into account the velocity of water in the tested object on the measurement line A (height of 0.065 m from the bottom) in a characteristic cross-section passing through the object axis (see Figure 6). The mesh contained 3,207,600, 6,311,981, 7,889,512, 11,569,230, and 14,115,049 cells.

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Figure 6

The velocity of the water depending on the size of the computational grid.

The quality of the generated computational meshes was checked using the criterion skewness angle QEAS [18]. This criterion is described by the following relationship:

QEAS=max{βmax−βeq180−βeq,βeq−βminβeq},

(1)

where βmaxβmin are the maximal and minimal angles (in degrees) between the edges of the cell, and βeq is the angle corresponding to an ideal cell, which for cubic cells is 90°.

Normalized in the interval [0;1], the value of QEAS should not exceed 0.75, which identifies the permissible skewness angle of the generated mesh. For the computed meshes, this value was equal to 0.55–0.65.

Moreover, when generating the computational grids in the studied facility, they were compacted in the areas of the highest gradients of the calculated values, where higher turbulence is to be expected (near the impeller). The obtained results of water velocity in the studied object at constant gas flow rate are shown in Figure 6.

The analysis of the obtained water velocity distributions (see Figure 6) along the line inside the object revealed that, with the density of the grid of nodal points, the velocity changed and its changes for the test cases of 7,889,512, 11,569,230, and 14,115,049 were insignificant. Therefore, it was assumed that a grid containing not less than 7,900,000 (7,889,512) cells would not affect the result of CFD calculations.

A single-block mesh of regular cells with a size of 0.0034 m was used in the numerical calculations. The total number of cells was approximately 7,900,000 (7,889,512). This grid resolution (see Figure 7) allowed the geometry of the system to be properly represented, maintaining acceptable computation time (about 3 days on a workstation with 2× CPU and 12 computing cores).

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Figure 7

Structured equidistant mesh used in numerical calculations: (a) mesh with smoothed, surface cells (the so-called FAVOR method) used in Flow-3D; (b) visualization of the applied mesh resolution.

The calculations were conducted with an explicit scheme. The timestep was selected by the program automatically and controlled by stability and convergence. From the moment of the initial velocity field generation (start of particle generation), it was 0.0001 s.

When modeling the degassing process, three fluids are present in the system: water, gas supplied through the rotor head (impeller), and the surrounding air. Modeling such a multiphase flow is a numerically very complex issue. The necessity to overcome the liquid backpressure by the gas flowing out from the impeller leads to the formation of numerical instabilities in the volume of fluid (VOF)-based approach used by Flow-3D software. Therefore, a mixed description of the analyzed flow was used here. In this case, water was treated as a continuous medium, while, in the case of gas bubbles, the discrete phase model (DPM) model was applied. The way in which the air surrounding the system was taken into account is later described in detail.

The following additional assumptions were made in the modeling:

  • —The liquid phase was considered as an incompressible Newtonian fluid.
  • —The effect of chemical reactions during the refining process was neglected.
  • —The composition of each phase (gas and liquid) was considered homogeneous; therefore, the viscosity and surface tension were set as constants.
  • —Only full turbulence existed in the liquid, and the effect of molecular viscosity was neglected.
  • —The gas bubbles were shaped as perfect spheres.
  • —The mutual interaction between gas bubbles (particles) was neglected.

2.3.1. Modeling of Liquid Flow 

The motion of the real fluid (continuous medium) is described by the Navier–Stokes Equation [20].

dudt=−1ρ∇p+ν∇2u+13ν∇(∇⋅ u)+F,

(2)

where du/dt is the time derivative, u is the velocity vector, t is the time, and F is the term accounting for external forces including gravity (unit components denoted by XYZ).

In the simulations, the fluid flow was assumed to be incompressible, in which case the following equation is applicable:

∂u∂t+(u⋅∇)u=−1ρ∇p+ν∇2u+F.

(3)

Due to the large range of liquid velocities during flows, the turbulence formation process was included in the modeling. For this purpose, the k–ε model turbulence kinetic energy k and turbulence dissipation ε were the target parameters, as expressed by the following equations [21]:

∂(ρk)∂t+∂(ρkvi)∂xi=∂∂xj[(μ+μtσk)⋅∂k∂xi]+Gk+Gb−ρε−Ym+Sk,

(4)

∂(ρε)∂t+∂(ρεui)∂xi=∂∂xj[(μ+μtσε)⋅∂k∂xi]+C1εεk(Gk+G3εGb)+C2ερε2k+Sε,

(5)

where ρ is the gas density, σκ and σε are the Prandtl turbulence numbers, k and ε are constants of 1.0 and 1.3, and Gk and Gb are the kinetic energy of turbulence generated by the average velocity and buoyancy, respectively.

As mentioned earlier, there are two gas phases in the considered problem. In addition to the gas bubbles, which are treated here as particles, there is also air, which surrounds the system. The boundary of phase separation is in this case the free surface of the water. The shape of the free surface can change as a result of the forming velocity field in the liquid. Therefore, it is necessary to use an appropriate approach to free surface tracking. The most commonly used concept in liquid–gas flow modeling is the volume of fluid (VOF) method [22,23], and Flow-3D uses a modified version of this method called TrueVOF. It introduces the concept of the volume fraction of the liquid phase fl. This parameter can be used for classifying the cells of a discrete grid into areas filled with liquid phase (fl = 1), gaseous phase, or empty cells (fl = 0) and those through which the phase separation boundary (fl ∈ (0, 1)) passes (free surface). To determine the local variations of the liquid phase fraction, it is necessary to solve the following continuity equation:

dfldt=0.

(6)

Then, the fluid parameters in the region of coexistence of the two phases (the so-called interface) depend on the volume fraction of each phase.

ρ=flρl+(1−fl)ρg,

(7)

ν=flνl+(1−fl)νg,

(8)

where indices l and g refer to the liquid and gaseous phases, respectively.

The parameter of fluid velocity in cells containing both phases is also determined in the same way.

u=flul+(1−fl)ug.

(9)

Since the processes taking place in the surrounding air can be omitted, to speed up the calculations, a single-phase, free-surface model was used. This means that no calculations were performed in the gas cells (they were treated as empty cells). The liquid could fill them freely, and the air surrounding the system was considered by the atmospheric pressure exerted on the free surface. This approach is often used in modeling foundry and metallurgical processes [24].

2.3.2. Modeling of Gas Bubble Flow 

As stated, a particle model was used to model bubble flow. Spherical particles (gas bubbles) of a given size were randomly generated in the area marked with green in Figure 7b. In the simulations, the gas bubbles were assumed to have diameters of 0.016 and 0.02 m corresponding to the gas flow rates of 10 and 30 dm3·min−1, respectively.

Experimental studies have shown that, as a result of turbulent fluid motion, some of the bubbles may burst, leading to the formation of smaller bubbles, although merging of bubbles into larger groupings may also occur. Therefore, to be able to observe the behavior of bubbles of different sizes (diameter), the calculations generated two additional particle types with diameters twice smaller and twice larger, respectively. The proportion of each species in the system was set to 33.33% (Table 2).

Table 2

Data assumed for calculations.

NoRotor Speed (Rotational Speed)
rpm
Bubbles Diameter
m
Corresponding Gas Flow Rate
dm3·min−1
NoRotor Speed (Rotational Speed)
rpm
Bubbles Diameter
m
Corresponding Gas Flow Rate
dm3·min−1
A2000.01610D2000.0230
0.0080.01
0.0320.04
B3000.01610E3000.0230
0.0080.01
0.0320.04
C5000.01610F5000.0230
0.0080.01
0.0320.04

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The velocity of the particle results from the generated velocity field (calculated from Equation (3) in the liquid ul around it and its velocity resulting from the buoyancy force ub. The effect of particle radius r on the terminal velocity associated with buoyancy force can be determined according to Stokes’ law.

ub=29 (ρg−ρl)μlgr2,

(10)

where g is the acceleration (9.81).

The DPM model was used for modeling the two-phase (water–air) flow. In this model, the fluid (water) is treated as a continuous phase and described by the Navier–Stokes equation, while gas bubbles are particles flowing in the model fluid (discrete phase). The trajectories of each bubble in the DPM system are calculated at each timestep taking into account the mass forces acting on it. Table 3 characterizes the DPM model used in our own research [18].

Table 3

Characteristic of the DPM model.

MethodEquations
Euler–LagrangeBalance equation:
dugdt=FD(u−ug)+g(ϱg−ϱ)ϱg+F.
FD (u − up) denotes the drag forces per mass unit of a bubble, and the expression for the drag coefficient FD is of the form
FD=18μCDReϱ⋅gd2g24.
The relative Reynolds number has the form
Re≡ρdg|ug−u|μ.
On the other hand, the force resulting from the additional acceleration of the model fluid has the form
F=12dρdtρg(u−ug),
where ug is the gas bubble velocity, u is the liquid velocity, dg is the bubble diameter, and CD is the drag coefficient.

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3. Results and Discussion

3.1. Calculations of Power and Mixing Time by the Flowing Gas Bubbles

One of the most important parameters of refining with a rotor is the mixing power induced by the spinning rotor and the outflowing gas bubbles (via impeller). The mixing power of liquid metal in a ladle of height (h) by gas injection can be determined from the following relation [15]:

pgVm=ρ⋅g⋅uB,

(11)

where pg is the mixing power, Vm is the volume of liquid metal in the reactor, ρ is the density of liquid aluminum, and uB is the average speed of bubbles, given below.

uB=n⋅R⋅TAc⋅Pm⋅t,

(12)

where n is the number of gas moles, R is the gas constant (8.314), Ac is the cross-sectional area of the reactor vessel, T is the temperature of liquid aluminum in the reactor, and Pm is the pressure at the middle tank level. The pressure at the middle level of the tank is calculated by a function of the mean logarithmic difference.

Pm=(Pa+ρ⋅g⋅h)−Paln(Pa+ρ⋅g⋅h)Pa,

(13)

where Pa is the atmospheric pressure, and h is the the height of metal in the reactor.

Themelis and Goyal [25] developed a model for calculating mixing power delivered by gas injection.

pg=2Q⋅R⋅T⋅ln(1+m⋅ρ⋅g⋅hP),

(14)

where Q is the gas flow, and m is the mass of liquid metal.

Zhang [26] proposed a model taking into account the temperature difference between gas and alloy (metal).

pg=QRTgVm[ln(1+ρ⋅g⋅hPa)+(1−TTg)],

(15)

where Tg is the gas temperature at the entry point.

Data for calculating the mixing power resulting from inert gas injection into liquid aluminum are given below in Table 4. The design parameters were adopted for the model, the parameters of which are shown in Figure 5.

Table 4

Data for calculating mixing power introduced by an inert gas.

ParameterValueUnit
Height of metal column0.7m
Density of aluminum2375kg·m−3
Process duration20s
Gas temperature at the injection site940K
Cross-sectional area of ladle0.448m2
Mass of liquid aluminum546.25kg
Volume of ladle0.23M3
Temperature of liquid aluminum941.15K

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Table 5 presents the results of mixing power calculations according to the models of Themelis and Goyal and of Zhang for inert gas flows of 10, 20, and 30 dm3·min−1. The obtained calculation results significantly differed from each other. The difference was an order of magnitude, which indicates that the model is highly inaccurate without considering the temperature of the injected gas. Moreover, the calculations apply to the case when the mixing was performed only by the flowing gas bubbles, without using a rotor, which is a great simplification of the phenomenon.

Table 5

Mixing power calculated from mathematical models.

Mathematical ModelMixing Power (W·t−1)
for a Given Inert Gas Flow (dm3·min−1)
102030
Themelis and Goyal11.4923.3335.03
Zhang0.821.662.49

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The mixing time is defined as the time required to achieve 95% complete mixing of liquid metal in the ladle [27,28,29,30]. Table 6 groups together equations for the mixing time according to the models.

Table 6

Models for calculating mixing time.

AuthorsModelRemarks
Szekely [31]τ=800ε−0.4ε—W·t−1
Chiti and Paglianti [27]τ=CVQlV—volume of reactor, m3
Ql—flow intensity, m3·s−1
Iguchi and Nakamura [32]τ=1200⋅Q−0.4D1.97h−1.0υ0.47υ—kinematic viscosity, m2·s−1
D—diameter of ladle, m
h—height of metal column, m
Q—liquid flow intensity, m3·s−1

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Figure 8 and Figure 9 show the mixing time as a function of gas flow rate for various heights of the liquid column in the ladle and mixing power values.

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Figure 8

Mixing time as a function of gas flow rate for various heights of the metal column (Iguchi and Nakamura model).

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Figure 9

Mixing time as a function of mixing power (Szekly model).

3.2. Determining the Bubble Size

The mechanisms controlling bubble size and mass transfer in an alloy undergoing refining are complex. Strong mixing conditions in the reactor promote impurity mass transfer. In the case of a spinning rotor, the shear force generated by the rotor motion separates the bubbles into smaller bubbles. Rotational speed, mixing force, surface tension, and liquid density have a strong influence on the bubble size. To characterize the kinetic state of the refining process, parameters k and A were introduced. Parameters kA, and uB can be calculated using the below equations [33].

k=2D⋅uBdB⋅π−−−−−−√,

(16)

A=6Q⋅hdB⋅uB,

(17)

uB=1.02g⋅dB,−−−−−√

(18)

where D is the diffusion coefficient, and dB is the bubble diameter.

After substituting appropriate values, we get

dB=3.03×104(πD)−2/5g−1/5h4/5Q0.344N−1.48.

(19)

According to the last equation, the size of the gas bubble decreases with the increasing rotational speed (see Figure 10).

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Figure 10

Effect of rotational speed on the bubble diameter.

In a flow of given turbulence intensity, the diameter of the bubble does not exceed the maximum size dmax, which is inversely proportional to the rate of kinetic energy dissipation in a viscous flow ε. The size of the gas bubble diameter as a function of the mixing energy, also considering the Weber number and the mixing energy in the negative power, can be determined from the following equations [31,34]:

  • —Sevik and Park:

dBmax=We0.6kr⋅(σ⋅103ρ⋅10−3)0.6⋅(10⋅ε)−0.4⋅10−2.

(20)

  • —Evans:

dBmax=⎡⎣Wekr⋅σ⋅1032⋅(ρ⋅10−3)13⎤⎦35 ⋅(10⋅ε)−25⋅10−2.

(21)

The results of calculating the maximum diameter of the bubble dBmax determined from Equation (21) are given in Table 7.

Table 7

The results of calculating the maximum diameter of the bubble using Equation (21).

ModelMixing Energy
ĺ (m2·s−3)
Weber Number (Wekr)
0.591.01.2
Zhang and Taniguchi
dmax
0.10.01670.02300.026
0.50.00880.01210.013
1.00.00670.00910.010
1.50.00570.00780.009
Sevik and Park
dBmax
0.10.2650.360.41
0.50.1390.190.21
1.00.1060.140.16
1.50.0900.120.14
Evans
dBmax
0.10.2470.3400.38
0.50.1300.1780.20
1.00.0980.1350.15
1.50.0840.1150.13

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3.3. Physical Modeling

The first stage of experiments (using the URO-200 water model) included conducting experiments with impellers equipped with four, eight, and 12 gas outlets (variants B4, B8, B12). The tests were carried out for different process parameters. Selected results for these experiments are presented in Figure 11Figure 12Figure 13 and Figure 14.

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Figure 11

Impeller variant B4—gas bubbles dispersion registered for a gas flow rate of 10 dm3·min−1 and rotor speed of (a) 200, (b) 300, (c) 400, and (d) 500 rpm.

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Figure 12

Impeller variant B8—gas bubbles dispersion registered for a gas flow rate of 10 dm3·min−1 and rotor speed of (a) 200, (b) 300, (c) 400, and (d) 500 rpm.

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Figure 13

Gas bubble dispersion registered for different processing parameters (impeller variant B12).

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Figure 14

Gas bubble dispersion registered for different processing parameters (impeller variant RT3).

The analysis of the refining variants presented in Figure 11Figure 12Figure 13 and Figure 14 reveals that the proposed impellers design model is not useful for the aluminum refining process. The number of gas outlet orifices, rotational speed, and flow did not affect the refining efficiency. In all the variants shown in the figures, very poor dispersion of gas bubbles was observed in the object. The gas bubble flow had a columnar character, and so-called dead zones, i.e., areas where no inert gas bubbles are present, were visible in the analyzed object. Such dead zones were located in the bottom and side zones of the ladle, while the flow of bubbles occurred near the turning rotor. Another negative phenomenon observed was a significant agitation of the water surface due to excessive (rotational) rotor speed and gas flow (see Figure 13, cases 20; 400, 30; 300, 30; 400, and 30; 500).

Research results for a ‘red triangle’ impeller equipped with three gas supply orifices (variant RT3) are presented in Figure 14.

In this impeller design, a uniform degree of bubble dispersion in the entire volume of the modeling fluid was achieved for most cases presented (see Figure 14). In all tested variants, single bubbles were observed in the area of the water surface in the vessel. For variants 20; 200, 30; 200, and 20; 300 shown in Figure 14, the bubble dispersion results were the worst as the so-called dead zones were identified in the area near the bottom and sidewalls of the vessel, which disqualifies these work parameters for further applications. Interestingly, areas where swirls and gas bubble chains formed were identified only for the inert gas flows of 20 and 30 dm3·min−1 and 200 rpm in the analyzed model. This means that the presented model had the best performance in terms of dispersion of gas bubbles in the model liquid. Its design with sharp edges also differed from previously analyzed models, which is beneficial for gas bubble dispersion, but may interfere with its suitability in industrial conditions due to possible premature wear.

3.4. Qualitative Comparison of Research Results (CFD and Physical Model)

The analysis (physical modeling) revealed that the best mixing efficiency results were obtained with the RT3 impeller variant. Therefore, numerical calculations were carried out for the impeller model with three outlet orifices (variant RT3). The CFD results are presented in Figure 15 and Figure 16.

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Figure 15

Simulation results of the impeller RT3, for given flows and rotational speeds after a time of 1 s: simulation variants (a) A, (b) B, (c) C, (d) D, (e) E, and (f) F.

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Figure 16

Simulation results of the impeller RT3, for given flows and rotational speeds after a time of 5.4 s.: simulation variants (a) A, (b) B, (c) C, (d) D, (e) E, and (f) F.

CFD results are presented for all analyzed variants (impeller RT3) at two selected calculation timesteps of 1 and 5.40 s. They show the velocity field of the medium (water) and the dispersion of gas bubbles.

Figure 15 shows the initial refining phase after 1 s of the process. In this case, the gas bubble formation and flow were observed in an area close to contact with the rotor. Figure 16 shows the phase when the dispersion and flow of gas bubbles were advanced in the reactor area of the URO-200 model.

The quantitative evaluation of the obtained results of physical and numerical model tests was based on the comparison of the degree of gas dispersion in the model liquid. The degree of gas bubble dispersion in the volume of the model liquid and the areas of strong turbulent zones formation were evaluated during the analysis of the results of visualization and numerical simulations. These two effects sufficiently characterize the required course of the process from the physical point of view. The known scheme of the below description was adopted as a basic criterion for the evaluation of the degree of dispersion of gas bubbles in the model liquid.

  • Minimal dispersion—single bubbles ascending in the region of their formation along the ladle axis; lack of mixing in the whole bath volume.
  • Accurate dispersion—single and well-mixed bubbles ascending toward the bath mirror in the region of the ladle axis; no dispersion near the walls and in the lower part of the ladle.
  • Uniform dispersion—most desirable; very good mixing of fine bubbles with model liquid.
  • Excessive dispersion—bubbles join together to form chains; large turbulence zones; uneven flow of gas.

The numerical simulation results give a good agreement with the experiments performed with the physical model. For all studied variants (used process parameters), the single bubbles were observed in the area of water surface in the vessel. For variants presented in Figure 13 (200 rpm, gas flow 20 and dm3·min−1) and relevant examples in numerical simulation Figure 16, the worst bubble dispersion results were obtained because the dead zones were identified in the area near the bottom and sidewalls of the vessel, which disqualifies these work parameters for further use. The areas where swirls and gas bubble chains formed were identified only for the inert gas flows of 20 and 30 dm3·min−1 and 200 rpm in the analyzed model (physical model). This means that the presented impeller model had the best performance in terms of dispersion of gas bubbles in the model liquid. The worst bubble dispersion results were obtained because the dead zones were identified in the area near the bottom and side walls of the vessel, which disqualifies these work parameters for further use.

Figure 17 presents exemplary results of model tests (CFD and physical model) with marked gas bubble dispersion zones. All variants of tests were analogously compared, and this comparison allowed validating the numerical model.

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Figure 17

Compilations of model research results (CFD and physical): A—single gas bubbles formed on the surface of the modeling liquid, B—excessive formation of gas chains and swirls, C—uniform distribution of gas bubbles in the entire volume of the tank, and D—dead zones without gas bubbles, no dispersion. (a) Variant B; (b) variant F.

It should be mentioned here that, in numerical simulations, it is necessary to make certain assumptions and simplifications. The calculations assumed three particle size classes (Table 2), which represent the different gas bubbles that form due to different gas flow rates. The maximum number of particles/bubbles (Table 1) generated was assumed in advance and related to the computational capabilities of the computer. Too many particles can also make it difficult to visualize and analyze the results. The size of the particles, of course, affects their behavior during simulation, while, in the figures provided in the article, the bubbles are represented by spheres (visualization of the results) of the same size. Please note that, due to the adopted Lagrangian–Eulerian approach, the simulation did not take into account phenomena such as bubble collapse or fusion. However, the obtained results allow a comprehensive analysis of the behavior of gas bubbles in the system under consideration.

The comparative analysis of the visualization (quantitative) results obtained with the water model and CFD simulations (see Figure 17) generated a sufficient agreement from the point of view of the trends. A precise quantitative evaluation is difficult to perform because of the lack of a refraction compensating system in the water model. Furthermore, in numerical simulations, it is not possible to determine the geometry of the forming gas bubbles and their interaction with each other as opposed to the visualization in the water model. The use of both research methods is complementary. Thus, a direct comparison of images obtained by the two methods requires appropriate interpretation. However, such an assessment gives the possibility to qualitatively determine the types of the present gas bubble dispersion, thus ultimately validating the CFD results with the water model.

A summary of the visualization results for impellers RT3, i.e., analysis of the occurring gas bubble dispersion types, is presented in Table 8.

Table 8

Summary of visualization results (impeller RT3)—different types of gas bubble dispersion.

No Exp.ABCDEF
Gas flow rate, dm3·min−11030
Impeller speed, rpm200300500200300500
Type of dispersionAccurateUniformUniform/excessiveMinimalExcessiveExcessive

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Tests carried out for impeller RT3 confirmed the high efficiency of gas bubble distribution in the volume of the tested object at a low inert gas flow rate of 10 dm3·min−1. The most optimal variant was variant B (300 rpm, 10 dm3·min−1). However, the other variants A and C (gas flow rate 10 dm3·min−1) seemed to be favorable for this type of impeller and are recommended for further testing. The above process parameters will be analyzed in detail in a quantitative analysis to be performed on the basis of the obtained efficiency curves of the degassing process (oxygen removal). This analysis will give an unambiguous answer as to which process parameters are the most optimal for this type of impeller; the results are planned for publication in the next article.

It should also be noted here that the high agreement between the results of numerical calculations and physical modelling prompts a conclusion that the proposed approach to the simulation of a degassing process which consists of a single-phase flow model with a free surface and a particle flow model is appropriate. The simulation results enable us to understand how the velocity field in the fluid is formed and to analyze the distribution of gas bubbles in the system. The simulations in Flow-3D software can, therefore, be useful for both the design of the impeller geometry and the selection of process parameters.

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4. Conclusions

The results of experiments carried out on the physical model of the device for the simulation of barbotage refining of aluminum revealed that the worst results in terms of distribution and dispersion of gas bubbles in the studied object were obtained for the black impellers variants B4, B8, and B12 (multi-orifice impellers—four, eight, and 12 outlet holes, respectively).

In this case, the control of flow, speed, and number of gas exit orifices did not improve the process efficiency, and the developed design did not meet the criteria for industrial tests. In the case of the ‘red triangle’ impeller (variant RT3), uniform gas bubble dispersion was achieved throughout the volume of the modeling fluid for most of the tested variants. The worst bubble dispersion results due to the occurrence of the so-called dead zones in the area near the bottom and sidewalls of the vessel were obtained for the flow variants of 20 dm3·min−1 and 200 rpm and 30 dm3·min−1 and 200 rpm. For the analyzed model, areas where swirls and gas bubble chains were formed were found only for the inert gas flow of 20 and 30 dm3·min−1 and 200 rpm. The model impeller (variant RT3) had the best performance compared to the previously presented impellers in terms of dispersion of gas bubbles in the model liquid. Moreover, its design differed from previously presented models because of its sharp edges. This can be advantageous for gas bubble dispersion, but may negatively affect its suitability in industrial conditions due to premature wearing.

The CFD simulation results confirmed the results obtained from the experiments performed on the physical model. The numerical simulation of the operation of the ‘red triangle’ impeller model (using Flow-3D software) gave good agreement with the experiments performed on the physical model. This means that the presented model impeller, as compared to other (analyzed) designs, had the best performance in terms of gas bubble dispersion in the model liquid.

In further work, the developed numerical model is planned to be used for CFD simulations of the gas bubble distribution process taking into account physicochemical parameters of liquid aluminum based on industrial tests. Consequently, the obtained results may be implemented in production practice.

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Funding Statement

This paper was created with the financial support grants from the AGH-UST, Faculty of Foundry Engineering, Poland (16.16.170.654 and 11/990/BK_22/0083) for the Faculty of Materials Engineering, Silesian University of Technology, Poland.

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Author Contributions

Conceptualization, K.K. and D.K.; methodology, J.P. and T.M.; validation, M.S. and S.G.; formal analysis, D.K. and T.M.; investigation, J.P., K.K. and S.G.; resources, M.S., J.P. and K.K.; writing—original draft preparation, D.K. and T.M.; writing—review and editing, D.K. and T.M.; visualization, J.P., K.K. and S.G.; supervision, D.K.; funding acquisition, D.K. and T.M. All authors have read and agreed to the published version of the manuscript.

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Institutional Review Board Statement

Not applicable.

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Informed Consent Statement

Not applicable.

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Data Availability Statement

Data are contained within the article.

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Conflicts of Interest

The authors declare no conflict of interest.

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Footnotes

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Application of Computational Fluid Dynamics in Chlorine-Dynamics Modeling of In-Situ Chlorination Systems for Cooling Systems

Jongchan Yi 1, Jonghun Lee 1, Mohd Amiruddin Fikri 2,3, Byoung-In Sang 4 and Hyunook Kim 1,*

Abstract

염소화는 상대적인 효율성과 저렴한 비용으로 인해 발전소 냉각 시스템에서 생물학적 오염을 제어하는​​데 선호되는 방법입니다. 해안 지역에 발전소가 있는 경우 바닷물을 사용하여 현장에서 염소를 전기화학적으로 생성할 수 있습니다. 이를 현장 전기염소화라고 합니다. 이 접근 방식은 유해한 염소화 부산물이 적고 염소를 저장할 필요가 없다는 점을 포함하여 몇 가지 장점이 있습니다. 그럼에도 불구하고, 이 전기화학적 공정은 실제로는 아직 초기 단계에 있습니다. 이 연구에서는 파일럿 규모 냉각 시스템에서 염소 붕괴를 시뮬레이션하기 위해 병렬 1차 동역학을 적용했습니다. 붕괴가 취수관을 따라 발생하기 때문에 동역학은 전산유체역학(CFD) 코드에 통합되었으며, 이후에 파이프의 염소 거동을 시뮬레이션하는데 적용되었습니다. 실험과 시뮬레이션 데이터는 강한 난류가 형성되는 조건하에서도 파이프 벽을 따라 염소 농도가 점진적인 것으로 나타났습니다. 염소가 중간보다 파이프 표면을 따라 훨씬 더 집중적으로 남아 있다는 사실은 전기 염소화를 기반으로 하는 시스템의 전체 염소 요구량을 감소시킬 수 있었습니다. 현장 전기 염소화 방식의 냉각 시스템은 직접 주입 방식에 필요한 염소 사용량의 1/3만 소비했습니다. 따라서 현장 전기염소화는 해안 지역의 발전소에서 바이오파울링 제어를 위한 비용 효율적이고 환경 친화적인 접근 방식으로 사용될 수 있다고 결론지었습니다.

Chlorination is the preferred method to control biofouling in a power plant cooling system due to its comparative effectiveness and low cost. If a power plant is located in a coastal area, chlorine can be electrochemically generated in-situ using seawater, which is called in-situ electrochlorination; this approach has several advantages including fewer harmful chlorination byproducts and no need for chlorine storage. Nonetheless, this electrochemical process is still in its infancy in practice. In this study, a parallel first-order kinetics was applied to simulate chlorine decay in a pilot-scale cooling system. Since the decay occurs along the water-intake pipe, the kinetics was incorporated into computational fluid dynamics (CFD) codes, which were subsequently applied to simulate chlorine behavior in the pipe. The experiment and the simulation data indicated that chlorine concentrations along the pipe wall were incremental, even under the condition where a strong turbulent flow was formed. The fact that chlorine remained much more concentrated along the pipe surface than in the middle allowed for the reduction of the overall chlorine demand of the system based on the electro-chlorination. The cooling system, with an in-situ electro-chlorination, consumed only 1/3 of the chlorine dose demanded by the direct injection method. Therefore, it was concluded that in-situ electro-chlorination could serve as a cost-effective and environmentally friendly approach for biofouling control at power plants on coastal areas.

Keywords

computational fluid dynamics; power plant; cooling system; electro-chlorination; insitu chlorination

Figure 1. Electrodes and batch experiment set-up. (a) Two cylindrical electrodes used in this study. (b) Batch experiment set-up for kinetic tests.
Figure 1. Electrodes and batch experiment set-up. (a) Two cylindrical electrodes used in this study. (b) Batch experiment set-up for kinetic tests.
Figure 2. Schematic diagram for pilot-scale cooling-water circulation system (a) along with a real picture of the system (b).
Figure 2. Schematic diagram for pilot-scale cooling-water circulation system (a) along with a real picture of the system (b).
Figure 3. Free chlorine decay curves in seawater with different TOC and initial chlorine concentration. Each line represents the predicted concentration of chlorine under a given condition. (a) Artificial seawater solution with 1 mg L−1 of TOC; (b) artificial seawater solution with 2 mg L−1 of TOC; (c) artificial seawater solution with 3 mg L−1 of TOC; (d) West Sea water (1.3 mg L−1 of TOC).
Figure 3. Free chlorine decay curves in seawater with different TOC and initial chlorine concentration. Each line represents the predicted concentration of chlorine under a given condition. (a) Artificial seawater solution with 1 mg L−1 of TOC; (b) artificial seawater solution with 2 mg L−1 of TOC; (c) artificial seawater solution with 3 mg L−1 of TOC; (d) West Sea water (1.3 mg L−1 of TOC).
Figure 4. Correlation between model and experimental data in the chlorine kinetics using seawater.
Figure 4. Correlation between model and experimental data in the chlorine kinetics using seawater.
Figure 5. Free chlorine concentrations in West Sea water under different current conditions in an insitu electro-chlorination system.
Figure 5. Free chlorine concentrations in West Sea water under different current conditions in an insitu electro-chlorination system.
Figure 6. Free chlorine distribution along the sampling ports under different flow rates. Each dot represents experimental data, and each point on the black line is the expected chlorine concentration obtained from computational fluid dynamics (CFD) simulation with a parallel first-order decay model. The red-dotted line is the desirable concentration at the given flow rate: (a) 600 L min−1 of flow rate, (b) 700 L min−1 of flow rate, (c) 800 L min−1 of flow rate, (d) 900 L min−1 of flow rate.
Figure 6. Free chlorine distribution along the sampling ports under different flow rates. Each dot represents experimental data, and each point on the black line is the expected chlorine concentration obtained from computational fluid dynamics (CFD) simulation with a parallel first-order decay model. The red-dotted line is the desirable concentration at the given flow rate: (a) 600 L min−1 of flow rate, (b) 700 L min−1 of flow rate, (c) 800 L min−1 of flow rate, (d) 900 L min−1 of flow rate.
Figure 7. Fluid contour images from CFD simulation of the electro-chlorination experiment. Inlet flow rate is 800 L min−1. Outlet pressure was set to 10.8 kPa. (a) Chlorine concentration; (b) expanded view of electrode side in image (a); (c) velocity magnitude; (d) pressure.
Figure 7. Fluid contour images from CFD simulation of the electro-chlorination experiment. Inlet flow rate is 800 L min−1. Outlet pressure was set to 10.8 kPa. (a) Chlorine concentration; (b) expanded view of electrode side in image (a); (c) velocity magnitude; (d) pressure.
Figure 8. Chlorine concentration contour in the simulation of full-scale in-situ electro-chlorination with different cathode positions. The pipe diameter is 2 m and the flow rate is 14 m3 s−1. The figure shows 10 m of the pipeline. (a) The simulation result when the cathode is placed on the surface of the pipe wall. (b) The simulation result when the cathode is placed on the inside of the pipe with 100 mm of distance from the pipe wall.
Figure 8. Chlorine concentration contour in the simulation of full-scale in-situ electro-chlorination with different cathode positions. The pipe diameter is 2 m and the flow rate is 14 m3 s−1. The figure shows 10 m of the pipeline. (a) The simulation result when the cathode is placed on the surface of the pipe wall. (b) The simulation result when the cathode is placed on the inside of the pipe with 100 mm of distance from the pipe wall.
Figure 9. Comparison of in-situ electro-chlorination and direct chlorine injection in full-scale applications. (a) Estimated chlorine concentrations along the pipe surface. (b) Relative chlorine demands.
Figure 9. Comparison of in-situ electro-chlorination and direct chlorine injection in full-scale applications. (a) Estimated chlorine concentrations along the pipe surface. (b) Relative chlorine demands.

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Figure 1- The experimental model [17]

와류형 우수 저류지의 수치 모델링에 대한 난류 슈미트 수의 영향 조사

Investigation of the Turbulent Schmidt Number Effects On Numerical Modelling Of Vortex-Type Stormwater Retention Ponds

S. M. Yamini1; H. Shamloo2; S. H. Ghafari3
1M.Eng., Dep. of Civil Engineering K.N. Toosi University of Technology, Valiasr St., Tehran, Iran.
smyamini@alumni.kntu.ac.ir
2Associate Professor, Dep. of Civil Engineering K.N. Toosi University of Technology, Valiasr St., Tehran, Iran.
hshamloo@kntu.ac.ir
3Ph.D., Dep. of Civil Engineering Univ. of Tehran, Enqelab St., Tehran, Iran. sarvenazghafari@ut.ac.ir

Abstract

정확하고 신뢰할 수 있는 CFD 모델링 결과를 얻는 것은 이러한 시뮬레이션에서 입력의 중요성 때문에 종종 정밀 조사의 대상입니다.

난류 모델링이 RANS(Reynolds-Averaged Navier-Stokes) 방정식을 기반으로 하는 경우 난류 스칼라 전송을 추정하려면 난류 흐름에서 질량 1에 대한 운동량 확산의 비율로 정의되는 난류 슈미트 수(Sct)의 정의가 필요합니다.

그러나 이 매개변수는 난류 흐름의 속성이므로 보편적인 값이 허용되지 않았습니다. 우수 저류지의 수치 연구에서 적절한 Sct를 설정하는 실제 역할은 수력 효율의 평가가 추적자 테스트의 출력 질량 농도를 기반으로 하기 때문에 가장 중요합니다.

본 연구에서는 FLOW-3D를 사용하여 와류형 우수 저류지의 여러 수치 시뮬레이션을 체계적으로 수행했습니다. 다양한 난류 슈미트 수의 범위는 메쉬 감도를 조사하기 위해 다른 수의 계산 셀에 의해 수행된 수치 시뮬레이션에 도입되었습니다.

또한 사용자 정의 또는 자동 계산 값으로 최대 난류 혼합 길이의 영향을 평가했습니다. 이 연구의 결과는 실험 결과와 밀접한 일치를 제공하는 Sct= 0.625와 함께 수리학적 직경의 7%와 동일한 최대 난류 혼합 길이의 일정한 값을 갖는 확립된 수치 모델입니다.

특히 수치적 무차원 RDT 곡선의 피크 값은 극적으로 감소하여 실험 결과와 거의 일치했습니다. 이것은 FLOW-3D가 난류 유동의 와류형 물리학에서 질량 확산도를 적절하게 예측하는 상당한 능력을 가지고 있다는 결론을 내립니다.

– Achieving accurate and reliable CFD modelling results often is the subject of scrutiny because of the importance of the inputs in those simulations. If turbulence modelling is based on Reynolds-Averaged Navier-Stokes (RANS) equations, estimating the turbulent scalar transport requires the definition of the turbulent Schmidt number (Sct), defined as the ratio of momentum diffusivity to mass one in a turbulent flow. However, no universal value has been accepted for this parameter as it is a property of turbulent flows.

The practical role of establishing a suitable Sct in numerical studies of stormwater retention ponds is of the utmost importance because the assessment of the hydraulic efficiency of them is based on output mass concentration of tracer tests. In this study, several numerical simulations of a vortex-type stormwater retention pond were systematically carried out using FLOW-3D. A range of various turbulent Schmidt numbers were introduced in numerical simulations performed by different number of computational cells to investigate mesh sensitivity.

Moreover, the effects of maximum turbulent mixing length as a user-defined or automatically computed value were assessed. The outcome of this study is an established numerical model with a constant value of maximum turbulent mixing length equal to 7% of the hydraulic diameter along with Sct= 0.625 which provides a close agreement with experimental results.

Noticeably, the peak values of numerical dimensionless RDT curves are dramatically decreased, resulted in a close match with experimental results. This concludes that FLOW-3D has a considerable ability to appropriately predict mass diffusivity in vortex-type physics of turbulent flows.

Keywords:

turbulent Schmidt number – maximum turbulent mixing length – CFD – mesh sensitivity – vortex-type
stormwater retention pond – environmental fluid mechanics

Figure 1- The experimental model [17]
Figure 1- The experimental model [17]
Figure 2- Schematic of boundary conditions in the numerical model
Figure 2- Schematic of boundary conditions in the numerical model
Figure 3- Positioning of mesh blocks
Figure 3- Positioning of mesh blocks

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Figure 1. (a) Top view of the microfluidic-magnetophoretic device, (b) Schematic representation of the channel cross-sections studied in this work, and (c) the magnet position relative to the channel location (Sepy and Sepz are the magnet separation distances in y and z, respectively).

Continuous-Flow Separation of Magnetic Particles from Biofluids: How Does the Microdevice Geometry Determine the Separation Performance?

1Department of Chemical and Biomolecular Engineering, ETSIIT, University of Cantabria, Avda. Los Castros s/n, 39005 Santander, Spain
2William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, 151 W. Woodruff Ave., Columbus, OH 43210, USA
*Author to whom correspondence should be addressed.
Sensors 202020(11), 3030; https://doi.org/10.3390/s20113030
Received: 16 April 2020 / Revised: 21 May 2020 / Accepted: 25 May 2020 / Published: 27 May 2020
(This article belongs to the Special Issue Lab-on-a-Chip and Microfluidic Sensors)

Abstract

The use of functionalized magnetic particles for the detection or separation of multiple chemicals and biomolecules from biofluids continues to attract significant attention. After their incubation with the targeted substances, the beads can be magnetically recovered to perform analysis or diagnostic tests. Particle recovery with permanent magnets in continuous-flow microdevices has gathered great attention in the last decade due to the multiple advantages of microfluidics. As such, great efforts have been made to determine the magnetic and fluidic conditions for achieving complete particle capture; however, less attention has been paid to the effect of the channel geometry on the system performance, although it is key for designing systems that simultaneously provide high particle recovery and flow rates. Herein, we address the optimization of Y-Y-shaped microchannels, where magnetic beads are separated from blood and collected into a buffer stream by applying an external magnetic field. The influence of several geometrical features (namely cross section shape, thickness, length, and volume) on both bead recovery and system throughput is studied. For that purpose, we employ an experimentally validated Computational Fluid Dynamics (CFD) numerical model that considers the dominant forces acting on the beads during separation. Our results indicate that rectangular, long devices display the best performance as they deliver high particle recovery and high throughput. Thus, this methodology could be applied to the rational design of lab-on-a-chip devices for any magnetically driven purification, enrichment or isolation.

Keywords: particle magnetophoresisCFDcross sectionchip fabrication

Korea Abstract

생체 유체에서 여러 화학 물질과 생체 분자의 검출 또는 분리를위한 기능화 된 자성 입자의 사용은 계속해서 상당한 관심을 받고 있습니다. 표적 물질과 함께 배양 한 후 비드를 자기 적으로 회수하여 분석 또는 진단 테스트를 수행 할 수 있습니다. 연속 흐름 마이크로 장치에서 영구 자석을 사용한 입자 회수는 마이크로 유체의 여러 장점으로 인해 지난 10 년 동안 큰 관심을 모았습니다. 

따라서 완전한 입자 포획을 달성하기 위한 자기 및 유체 조건을 결정하기 위해 많은 노력을 기울였습니다. 그러나 높은 입자 회수율과 유속을 동시에 제공하는 시스템을 설계하는 데있어 핵심이기는 하지만 시스템 성능에 대한 채널 형상의 영향에 대해서는 덜주의를 기울였습니다. 

여기에서 우리는 자기 비드가 혈액에서 분리되고 외부 자기장을 적용하여 버퍼 스트림으로 수집되는 YY 모양의 마이크로 채널의 최적화를 다룹니다. 비드 회수 및 시스템 처리량에 대한 여러 기하학적 특징 (즉, 단면 형상, 두께, 길이 및 부피)의 영향을 연구합니다. 

이를 위해 분리 중에 비드에 작용하는 지배적인 힘을 고려하는 실험적으로 검증 된 CFD (Computational Fluid Dynamics) 수치 모델을 사용합니다. 우리의 결과는 직사각형의 긴 장치가 높은 입자 회수율과 높은 처리량을 제공하기 때문에 최고의 성능을 보여줍니다. 

따라서 이 방법론은 자기 구동 정제, 농축 또는 분리를 위한 랩온어 칩 장치의 합리적인 설계에 적용될 수 있습니다.

Figure 1. (a) Top view of the microfluidic-magnetophoretic device, (b) Schematic representation of the channel cross-sections studied in this work, and (c) the magnet position relative to the channel location (Sepy and Sepz are the magnet separation distances in y and z, respectively).
Figure 1. (a) Top view of the microfluidic-magnetophoretic device, (b) Schematic representation of the channel cross-sections studied in this work, and (c) the magnet position relative to the channel location (Sepy and Sepz are the magnet separation distances in y and z, respectively).
Figure 2. (a) Channel-magnet configuration and (b–d) magnetic force distribution in the channel midplane for 2 mm, 5 mm and 10 mm long rectangular (left) and U-shaped (right) devices.
Figure 2. (a) Channel-magnet configuration and (b–d) magnetic force distribution in the channel midplane for 2 mm, 5 mm and 10 mm long rectangular (left) and U-shaped (right) devices.
Figure 3. (a) Velocity distribution in a section perpendicular to the flow for rectangular (left) and U-shaped (right) cross section channels, and (b) particle location in these cross sections.
Figure 3. (a) Velocity distribution in a section perpendicular to the flow for rectangular (left) and U-shaped (right) cross section channels, and (b) particle location in these cross sections.
Figure 4. Influence of fluid flow rate on particle recovery when the applied magnetic force is (a) different and (b) equal in U-shaped and rectangular cross section microdevices.
Figure 4. Influence of fluid flow rate on particle recovery when the applied magnetic force is (a) different and (b) equal in U-shaped and rectangular cross section microdevices.
Figure 5. Magnetic bead capture as a function of fluid flow rate for all of the studied geometries.
Figure 5. Magnetic bead capture as a function of fluid flow rate for all of the studied geometries.
Figure 6. Influence of (a) magnetic and fluidic forces (J parameter) and (b) channel geometry (θ parameter) on particle recovery. Note that U-2mm does not accurately fit a line.
Figure 6. Influence of (a) magnetic and fluidic forces (J parameter) and (b) channel geometry (θ parameter) on particle recovery. Note that U-2mm does not accurately fit a line.
Figure 7. Dependence of bead capture on the (a) functional channel volume and (b) particle residence time (tres). Note that in the curve fitting expressions V represents the functional channel volume and that U-2mm does not accurately fit a line.
Figure 7. Dependence of bead capture on the (a) functional channel volume and (b) particle residence time (tres). Note that in the curve fitting expressions V represents the functional channel volume and that U-2mm does not accurately fit a line.

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유압 헤드 계산에서는 유선이 평행하다고 가정

FLOW-3D Output variables(출력 변수)

Output variables(출력 변수)

FLOW-3D에서 주어진 시뮬레이션의 정확한 출력은 어떤 물리적 모델, 출력 위젯에 정의된 추가 출력 및 특정 구성 요소별 출력에 따라 달라집니다. 이 문서는 FLOW-3D의 출력에 대해 좀 더 복잡한 출력 변수 중 일부를 참조하는 역할을 합니다.

FLOW-3D Additional output
FLOW-3D Additional output

Distance Traveled by Fluid(유체로 이동 한 거리)

때로는 유체 입자가 이동한 거리가 중요한 경우도 있습니다. FLOW-3D에서 사용자는 모델 설정 ‣ 출력 위젯에서 유체가 이동한 거리에 대한 출력을 요청할 수 있습니다. 이 기능은 유체가 흐름 영역(경계 또는 질량 소스를 통해)에 들어간 시간 또는 유체가 도메인을 통해 이동한 거리를 계산합니다. 이 기능은 모든 시뮬레이션에도 사용할 수 있으며, 특별한 모델을 사용할 필요가 없으며, 흐름에도 영향을 미치지 않습니다. 이 모델을 사용하려면 출력 위젯으로 이동하고 추가 출력 섹션에서 “Distance traveled by fluid” 옆의 체크상자를 선택하십시오.

 노트

추가 출력 섹션은 출력 위젯의 모든 탭에서 사용할 수 있습니다.

유체 도착 시간

유체 도착 시간을 아는 것은 종종 유용합니다. 예를 들어 주조 시뮬레이션에서 주입 시간을 결정하는 데 사용할 수 있습니다. 제어 볼륨은 충전 프로세스 동안 여러 번 채워지고 비워지기 때문에 계산 셀이 채워지는 처음과 마지막 시간 모두 기록되고, 후 처리를 위해 저장될 수 있습니다. 이 작업은 출력 위젯과 추가 출력 섹션 내에서 유체 도착 시간 확인란을 선택하여 수행됩니다.

 노트

이 출력 옵션은 1 유체 자유 표면 흐름에만 사용할 수 있습니다.

유체 체류 시간

때로는 유체가 계산 영역 내에서 보내는 시간인 체류시간을 아는 것이 유용합니다. 이는 출력 ‣ Output ‣ Additional Output ‣ Fluid residence time 확인란을 선택하여 수행합니다. 여기서 S로 지정된 이 변수에 대한 전송 방정식은 단위 소스 항과 함께 Solve됩니다.

유체 체류 시간(Fluid residence time)
유체 체류 시간(Fluid residence time)

여기에서 t는 시간이며 u는 유체 속도입니다.

S의 단위는 시간이다. 계산 도메인에 들어가는 모든 유체에 대한 S의 초기값은 0입니다.

의 값은 항상 second order체계를 가진 데이터로부터 근사치를 구합니다.

이 출력 옵션은 1 유체 및 2 유체 유량 모두에 사용할 수 있습니다.

 노트

경계 조건 또는 소스에서 도메인으로 유입되는 유체가 이미 도메인에 있는 유체와 혼합될 때 체류가 감소하는 것처럼 보일 수 있습니다.

Wall Contact Time

벽면 접촉 시간 출력은 (1)개별 유체 요소가 특정 구성 요소와 접촉하는 시간 및 (2)특정 구성 요소가 유체와 접촉하는 시간을 추적합니다. 이 모델은 액체 금속이 모래 오염물과 접촉했을 때 오염과 상관 관계가 있는 proxy 변수를 제공하기 위한 것입니다. 이 출력은 최종 주조물에서 오염된 유체가 어디에 있는지 확인하는 데 사용될 수 있습니다. 접촉 시간 모델의 또 다른 해석은, 예를 들어, 용해를 통해 다소 일정한 비율로 화학물질을 방출하는 물에 잠긴 물체에 의한 강의 물의 오염입니다.

모델은 Model Setup ‣ Output ‣ Wall contact time 박스를 확인하여 활성화됩니다. 또한 Model Setup ‣ Output ‣ Geometry Data section의 각 구성요소에 대해 해당 구성요소를 계산에 포함하기 위해 반드시 설정해야 하는 Contact time flag가 있습니다.

 추가 정보

Wall Contact Time with Fluid and Component Properties: Contact Time with Fluid for more information on the input variables를 참조하십시오.

 노트

이 모델은 실제 구성 요소, 즉 고체, 다공성 매체, 코어 가스 및 충전 퇴적물 구성 요소로 제한됩니다. 접촉 시간은 유체 # 1과 관련해서만 계산됩니다.

2. 형상 데이터
2. 형상 데이터

Component wetted are

Fluid 1과 접촉하는 구성 요소의 표면 영역은 관심 구성 요소에 대한 Model Setup ‣ Output ‣ Geometry Data ‣ Wetted area 옵션을 활성화하여 History Data로 출력 될 수 있습니다.

구성 요소의 힘과 토크

Forces

Model Setup ‣ Output ‣ Geometry Data ‣ Forces 옵션을 활성화하면 부품에 대한 압력, 전단력, 탄성 및 벽 접착력을 History Data에 출력할 수 있습니다.

압력을 가지지 않은 셀(즉, 도메인 외부에 있거나 다른 구성 요소 안에 있는 셀)이 구성 요소 주변의 각 셀에 대한 압력 영역 제품을 합산하는 동안 어떻게 처리되는지를 제어하는 압력 계산에 대한 몇 가지 추가 옵션이 있습니다. 기본 동작은 이러한 셀에서 사용자 정의 기준 압력을 사용하는 것입니다. 지정되지 않은 경우 기준 압력은 초기 무효 압력인 PVOID로 기본 설정됩니다. 또는, 코드는 Reference pressure is code calculated 옵션을 선택하여 구성요소의 노출된 표면에 대한 평균 압력을 사용할 수 있습니다.

마지막으로, 일반 이동 물체의 경우, 규정된/제약을 받는 대로 물체를 이동시키는 힘을 나타내는 잔류 힘의 추가 출력이 있습니다.

Torques

Model Setup ‣ Output ‣ Force 옵션이 활성화되면 구성 요소의 토크가 계산되고 History Data에 출력됩니다. 토크는 힘-모멘트에 대한 기준점 X, 힘-모멘트에 대한 기준점 Y, 정지 구성 요소에 대한 힘-모멘트 입력에 대한 기준점 Z에 의해 지정된 지점에 대해 보고됩니다. 참조점의 기본 위치는 원점입니다.

General Moving Objects에는 몇 가지 추가 참고 사항이 있습니다. 첫째, 토크는 (1) 6-DOF 동작의 질량 위치 중심 또는 (2)고정축 및 고정점 회전의 회전 축/점에 대해 보고됩니다. 힘에서 행해지는 것과 마찬가지로, 규정된/제한된 바와 같이 물체를 이동시키는 토크를 나타내는 잔류 토크의 출력도 있습니다.

 노트

힘 및 토크 출력은 각 지오메트리 구성 요소의 일반 히스토리 데이터에 기록됩니다. 출력은 개별 힘/토크 기여 (예: 압력, 전단, 탄성, 벽 접착) 및 개별 기여도의 합으로 계산된 총 결합력/토크로 제공됩니다.

Buoyancy center and metacentric height (부력 중심 및 메타 중심 높이)

일반 이동 객체의 부력과 안정성에 대한 정보는 각 구성 요소에 대해 모델 설정 Setup 출력 ‣ 기하학적 데이터 ‣ 부력 중심 및 도량형 높이 옵션을 활성화하여 History Data에서 출력할 수 있습니다. 이렇게 하면 구성 요소의 중심 위치와 중심 높이가 출력됩니다.

  1. Advanced

FLOW-3D Advanced Output Option
FLOW-3D Advanced Output Option

Fluid vorticity & Q-criterion(유체 와동 및 Q 기준)

와동구성 요소뿐만 아니라 와동 구조를 위한 Q-criterion을 계산하고 내보내려면 Model Setup ‣ Output ‣ Advanced 탭에서 해당 확인란을 클릭하여 유체 와동 & Q-criterion을 활성화하십시오.

여기에서:

:  소용돌이 벡터의 다른 구성 요소

 Q-criterion은 속도 구배 텐서의 2차 불변성을 갖는 연결된 유체 영역으로 소용돌이를 정의합니다. 이는 전단 변형률과 와류 크기 사이의 국부적 균형을 나타내며, 와류 크기가 변형률의 크기보다 큰 영역으로 와류를 정의합니다.

Hydraulic Data and Total Hydraulic Head 3D

Hydraulic Data

깊이 기준 유압 데이터를 요청하려면 출력 ‣ 고급으로 이동한 후 유압 데이터 옆의 확인란을 선택하십시오(심층 평균 값과 중력을 -Z 방향으로 가정).

이 옵션은 FLOW-3D가 유압 시뮬레이션에 유용할 수 있는 추가 깊이 평균 데이터를 출력하도록 합니다.

  • Flow depth
  • Maximum flow depth
  • Free surface elevation
  • Velocity
  • Offset velocity
  • Froude number
  • Specific hydraulic head
  • Total hydraulic head

이 수량 각각에 대해 하나의 값 이 메쉬의 모든 (x, y) 위치에서 계산되고 수직 열의 모든 셀에 저장됩니다 (이 수량이 깊이 평균이기 때문에 z 방향으로 데이터의 변화가 없습니다). 변수는 정확도를 보장하기 위해주기마다 계산됩니다. 모든 경우에,  깊이 평균 속도, z- 방향  의 중력 가속도, 유체 깊이, 및 컬럼 내 유체의 최소 z- 좌표입니다.

  • 자유 표면 고도는 수직 기둥의 맨 위 유체 요소에 있는 자유 표면의 z-좌표로 계산됩니다.
  • The Froude number 은   

식으로 계산됩니다.

  • 유체 깊이는 깊이 평균 메쉬 열의 모든 유체의 합으로 계산됩니다.

특정 유압 헤드 

및 총 유압 헤드

변수는 다음에서 계산됩니다.  

 노트

  • 깊이 기준 유압 출력 옵션은 예리한 인터페이스가 있고 중력이 음의 z 방향으로 향할 때에만 유체 1에 유효합니다.
  • 유압 헤드 계산은 스트림 라인이 평행하다고 가정한다는 점을 유념해야 합니다. 예를 들어 플럭스 표면이 재순환 흐름 영역에 배치되는 경우 이 문제가 발생할 수 있습니다. 이 경우, 유량 표면에서 보고된 유량 평균 유압 헤드는 헤드의 계산에서 흐름 방향이 무시되기 때문에 예상보다 클 수 있습니다.

Total Hydraulic Head 3D(총 유압 헤드 3D)

또한 총 유압 헤드 3D 옵션을 확인하여 국부적(3D) 속도 필드, 플럭스 표면에서의 유압 에너지(배플 참조) 및 플럭스 기반 유압 헤드를 사용하여 유체 1의 총 헤드를 계산할 수 있다. 3D 계산은 국부 압력을 사용하여 수행되며(즉, 압력이 유체 깊이와 관련이 있다고 가정하지 않음) 원통 좌표와 호환됩니다.

 노트

  • 유압 헤드 계산은 스트림 라인이 평행하다고 가정한다는 점을 유념해야 한다. 예를 들어 플럭스 표면이 재순환 흐름 영역에 배치되는 경우 문제가 발생할 수 있습니다. 이 경우, 플럭스 표면에서 보고된 유량 평균 유압 헤드는 헤드의 계산 시 흐름 방향이 무시되기 때문에 예상보다 클 수 있습니다.
  • 3D 유압 헤드 계산은 입력 파일에 중력이 정의되지 않은 경우 중력 벡터의 크기를 1로 가정합니다.

Flux-averaged hydraulic head

특정 위치 (즉, 배플)의 플럭스 평균 유압 헤드는 다음과 같이 계산됩니다.

Flux-averaged hydraulic head
Flux-averaged hydraulic head

유압 헤드 계산에서는 유선이 평행하다고 가정합니다. 예를 들어 플럭스 표면이 재순환 흐름 영역에 배치된 경우 (예: 아래에 표시된 것과 같이) 문제가 될 수 있습니다.

유압 헤드 계산에서는 유선이 평행하다고 가정




유압 헤드 계산에서는 유선이 평행하다고 가정

이 경우 플럭스 표면에 보고된 플럭스 평균 유압 헤드는 헤드 계산 시 흐름 방향이 무시되므로 예상보다 클 수 있습니다.

FLOW-3D에는 History Probes, Flux surface, Sampling Volumes의 세 가지 주요 측정 장치가 있습니다. 이러한 장치를 시뮬레이션에 추가하는 방법은 모델 설정 섹션에 설명되어 있습니다(측정 장치 참조). 이들의 출력은 기록 데이터 편집 시간 간격으로 flsgrf 파일의 일반 기록 데이터 카탈로그에 저장됩니다. 이러한 결과는 Analyze ‣ Probe 탭에서 Probe Plots을 생성하여 액세스할 수 있습니다.

히스토리 프로브 출력

히스토리 프로브를 생성하는 단계는 모델 설정 섹션에 설명되어 있습니다(기록 프로브 참조). 시뮬레이션에 사용된 물리 모델에 따라 각각의 History Probe에서 서로 다른 출력을 사용할 수 있습니다. 프로브를 FSI/TSE로 지정하면 유한 요소 메시 안에 들어가야 하는 위치에서 응력/스트레인 데이터만 제공한다. 유체 프로브가 솔리드 형상 구성 요소에 의해 차단된 영역 내에 위치하는 경우, 기하학적 구조와 관련된 수량(예: 벽 온도)만 계산된다. 일반적으로 프로브 좌표에 의해 정의된 위치에서 이러한 양을 계산하려면 보간이 필요하다.

플럭스 표면 출력

플럭스 표면은 이를 통과하는 수량의 흐름을 측정하는데 사용되는 특별한 물체입니다. 플럭스 표면을 만드는 단계는 모델 설정 섹션에 설명되어 있습니다(플럭스 표면 참조). 각 플럭스 표면에 대해 계산된 수량은 다음과 같습니다.

  • Volume flow rate for fluid #1
  • Volume flow rate for fluid #2 (for two-fluid problems only)
  • Combined volume flow rate (for two-fluid problems only)
  • Total mass flow rate
  • Flux surface area wetted by fluid #1
  • Flux-averaged hydraulic head when 3D Hydraulic Head is requested from additional output options
  • Hydraulic energy flow when hydraulic data output is requested
  • Total number of particles of each defined species in each particle class crossing flux surface when the particle model is active
  • Flow rate for all active and passive scalars this includes scalar quantities associated with active physical models (eg. suspended sediment, air entrainment, ect.)

 노트

  • 유속과 입자수의 기호는 유동 표면을 설명하는 함수의 기호에 의해 정의된 대로 흐름이나 입자가 플럭스 표면의 음에서 양으로 교차할 때 양의 부호가 됩니다.
  • 플럭스 표면은 각 표면의 유량과 입자 수가 정확하도록 그들 사이에 적어도 두 개의 메쉬 셀이 있어야 합니다.
  • 유압 데이터 및 총 유압 헤드 3D 옵션을 사용할 때는 유압 헤드 계산이 스트림 라인이 평행하다고 가정한다는 점을 유념해야 한다. 예를 들어 플럭스 표면이 재순환 흐름 영역에 배치되는 경우 이 문제가 발생할 수 있습니다. 이 경우, 유량 표면에서 보고된 유량 평균 유압 헤드는 헤드의 계산에서 흐름 방향이 무시되기 때문에 예상보다 클 수 있습니다.

샘플링 볼륨 출력

샘플링 볼륨은 해당 범위 내에서 볼륨을 측정하는 3 차원 데이터 수집 영역입니다. 샘플링 볼륨을 만드는 단계는 모델 설정 섹션에 설명되어 있습니다(샘플링 볼륨 참조). 각 샘플링 볼륨의 계산 수량은 다음과 같습니다.

  • 시료채취량 내에서 #1 유체 총량
  • 시료채취량 내 #1 유체질량 중심
  • 샘플링 용적 가장자리에 위치한 솔리드 표면을 포함하여 샘플링 용적 내의 모든 벽 경계에 작용하는 좌표계의 원점에 상대적인 유압력 및 모멘트.
  • 샘플링 용적 내 총 스칼라 종량: 이것은 부피 적분으로 계산되므로 스칼라 양이 질량 농도를 나타내면 샘플링 용적 내의 총 질량이 계산된다. 거주 시간과 같은 일부 종의 경우, 평균 값이 대신 계산됩니다.
  • 샘플링 볼륨 내의 입자 수: 각 샘플링 볼륨 내에 있는 각 입자 등급의 정의된 각 종별 입자 수(입자 모델이 활성화된 경우)
  • 운동 에너지, 난류 에너지, 난류 소실율 및 와류에 대한 질량 평균
  • 표본 체적의 6개 경계 각각에서 열 유속: 유체 대류, 유체 및 고체 성분의 전도 및 유체/구성 요소 열 전달이 포함됩니다. 각 플럭스의 기호는 좌표 방향에 의해 결정되는데, 예를 들어, 양방향의 열 플럭스도 양수입니다. 출력에서 확장 또는 최대 디버그 수준을 선택하지 않는 한 이러한 디버그 수준은 fsplt에 자동으로 표시되지 않습니다.

FLOW-3D 및TruVOF는 미국 및 기타 국가에서 등록 상표입니다.

General Applications Bibliography

다음은 일반 응용 분야의 기술 문서 모음입니다.
이 모든 논문은 FLOW-3D  결과를 포함하고 있습니다. 복잡한 다중 물리와 관련된 문제를 성공적으로 시뮬레이션하기 위해 FLOW-3D를 사용 하는 방법에 대해 자세히 알아보십시오.

Below is a collection of technical papers in our General Applications Bibliography. All of these papers feature FLOW-3D results. Learn more about how FLOW-3D can be used to successfully simulate problems that involve complex multiphysics.

2024년 3월 20일 Upate

204-23   Togo Shinonaga, Hibiki Tajima, Yasuhiro Okamoto, Akira Okada, Application of large-area electron beam irradiation to micro-edge filleting, Journal of Manufacturing Processes, 107; pp. 65-73, 2023. doi.org/10.1016/j.jmapro.2023.10.039

167-23   Xiaoyong Cheng, Zhixian Cao, Ji Li, Alistair Borthwick, A numerical study of the settling of non-spherical particles in quiescent water, Physics of Fluids, 35.9; 2023. doi.org/10.1063/5.0165555

109-23 Dileep Karnam, Yu-Lung Lo, Chia-Hua Yang, Simulation study and parameter optimization of laser TSV using artificial neural networks, Journal of Materials Research and Technology, 25; pp. 3712-3727, 2023. doi.org/10.1016/j.jmrt.2023.06.199

66-23   Erik Holmen Olofsson, Michael Roland, Jon Spangenberg, Ninna Halberg Jokil, Jesper Henri Hattel, A CFD model with free surface tracking: predicting fill level and residence time in a starve-fed single-screw extruder, The International Journal of Advanced Manufacturing Technology, 126; pp. 3579-3591, 2023. doi.org/10.1007/s00170-023-11329-w

20-23   Giampiero Sciortino, Valentina Lombardi, Pietro Prestininzi, Modelling of cantilever-based flow energy harvesters featuring C-shaped vibration inducers: The role of the fluid/beam interaction, Applied Sciences, 13.1; 416, 2023. doi.org/10.3390/app13010416

134-22   Guozheng Ma, Shuying Chen, Haidou Wang, Impact spread behavior of flying droplets and properties of splats, Micro Process and Quality Control of Plasma Spraying, pp. 87-202, 2022. doi.org/10.1007/978-981-19-2742-3_3

111-22   Chia-Lin Chiu, Chia-Ming Fan, Chia-Ren Chu, Numerical analysis of two spheres falling side by side, Physics of Fluids, 34; 072112, 2022. doi.org/10.1063/5.0096534

58-21   Ruizhe Liu, Haidong Zhao, Experimental study and numerical simulation of infiltration of AlSi12 alloys into Si porous preforms with micro-computed tomography inspection characteristics, Journal of the Ceramic Society of Japan, 129.6; pp. 315-322, 2021. doi.org/10.2109/jcersj2.21018

56-20   Nils Steinau, CFD modeling of ascending Strombolian gas slugs through a constricted volcanic conduit considering a non-linear rheology, Thesis, Universität Hamburg, Hamburg, Germany, 2020.

30-20   Bita Bayatsarmadi, Mike Horne, Theo Rodopoulos and Dayalan Gunasegaram, Intensifying diffusion-limited reactions by using static mixer electrodes in a novel electrochemical flow cell, Journal of The Electrochemical Society, 167.6, 2020. doi.org/10.1149/1945-7111/ab7e8f

75-19   Raphaël Comminal, Marcin Piotr Serdeczny, Navid Ranjbar, Mehdi Mehrali, David Bue Pedersen, Henrik Stang, Jon Spangenberg, Modelling of material deposition in big area additive manufacturing and 3D concrete printing, Proceedings, Advancing Precision in Additive Manufacturing, Nantes, France, September 16-18, 2019.

35-19     Sung-Won Ha, Tae-Won Kim, Joo-Hwan Choi, and Young-Jin Park, Study for flow phenomenon in the circulation water pump chamber using the Flow-3D model, Journal of the Korea Academia-Industrial Cooperation Society, Vol. 20, No. 4, pp. 580-589, 2019. doi: 10.5762/KAIS.2019.20.4.580

27-19     Rolands Cepuritis, Elisabeth L. Skare, Evgeny Ramenskiy, Ernst Mørtsell, Sverre Smeplass, Shizhao Li, Stefan Jacobsen, and Jon Spangeberg, Analysing limitations of the FlowCyl as a one-point viscometer test for cement paste, Construction and Building Materials, Vol. 218, pp. 333-340, 2019. doi: 10.1016.j.conbuildmat.2019.05.127

26-19     Shanshan Hu, Lunliang Duan, Qianbing Wan, and Jian Wang, Evaluation of needle movement effect on root canal irrigation using a computational fluid dynamics model, BioMedical Engineering OnLine, Vol. 18, No. 52, 2019. doi: 10.1186/s12938-019-0679-5

83-18   Elisabeth Leite Skare, Stefan Jacobsen, Rolands Cepuritis, Sverre Smeplass and Jon Spangenberg, Decreasing the magnitude of shear rates in the FlowCyl, Proceedings of the 12th fib International PhD Symposium in Civil Engineering, Prague, Czech Republic, August 29-31, 2018.

71-18   Marc Bascompta, Jordi Vives, Lluís Sanmiqeul and José Juan de Felipe, CFD friction factors verification in an underground mine, Proceedings of the 4th World Congress on Mechanical, Chemical, and Material Engineering, August 16 – 18, 2018, Madrid, Spain, Paper No. MMME 105, 2018. doi.org/10.11159/mmme18.105

56-18   J. Spangenberg, A. Uzala, M.W. Nielsen and J.H. Hattel, A robustness analysis of the bonding process of joints in wind turbine blades, International Journal of Adhesion and Adhesives, vol. 85, pp. 281-285, 2018. doi.org/10.1016/j.ijadhadh.2018.06.009

21-18   Zhang Weikang and Gong Hongwei, Numerical Simulation Study on Characteristics of Airtight Water Film with Flow Deflectors, IOP Conference Series: Earth and Environmental Science vol. 153, no. 3, pp. 032025, 2018. doi.org/10.1088/1755-1315/153/3/032025

59-17  Han Eol Park and In Cheol Bang, Design study on mixing performance of rotational vanes in subchannel with fuel rod bundles, Transactions of the Korean Nuclear Society Autumn Meeting, Gyeongju, Korea, October 26-27, 2017.

58-17  Jian Zhou, Claudia Cenedese, Tim Williams and Megan Ball, On the propagation of gravity currents over and through a submerged array of circular cylinders, Journal of Fluid Mechanics, Vol. 831, pp. 394-417, 2017. doi.org/10.1017/jfm.2017.604

24-17   Zhiyuan Ge, Wojciech Nemec, Rob L. Gawthorpe, Atle Rotevatn and Ernst W.M. Hansen, Response of unconfined turbidity current to relay-ramp topography: insights from process-based numerical modelling, doi: 10.1111/bre.12255 This article is protected by copyright. All rights reserved.

06-17   Masoud Hosseinpoor, Kamal H. Khayat, Ammar Yahia, Numerical simulation of self-consolidating concrete flow as a heterogeneous material in L-Box set-up: coupled effect of reinforcing bars and aggregate content on flow characteristics, A. Mater Struct (2017) 50: 163. doi:10.1617/s11527-017-1032-8

94-16   Mehran Seyed Ahmadi, Markus Bussmann and Stavros A. Argyropoulos, Mass transfer correlations for dissolution of cylindrical additions in liquid metals with gas agitation, International Journal of Heat and Mass Transfer, Volume 97, June 2016, Pages 767-778

83-16   Masoud Hosseinpoor, Numerical simulation of fresh SCC flow in wall and beam elements using flow dynamics models, Ph.D. Thesis: University of Sherbrooke, September 2016.

51-16   Aditi Verma, Application of computational transport analysis – Oil spill dynamics, Master Thesis: State University of New York at Buffalo, 2016, 56 pages; 1012775

37-16   Hannah Dietterich, Einat Lev, and Jiangzhi Chen, Benchmarking computational fluid dynamics models for lava flow simulation, Geophysical Research Abstracts, Vol. 18, EGU2016-2202, 2016, EGU General Assembly 2016, © Author(s) 2016. CC Attribution 3.0 License.

 19-16   A.J. Vellinga, M.J.B. Cartigny, E.W.M. Hansen, P.J. Tallinga, M.A. Clare, E.J. Sumner and J.T. Eggenhuisen, Process-based Modelling of Turbidity Currents – From Computational Fluid-dynamics to Depositional Signature, Second Conference on Forward Modelling of Sedimentary Systems, 25 April 2016, DOI: 10.3997/2214-4609.201600374

106-15    Hidetaka Oguma, Koji Tsukimoto, Saneyuki Goya, Yoshifumi Okajima, Kouichi Ishizaka, and Eisaku Ito, Development of Advanced Materials and Manufacturing Technologies for High-efficiency Gas Turbines, Mitsubishi Heavy Industries Technical Review Vol. 52 No. 4, December 2015

93-15   James M. Brethour, Modelling of Cavitation within Highly Transient Flows with the Volume of Fluid Method, 1st Pan-American Congress on Computational Mechanics, April 27-29, 2015

90-15   Troy Shinbrot, Matthew Rutala, Andrea Montessori, Pietro Prestininzi and Sauro Succi, Paradoxical ratcheting in cornstarch, Phys. Fluids 27, 103101 (2015); http://dx.doi.org/10.1063/1.4934709

84-15   Nicolas Roussel, Annika Gram, Massimiliano Cremonesi, Liberato Ferrara, Knut Krenzer, Viktor Mechtcherine, Sergiy Shyshko, Jan Skocec, Jon Spangenberg, Oldrich Svec, Lars Nyholm Thrane and Ksenija Vasilic, Numerical simulations of concrete flow: A benchmark comparison, Cem. Concr. Res. (2015), http://dx.doi.org/10.1016/j.cemconres.2015.09.022

02-15   David Souders, FLOW-3D Version 11 Enhances CFD Simulation, Desktop Engineering, January 2015

125-14   Herbert Obame Mve, Romuald Rullière, Rémi Goulet and Phillippe Haberschill, Numerical Analysis of Heat Transfer of a Flow Confined by Wire Screen in Lithium Bromide Absorption Process, Defect and Diffusion Forum, ISSN: 1662-9507, Vol. 348, pp 40-50, doi:10.4028/www.scientific.net/DDF.348.40, © 2014 Trans Tech Publications, Switzerland

55-14   Agni Arumugam Selvi, Effect of Linear Direction Oscillation on Grain Refinement, Master’s Thesis: The Ohio State University, Graduate Program in Mechanical Engineering, Copyright by Agni Arumugam Selvi, 2014

99-13   R. C. Givler and M. J. Martinez, Computational Model of Miniature Pulsating Heat Pipes, SANDIA REPORT, SAND2012-4750, Unlimited Release, Printed January 2013.

82-13    Shizhao Li, Jon Spangenberg, Jesper Hattel, A CFD Approach for Prediction of Unintended Porosities in Aluminum Syntactic Foam A Preliminary Study, 8th International Conference on Porous Metals and Metallic Foams (METFOAM 2013), Raleigh, NC, June 2013

81-13   S. Li, J. Spangenberg, J. H. Hattel, A CFD Model for Prediction of Unintended Porosities in Metal Matrix Composites A Preliminary Study, 19th International Conference on Composite Materials (ICCM 2013), Montreal, Canada, July 2013

78-13   Haitham A. Hussein, Rozi Abdullah, Sobri, Harun and Mohammed Abdulkhaleq, Numerical Model of Baffle Location Effect on Flow Pattern in Oil and Water Gravity Separator Tanks, World Applied Sciences Journal 26 (10): 1351-1356, 2013, ISSN 1818-4952, DOI: 10.5829/idosi.wasj.2013.26.10.1239, © IDOSI Publications, 2013

74-13  Laetitia Martinie, Jean-Francois Lataste, and Nicolas Roussel, Fiber orientation during casting of UHPFRC: electrical resistivity measurements, image analysis and numerical simulations, Materials and Structures, DOI 10.1617/s11527-013-0205-3, November 2013. Available for purchase online at SpringerLink.

67-13 Stefan Jacobsen, Rolands Cepuritis, Ya Peng, Mette R. Geiker, and Jon Spangenberg, Visualizing and simulating flow conditions in concrete form filling using Pigments, Construction and Building Materials 49 (2013) 328–342, © 2013 Elsevier Ltd. All rights reserved. Available for purchase at ScienceDirect.

60-13 Huey-Jiuan Lin, Fu-Yuan Hsu, Chun-Yu Chiu, Chien-Kuo Liu, Ruey-Yi Lee, Simulation of Glass Molding Process for Planar Type SOFC Sealing Devices, Key Engineering Materials, 573, 131, September 2013. Available for purchase at Scientific.net.

32-13 M A Rashid, I Abustan and M O Hamzah, Numerical simulation of a 3-D flow within a storage area hexagonal modular pavement systems, 4th International Conference on Energy and Environment 2013 (ICEE 2013), IOP Conf. Series: Earth and Environmental Science 16 (2013) 012056 doi:10.1088/1755-1315/16/1/012056. Full paper available at IOP.

105-12 Jon Spangenberg, Numerisk modellering af formfyldning ved støbning i selvkompakterende beton, Ph.D. Thesis: Technical University of Denmark, ID: 0eeede98-fb07-4800-86e2-0a6baeb1e7a3, 2012.

100-12 Nurul Hasan, Validation of CFD models using FLOW-3D for a Submerged Liquid Jet, Ninth International Conference on CFD in the Minerals and Process Industries, CSIRO, Melbourne, Australia, 10-12 December 2012.

87-12  Abustan, Ismail, Hamzah, Meor Othman and Rashid, Mohd Aminur, A 3-Dimensional Numerical Study of a Flow within a Permeable Pavement, OIDA International Journal of Sustainable Development, Vol. 04, No. 02, pp. 37-44, April 2012.

86-12 Abustan, Ismail, Hamzah, Meor Othman and Rashid, Mohd Aminur, Review of Permeable Pavement Systems in Malaysia Conditions, OIDA International Journal of Sustainable Development, Vol. 04, No. 02, pp. 27-36, April 2012.

85-12  Mohd Aminur Rashid, Ismail Abustan, Meor Othman Hamzah, Infiltration Characteristic Modeling Using FLOW-3D within a Modular Pavement, Procedia Engineering, Volume 50, 2012, Pages 658-667, ISSN 1877-7058, 10.1016/j.proeng.2012.10.072.

73-12  Mohd Aminur Rashid, Ismail Abustan, Meor Othman Hamzah, Infiltration Characteristic Modeling Using FLOW-3D within a Modular Pavement, Procedia Engineering, Volume 50, 2012, Pages 658-667, ISSN 1877-7058, 10.1016/j.proeng.2012.10.072.

65-12  X.H. Yang, T.J. Lu, T. Kim, Influence of non-conducting pore inclusions on phase change behavior of porous media with constant heat flux boundaryInternational Journal of Thermal Sciences, Available online 10 October 2012. Available online at SciVerse.

56-12  Giancarlo Alfonsi, Agostino Lauria, Leonardo Primavera, Flow structures around large-diameter circular cylinder, Journal of Flow Visualization and Image Processing, DOI: 10.1615/JFlowVisImageProc.2012005088, 2012. Available for purchase online at Begell Digital Library.

49-12  M. Janocko, M.B.J. Cartigny, W. Nemec, E.W.M. Hansen, Turbidity current hydraulics and sediment deposition in erodible sinuous channels: laboratory experiments and numerical simulations, Marine and Petroleum Geology, Available online 17 September 2012. Available for purchase online at SciVerse.

32-12  Fatih Karadagli, Bruce E. Rittmann, Drew C. McAvoy, and John E. Richardson, Effect of Turbulence on the Disintegration Rate of Flushable Consumer Products, Water Environment Research, Volume 84, Number 5, May 2012

31-12    D. Valero Huerta and R. García-Bartual, Optimization of Air Conditioning Diffusers Location in Large Agricultural Warehouses Using CFD Techniques, International Conference of Agricultural Engineering (CIGR-AgEng2012) Valencia, Spain, July 8-12, 2012

16-12 Yi Fan Fu, Wei Dong, Ying Li, Yi Tan, Ming Hui Yi, Akira Kawasaki, Simulation of the Effects of the Physical Properties on Particle Formation of Pulsated Orifice Ejection Method (POEM), 2012, Advanced Materials Research, 509, 161. Available for purchase online at Scientific.Net.

92-11  Giancarlo Alfonsi, Agostino Lauria, Leonardo Primavera, The lower vertical structure past the Ahmed car model, International Conference on Computational Science, ICCS 2011. Available for purchase online at Begell Digital Library.

80-11  Ismail Abustan, Meor Othman Hamzah, Mohd Aminur Rashid, A 3-Dimensional Numerical Study of a Flow within a Permeable Pavement, OIDA International Conference on Sustainable Development, ISSN 1923-6670, Putrajaya, Malaysia, 5-7th December 2011

66-11   H. Kondo, T. Furukawa, Y. Hirakawa, K. Nakamura, M. Ida, K.Watanabe, T. Kanemura, E. Wakai, H. Horiike, N. Yamaoka, H. Sugiura, T. Terai, A. Suzuki, J. Yagi, S. Fukada, H. Nakamura, I. Matsushita, F. Groeschel, K. Fujishiro, P. Garin and H. Kimura, IFMIF-EVEDA lithium test loop design and fabrication technology of target assembly as a key componentNuclear Fusion Volume 51 Number 12, doi:10.1088/0029-5515/51/12/123008

49-11     N.I. Vatin, A.A. Girgidov, K.I. Strelets, Numerical modelling the three-dimensional velocity field in the cyclone, Inzhenerno-Stroitel’nyi Zhurnal, No. 4, 2011. In Russian.

41-11    Maiko Hosoda, Taichi Hirano, and Keiji Sakai, Low-Viscosity Measurement by Capillary Electromagnetically Spinning Technique, © 2011 The Japan Society of Applied Physics, Japanese Journal of Applied Physics, July 20, 2011.

18-11  Ortloff, C.R., Vogel, M., Spray cooling heat transfer — Test and CFD analysis, Semiconductor Thermal Measurement and Management Symposium (SEMI-THERM), 2011 27th Annual IEEE, 20-24 March 2011, pp 245 – 252, San Jose, CA, 10.1109/STHERM.2011.5767208.

82-10   Dr. John Abbott, Two problems on the flow of viscous sheets of molten glass, 26th Annual Workshop on Mathematical Problems in Industry, Rensselear Polytechnic Institute, June 14-18, 2010

57-10  Chouet, B. A., Dawson, P. B., James, M. R. and Lane, S. J., Seismic source mechanism of degassing bursts at Kilauea Volcano, Hawaii: Results from waveform inversion in the 10–50 s band, J. Geophys. Res., 115, B09311, doi:10.1029/2009JB006661, September 2010. Available online at JOURNAL OF GEOPHYSICAL RESEARCH.

55-10 Pamela Waterman, FEA and CFD: Getting Better All the Time, Desktop Engineering, December 2010.

53-10  Nicolas Fries, Capillary transport processes in porous materials – experiment and model, Cuvillier Verlag Göttingen; 2010; ISBN 978-3-86955-507-2. Available at www.cuvillier.de  and www.amazon.de.

45-10  Meiring Beyers, Thomas Harms, and Johan Stander, Mitigating snowdrift at the elevated SANAE IV research station in Antarctica CFD simulation and field application, The Fifth International Symposium on Computational Wind Engineering (CWE2010), Chapel Hill, North Carolina, USA, May 23-27, 2010.

31-10 J. Spangenberg, N. Roussel, J.H. Hattel, J. Thorborg, M.R. Geiker, H. Stang and J. Skocek, Prediction of the Impact of Flow-Induced Inhomogeneities in Self-Compacting Concrete (SCC), Ch. 25 of “Design, Production and Placement of Self-Consolidating Concrete,” RILEM Bookseries, 2010, Volume 1, Part 5, 209-215, DOI: 10.1007/978-90-481-9664-7_18. Available online at Springer Link.

28-10 Sirisha Burra, Daniel P. Nicolella, W. Loren Francis, Christopher J. Freitas, Nicholas J. Mueschke, Kristin Poole, and Jean X. Jiang, Dendritic processes of osteocytes are mechanotransducers that induce the opening of hemichannels, Proc Natl Acad Sci U S A. 2010 Jul 19. [Epub ahead of print], Available for purchase at PNAS.

19-10 Michael T. Tolley, Michael Kalontarov, Jonas Neubert, David Erickson and Hod Lipson, Stochastic Modular Robotic Systems A Study of Fluidic Assembly Strategies, IEEE Transactions on Robotics, Vol. 26, NO. 3, June 2010

59-17   Han Eol Park and In Cheol Bang, Design study on mixing performance of rotational vanes in subchannel with fuel rod bundles, Transactions of the Korean Nuclear Society Autumn Meeting, Gyeongju, Korea, October 26-27, 2017.

44-09 Micah Fuller, Fabian Bombardelli, Deb Niemeier, Particulate Matter Modeling in Near-Road Vegetation Environments, Contract AQ-04-01: Developing Effective and Quantifiable Air Quality Mitigation Measures, UC Davis, Caltrans, September 2009

28-09 D. C. Lo, Dong-Taur Su and Jan-Ming Chen (2009), Application of Computational Fluid Dynamics Simulations to the Analysis of Bank Effects in Restricted Waters, Journal of Navigation, 62, pp 477-491, doi:10.1017/S037346330900527X; Purchase the article online (clicking on this link will take you to the Cambridge Journals website).

24-09 Richard C. Givler and Mario J. Martinez, Modeling of Pulsating Heat Pipes, Sandia Report, SAND2009-4520, Sandia National Laboratories, August 2009.

45-08  J. Saeki, Seikei Kakou, Three-Dimensional Flow Analysis of a Thermosetting Compound in a Motor Stator, 20, 750-754 (2008) [in Japanese] (Zipped file contains paper and appendices)

38-08 Yoshifumi Kuriyama, Ken’ichi Yano and Masafumi Hamaguchi, Trajectory Planning for Meal Assist Robot Considering Spilling Avoidance, 17th IEEE International Conference on Control Applications, Part of 2008 1EEE Multi-conference on Systems and Control, San Antonio, Texas, September 3-5, 2008

29-08 Ernst W.M. Hansen, Wojciech Nemec and Snorre Heimsund, Numerical CFD simulations — a new tool for the modelling of turbidity currents and sand dispersal in deep-water basins, Production Geoscience 2008 in Stavanger, Norway, © 2008

17-08 James, M. R., Lane, S. J. & Corder, S. B., Modelling the rapid near-surface expansion of gas slugs in low-viscosity magmas, In Lane S. J., Gilbert J. S. (eds) Fluid Motion in Volcanic Conduits: A Source of Seismic and Acoustic Signals. Geol. Soc., London, Spec. Pub., 307, 147-167, doi: 10.1144/SP307.9. 2008

16-08 Stefano Malavasi, Nicola Trabucchi, Numerical Investigation of the Flow Around a Rectangular Cylinder Near a Solid Wall, BBAA VI International Colloquium on: Bluff Bodies Aerodynamics & Applications, Milano, Italy, July 2008

41-07 Nicolas Roussel, Mette R. Geiker, Frederic Dufour, Lars N. Thrane and Peter Szabo, Computational modeling of concrete flow General Overview, Cement and Concrete Research 37 (2007) 1298-1307, © 2007 Elsevier Ltd.

40-07 Nemec, W., Heimsund, S., Xu, J. & Hansen, E.W.M., Numerical CFD simulation of turbidity currents, British Sedimentological Research Group (BSRG) Annual Meeting, Birmingham, 17-18 December 2007

39-07 Heimsund, S, Xu, J. & Nemec, W., Numerical Simulation of Recent Turbidity Currents in the Monterey Canyon System, Offshore California, American Geophysical Union Fall Meeting, 10-14 December 2007

32-07 James, M. R., Lane, S. J. & Corder, S. B., Modeling the near-surface expansion of gas slugs in basaltic magmaEos Trans. A.G.U., 88(52), Fall Meet. Suppl.. Abs. V12B-03. 2007

31-07 James, M. R., Lane, S. J. and Corder, S. B., Degassing low-viscosity magma: Quantifying the transition between passive bubble-burst and explosive activityE.G.U. Geophys. Res. Abstr., 905336, SRef-ID: 1607-7962/gra/EGU2007-A-05336. 2007

35-06  S. Green and C. Manepally, Software Validation Report for FLOW-3D Version 9.0, Center for Nuclear Waste Regulatory Analyses, August 2006

33-06 N. Roussel, Correlation between yield stress and slump: Comparison between numerical simulations and concrete rheometers results, © RILEM 2006, Materials and Structures (2006) 39:501-509, Purchase online at Springer Link.

32-06 Heimsund, S., Möller, N. and Guargena, C., FLOW-3D simulation of the Ormen Lange field, mid-Norway, In: Hoyanagi, K., Takano, O. and Kano, K. (Ed.), Abstracts, International Association of Sedimentologists 17th International Sedimentological Congress, Fukuoka, Vol. B, p. 107, 2006

10-06 Gengsheng Wei, An Implicit Method to Solve Problems of Rigid Body Motion Coupled with Fluid Flow, Flow Science Technical Note #76, FSI-05-TN76.

8-06 Gengsheng Wei, Three-Dimensional Collision Modeling for Rigid Bodies and its Coupling with Fluid Flow Computation, Flow Science Technical Note #75, FSI-06-TN75.

34-05  Young Bae Kim, Kyung Do Kim, Sang Eui Hong, Jong Goo Kim, Man Ho Park, and Ju Hyun Kim, and Jae Keun Kweon, 3D Simulation of PU Foaming Flow in a Refrigerator Cabinet, Appliance Magazine.com, January 2005.

33-05 N. Roussel, Fifty-cent rheo-meter for yield stress measurements From slump to spreading flow, @2005 by The Society of Rheolgoy, Inc., J. Rheol. 49(3), 705-718 May/June (2005)

32-05 Heimsund, S., Möller, N., Guargena, C. and Thompson, L., Field-scale modeling of turbidity currents by FLOW-3D simulations, In: Workshop Abstracts, Modeling of Turbidity Currents and Related Gravity Currents, University of California, Santa Barbara, 2 p., (2005)

15-05 Gengsheng Wei, A Fixed-Mesh Method for General Moving Objects, Flow Science Technical Note #73, FSI-05-TN73

14-05 James M. Brethour, Incremental Thermoelastic Stress Model, Flow Science Technical Note #72, FSI-05-TN72

9-05 Gengsheng Wei, A Fixed-Mesh Method for General Moving Objects in Fluid Flow, Modern Physics Letters B, Vol. 19, Nos. 28-29 (2005) 1719-1722

1-05 C.W. Hirt, Electro-Hydrodynamics of Semi-Conductive Fluids: With Application to Electro-Spraying Flow Science Technical Note #70, FSI-05-TN70

35-04  J. Saeki, T. Kono and T. Teramae, Seikei Kakou, Formulation of Mathematical Models for Estimating Residual Stress and Strain Components Correlated with 3-D Flow of Thermosetting Compounds, 16, 5, 309-316 (2004) [in Japanese]. (Zipped file contains paper and appendices)

31-04 Heimsund, S., Möller, N., Guargena, C. and Thompson, L., The control of seafloor topography on turbidite sand dispersal in the Ormen Lange field: a large-scale application of FLOW-3D simulations, In: Martinsen, O.J. (Ed.), Abstracts and Proceedings of the Geological Society of Norway (NGF), Deep Water Sedimentary Systems of Arctic and North Atlantic Margins, Stavanger, 3, p. 25, (2004)

26-04 Beyers, J.H.M., Harms, T.M. and Sundsbø, P.A., 2004, Numerical simulation of three dimensional, transient snow drifting around a cube, Journal of wind engineering and industrial aerodynamics, vol. 92, pp. 725-747, ISSN 0167-6105

25-04 Beyers, J.H.M, Harms, T.M. and Sundsbø, P.A., 2004, Numerical simulation of snow drifting around an elevated obstacle, Proceedings of the 5th conference on snow engineering, Davos, Switzerland, pp.185-191

17-04 Michael Barkhudarov, Multi-Block Gridding Technique for FLOW-3D (Revised), Flow Science Technical Note #59-R2, FSI-00-TN59-R2

36-03 Heimsund, S., Hansen, E.W.M. and Nemec, W., Numerical CFD simulation of turbidity currents and comparison with laboratory data, In: Hodgetts, D., Hodgson, D. and Smith, R. (Ed.), Slope Modelling Workshop Abstracts, Experimental, Reservoir and Forward Modelling of Turbidity Currents and Deep-Water Sedimentary Systems, Liverpool Univ., p. 13., (2003b)

35-03 Heimsund, S., Hansen, E.W.M. and Nemec, W. Computational 3-D fluid-dynamics model for sediment transport, erosion and deposition by turbidity currents, In: Nakrem, H.A. (Ed.), Abstracts and Proceedings of the Geological Society of Norway (NGF), Den 18. Vinterkonferansen, Oslo, 1, p. 39., (2003a)

33-03 Beyers, J.H.M., Sundsbø, P.A. and Harms, T.M., 2003, Numerical simulation and verification of drifting snow around a cube, Proceedings of the 11th international conference on wind engineering, Texas Tech University, Lubbock, Texas, USA, pp. 1886-1893

27-03 Jun Zeng, Daniel Sobek and Tom Korsmeyer, Electro-Hydrodynamic Modeling of Electrospray Ionization CAD for a µFluidic Device-Mass Spectrometer Interface, Agilent Technologies Inc, paper presented at Transducers 2003, June 03 Boston (note: Reference #10 is to FLOW-3D)

25-03 J. M Brethour, Moving Boundaries an Eularian Approach, Moving Boundaries VII, Computational Modelling of Free and Moving Boundary Problems, A. A. Mammoli & C.A. Brebbia, WIT Press

19-03 James Brethour, Incremental Elastic Stress Model, Flow Science Technical Note (FSI-03-TN64)

18-03 Michael Barkhudarov, Semi-Lagrangian VOF Advection Method for FLOW-3D, Flow Science Technical Note (FSI-03-TN63)

11-02 Junichi Saeki and Tsutomu Kono, Three-Dimensional Flow Analysis of a Thermosetting Compound during Mold Filling, Polymer Processing Society 18th Annual Meeting, June 2002, Guimares, Portugal.

46-01 Yasunori Iwai, Takumi Hayashi, Toshihiko Yamanishi, Kazuhiro Kobayashi and Masataka Nishi, Simulation of Tritium Behavior after Intended Tritium Release in Ventilated Room, Journal of Nuclear Science and Technology, Vol. 38, No. 1, p. 63-75, January 2001

23-01 Borre Bang, Dag Lukkassen, Application of Homogenization Theory Related to Stokes Flow in Porous Media, Applications of Mathematics, Narvik, Norway, No 4, pp. 309-319.

15-01 Ernst Hansen, SINTEF Energy Research, Trondheim, Norway, Computer Simulation Helps Increase Flow Rate in Three-Phase Separator, Drilling Marketplace, Vol 55, No 10, May 15, 2001, pp.14

10-01 Ernst Hansen, SINTEF Energy Research, Phenomeological Modeling and Simulation of Fluid Flow and Separation Behaviour in Offshore Gravity Separators, PVP-Col 431, Emerging Technologies for Fluids, Structures and Fluids, Structures and Fluid Structure Interaction — 2001, ASME 2001, pp. 23-29

7-01 C. Bohm, D. A. Weiss, and C. Tropea, Multi-droplet Impact onto Solid Walls Droplet-droplet Interaction and Collision of Kinemeatic Discontinuities, DaimlerChrysler Research and Technology, ILASS-Europe 2000, September 11-13, 2000

6-01 Ernst Hansen, Simulation Raises Separator Flow RateEngineering Talk, March 21, 2001

3-01 M. Sick, H. Keck, G. Vullioud, and E. Parkinson, New Challenges in Pelton Research

1-01 Y. Darsht, K. Kuvanov, A. Puzanov, I. Kholkin, FLOW-3D in Designing Hydraulic Systems for Heavy Machinery  (in Russian), SAPR I Grafika (CAD and Graphics), August 2000, pp. 50-55.

22-00 A. K. Temu, O. K. Sønju and E. W. M. Hansen, Criteria for Minimum Particle Deposition onto a Cylinder in Crossflow, International Symposium on Multiphase Flow and Transport Phenomena, November 2000, Tekirova, Antalya, Turkey

21-00 Claus Maier, Stefan aus der Wiesche and Eberhard P. Hofer, Impact of Microdrops on Solid Surfaces for DNA-Synthesis, Department of Measurement, Control and Microtechnology, University of Ulm, Technical Proceedings of the 2000 International Conference on Modeling and Simulation of Microsystems, pp. 586-589

11-00 Thomas K. Thiis, A Comparison of Numerical Simulations and Full-scale Measurements of Snowdrifts around Buildings, Wind and Structures – ISSN: 1226-6116,Vol. 3, nr. 2 (2000), pp. 73-81

10-00 P.A. Sundsbo and B. Bang, Snow drift control in residential areas-Field measurements and numerical simulations, Fourth International Conference on Snow Engineering, pp. 377-382

9-00 Thomas K. Thiis and Christian Jaedicke, The Snowdrift Pattern Around Two Cubical Obstacles with Varying Distance—Measurement and Numerical Simulations, Snow Engineering, edited by Hjorth-Hansen, et al, Balkema, Rotterdam, 2000, pp.369-375.

8-00 Thomas K. Thiis and Christian Jaedicke, Changes in the Snowdrift Pattern Caused by a Building Extension—Investigations Through Scale Modeling and Numerical Simulations, Snow Engineering, edited by Hjorth-Hansen, et al, Balkema, Rotterdam, 2000, pp. 363-368

7-00 Bruce Letellier, Louis Restrepo, and Clinton Shaffer, Near-Field Dispersion of Fission Products in Complex Terrain Using a 3-D Turbulent Fluid-Flow Model, CCPS International Conference, San Francisco, CA, September 28-October 1, 1999

6-00 Bruce Letellier, Patrick McClure, and Louis Restrepo, Source-Term and Building-Wake Consequence Modeling for the GODIVA IV Reactor at Los Alamos National Laboratory, 1999 Safety Analysis Workshop, Portland, Oregon, June 13-18, 1999

11-99 Thomas K. Thiis and Yngvar Gjessing, Large-scale Measurements of Snowdrifts Around Flat-roofed and Single-pitch-roofed Buildings, Cold Regions Science and Technology 30, Narvik, Norway, May 17, 1999, pp. 175-181

3-99 A. A. Gubaidullin, Jr., T. N. Dinh, and B. R. Sehgal, Analysis of Natural Convection Heat Transfer and Flows in Internally Heated Stratified Liquid, accepted for publication 33rd Natl. Heat Transfer Conf. CD proceedings, Albuquerque, NM, August 15-17, 1999

20-98 Mark W. Silva, A Computational Study of Highly Viscous Impinging Jets, published by the Amarillo National Resource Center for Plutonium, ANRCP-1998-18, November 1998

17-98 P. A. Sundsbo and B. Bang, 1998, Calculation of Snowdrift Around Roadside Safety Barriers, Proc of the International Snow Science Workshop, Sept. 1998, Sunriver, Oregon, USA 279-283

11-98 P-A Sundsbo, Numerical simulations of wind deflection fins to control snow accumulation in building steps, Journal of Wind Engineering and Industrial Aerodynamics 74-76 (1998) 543-552

23-97  P.E. O’Donoghue, M.F. Kanninen, C.P. Leung, G. Demofonti, and S. Venzi, The development and validation of a dynamic propagation model for gas transmission pipelines, Intl J. Pres. Ves. & Piping 70 (1997) 11-25, P11 : S0308 – 0161 (96) 00012 – 9.

22-97  Christopher J. Matice, Simulation of High Speed Filling, Presented at High Speed Processing & Filling of Plastic Containers, SME, Chicago, Illinois, November 11, 1997.

12-97 B. Entezam and W. K. Van Moorhem, University of Utah, Salt Lake City, UT and J. Majdalani, Marquette University, Milwaukee, WI, Modeling of a Rijke-Tube Pulse Combustor Using Computational Fluid Dynamics, presented at 33rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Seattle, WA, July 6-9, 1997.

11-97 B. Entezam, Computational and Experimental Investigation of Unsteady Flowfield Inside the Rijke Tube, doctoral thesis submitted to University of Utah, Dept. Mechanical Engineering, Salt Lake City, UT, June 1997

2-97 K. Fujisaki, T. Ueyama, and K. Okazawa, Magnetohydrodynamic Calculation of In-Mold Electromagnetic Stirring, Nippon Steel Corp., IEEE Transactions on Magnetics, Vol. 33, No. 2, March 1997

1-97 P. A. Sundsbo, Four Layer Modelling and Numerical Simulations of Snow Drift, to be submitted to the Journal of Glaciology, 1997

23-96 Andy K Palmer, Computational Fluid Dynamic Software Comparison and Electrostatic Precipitator Modeling, Presented to the Faculty of California State University, Summer 1996

21-96 P. A. Sundsbo, Computer Simulation of Snow-Drift around Structures, Proceedings of the 4th Symposium on Building Physics in the Nordic Countries, Vol. 2, 533-539, Finland, 9-10 Sep. 1996

20-96 P. A. Sundsbo and E.W.M. Hansen, Modelling and Numerical Simulation of Snow-Drift around Snow Fences, Proceedings of the 3rd International Conference on Snow Engineering, Sendai, Japan, 26-31 May 1996

19-96 P. A. Sundsbo, Numerical Modelling and Simulation of Snow Accumulations around Porous FencesProceedings of the International Snow Science Workshop, Banff, Alberta, Canada, 6-10 Oct. 1996

18-96 T. Iverson, Editor, Applied Modelling and Simulation, Proceedings of the 38th SIMS Simulation Conference, Norwegian University of Science and Technology, Trondheim, Norway, June 11-13, 1996

17-96 C. L. Parish, Modeling Compressible Flow Through an Orifice Stack Using Numerical Methods, thesis submitted for M.S. Mech. Engineering, NM State University, Las Cruces, NM, December 1996

15-96 T. Wiik and R. K. Calay, A Study of Balcony on Flow-Field and Wind Loads for Low-Rise Buildings, Fourth Symposium on Building Physics in the Nordic Countries, Dipoli, Espoo, Finland, September 1996

14-96 T. Wiik, E.W.M. Hansen, The Assessment of Wind Loads on Roof Overhang of Low-Rise Buildings, Second International Symposium Wind Engineering, Fort Collins, CO, September 1996

13-96 T. Wiik, R. K. Calay, and A. Holdo, A Study of Effects of Eaves on Flow-Field and Wind Loads for Low-Rise Houses, Third International Colloquium on Bluff Body Aerodynamics and Applications, Blacksburg, Virginia, August 1996

11-96 Y. Miyamoto and M. Harada, A Flow Analysis accompanied by Formation of the Liquid Droplets shown with an Animation Display Technique, SEA Corporation, presented at Visualization Information Conference, Tokyo, Japan, July 17, 1996

8-96 J. Bakken, E. Naess, T. Engebretsen, and E. W. M. Hansen, Fluid Flow in Porous Media, proceedings of the 38th SIMS Simulations Conference, Norwegian Univ. of Science & Technology, Trondheim, Norway, June 11-13, 1996

7-96E. W. M. Hansen, Performance of Oil/Water Gravity Separators Imposed to Motion, proceedings of the 38th SIMS Simulations Conference, Norwegian Univ. of Science & Technology, Trondheim, Norway, June 11-13, 1996

8-95 J. J. Francis, Computational Hydrodynamic Study of Flow through a Vertical Slurry Heat Exchanger, NSF Summer Research Program, Dept. Mech. Engineering, Univ. of Nevada Las Vegas, August 9, 1995

4-94 J. L. Ditter and C. W. Hirt, A Scalable Model for Mixing Vessels, Flow Science report, FSI-94-00-1, presented at the 1994 ASME Fluids Engineering Summer Meeting, Incline Village, NV, June 1994

3-94 A. Nielsen, B. Bang, P. A. Sundsbo and T. Wiik, Computer Simulation of Windspeed, Windpressure and Snow Accumulation around Buildings (SNOW-SIM), 1st International Conference on HVAC in Cold Climate, Rovaniemi, Finland, from Narvik Institute of Technology, Narvik, Norway, March 1994

2-94 J. M. Sicilian, Addition of an Extended Bubble Model to FLOW-3D, Flow Science report, FSI-94-58-1, March 1994

1-94 T. Hong, C. Zhu, P. Cal and L-S Fan, Numerical Modeling of Basic Modes of Formation and Interactions of Bubbles in Liquids, Dept. Chem. Engineering, Ohio State University, Columbus, OH 43210, March 1994

14-93 J. L. Ditter and C. W. Hirt, A Scalable Model for Stir Tanks, Flow Science Technical Note #38, December 1993 (FSI-93-TN38)

13-93 J. Partinen, N. Saluja and J. K. Kirtley, Jr., Experimental and Computational Investigation of Rotary Electromagnetic Stirring in a Woods Metal System, Dept. of Math, Science and Engr. and Dept. of Electrical Engr. and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139-4307

12-93 J. Partinen, N. Saluja and J. K. Kirtley, Jr., Modeling of Surface Deformation in an Electromagnetically Stirred Metallic Melt, Dept. of Math, Science, and Engr. and Dept. of Electrical Engr. and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139-4307

10-93 C. Philippe, Summary Report on Test Calculations with FLOW-3D/CAST93, (coupled-rigid-body dynamics model), ESTEC, Noordwijk, The Netherlands, September 17, 1993

5-93 J. M. Sicilian, J. L. Ditter and C. L. Bronisz, FLOW-3D Analyses of CFD Triathlon Benchmark, Flow Science report, presented at the ASME Fluids Engineering Conference, Washington DC, June 20-24, 1993

4-93 T. Wiik, Ventilation of the Attic due to Wind Loads on Low-Rise Buildings, paper for 3rd Symposium of Building Physics in Nordic Countries, Narvik Institute of Technology, Narvik, Norway, summer 1993

3-93 E. W. M. Hansen, Modelling and Simulation of Separation Effects and Fluid Flow Behaviour in Process-Units, SIMS’93 – 35th Simulation Conference, Kongsberg, Norway, June 9-11, 1993

2-93 M. A. Briones, R. S. Brodsky and J. J. Chalmers, Computer Simulation of the Rupture of a Gas Bubble at a Gas-Liquid Interface and its Implications in Animal Cell Damage, Dept. Chemical Engineering, Ohio State University, Manuscript No. RB68, April 1993

11-92 G. Trapaga, E. F. Matthys, J. J. Valencia and J. Szekely, Fluid Flow, Heat Transfer, and Solidification of Molten Metal Droplets Impinging on Substrates: Comparison of Numerical and Experimental Results, Metallurgical Transactions B, Vol. 23B, pp. 701-718, December 1992

10-92 J. B. Dalin, J. M. Le Guilly, P. Le Roy and E. Maas, Numerical Simulations Applied to the Production of Automotive Foundry Components, Numerical Methods in Industrial Forming Processes, Wood & Zienkiewicz (eds), Balkema, Rotterdam, 1992

5-92 C. W. Hirt, Volume-Fraction Techniques: Powerful Tools for Flow Modeling, Flow Science report (FSI-92-00-02), presented at the Computational Wind Engineering Conference, University of Tokyo, August 1992

3-92 C. L. Bronisz and C.W. Hirt, Lubricant Flow in a Rotary Lip Seal, Flow Science Technical Note #33, February 1992 (FSI-92-TN33)

16-91 A. Nielsen, SNOW-SIM – Computer Model for Simulation of Wind and Snow Loads on Buildings and Structures, Building Science, Narvik Institute of Technology, Narvik, Norway, (not dated)

15-91 E. W. M. Hansen, H. Heitmann, B. Laska, A. Ellingsen, O. Ostby, T. B. Morrow and F. T. Dodge, Fluid Flow Modelling of Gravity Separators, SINTEF, Norway and Southwest Research Institute, Texas, Elsevier Science Publishers, 1991

14-91 E. W. M. Hansen, H. Heitmann, B. Laska and M. Loes, Numerical Simulation of Fluid Flow Behaviour Inside, and Redesign of a Field Separator, SINTEF, Norway and STATOIL, Norway (not dated)

13-91 G. Trapaga and J. Szekely, Mathematical Modeling of the Isothermal Impingement of Liquid Droplets in Spraying Processes, Metallurgical Transactions, Vol. 22B, pp. 901-914, December 1991

11-91 N. Saluja and J. Szekely, Velocity Fields and Free Surface Phenomena in an Inductively Stirred Mercury Pool, European Journal of Mechanics, B/Fluids, Vol. 10, No. 5, pp. 563-572, Oct. 1991

4-90 J. M. Sicilian, A Note on Implementing Specified Velocities and Momentum Sources, Flow Science report, September 1990 (FSI-90-00-5)

13-90 P. Jonsson, N. Saluja, O. J. Ilegbusi, and J. Szekely, Fluid Flow Phenomena in the Filling of Cylindrical Molds Using Newtonian (Turbulent) and Non-Newtonian (Power Law) Fluids, submitted to Trans. of the American Foundrymen’s Soc., June 1990

12-90 N. Saluja, O. J. Ilegbusi, and J. Szekely, On the Computation of the Velocity Fields and the Dynamic Free Surface Generated in a Liquid Metal Column by a Rotating Magnetic Field, submitted to J. Fluid Mech., July 1990

7-90 C. L. Bronisz and C. W. Hirt, Modeling Unsaturated Flow in Porous Media: A FLOW-3D Extension, Flow Science report, July 1990 (FSI-90-48-2)

5-90 C. L. Bronisz and C. W. Hirt, Hydrodynamic Ram Simulations Using FLOW-3D, Flow Science report, May 1990 (FSI-90-49-1)

3-90 C. W. Hirt, Turbojet Plume Flow Analysis, Flow Science report, February 1990 (FSI-90-45-1)

5-89 K. S. Eckhoff and E. W. M. Hansen, Mathematical Modelling and Numerical Investigation of Separation in Two-Phase Rotating Flow, SINTEF-Foundation for Scientific and Industrial Research at the Norwegian Institute of Technology, Trondheim, Norway, Report No. OR 22 1907.00.01.89, 29 April 1989

2-89 J. M. Sicilian and J. R. Tegart, Comparisons of FLOW-3D Calculations with Very Large Amplitude Slosh Data, presented at the Symposium on Computational Experiments, PVP ASME Conference, Honolulu, HI, July 22-27, 1989

2-88 J. M. Sicilian and C. W. Hirt, AFT Field Joint: CFD Analysis Using the FLOW-3D Program, in Redesigned Solid Rocket Motor Circumferential Flow Technical Interchange Meeting Final Report, NASA-TWR-17788, February 1988

14-87 C. J. Freitas, S. T. Green, and T. B. Morrow, Fluid Dynamics Associated with Ductile Pipeline Fracture, Southwest Research Institute report presented at ASME Winter Annual Meeting, Boston, MA, December 1987

13-87 J. Sicilian, The FLOW-3D Model for Thermal Conduction in Solids, Flow Science report, Dec. 1987 (FSI-87-00-4)

7-87 C.W. Hirt, Vectored Nozzle Flow with Turbulence Modeling, Flow Science report, Sept. 1987 (FSI-87-29-1)

4-87 J.M. Sicilian, C.W. Hirt, and R. P. Harper, FLOW-3D: Computational Modeling Power for Scientists and Engineers, Flow Science report, 1987 (FSI-87-00-1)

3-86 J. M. Sicilian, Natural-Convection Heat-Transfer Analysis, Flow Science Technical Note #4, June 1986 (FSI-86-00-TN4)

2-86 J. Navickas and C. R. Cross, Air Circulation Characteristics and Convective Losses in a 5-MW Molten Salt Cavity Solar Receiver, ASME 8th Annual Conference on Solar Engineering, Anaheim, California, April 13-16, 1986

5-85 C. W. Hirt and R. P. Harper, Calculations of Vent Clearing in a Chemical Process Tank, Flow Science report, December 1985 (FSI-85-28-1)

2-84 Applications of SOLA-3D/FSI to Fluid Slosh, Flow Science report, May 1984