이 연구에서는 세 가지 다른 말뚝 뚜껑 높이에서 직사각형 말뚝 캡이 있는 복잡한 부두 주변의 지역 세굴 및 관련 흐름 유체 역학을 조사합니다. 말뚝 캡 높이가 초기 모래층에 대해 선택되었으며, 말뚝 캡이 흐름에 노출되지 않고(사례 I), 부분적으로 노출되고(사례 II) 완전히 노출(사례 III)되도록 했습니다. 실험은 맑은 물 세굴 조건 하에서 재순환 수로에서 수행되었으며, 입자 이미지 유속계 (PIV) 기술을 사용하여 다른 수직면에서 순간 유속을 얻었습니다. 부분적으로 노출된 파일 캡 케이스는 최대 수세미 깊이(MSD)를 보여주었습니다. 사례 II에서 MSD가 발생한 이유는 난류 유동장 분석을 통해 밝혀졌는데, 이는 말뚝 캡이 흐름에 노출됨에 따라 더 높은 세굴 깊이를 담당하는 말뚝 가장자리에서 와류 생성에 지배적으로 영향을 미친다는 것을 보여주었습니다. 유동장에 대한 파일 캡의 영향은 평균 속도, 소용돌이, 레이놀즈 전단 응력 및 난류 운동 에너지 윤곽을 통해 사례 III에서 두드러지게 나타났지만 파일 캡이 베드에서 떨어져 있었기 때문에 파일 캡 모서리는 수세미에 직접적인 영향을 미치지 않았습니다.
In this study, the local scour and the associated flow hydrodynamics around a complex pier with rectangular pile-cap at three different pile-cap elevations are investigated. The pile-cap elevations were selected with respect to the initial sand bed, such that the pile-cap was unexposed (case I), partially exposed (case II), and fully exposed (case III) to the flow. The experiments were performed in a recirculating flume under clear-water scour conditions, and the instantaneous flow velocity was obtained at different vertical planes using the particle image velocimetry (PIV) technique. The partially exposed pile-cap case showed the maximum obtained scour-depth (MSD). The reason behind the MSD occurrence in case II was enunciated through the analysis of turbulent flow field which showed that as the pile-cap got exposed to the flow, it dominantly affected the generation of vortices from the pile-cap corners responsible for the higher scour depth. The effect of the pile-cap on the flow field was prominently seen in case III through the mean velocities, vorticity, Reynolds shear stresses and turbulent kinetic energy contours, but since the pile-cap was away from the bed, the pile-cap corners did not show any direct effect on the scour.
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The hydrodynamics of coral reefs strongly influences their biological functioning, impacting processes such as nutrient availability and uptake, recruitment success and bleaching. For example, coral reefs located in oligotrophic regions depend on upwelling for nutrient supply. Coral reefs at Sodwana Bay, located on the east coast of South Africa, are an example of high latitude marginal reefs. These reefs are subjected to complex hydrodynamic forcings due to the interaction between the strong Agulhas current and the highly variable topography of the region. In this study, we explore the reef scale hydrodynamics resulting from the bathymetry for two steady current scenarios at Two-Mile Reef (TMR) using a combination of field data and numerical simulations. The influence of tides or waves was not considered for this study as well as reef-scale roughness. Tilt current meters with onboard temperature sensors were deployed at selected locations within TMR. We used field observations to identify the dominant flow conditions on the reef for numerical simulations that focused on the hydrodynamics driven by mean currents. During the field campaign, southerly currents were the predominant flow feature with occasional flow reversals to the north. Northerly currents were associated with greater variability towards the southern end of TMR. Numerical simulations showed that Jesser Point was central to the development of flow features for both the northerly and southerly current scenarios. High current variability in the south of TMR during reverse currents is related to the formation of Kelvin-Helmholtz type shear instabilities along the outer edge of an eddy formed north of Jesser Point. Furthermore, downward vertical velocities were computed along the offshore shelf at TMR during southerly currents. Current reversals caused a change in vertical velocities to an upward direction due to the orientation of the bathymetry relative to flow directions.
A predominant southerly current was measured at Two-Mile Reef with occasional reversals towards the north.
Field observations indicated that northerly currents are spatially varied along Two-Mile Reef.
Simulation of reverse currents show the formation of a separated flow due to interaction with Jesser Point with Kelvin–Helmholtz type shear instabilities along the seaward edge.
지금까지 Sodwana Bay에서 자세한 암초 규모 유체 역학을 모델링하려는 시도는 없었습니다. 이러한 모델의 결과는 규모가 있는 산호초 사이의 흐름이 산호초 건강에 어떤 영향을 미치는지 탐색하는 데 사용할 수 있습니다. 이 연구에서는 Sodwana Bay의 유체역학을 탐색하는 데 사용할 수 있는 LES 모델을 개발하기 위한 단계별 접근 방식을 구현합니다. 여기서 우리는 이 초기 단계에서 파도와 조수의 영향을 배제하면서 Agulhas 해류의 유체역학에 초점을 맞춥니다. 이 접근법은 흐름의 첫 번째 LES를 제시하고 Sodwana Bay의 산호초에서 혼합함으로써 향후 연구의 기초를 제공합니다.
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Experimental and numerical study of flow at a 90 degree lateral turnout with enhanced roughness coefficient and invert level changes
Maryam Bagheria, Seyed M. Ali Zomorodianb, Masih Zolghadrc, H. Md. Azamathulla d,* and C. Venkata Siva Rama Prasade a Hydraulic Structures, Department of Water Engineering, Shiraz University, Shiraz, Iran b Department of Water Engineering, College of Agriculture, Shiraz University, Shiraz, Iran c Department of Water Sciences Engineering, College of Agriculture, Jahrom University, Jahrom, Iran d Civil & Environmental Engineering, The University of the West Indies, St. Augustine Campus, Port of Spain, Trinidad e Department of Civil Engineering, St. Peters Engineering College, Hyderabad, India *Corresponding author. E-mail: email@example.com
측면 분기기(흡입구)의 상류측에서 유동 분리는 분기기 입구에서 맴돌이 전류를 일으키는 중요한 문제입니다. 이는 흐름의 유효 폭, 분기 용량 및 효율성을 감소시킵니다. 따라서 분리구역의 크기를 파악하고 그 크기를 줄이기 위한 방안을 제시하는 것이 필수적이다.
본 연구에서는 분리 구역의 크기를 줄이기 위한 방법으로 분출구 입구에 7가지 유형의 조면화 요소와 4가지 다른 방류가 있는 3가지 다른 베드 인버트 레벨의 설치(총 84회 실험)를 조사했습니다. 또한 3D 전산 유체 역학(CFD) 모델을 사용하여 분리 구역의 흐름 패턴과 치수를 평가했습니다.
결과는 조도 계수를 향상시키면 분리 영역 치수를 최대 38%까지 줄일 수 있는 반면 드롭 구현 효과는 사용된 조도 계수에 따라 이 영역을 다르게 축소할 수 있음을 보여주었습니다. 두 방법을 결합하면 분리 구역 치수를 최대 63%까지 줄일 수 있습니다.
Flow separation at the upstream side of lateral turnouts (intakes) is a critical issue causing eddy currents at the turnout entrance. It reduces the effective width of flow, turnout capacity and efficiency. Therefore, it is essential to identify the dimensions of the separation zone and propose remedies to reduce its dimensions.
Installation of 7 types of roughening elements at the turnout entrance and 3 different bed invert levels, with 4 different discharges (making a total of 84 experiments) were examined in this study as a method to reduce the dimensions of the separation zone. Additionally, a 3-D Computational Fluid Dynamic (CFD) model was utilized to evaluate the flow pattern and dimensions of the separation zone.
Results showed that enhancing the roughness coefficient can reduce the separation zone dimensions up to 38% while the drop implementation effect can scale down this area differently based on the roughness coefficient used. Combining both methods can reduce the separation zone dimensions up to 63%.
discharge ratio, flow separation zone, intake, three dimensional simulation
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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.
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.
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 1, Figure 2, Figure 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 1, Figure 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.
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.
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.
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 . This criterion is described by the following relationship:
where βmax, βmin 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).
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 .
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 X, Y, Z).
In the simulations, the fluid flow was assumed to be incompressible, in which case the following equation is applicable:
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 :
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:
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.
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.
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 .
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).
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.
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 .
Characteristic of the DPM model.
Balance 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.
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 :
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.
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.
where Pa is the atmospheric pressure, and h is the the height of metal in the reactor.
Themelis and Goyal  developed a model for calculating mixing power delivered by gas injection.
where Q is the gas flow, and m is the mass of liquid metal.
Zhang  proposed a model taking into account the temperature difference between gas and alloy (metal).
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.
Data for calculating mixing power introduced by an inert gas.
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.
Mixing power calculated from mathematical models.
Mixing Power (W·t−1) for a Given Inert Gas Flow (dm3·min−1)
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.
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 k, A, and uB can be calculated using the below equations .
where D is the diffusion coefficient, and dB is the bubble diameter.
After substituting appropriate values, we get
According to the last equation, the size of the gas bubble decreases with the increasing rotational speed (see 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]:
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 11, Figure 12, Figure 13 and Figure 14.
Gas bubble dispersion registered for different processing parameters (impeller variant RT3).
The analysis of the refining variants presented in Figure 11, Figure 12, Figure 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.
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.
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.
Summary of visualization results (impeller RT3)—different types of gas bubble dispersion.
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.
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.
This paper was created with the financial support grants from the AGH-UST, Faculty of Foundry Engineering, Poland (18.104.22.1684 and 11/990/BK_22/0083) for the Faculty of Materials Engineering, Silesian University of Technology, Poland.
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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Aneesh Kumar J1, a, K. Krishnakumar1, b and S. Savithri2, c 1 Department of Mechanical Engineering, College of Engineering, Thiruvananthapuram, Kerala, 2 Computational Modelling& Simulation Division, Process Engineering & Environmental Technology Division CSIR-National Institute for Interdisciplinary Science & Technology Thiruvananthapuram, Kerala, India. a firstname.lastname@example.org, b email@example.com, c firstname.lastname@example.org, email@example.com Key words: Mold filling, centrifugal casting process, computer simulation, FLOW- 3D™
원심 주조 공정은 기능적으로 등급이 지정된 재료, 즉 구성 요소 간에 밀도 차이가 큰 복합 재료 또는 금속 재료를 생산하는 데 사용되는 잠재적인 제조 기술 중 하나입니다. 이 공정에서 유체 흐름이 중요한 역할을 하며 복잡한 흐름 공정을 이해하는 것은 결함 없는 주물을 생산하는 데 필수입니다. 금형이 고속으로 회전하고 금형 벽이 불투명하기 때문에 흐름 패턴을 실시간으로 시각화하는 것은 불가능합니다. 따라서 현재 연구에서는 상용 CFD 코드 FLOW-3D™를 사용하여 수직 원심 주조 공정 중 단순 중공 원통형 주조에 대한 금형 충전 시퀀스를 시뮬레이션했습니다. 수직 원심주조 공정 중 다양한 방사 속도가 충전 패턴에 미치는 영향을 조사하고 있습니다.
Centrifugal casting process is one of the potential manufacturing techniques used for producing functionally graded materials viz., composite materials or metallic materials which have high differences of density among constituents. In this process, the fluid flow plays a major role and understanding the complex flow process is a must for the production of defect-free castings. Since the mold spins at a high velocity and the mold wall being opaque, it is impossible to visualise the flow patterns in real time. Hence, in the present work, the commercial CFD code FLOW-3D™, has been used to simulate the mold filling sequence for a simple hollow cylindrical casting during vertical centrifugal casting process. Effect of various spinning velocities on the fill pattern during vertical centrifugal casting process is being investigated.
 W. Shi-Ping, L. Chang-yun, G. Jing-jie, S. Yan-qing, L. Xiu-qiao, F. Heng-zhi, Numerical simulation and experimental investigation of two filling methods in vertical centrifugal casting, Trans. Nonferrous Met. Soc. China 16 (2006) 1035-1040. 10.1016/s1003-6326(06)60373-7  G. Chirita, D. Soares, F.S. Silva, Advantages of the centrifugal casting technique for the production of structural components with Al-Si alloys, Mater. Des. 29 (2008) 20-27. 10.1016/j.matdes.2006.12.011  A. Kermanpur, Sh. Mahmoudi, A. Hajipour, Numerical simulation of metal flow and solidification in the multi-cavity casting moulds of automotive components, J. Mater. Proc. Tech. 206 (208) 62-68. 10.1016/j.jmatprotec.2007.12.004  D. McBride et. al. Complex free surface flows in centrifugal casting: Computational modelling and validation experiments, Computers & Fluids 82 (2013) 63-72. 10.1016/j.compfluid.2013.04.021
Analysis of behavior and hydraulic characteristics of flow over the dam spillway is a complicated task that takes lots of money and time in water engineering projects planning. To model those hydraulic characteristics, several methods such as physical and numerical methods can be used. Nowadays, by utilizing new methods in computational fluid dynamics (CFD) and by the development of fast computers, the numerical methods have become accessible for use in the analysis of such sophisticated flows. The CFD softwares have the capability to analyze two- and three-dimensional flow fields. In this paper, the flow pattern at the guide wall of the Kamal-Saleh dam was modeled by Flow 3D. The results show that the current geometry of the left wall causes instability in the flow pattern and making secondary and vortex flow at beginning approach channel. This shape of guide wall reduced the performance of weir to remove the peak flood discharge.
댐 여수로 흐름의 거동 및 수리학적 특성 분석은 물 공학 프로젝트 계획에 많은 비용과 시간이 소요되는 복잡한 작업입니다. 이러한 수력학적 특성을 모델링하기 위해 물리적, 수치적 방법과 같은 여러 가지 방법을 사용할 수 있습니다. 요즘에는 전산유체역학(CFD)의 새로운 방법을 활용하고 빠른 컴퓨터의 개발로 이러한 정교한 흐름의 해석에 수치 방법을 사용할 수 있게 되었습니다. CFD 소프트웨어에는 2차원 및 3차원 유동장을 분석하는 기능이 있습니다. 본 논문에서는 Kamal-Saleh 댐 유도벽의 흐름 패턴을 Flow 3D로 모델링하였다. 결과는 왼쪽 벽의 현재 형상이 흐름 패턴의 불안정성을 유발하고 시작 접근 채널에서 2차 및 와류 흐름을 만드는 것을 보여줍니다. 이러한 형태의 안내벽은 첨두방류량을 제거하기 위해 둑의 성능을 저하시켰다.
Spillways are one of the main structures used in the dam projects. Design of the spillway in all types of dams, specifically earthen dams is important because the inability of the spillway to remove probable maximum flood (PMF) discharge may cause overflow of water which ultimately leads to destruction of the dam (Das and Saikia et al. 2009; E 2013 and Novak et al. 2007). So study on the hydraulic characteristics of this structure is important. Hydraulic properties of spillway including flow pattern at the entrance of the guide walls and along the chute. Moreover, estimating the values of velocity and pressure parameters of flow along the chute is very important (Chanson 2004; Chatila and Tabbara 2004). The purpose of the study on the flow pattern is the effect of wall geometry on the creation transverse waves, flow instability, rotating and reciprocating flow through the inlet of spillway and its chute (Parsaie and Haghiabi 2015a, b; Parsaie et al. 2015; Wang and Jiang 2010). The purpose of study on the values of velocity and pressure is to calculate the potential of the structure to occurrence of phenomena such as cavitation (Fattor and Bacchiega 2009; Ma et al. 2010). Sometimes, it can be seen that the spillway design parameters of pressure and velocity are very suitable, but geometry is considered not suitable for conducting walls causing unstable flow pattern over the spillway, rotating flows at the beginning of the spillway and its design reduced the flood discharge capacity (Fattor and Bacchiega 2009). Study on spillway is usually conducted using physical models (Su et al. 2009; Suprapto 2013; Wang and Chen 2009; Wang and Jiang 2010). But recently, with advances in the field of computational fluid dynamics (CFD), study on hydraulic characterist–ics of this structure has been done with these techniques (Chatila and Tabbara 2004; Zhenwei et al. 2012). Using the CFD as a powerful technique for modeling the hydraulic structures can reduce the time and cost of experiments (Tabbara et al. 2005). In CFD field, the Navier–Stokes equation is solved by powerful numerical methods such as finite element method and finite volumes (Kim and Park 2005; Zhenwei et al. 2012). In order to obtain closed-form Navier–Stokes equations turbulence models, such k − ε and Re-Normalisation Group (RNG) models have been presented. To use the technique of computational fluid dynamics, software packages such as Fluent and Flow 3D, etc., are provided. Recently, these two software packages have been widely used in hydraulic engineering because the performance and their accuracy are very suitable (Gessler 2005; Kim 2007; Kim et al. 2012; Milési and Causse 2014; Montagna et al. 2011). In this paper, to assess the flow pattern at Kamal-Saleh guide wall, numerical method has been used. All the stages of numerical modeling were conducted in the Flow 3D software.
Materials and methods
Firstly, a three-dimensional model was constructed according to two-dimensional map that was prepared for designing the spillway. Then a small model was prepared with scale of 1:80 and entered into the Flow 3D software; all stages of the model construction was conducted in AutoCAD 3D. Flow 3D software numerically solved the Navier–Stokes equation by finite volume method. Below is a brief reference on the equations that used in the software. Figure 1 shows the 3D sketch of Kamal-Saleh spillway and Fig. 2 shows the uploading file of the Kamal-Saleh spillway in Flow 3D software.
Review of the governing equations in software Flow 3D
Continuity equation at three-dimensional Cartesian coordinates is given as Eq (1).
where u, v, z are velocity component in the x, y, z direction; Ax, Ay, Az cross-sectional area of the flow; ρ fluid density; PSOR the source term; vf is the volume fraction of the fluid and three-dimensional momentum equations given in Eq (2).
where P is the fluid pressure; Gx, Gy, Gz the acceleration created by body fluids; fx, fy, fz viscosity acceleration in three dimensions and vf is related to the volume of fluid, defined by Eq. (3). For modeling of free surface profile the VOF technique based on the volume fraction of the computational cells has been used. Since the volume fraction F represents the amount of fluid in each cell, it takes value between 0 and 1.
Flow 3D offers five types of turbulence models: Prantl mixing length, k − ε equation, RNG models, Large eddy simulation model. Turbulence models that have been proposed recently are based on Reynolds-averaged Navier–Stokes equations. This approach involves statistical methods to extract an averaged equation related to the turbulence quantities.
Steps of solving a problem in Flow 3D software
(1) Preparing the 3D model of spillway by AutoCAD software. (2) Uploading the file of 3D model in Flow 3D software and defining the problem in the software and checking the final mesh. (3) Choosing the basic equations that should be solved. (4) Defining the characteristics of fluid. (5) Defining the boundary conditions; it is notable that this software has a wide range of boundary conditions. (6) Initializing the flow field. (7) Adjusting the output. (8) Adjusting the control parameters, choice of the calculation method and solution formula. (9) Start of calculation. Figure 1 shows the 3D model of the Kamal-Saleh spillway; in this figure, geometry of the left and right guide wall is shown.
Figure 2 shows the uploading of the 3D spillway dam in Flow 3D software. Moreover, in this figure the considered boundary condition in software is shown. At the entrance and end of spillway, the flow rate or fluid elevation and outflow was considered as BC. The bottom of spillway was considered as wall and left and right as symmetry.
Calibration of the Flow 3D for modeling the effect of geometry of guide wall on the flow pattern is included for comparing the results of Flow 3D with measured water surface profile. Calibration the Flow 3D software could be conducted in two ways: first, changing the value of upstream boundary conditions is continued until the results of water surface profile of the Flow 3D along the spillway successfully covered the measurement water surface profile; second is the assessment the mesh sensitivity. Analyzing the size of mesh is a trial-and-error process where the size of mesh is evaluated form the largest to the smallest. With fining the size of mesh the accuracy of model is increased; whereas, the cost of computation is increased. In this research, the value of upstream boundary condition was adjusted with measured data during the experimental studies on the scaled model and the mesh size was equal to 1 × 1 × 1 cm3.
Results and discussion
The behavior of water in spillway is strongly affected by the flow pattern at the entrance of the spillway, the flow pattern formation at the entrance is affected by the guide wall, and choice of an optimized form for the guide wall has a great effect on rising the ability of spillway for easy passing the PMF, so any nonuniformity in flow in the approach channel can cause reduction of spillway capacity, reduction in discharge coefficient of spillway, and even probability of cavitation. Optimizing the flow guiding walls (in terms of length, angle and radius) can cause the loss of turbulence and flow disturbances on spillway. For this purpose, initially geometry proposed for model for the discharge of spillway dam, Kamal-Saleh, 80, 100, and 120 (L/s) were surveyed. These discharges of flow were considered with regard to the flood return period, 5, 100 and 1000 years. Geometric properties of the conducting guidance wall are given in Table 1.Table 1 Characteristics and dimensions of the guidance walls tested
Results of the CFD simulation for passing the flow rate 80 (L/s) are shown in Fig. 3. Figure 3 shows the secondary flow and vortex at the left guide wall.
For giving more information about flow pattern at the left and right guide wall, Fig. 4 shows the flow pattern at the right side guide wall and Fig. 5 shows the flow pattern at the left side guide wall.
With regard to Figs. 4 and 5 and observing the streamlines, at discharge equal to 80 (L/s), the right wall has suitable performance but the left wall has no suitable performance and the left wall of the geometric design creates a secondary and circular flow, and vortex motion in the beginning of the entrance of spillway that creates cross waves at the beginning of spillway. By increasing the flow rate (Q = 100 L/s), at the inlet spillway secondary flows and vortex were removed, but the streamline is severely distorted. Results of the guide wall performances at the Q = 100 (L/s) are shown in Fig. 6.
Also more information about the performance of each guide wall can be derived from Figs. 7 and 8. These figures uphold that the secondary and vortex flows were removed, but the streamlines were fully diverted specifically near the left side guide wall.
As mentioned in the past, these secondary and vortex flows and diversion in streamline cause nonuniformity and create cross wave through the spillway. Figure 9 shows the cross waves at the crest of the spillway.
The performance of guide walls at the Q = 120 (L/s) also was assessed. The result of simulation is shown in Fig. 10. Figures 11 and 12 show a more clear view of the streamlines near to right and left side guide wall, respectively. As seen in Fig. 12, the left side wall still causes vortex flow and creation of and diversion in streamline.
The results of the affected left side guide wall shape on the cross wave creation are shown in Fig. 13. As seen from Fig. 3, the left side guide wall also causes cross wave at the spillway crest.
As can be seen clearly in Figs. 9 and 13, by moving from the left side to the right side of the spillway, the cross waves and the nonuniformity in flow is removed. By reviewing Figs. 9 and 13, it is found that the right side guide wall removes the cross waves and nonuniformity. With this point as aim, a geometry similar to the right side guide wall was considered instead of the left side guide wall. The result of simulation for Q = 120 (L/s) is shown in Fig. 14. As seen from this figure, the proposed geometry for the left side wall has suitable performance smoothly passing the flow through the approach channel and spillway.
More information about the proposed shape for the left guide wall is shown in Fig. 15. As seen from this figure, this shape has suitable performance for removing the cross waves and vortex flows.
Figure 16 shows the cross section of flow at the crest of spillway. As seen in this figure, the proposed shape for the left side guide wall is suitable for removing the cross waves and secondary flows.
Analysis of behavior and hydraulic properties of flow over the spillway dam is a complicated task which is cost and time intensive. Several techniques suitable to the purposes of study have been undertaken in this research. Physical modeling, usage of expert experience, usage of mathematical models on simulation flow in one-dimensional, two-dimensional and three-dimensional techniques, are some of the techniques utilized to study this phenomenon. The results of the modeling show that the CFD technique is a suitable tool for simulating the flow pattern in the guide wall. Using this tools helps the designer for developing the optimal shape for hydraulic structure which the flow pattern through them are important.
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by Faizal Yusuf, M.A.Sc., P.Eng. Specialist Engineer in the Hydrotechnical Department at BC Hydro
BC Hydro, a public electric utility in British Columbia, uses FLOW-3D to investigate complex hydraulics issues at several existing dams and to assist in the design and optimization of proposed facilities.
Faizal Yusuf, M.A.Sc., P.Eng., Specialist Engineer in the Hydrotechnical department at BC Hydro, presents three case studies that highlight the application of FLOW-3D to different types of spillways and the importance of reliable prototype or physical hydraulic model data for numerical model calibration.
W.A.C. Bennett Dam At W.A.C. Bennett Dam, differences in the spillway geometry between the physical hydraulic model from the 1960s and the prototype make it difficult to draw reliable conclusions on shock wave formation and chute capacity from physical model test results. The magnitude of shock waves in the concrete-lined spillway chute are strongly influenced by a 44% reduction in the chute width downstream of the three radial gates at the headworks, as well as the relative openings of the radial gates. The shock waves lead to locally higher water levels that have caused overtopping of the chute walls under certain historical operations.Prototype spill tests for discharges up to 2,865 m3/s were performed in 2012 to provide surveyed water surface profiles along chute walls, 3D laser scans of the water surface in the chute and video of flow patterns for FLOW-3D model calibration. Excellent agreement was obtained between the numerical model and field observations, particularly for the location and height of the first shock wave at the chute walls (Figure 1).
W.A.C에서 Bennett Dam, 1960년대의 물리적 수력학 모델과 프로토타입 사이의 여수로 형상의 차이로 인해 물리적 모델 테스트 결과에서 충격파 형성 및 슈트 용량에 대한 신뢰할 수 있는 결론을 도출하기 어렵습니다. 콘크리트 라이닝 방수로 낙하산의 충격파 크기는 방사형 게이트의 상대적인 개구부뿐만 아니라 헤드워크에 있는 3개의 방사형 게이트 하류의 슈트 폭이 44% 감소함에 따라 크게 영향을 받습니다. 충격파는 특정 역사적 작업에서 슈트 벽의 범람을 야기한 국부적으로 더 높은 수위로 이어집니다. 최대 2,865m3/s의 배출에 대한 프로토타입 유출 테스트가 2012년에 수행되어 슈트 벽을 따라 조사된 수면 프로필, 3D 레이저 스캔을 제공했습니다. FLOW-3D 모델 보정을 위한 슈트의 수면 및 흐름 패턴 비디오. 특히 슈트 벽에서 첫 번째 충격파의 위치와 높이에 대해 수치 모델과 현장 관찰 간에 탁월한 일치가 이루어졌습니다(그림 1).
The calibrated FLOW-3D model confirmed that the design flood could be safely passed without overtopping the spillway chute walls as long as all three radial gates are opened as prescribed in existing operating orders with the outer gates open more than the inner gate.
The CFD model also provided insight into the concrete damage in the spillway chute. Cavitation indices computed from FLOW-3D simulation results were compared with empirical data from the USBR and found to be consistent with the historical performance of the spillway. The numerical analysis supported field inspections, which concluded that deterioration of the concrete conditions in the chute is likely not due to cavitation.
Strathcona Dam FLOW-3D was used to investigate poor approach conditions and uncertainties with the rating curves for Strathcona Dam spillway, which includes three vertical lift gates on the right abutment of the dam. The rating curves for Strathcona spillway were developed from a combination of empirical adjustments and limited physical hydraulic model testing in a flume that did not include geometry of the piers and abutments.
Numerical model testing and calibration was based on comparisons with prototype spill observations from 1982 when all three gates were fully open, resulting in a large depression in the water surface upstream of the leftmost bay (Figure 2). The approach flow to the leftmost bay is distorted by water flowing parallel to the dam axis and plunging over the concrete retaining wall adjacent to the upstream slope of the earthfill dam. The flow enters the other two bays much more smoothly. In addition to very similar flow patterns produced in the numerical model compared to the prototype, simulated water levels at the gate section matched 1982 field measurements to within 0.1 m.
보정된 FLOW-3D 모델은 외부 게이트가 내부 게이트보다 더 많이 열려 있는 기존 운영 명령에 규정된 대로 3개의 방사형 게이트가 모두 열리는 한 여수로 낙하산 벽을 넘지 않고 설계 홍수를 안전하게 통과할 수 있음을 확인했습니다.
CFD 모델은 방수로 낙하산의 콘크리트 손상에 대한 통찰력도 제공했습니다. FLOW-3D 시뮬레이션 결과에서 계산된 캐비테이션 지수는 USBR의 경험적 데이터와 비교되었으며 여수로의 역사적 성능과 일치하는 것으로 나타났습니다. 수치 분석은 현장 검사를 지원했으며, 슈트의 콘크리트 상태 악화는 캐비테이션 때문이 아닐 가능성이 높다고 결론지었습니다.
Strathcona 댐 FLOW-3D는 Strathcona Dam 여수로에 대한 등급 곡선을 사용하여 열악한 접근 조건과 불확실성을 조사하는 데 사용되었습니다. 여기에는 댐의 오른쪽 접합부에 3개의 수직 리프트 게이트가 포함되어 있습니다. Strathcona 여수로에 대한 등급 곡선은 경험적 조정과 교각 및 교대의 형상을 포함하지 않는 수로에서 제한된 물리적 수리 모델 테스트의 조합으로 개발되었습니다.
수치 모델 테스트 및 보정은 세 개의 수문이 모두 완전히 개방된 1982년의 프로토타입 유출 관측과의 비교를 기반으로 했으며, 그 결과 가장 왼쪽 만의 상류 수면에 큰 함몰이 발생했습니다(그림 2). 최좌단 만으로의 접근 흐름은 댐 축과 평행하게 흐르는 물과 흙채움댐의 상류 경사면에 인접한 콘크리트 옹벽 위로 떨어지는 물에 의해 왜곡됩니다. 흐름은 훨씬 더 원활하게 다른 두 베이로 들어갑니다. 프로토타입과 비교하여 수치 모델에서 생성된 매우 유사한 흐름 패턴 외에도 게이트 섹션에서 시뮬레이션된 수위는 1982년 현장 측정과 0.1m 이내로 일치했습니다.
The calibrated CFD model produces discharges within 5% of the spillway rating curve for the reservoir’s normal operating range with all gates fully open. However, at higher reservoir levels, which may occur during passage of large floods (as shown in Figure 3), the difference between simulated discharges and the rating curves are greater than 10% as the physical model testing with simplified geometry and empirical corrections did not adequately represent the complex approach flow patterns. The FLOW-3D model provided further insight into the accuracy of rating curves for individual bays, gated conditions and the transition between orifice and free surface flow.
보정된 CFD 모델은 모든 게이트가 완전히 열린 상태에서 저수지의 정상 작동 범위에 대한 여수로 등급 곡선의 5% 이내에서 배출을 생성합니다. 그러나 대규모 홍수가 통과하는 동안 발생할 수 있는 더 높은 저수지 수위에서는(그림 3 참조) 단순화된 기하학과 경험적 수정을 사용한 물리적 모델 테스트가 그렇지 않았기 때문에 모의 배출과 등급 곡선 간의 차이는 10% 이상입니다. 복잡한 접근 흐름 패턴을 적절하게 표현합니다. FLOW-3D 모델은 개별 베이, 게이트 조건 및 오리피스와 자유 표면 흐름 사이의 전환에 대한 등급 곡선의 정확도에 대한 추가 통찰력을 제공했습니다.
John Hart Dam The John Hart concrete dam will be modified to include a new free crest spillway to be situated between an existing gated spillway and a low level outlet structure that is currently under construction. Significant improvements in the design of the proposed spillway were made through a systematic optimization process using FLOW-3D.
The preliminary design of the free crest spillway was based on engineering hydraulic design guides. Concrete apron blocks are intended to protect the rock at the toe of the dam. A new right training wall will guide the flow from the new spillway towards the tailrace pool and protect the low level outlet structure from spillway discharges.
FLOW-3D model results for the initial and optimized design of the new spillway are shown in Figure 4. CFD analysis led to a 10% increase in discharge capacity, significant decrease in roadway impingement above the spillway crest and improved flow patterns including up to a 5 m reduction in water levels along the proposed right wall. Physical hydraulic model testing will be used to confirm the proposed design.
존 하트 댐 John Hart 콘크리트 댐은 현재 건설 중인 기존 배수로와 저층 배수로 사이에 위치할 새로운 자유 마루 배수로를 포함하도록 수정될 것입니다. FLOW-3D를 사용한 체계적인 최적화 프로세스를 통해 제안된 여수로 설계의 상당한 개선이 이루어졌습니다.
자유 마루 여수로의 예비 설계는 엔지니어링 수력학 설계 가이드를 기반으로 했습니다. 콘크리트 앞치마 블록은 댐 선단부의 암석을 보호하기 위한 것입니다. 새로운 오른쪽 훈련 벽은 새 여수로에서 테일레이스 풀로 흐름을 안내하고 여수로 배출로부터 낮은 수준의 배출구 구조를 보호합니다.
새 여수로의 초기 및 최적화된 설계에 대한 FLOW-3D 모델 결과는 그림 4에 나와 있습니다. CFD 분석을 통해 방류 용량이 10% 증가하고 여수로 마루 위의 도로 충돌이 크게 감소했으며 최대 제안된 오른쪽 벽을 따라 수위가 5m 감소합니다. 제안된 설계를 확인하기 위해 물리적 수압 모델 테스트가 사용됩니다.
BC Hydro has been using FLOW-3D to investigate a wide range of challenging hydraulics problems for different types of spillways and water conveyance structures leading to a greatly improved understanding of flow patterns and performance. Prototype data and reliable physical hydraulic model testing are used whenever possible to improve confidence in the numerical model results.
다양한 유형의 여수로 및 물 수송 구조로 인해 흐름 패턴 및 성능에 대한 이해가 크게 향상되었습니다. 프로토타입 데이터와 신뢰할 수 있는 물리적 유압 모델 테스트는 수치 모델 결과의 신뢰도를 향상시키기 위해 가능할 때마다 사용됩니다.
About Flow Science, Inc. Based in Santa Fe, New Mexico USA, Flow Science was founded in 1980 by Dr. C. W. (Tony) Hirt, who was one of the principals in pioneering the “Volume-of-Fluid” or VOF method while working at the Los Alamos National Lab. FLOW-3D is a direct descendant of this work, and in the subsequent years, we have increased its sophistication with TruVOF, boasting pioneering improvements in the speed and accuracy of tracking distinct liquid/gas interfaces. Today, Flow Science products offer complete multiphysics simulation with diverse modeling capabilities including fluid-structure interaction, 6-DoF moving objects, and multiphase flows. From inception, our vision has been to provide our customers with excellence in flow modeling software and services.
이 연구에서 FLOW 3D 전산 유체 역학(CFD) 소프트웨어를 사용하여 파키스탄 Mirani 댐 방수로에 대한 에너지 소산 옵션으로 미국 매립지(USBR) 유형 II 및 USBR 유형 III 유역의 성능을 추정했습니다. 3D Reynolds 평균 Navier-Stokes 방정식이 해결되었으며, 여기에는 여수로 위의 자유 표면 흐름을 캡처하기 위해 공기 유입, 밀도 평가 및 드리프트-플럭스에 대한 하위 그리드 모델이 포함되었습니다. 본 연구에서는 5가지 모델을 고려하였다. 첫 번째 모델에는 길이가 39.5m인 USBR 유형 II 정수기가 있습니다. 두 번째 모델에는 길이가 44.2m인 USBR 유형 II 정수기가 있습니다. 3번째와 4 번째모델에는 길이가 각각 48.8m인 USBR 유형 II 정수조와 39.5m의 USBR 유형 III 정수조가 있습니다. 다섯 번째 모델은 네 번째 모델과 동일하지만 마찰 및 슈트 블록 높이가 0.3m 증가했습니다. 최상의 FLOW 3D 모델 조건을 설정하기 위해 메쉬 민감도 분석을 수행했으며 메쉬 크기 0.9m에서 최소 오차를 산출했습니다. 세 가지 경계 조건 세트가 테스트되었으며 최소 오류를 제공하는 세트가 사용되었습니다. 수치적 검증은 USBR 유형 II( L = 48.8m), USBR 유형 III( L = 35.5m) 및 USBR 유형 III 의 물리적 모델 에너지 소산을 0.3m 블록 단위로 비교하여 수행되었습니다( L= 35.5m). 통계 분석 결과 평균 오차는 2.5%, RMSE(제곱 평균 제곱근 오차) 지수는 3% 미만이었습니다. 수리학적 및 경제성 분석을 바탕으로 4 번째 모델이 최적화된 에너지 소산기로 밝혀졌습니다. 흡수된 에너지 백분율 측면에서 물리적 모델과 수치적 모델 간의 최대 차이는 5% 미만인 것으로 나타났습니다.
In this study, the FLOW 3D computational fluid dynamics (CFD) software was used to estimate the performance of the United States Bureau of Reclamation (USBR) type II and USBR type III stilling basins as energy dissipation options for the Mirani Dam spillway, Pakistan. The 3D Reynolds-averaged Navier–Stokes equations were solved, which included sub-grid models for air entrainment, density evaluation, and drift–flux, to capture free-surface flow over the spillway. Five models were considered in this research. The first model has a USBR type II stilling basin with a length of 39.5 m. The second model has a USBR type II stilling basin with a length of 44.2 m. The 3rd and 4th models have a USBR type II stilling basin with a length of 48.8 m and a 39.5 m USBR type III stilling basin, respectively. The fifth model is identical to the fourth, but the friction and chute block heights have been increased by 0.3 m. To set up the best FLOW 3D model conditions, mesh sensitivity analysis was performed, which yielded a minimum error at a mesh size of 0.9 m. Three sets of boundary conditions were tested and the set that gave the minimum error was employed. Numerical validation was done by comparing the physical model energy dissipation of USBR type II (L = 48.8 m), USBR type III (L =35.5 m), and USBR type III with 0.3-m increments in blocks (L = 35.5 m). The statistical analysis gave an average error of 2.5% and a RMSE (root mean square error) index of less than 3%. Based on hydraulics and economic analysis, the 4th model was found to be an optimized energy dissipator. The maximum difference between the physical and numerical models in terms of percentage energy absorbed was found to be less than 5%.
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A. Safarzadeh1*, P. Mohsenzadeh2, S. Abbasi3 1 Professor of Civil Eng., Water Engineering and Mineral Waters Research Center, Univ. of Mohaghegh Ardabili,Ardabil, Iran 2 M.Sc., Graduated of Civil-Hydraulic Structures Eng., Faculty of Eng., Univ. of Mohaghegh Ardabili, Ardabil, Iran 3 M.Sc., Graduated of Civil -Hydraulic Structures Eng., Faculty of Eng., Univ. of Mohaghegh Ardabili, Ardabil, Iran Safarzadeh@uma.ac.ir
유체 이동에 의해 생성된 RBF는 Ls-Dyna에서 Fluent, ICFD ALE 및 SPH 방법으로 시뮬레이션되었습니다. RBF의 과예측은 유체가 메인 도메인에서 고속으로 분리될 때 발생합니다. 이 과잉 예측은 요소 크기, 시간 단계 크기 및 유체 모델에 따라 다릅니다. 유체 성능을 검증하려면 최대 RBF보다 임펄스가 권장됩니다.
Dam break is a very important problem due to its effects on economy, security, human casualties and environmental consequences. In this study, 3D flow due to dam break over the porous substrate is numerically simulated and the effect of porosity, permeability and thickness of the porous bed and the water depth in the porous substrate are investigated. Classic models of dam break over a rigid bed and water infiltration through porous media were studied and results of the numerical simulations are compared with existing laboratory data. Validation of the results is performed by comparing the water surface profiles and wave front position with dam break on rigid and porous bed. Results showed that, due to the effect of dynamic wave in the initial stage of dam break, a local peak occurs in the flood hydrograph. The presence of porous bed reduces the acceleration of the flood wave relative to the flow over the solid bed and it decreases with the increase of the permeability of the bed. By increasing the permeability of the bed, the slope of the ascending limb of the flood hydrograph and the peak discharge drops. Furthermore, if the depth and permeability of the bed is such that the intrusive flow reaches the rigid substrate under the porous bed, saturation of the porous bed, results in a sharp increase in the slope of the flood hydrograph. The maximum values of the peak discharge at the end of the channel with porous bed occurred in saturated porous bed conditions.
댐 붕괴는 경제, 보안, 인명 피해 및 환경적 영향으로 인해 매우 중요한 문제입니다. 본 연구에서는 다공성 기재에 대한 댐 파괴로 인한 3차원 유동을 수치적으로 시뮬레이션하고 다공성 기재의 다공성, 투과도 및 다공성 층의 두께 및 수심의 영향을 조사합니다. 단단한 바닥에 대한 댐 파괴 및 다공성 매체를 통한 물 침투의 고전 모델을 연구하고 수치 시뮬레이션 결과를 기존 실험실 데이터와 비교합니다. 결과 검증은 강체 및 다공성 베드에서 댐 파단과 수면 프로파일 및 파면 위치를 비교하여 수행됩니다. 그 결과 댐파괴 초기의 동적파동의 영향으로 홍수수문곡선에서 국부첨두가 발생하는 것으로 나타났다. 다공성 베드의 존재는 고체 베드 위의 유동에 대한 홍수파의 가속을 감소시키고 베드의 투과성이 증가함에 따라 감소합니다. 베드의 투수성을 증가시켜 홍수 수문곡선의 오름차순 경사와 첨두방류량이 감소한다. 더욱이, 만약 층의 깊이와 투과성이 관입 유동이 다공성 층 아래의 단단한 기질에 도달하는 정도라면, 다공성 층의 포화는 홍수 수문곡선의 기울기의 급격한 증가를 초래합니다. 다공층이 있는 채널의 끝단에서 최대 방전 피크값은 포화 다공층 조건에서 발생하였다.
Keywords: Dams Break, 3D modeling, Porous Bed, Permeability, Flood wave
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Shen Zhen-dong*1, 2, Zhang Yang1, 2 1Zhejiang Guangchuan Engineering Consultation Co., Ltd., Hangzhou, 310020, Zhejiang, China 2Zhejiang Institute of Hydraulics &Estuary, Hangzhou 310020, Zhejiang, China E-mail: firstname.lastname@example.org
최근 몇 년 동안 생태학적 수자원 보존 공학의 발전으로 많은 새로운 댐 디자인이 등장했습니다. 본 논문에서는 체계적인 소면보 연구와 조사를 바탕으로 새로운 종류의 입상 혼합물 위어를 제시하였습니다.
입상보의 수치해석은 Flow-3D를 이용하여 수행하였으며, 그 결과를 물리적 모델 실험결과와 비교하였습니다. 유속, 유속 분포 및 둑의 파손에 대한 수치 시뮬레이션 결과는 실험 결과와 잘 일치하며, 이는 3차원 수학적 모델이 물리적 모델 실험과 결합되어 모든 입상 혼합물 둑을 시뮬레이션할 수 있음을 나타냅니다.
이 방법을 이용하여 특성 및 수리학적 매개변수를 분석하면 생태보의 후속 연구를 위한 기술적 지원을 제공할 수 있습니다.
In recent years, with the development of ecological water conservancy engineering, many new weir designs have also emerged. This paper has put forward a new kind of granular mixtures weir based on the systematic carding weir researches, combined with investigation. The numerical simulation of granular weir is carried out by using Flow-3D,and the results are compared with the physical model experiment results. The numerical simulation results of the flow velocity, flow distribution and the failure of the weir are in good agreement with the experimental results, which indicates that the 3-D mathematical model can be combined with physical model experiments to simulate the granular mixtures weir in all directions. Using this method to analysis the characteristics and hydraulic parameters can provide technical support for the follow-up research of ecological weir.
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본 논문은 경사가 완만한 수로에서 손상되거나 손상되지 않은 교각 주변의 유동 패턴을 분석했습니다. 실험은 길이가 12m이고 기울기가 0.008인 직선 수로에서 수행되었습니다. Acoustic Doppler Velocimeter(ADV)를 이용하여 3차원 유속 데이터를 수집하였고, 그 결과를 PIV(Particle Image Velocimetry) 데이터와 분석하여 비교하였습니다.
다중 블록 옵션이 있는 취수구의 퇴적물 시뮬레이션(SSIIM)은 이 연구에서 흐름의 수치 시뮬레이션을 위해 통합되었습니다. 일반적으로 비교에서 얻은 결과는 수치 데이터와 실험 데이터 간의 적절한 일치를 나타냅니다. 결과는 모든 경우에 수로 입구에서 2m 거리에서 기복적 수압 점프가 발생했음을 보여주었습니다.
경사진 수로의 최대 베드 전단응력은 2개의 손상 및 손상되지 않은 교각을 설치하기 위한 수평 수로의 12배였습니다. 이와 같은 경사수로 교각의 위치에 따라 상류측 수위는 수평수로의 유사한 조건에 비해 72.5% 감소한 반면, 이 감소량은 경사면에서 다른 경우에 비해 8.3% 감소하였다. 채널 또한 두 교각이 있는 경우 최대 Froude 수는 수평 수로의 5.7배였습니다.
This paper analyzed the flow pattern around damaged and undamaged bridge piers in a channel with a mild slope. The experiments were carried out on a straight channel with a length of 12 meters and a slope of 0.008. Acoustic Doppler velocimeter (ADV) was employed to collect three-dimensional flow velocity data, and the results were analyzed and compared with particle image velocimetry (PIV) data. Sediment Simulation in Intakes with Multiblock option (SSIIM) was incorporated for the numerical simulation of the flow in this study. Generally, the results obtained from the comparisons referred to the appropriate agreement between the numerical and the experimental data. The results showed that an undular hydraulic jump occurred at a distance of two meters from the channel entrance in every case; the maximum bed shear stress in the sloped channel was 12 times that in a horizontal channel for installing two damaged and undamaged piers. With this position of the piers in the sloped channel, the upstream water level underwent a 72.5% reduction compared to similar conditions in a horizontal channel, while the amount of this water level decrease was equal to 8.3% compared to the other cases in a sloped channel. In addition, with the presence of both piers, the maximum Froude number was 5.7 times that in a horizontal channel.
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Flow aeration in chute spillway is one of the most effective and economic ways to prevent cavitation damage. Surface damage is significantly reduced when very small values of air are scattered in a water prism. A structure known as an aerator may be used for this purpose. Besides, ramp angle is one of the factors influencing aerator efficiency. In this research, the value of air entraining the flow through the Jarreh Dam’s spillway at the ramp angles of 6, 8 and 10 degrees, as three different scenarios, was simulated using the Flow-3D software. In order to validate the results of the inlet air into the flowing fluid at a ramp angle of 6 degrees, the observational results of the dam spillway physical model from the laboratory of TAMAB Company in Iran were used. According to the results, raising the ramp angle increases the inlet air to the water jet nappe, and a ten-degree ramp angle provides the best aeration efficiency. The Flow-3D model can also simulate the two-phase water-air flow on spillways, according to the results.
슈트 여수로의 흐름 폭기는 캐비테이션 손상을 방지하는 가장 효과적이고 경제적인 방법 중 하나입니다. 수중 프리즘에 아주 작은 양의 공기가 흩어지면 표면 손상이 크게 줄어듭니다. 이를 위해 폭기 장치로 알려진 구조를 사용할 수 있습니다. 또한, 램프 각도는 폭기 효율에 영향을 미치는 요인 중 하나입니다. 이 연구에서는 FLOW-3D 소프트웨어를 사용하여 3가지 다른 시나리오인 6, 8 및 10도의 램프 각도에서 Jarreh 댐의 방수로를 통해 흐름을 동반하는 공기의 값을 시뮬레이션했습니다. 6도의 경사각에서 유동 유체로 유입되는 공기의 결과를 검증하기 위해이란 TAMAB Company의 실험실에서 댐 방수로 물리적 모델의 관찰 결과를 사용했습니다. 결과에 따르면 램프 각도를 높이면 워터제트 기저귀로 유입되는 공기가 증가하고 10도 램프 각도는 최고의 폭기 효율을 제공합니다. Flow-3D 모델은 결과에 따라 여수로의 2단계 물-공기 흐름을 시뮬레이션할 수도 있습니다.
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NUMERICAL SIMULATION OF FLOW PATTERN IN SERIES OF IMPERMEABLE GROYNES IN FIXED BED
Kafle, Mukesh Raj1 1Asst. Professor, Department of Civil Engineering, Institute of Engineering, Pulchowk Campus, Nepal Email: email@example.com
This paper presents a numerical simulation of recirculating flow patterns in groyne fields. Moreover, it entails the concept determination of proper spacing of vertical unsubmerged and impermeable groynesin seriesto control the bank erosion. Flow pattern between the groynes varies along their space. The flow in groyne field may significantly affect the flow change, bed change, bank erosion and condition of habitat. In this regard, an assessment of flow along the space of groynes will yield important data needed to diversify the object of groyne installation. So, knowledge about determination of the proper spacing of groynes in groyne field is important. Space of vertical groynes was set from 1.5 to 10 times the length of groynes. The velocity field between groynes was simulated by using Computational Fluid Dynamics (CFD) model Nays 2D. Simulated velocity field was compared with existing experimentaldata for the same parameter, which agreed satisfactorily. Based on simulated results,the optimal spacing of vertical groynes to control the bank erosion was recommended.
이 논문은 groyne 필드에서 재순환 흐름 패턴의 수치 시뮬레이션을 제공합니다. 더욱이, 그것은 제방 침식을 제어하기 위해 수직 비침수 및 불침투성 그로이네신 시리즈의 적절한 간격의 개념 결정을 수반합니다. groynes 사이의 흐름 패턴은 공간에 따라 다릅니다. groyne field의 흐름은 흐름 변화, 하상 변화, 제방 침식 및 서식지 상태에 중대한 영향을 미칠 수 있습니다. 이와 관련하여, groyne 공간을 따른 흐름의 평가는 groyne 설치 대상을 다양화하는 데 필요한 중요한 데이터를 산출할 것입니다. 따라서, groyne field에서 groyne의 적절한 간격 결정에 대한 지식이 중요합니다. 수직 여백의 간격은 여아 길이의 1.5배에서 10배 사이로 설정하였다. groyne 사이의 속도장은 CFD(Computational Fluid Dynamics) 모델 Nays 2D를 사용하여 시뮬레이션되었습니다. 시뮬레이션된 속도장은 동일한 매개변수에 대해 기존 실험 데이터와 비교되었으며 만족스럽게 일치했습니다. 모의 결과를 바탕으로 제방 침식을 억제하기 위한 최적의 수직 제방 간격을 제안하였다.
Introduction Spur dikes or groynes are used to protect river banks from erosion and also keep the channel navigable.Depending upon the flow characteristics, spur-dikes may be classified as submerged and unsubmerged. Also, based on the permeability, spur dikes are further classified as permeable and impermeable. Herein, un-submerged !impermeable spur dikes are dealt. These structures are built from the river bank into the stream flow and usually built in group. Construction of groyne against the flow causes significant changes in flow pattern in channel. Those changes may result in scour phenomenon around groynes which may lead structure instability and changes in river morphology. Moreover, in series of groynes, spacing of groynes leads different types of recirculating flow patterns.Therefore, investigating the characteristics of flow pattern around groynes have been a great interest in river engineering. Numerous researchers like Sukhodolov et al. (2002), Hao Zhang et al.(2009), Beheshti (2010), Duan (2009), Naji(2010), Karami(2011) made a variety of experiments in order to determine the flow pattern around groynes. Most of these researchers studied effect of single groyne, while using series of groynes is more effective in protection of rivers. Besides experimental studies, variety of CFD models have been developed for computing flow pattern around hydraulic structures; like Fluent, Flow 3D, Nays 2D, Nays CUBE and SSIIM. In this study, Nays 2D numerical modelling has been used to investigate flow and recirculating pattern around a series of groynes and streamlines including components of velocities.
Flow pattern in groyne fields Under conditions where the groynes are not submerged, the groyne fields are not really part of the wetted cross section of a river. Because of that, the flow pattern in the groyne-field is not directly the result of the discharge in the main channel. Reducing the main stream velocity has no effect on the flow pattern itself, whereas lowering the water level does (Uijttewaal et al.2001). Moreover, the flow pattern inside a groyne field may change with the change of its geometry, location along the river (inner curve, outer curve, or straight part), and/ or the groynes orientation( Przedwojski et al.1995). However, there is an indirect effect of the discharge on the flow pattern in the groyne field. Because of the flow that is diverted from the main channel into the groyne fields, water flows into the groyne field with low velocity through the downstream half of the interfacial section between the groyne field and the main channel. This water flows back to the main channel through a small width of, just downstream the upstream groyne of the groyne field ( Termes et al.1991). Flow separates on a groyne head and forms a secondary flow represented by a large scale vortex with a vertical axis of rotation called primary gyre. Deflection of the flow inside the groyne field by banks and upstream groynes leads to the development of a secondary gyre with an opposite direction of rotation to the primary gyre. Location, mutual interactions, and energy exchange between gyres are the factors that create a specific recirculation pattern, and, consequently assuming correspondence with sedimentation processes, they define deposition patterns.
Model Formulation The CFD model selected for this study is the publically available software NAYS 2D (iRIC 2.0), which is an analytical solver for calculation of unsteady two-dimensional plane flow and riverbed deformation using boundary-fitted coordinates within general curvilinear coordinates. A numerical channel of length 8.0m and width 0.9m was created with grid size of 0.01m im stream wise and 0.03m in cross stream directions. Groynes or spur dikes of length 0.15 and width 0.01m were chosen in series. Groyne field with various aspect ratio (b/x) 0.7, 0.25, 0.17, 0.125 and 0.10, where b=length of spur dike, x=spacing of two dikes. Discharge of 0.0175 m3 /s was applied. For boundary conditions, water surface at downstream and velocity at upstream were considered as uniform flow. Relaxation coefficient for water surface calculation was considered as 0.8. For the finite-difference method, the CIP method was applied to the advection terms in equations of motion. For the turbulent field calculation, Constant eddy viscosity, Zero-equation model and k-G models were applied and compared. The model!s accuracy in predicting the velocity magnitudes is evaluated using statistical parameters- mean absolute error (MAE), mean square error(MSE), and root mean square error (RMSE). The comparison of results shows the importance of selecting an appropriate turbulence model in simulating flow field around a spur dike. From the comparison, k-I model is found superior over zero energy model and eddy viscosity model. So, k-I model is chosen as appropriate turbulence closure model.
Model!s Validation The capability of CFD model Nays 2D to simulate the velocity field and recirculation pattern in groyne field was compared with experimental data of laboratory experiments by Sukhodolov et al. (2002). The numerical simulation was validated for aspect ratio (R=b/x=0.7) and R=0.25. For aspect ratio R=0.7, one gyre system occupies the whole area of the groyne field. The areas with lower-than-average velocity values are clearly seen in the central part of the gyre and near its corners. Velocities increase towards the margins of the gyre. For aspect ratio R=0.25, two gyre velocity fields were observed in the groyne field. In the downstream part of the groyne field a large gyre, covering two-thirds of the area is clearly visible. The left part(upstream) contains second gyre rotating much more slowly and in the direction opposed to the primary gyre. The simulated and observed velocity field pattern and gyre found satisfactorily agreed. Now, after validation, the model was used for further analysis of velocity field for various aspect ratios.
Results and Discussions The calibrated model was applied to five different cases of un-submerged and impermeable groyne fields with aspect ratios R=0.70,0.25,0.17,0.125 & 0.10 and flow pattern was numerically simulated. For aspect ratio R=0.7 i.e x/b=1.5, Fig 1(a) only one lateral primary gyre was formed inside the groyne field. The circulation pattern in this case is distinguished by the main flow that is deflected outside the groyne field. The developed primary gyre prevents the main flow from penetrating the groyne field. Therefore, this pattern is desirable for navigation purposes as a continuous deep channel is maintained along the face of the groyne field. Simulated velocity pattern satisfactorily agrees with the observed velocity field Fig 1(b) for the same aspect ratio by Sukhodolov (2002). The spacing of the groyne was further increased maintaining aspect ratio R= 0.25 i. e x/b=4 Fig 2(a) and flow pattern inside the groyne field was simulated. In this case, in the downstream part of the groyne field, a primary gyre occupying almost two-third area was formed. In addition, deflection of the flow inside the groyne field by banks and upstream groynes leads to the development of a secondary gyre with an opposite direction of rotation to the primary gyre covering almost one-third part of the groyne field. Likewise in the first case, the main current is maintained deflected outside the groyne field. Simulated velocity pattern satisfactorily agrees with the observed velocity field Fig 2(b) for the same aspect ratio by Sukhodolov (2002). The spacing of the groyne was further increased maintaining aspect ratio R=0.17 i.e x/b=6. In this case the flow pattern was similar to the aspect ratio R=0.25. The spacing of the groynes was further increased maintaining aspect ratio R=0.125 i. e x/b=8. In this case, similar to the previous scenarios two longitudinal gyres but with different positions are formed. The main current is directed in to the groyne field (Fig 3) creating a much more stronger eddy near the upstream groyne and greater turbulence along the upstream face and at the groyne lower head. As the spacing between groynes increased maintaining aspect ratio R=0.10 i. e x/b=10 (Fig 4), still primary and secondary gyres are generated. The formed gyres deflect the main flow thus preventing to enter in to the groyne field in upstream part. However, in the downstream of the primary gyre and just upstream of the second groyne, the flow attacks the bank directly. The resultant velocity profiles at the deflected region y/b=3 were plotted and how the spacing of second groyne affect the result was analyzed. Spacing of groynes makes little change in upstream resultant velocity. However, in the deflected region, its effect is significant. Higher value of spacing of groyne leads higher average deviation in resultant velocity. For aspect ratio R=0.7, the average deviation estimated as 0.02%. In the case of aspect ratio R=0.25, this value was reached to 1.57%. Further increment of spacing i. e decreasing the aspect ratio R=0.17, average deviation was found 3.82%. For the aspect ratio R=0.125, that value was estimated as 4.16%.
Conclusions Geometry of the groyne fields; width and length of the groyne field mainly cause the specific flow patterns including number and shape of eddies or gyres. Eddies developed inside the groyne field deflects the main flow preventing it entering into the dead zone. An aspect ratio close to unity gives rise to a single eddy. A smaller aspect ratio (higher spacing between groynes) gives room to two stationary eddies, a large one called primary eddy, in the downstream part of the groyne field, and a smaller secondary eddy emerges near the upstream groyne. The extreme long groyne field -case of length to width ratio of larger thaneight shows penetration of main flow into the groyne field. The two eddies remain in a relatively stable position, while the main flow zone starts to penetrate into groyne field further downstream. In all cases, there is an eddy detaches from the upstream groyne tip that travels along the main channel groyne field interface and eventually merges with the primary eddy. The simulated results indicate that the spacing of groynes or spur dikes from the controlling of bank erosion point of view should be limited within six times the length of groyne.
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Liril D.SilviaDinesh K.ChandrakercSumanaGhoshaArup KDasb aDepartment of Chemical Engineering, Indian Institute of Technology, Roorkee, India bDepartment of Mechanical Engineering, Indian Institute of Technology, Roorkee, India cReactor Engineering Division, Bhabha Atomic Research Centre, Mumbai, India
Present work reports numerical understanding of interfacial dynamics during co-flow of vapor and liquid phases of water inside a typical Boiling Water Reactor (BWR), consisting of a nuclear fuel rod bundle assembly of 7 pins in a circular array. Two representative spacings between rods in a circular array are used to carry out the simulation. In literature, flow boiling in a nuclear reactor is dealt with mechanistic models or averaged equations. Hence, in the present study using the Volume of Fluid (VOF) based multiphase model, a detailed numerical understanding of breaking and making in interfaces during flow boiling in BWR is targeted. Our work will portray near realistic vapor bubble and liquid flow dynamics in rod bundle scenario. Constant wall heat flux for fuel rod and uniform velocity of the liquid at the inlet patch is applied as a boundary condition. The saturation properties of water are taken at 30 bar pressure. Flow boiling stages involving bubble nucleation, growth, merging, local dry-out, rewetting with liquid patches, and complete dry-out are illustrated. The dry-out phenomenon with no liquid presence is numerically observed with phase fraction contours at various axial cut-sections. The quantification of the liquid phase fraction at different axial planes is plotted over time, emphasizing the progressive dry-out mechanism. A comparison of liquid-vapor distribution for inner and outer rods reveals that the inner rod’s dry-out occurs sooner than that of the outer rod. The heat transfer coefficient to identify the heat dissipation capacity of each case is also reported.
현재 작업은 원형 배열에 있는 7개의 핀으로 구성된 핵연료봉 다발 어셈블리로 구성된 일반적인 끓는 물 원자로(BWR) 내부의 물의 증기 및 액체상의 동시 흐름 동안 계면 역학에 대한 수치적 이해를 보고합니다.
원형 배열의 막대 사이에 두 개의 대표적인 간격이 시뮬레이션을 수행하는 데 사용됩니다. 문헌에서 원자로의 유동 비등은 기계론적 모델 또는 평균 방정식으로 처리됩니다.
따라서 VOF(Volume of Fluid) 기반 다상 모델을 사용하는 본 연구에서는 BWR에서 유동 비등 동안 계면의 파괴 및 생성에 대한 자세한 수치적 이해를 목표로 합니다.
우리의 작업은 막대 번들 시나리오에서 거의 사실적인 증기 기포 및 액체 흐름 역학을 묘사합니다. 연료봉에 대한 일정한 벽 열유속과 입구 패치에서 액체의 균일한 속도가 경계 조건으로 적용됩니다. 물의 포화 특성은 30bar 압력에서 취합니다.
기포 핵 생성, 성장, 병합, 국소 건조, 액체 패치로 재습윤 및 완전한 건조를 포함하는 유동 비등 단계가 설명됩니다. 액체가 존재하지 않는 건조 현상은 다양한 축 단면에서 위상 분율 윤곽으로 수치적으로 관찰됩니다.
다른 축 평면에서 액상 분율의 정량화는 점진적인 건조 메커니즘을 강조하면서 시간이 지남에 따라 표시됩니다. 내부 막대와 외부 막대의 액-증기 분포를 비교하면 내부 막대의 건조가 외부 막대보다 더 빨리 발생함을 알 수 있습니다. 각 경우의 방열 용량을 식별하기 위한 열 전달 계수도 보고됩니다.
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측면 분기기(흡입구)의 상류 측에서 흐름 분리는 분기기 입구에서 와류를 일으키는 중요한 문제입니다. 이는 흐름의 유효 폭, 출력 용량 및 효율성을 감소시킵니다. 따라서 분리지대의 크기를 파악하고 크기를 줄이기 위한 방안을 제시하는 것이 필수적이다. 본 연구에서는 분리 구역의 치수를 줄이기 위한 방법으로 7가지 유형의 거칠기 요소를 분기구 입구에 설치하고 4가지 다른 배출(총 84번의 실험을 수행)과 함께 3개의 서로 다른 베드 반전 레벨을 조사했습니다. 또한 3D CFD(Computational Fluid Dynamics) 모델을 사용하여 분리 영역의 흐름 패턴과 치수를 평가했습니다. 결과는 거칠기 계수를 향상시키면 분리 영역 치수를 최대 38%까지 줄일 수 있는 반면, 드롭 구현 효과는 사용된 거칠기 계수를 기반으로 이 영역을 다르게 축소할 수 있음을 보여주었습니다. 두 가지 방법을 결합하면 분리 영역 치수를 최대 63%까지 줄일 수 있습니다.
Flow separation at the upstream side of lateral turnouts (intakes) is a critical issue causing eddy currents at the turnout entrance. It reduces the effective width of flow, turnout capacity and efficiency. Therefore, it is essential to identify the dimensions of the separation zone and propose remedies to reduce its dimensions. Installation of 7 types of roughening elements at the turnout entrance and 3 different bed invert levels, with 4 different discharges (making a total of 84 experiments) were examined in this study as a method to reduce the dimensions of the separation zone. Additionally, a 3-D Computational Fluid Dynamic (CFD) model was utilized to evaluate the flow pattern and dimensions of the separation zone. Results showed that enhancing the roughness coefficient can reduce the separation zone dimensions up to 38% while the drop implementation effect can scale down this area differently based on the roughness coefficient used. Combining both methods can reduce the separation zone dimensions up to 63%.
Turnouts or intakes are amongst the oldest and most widely used hydraulic structures in irrigation networks. Turnouts are also used in water distribution, transmission networks, power generation facilities, and waste water treatment plants etc. The flows that enter a turnout have a strong momentum in the direction of the main waterway and that is why flow separation occurs inside the turnout. The horizontal vortex formed in the separation area is a suitable place for accumulation and deposition of sediments. The separation zone is a vulnerable area for sedimentation and for reduction of effective flow due to a contracted flow region in the lateral channel. Sedimentaion in the entrance of the intake can gradually be transfered into the lateral channel and decrease the capacity of the higher order channels over time (Jalili et al. 2011). On the other hand, the existence of coarse-grained materials causes erosion and destruction of the waterway side walls and bottom. In addition, sedimentation creates conditions for vegetation to take root and damage the waterway cover, which causes water to leak from its perimeter. Therefore, it is important to investigate the pattern of the flow separation area in turnouts and provide solutions to reduce the dimensions of this area.
The three-dimensional flow structure at turnouts is quite complex. In an experimental study by Neary & Odgaard (1993) in a 90-degree water turnout it was found that the secondary currents and separation zone varies from the bed to the water surface. They also found that at a 90-degree water turnout, the bed roughness and discharge ratio play a critical role in flow structure. They asserted that an explanation of sediment behavior at a diversion entrance requires a comprehensive understanding of 3D flow patterns around the lateral-channel entrance. In addition, they suggested that there is a strong similarity between flow in a channel bend and a diversion channel, and that this similarity can rationalize the use of bend flow models for estimation of 3D flow structures in diversion channels.
Some of the distinctive characteristics of dividing flow in a turnout include a zone of separation immediately near the entrance of the lateral turnout (separation zone), a contracted flow region in the branch channel (contracted flow), and a stagnation point near the downstream corner of the junction (stagnation zone). In the region downstream of the junction, along the continuous far wall, separation due to flow expansion may occur (Ramamurthy et al. 2007), that is, a separation zone. This can both reduce the turnout efficiency and the effective width of flow while increasing the sediment deposition in the turnout entrance (Jalili et al. 2011). Installation of submerged vanes in the turnout entrance is a method which is already applied to reduce the size of flow separation zones. The separation zone draws sediments and floating materials into themselves. This reduces effective cross-section area and reduces transmission capacity. These results have also been obtained in past studies, including by Ramamurthy et al. (2007) and in Jalili et al. (2011). Submerged vanes (Iowa vanes) are designed in order to modify the near-bed flow pattern and bed-sediment motion in the transverse direction of the river. The vanes are installed vertically on the channel bed, at an angle of attack which is usually oriented at 10–25 degrees to the local primary flow direction. Vane height is typically 0.2–0.5 times the local water depth during design flow conditions and vane length is 2–3 times its height (Odgaard & Wang 1991). They are vortex-generating devices that generate secondary circulation, thereby redistributing sediment within the channel cross section. Several factors affect the flow separation zone such as the ratio of lateral turnout discharge to main channel discharge, angle of lateral channel with respect to the main channel flow direction and size of applied submerged vanes. Nakato et al. (1990) found that sediment management using submerged vanes in the turnout entrance to Station 3 of the Council Bluffs plant, located on the Missouri River, is applicable and efficient. The results show submerged vanes are an appropriate solution for reduction of sediment deposition in a turnout entrance. The flow was treated as 3D and tests results were obtained for the flow characteristics of dividing flows in a 90-degree sharp-edged, junction. The main and lateral channel were rectangular with the same dimensions (Ramamurthy et al., 2007).
Keshavarzi & Habibi (2005) carried out experiments on intake with angles of 45, 67, 79 and 90 degrees in different discharge ratios and reported the optimum angle for inlet flow with the lowest flow separation area to be about 55 degrees. The predicted flow characteristics were validated using experimental data. The results indicated that the width and length of the separation zone increases with the increase in the discharge ratio Qr (ratio of outflow per unit width in the turnout to inflow per unit width in the main channel).
Abbasi et al. (2004) performed experiments to investigate the dimensions of the flow separation zone at a lateral turnout entrance. They demonstrated that the length and width of the separation zone decreases with the increasing ratio of lateral turn-out discharge. They also found that with a reducing angle of lateral turnout, the length of the separation zone scales up and width of separation zone reduces. Then they compared their observations with results of Kasthuri & Pundarikanthan (1987) who conducted some experiments in an open-channel junction formed by channels of equal width and an angle of lateral 90 degree turnout, which showed the dimensions of the separation zone in their experiments to be smaller than in previous studies. Kasthuri & Pundarikanthan (1987) studied vortex and flow separation dimensions at the entrance of a 90 degree channel. Results showed that increasing the diversion discharge ratio can reduce the length and width of the vortex area. They also showed that the length and width of the vortex area remain constant at diversion ratios greater than 0.7. Karami Moghaddam & Keshavarzi (2007) analyzed the flow characteristics in turnouts with angles of 55 and 90 degrees. They reported that the dimensions of the separation zone decrease by increasing the discharge ratio and reducing the turnout angle with respect to the main channel. Studies about flow separation zone can be found in Jalili et al. (2011), Nikbin & Borghei (2011), Seyedian et al. (2008).
Jamshidi et al. (2016) measured the dimensions of a flow separation zone in the presence of submerged vanes with five arrangements (parallel, stagger, compound, piney and butterflies). Results showed that the ratio of the width to the length of the separation zone (shape index) was between 0.2 and 0.28 for all arrangements.
Karami et al. (2017) developed a 3D computational fluid dynamic (CFD) code which was calibrated by measured data. They used the model to evaluate flow pattern, diversion ratio of discharge, strength of the secondary flow, and dimensions of the vortex inside the channel in various dikes and submerged vane installation scenarios. Results showed that the diversion ratio of discharge in the diversion channel is dependent on the width of the flow separation area in the main channel. A dike, perpendicular to the flow, doubles the ratio of diverted discharge and reduces the suspended sediment load compared with the base-line situation by creating outer arch conditions. In addition, increasing the longitudinal distance between vanes increases the velocity gradient between the vanes and leads to a more severe erosion of the bed near the vanes.Figure 1VIEW LARGEDOWNLOAD SLIDE
Laboratory channel dimensions.
Al-Zubaidy & Hilo (2021) used the Navier–Stokes equation to study the flow of incompressible fluids. Using the CFD software ANSYS Fluent 19.2, 3D flow patterns were simulated at a diversion channel. Their results showed good agreement using the comparison between the experimental and numerical results when the k-omega turbulence viscous model was employed. Simulation of the flow pattern was then done at the lateral channel junction using a variety of geometry designs. These improvements included changing the intake’s inclination angle and chamfering and rounding the inner corner of the intake mouth instead of the sharp edge. Flow parameters at the diversion including velocity streamlines, bed shear stress, and separation zone dimensions were computed in their study. The findings demonstrated that changing the 90° lateral intake geometry can improve the flow pattern and bed shear stress at the intake junction. Consequently, sedimentation and erosion problems are reduced. According to the conclusions of their study, a branching angle of 30° to 45° is the best configuration for increasing branching channel discharge, lowering branching channel sediment concentration.
The review of the literature shows that most of the studies deal with turnout angle, discharge ratio and implementation of vanes as techniques to reduce the area of the separation zone. This study examines the effect of roughness coefficient and drop implementation at the entrance of a 90-degree lateral turnout on the dimensions of the separation zone. As far as the authors are aware, these two variables have never been studied as a remedy to decrease the separation zone dimensions whilst enhancing turnout efficiency. Additionally, a three-dimensional numerical model is applied to simulate the flow pattern around the turnout. The numerical results are verified against experimental data.
The experiments were conducted in a 90 degree dividing flow laboratory channel. The main channel is 15 m long, 0.5 m wide and 0.4 m high and the branch channel is 3 m long, 0.35 m wide and 0.4 m high, as shown in Figure 1. The tests were carried out at 9.65 m from the beginning of the flume and were far enough from the inlet, so we were sure that the flow was fully developed. According to Kirkgöz & Ardiçlioğlu (1997) the length of the developing region would be approximantly 65 and 72 times the flow depth. In this study, the depth is 9 cm, which makes this condition.
Both the main and lateral channel had a slope of 0.0003 with side walls of concrete. A 100 hp pump discharged the water into a stilling basin at the entrance of the main flume. The discharge was measured using an ultrasonic discharge meter around the discharge pipe. Eighty-four experiments in total were carried out at range of 0.1<Fr<0.4 (Froude numbers in main channel and upstream of turnout). The depth of water in the main channel in the experiments was 9 cm, in which case the effect of surface tension can be considered; according to research by Zolghadr & Shafai Bejestan (2020) and Zolghadr et al. (2021), when the water depth is more than 6 cm, the effect of surface tension is reduced and can be ignored given that the separation phenomenon occurs in the boundary layer, the height of the roughness creates disturbances in growth and development of the boundary layer and, as a result, separation growth is also faced with disruption and its dimensions grow less compared to smooth surfaces. Similar conditions occur in case of drop implementation. A disturbance occurs in the growth of the boundary layer and as a result the separation zone dimensions decrease. In order to investigate the effect of roughness coefficient and drop implementation on the separation zone dimensions, four different discharges (16, 18, 21, 23 l/s) in subcritical conditions, seven Manning (Strickler) roughness coefficients (0.009, 0.011, 0.017, 0.023, 0.028, 0.030, 0.032) as shown in Figure 2 and three invert elevation differences between the main channel and lateral turnout invert (0, 5 and 10 cm) at the entrance of the turnout were considered. The Manning roughness coefficient values were selected based on available and feasible values for real conditions, so that 0.009 is equivalent to galvanized sheet roughness and selected for the baseline tests. 0.011 is for concrete with neat surface, 0.017 and 0.023 are for unfinished and gunite concrete respectively. 0.030 and 0.032 values are for concrete on irregular excavated rock (Chow 1959). The roughness coefficients were created by gluing sediment particles on a thin galvanized sheet which was installed at the upstream side of the lateral turnout. The values of roughness coefficients were calculated based on the Manning-Strickler formula. For this purpose, some uniformly graded sediment samples were prepared and the Manning roughness coefficient of each sample was determined with respect to the median size (D50) value pasted into the Manning-Strickler formula. Some KMnO4 was sifted in the main channel upstream to visualize and measure the dimensions of the separation zone. Consequently, when KMnO4 approached the lateral turnout a photo of the separation zone was taken from a top view. All the experiments were recorded and several photos were taken during the experiment after stablishment of steady flow conditions. The photos were then imported to AutoCAD to measure the separation zone dimensions. Because all the shooting was done with a high-definition camera and it was possible to zoom in, the results are very accurate.Figure 2VIEW LARGEDOWNLOAD SLIDE
The velocity values were also recorded by a one-dimensional velocity meter at 15 cm distance from the turnout entrance and in transverse direction (perpendicular to the flow direction).
The water level was also measured by depth gauges with a accuracy of 0.1 mm, and velocity in one direction with a single-dimensional KENEK LP 1100 with an accuracy of ±0.02 m/s (0–1 m/s), ± 0.04 m/s (1–2 m/s), ± 0.08 m/s (2–4 m/s), ±0.10 m/s (4–5 m/s).
ListenA FLOW-3D numerical model was utilized as a solver of the Navier-Stokes equation to simulate the three-dimensional flow field at the entrance of the turnout. The governing equations included continuity momentum equations. The continuity equation, regardless of the density of the fluid in the form of Cartesian coordinates x, y, and z, is as follows:
(1)where u, v, and w represent the velocity components in the x, y, and z directions, respectively; Ax, Ay, and Az are the surface flow fractions in the x, y, and z directions, respectively; VF denotes flow volume fraction; r is the density of the fluid; t is time; and Rsor refers to the source of the mass. Equations (2)–(4) show momentum equations in x, y and z dimensions respectively :
(4)where Gx, Gy, and Gz are the accelerations caused by gravity in the x, y, and z directions, respectively; and fx, fy, and fz are the accelerations caused by viscosity in the x, y, and z directions, respectively.
The turbulence models used in this study were the renormalized group (RNG) models. Evaluation of the concordance of the mentioned models with experimental studies showed that the RNG model provides more accurate results.
Two blocks of mesh were used to simulate the main channels and lateral turnout. The meshes were denser in the vicinity of the entrance of the turnout in order to increase the accuracy of computations. Boundary conditions for the main mesh block included inflow for the channel entrance (volumetric flow rate), outflow for the channel exit, ‘wall’ for the bed and the right boundary and ‘symmetry’ for the top (free surface) and left boundaries (turnout). The side wall roughness coefficient was given to the software as the Manning number in surface roughness of any component. Considering the restrictions in the available processor, a main mesh block with appropriate mesh size was defined to simulate the main flow field in the channel, while the nested mesh-block technique was utilized to create a very dense solution field near the roughness plate in order to provide accurate results around the plates and near the entrance of the lateral turnout. This technique reduced the number of required mesh elements by up to 60% in comparison with the method in which the mesh size of the main solution field was decreased to the required extent.
The numerical outputs are verified against experimental data. The hydraulic characteristics of the experiment are shown in Table 1.Table 1
During the experiments, the dimensions of the separation zone were recorded with an HD camera. Some photos were imported to AutoCad software. Then, the separation zones dimensions were measured and compared in different scenarios.
At the beginning, the flow pattern in the separation zone for four different hydraulic conditions was studied for seven different Manning roughness coefficients from 0.009 to 0.032. To compare the obtained results, roughness of 0.009 was considered as the base line. The percentage of reduction in separation zone area in different roughness coefficients is shown in Figure 3. According to this figure, by increasing the roughness of the turnout side wall, the separation zone area ratio reduces (ratio of separation zone area to turnout area). In other words, in any desired Froud number, the highest dimensions of the separation zone area are related to the lowest roughness coefficients. In Figure 3, ‘A’ is the area of the separation zone and ‘Ai’ represents the total area of the turnout.Figure 3VIEW LARGEDOWNLOAD SLIDE
Effect of roughness on separation zone dimensions.
It should be mentioned that the separation zone dimensions change with depth, so that the area is larger at the surface than near the bed. This study measured the dimensions of this area at the surface. Figure 4 show exactly where the roughness elements were located.Figure 5VIEW LARGEDOWNLOAD SLIDE
Comparison of separation zone for n=0.023 and n=0.032.
Figure 5 shows images of the separation zone at n=0.023 and n=0.032 as examples, and show that the separation area at n=0.032 is smaller than that of n=0.023.
The difference between the effect of the two 0.032 and 0.030 roughnesses is minor. In other words, the dimensions of the separation zone decreased by increasing roughness up to 0.030 and then remained with negligable changes.
In the next step, the effect of intake invert relative to the main stream (drop) on the dimensions of the separation zone was investigated. To do this, three different invert levels were considered: (1) without drop; (2) a 5 cm drop between the main canal and intake canal; and (3) a 10 cm drop between the main canal and intake canal. The without drop mode was considered as the control state. Figure 6 shows the effect of drop implementation on separation zone dimensions. Tables 2 and 3 show the reduced percentage of separation zone areas in 5 and 10 cm drop compared to no drop conditions as the base line. It was found that the best results were obtained when a 10 cm drop was implemented.Table 2
Decrease percentage of separation zone area in 5 cm drop
Decrease percentage of separation zone area in 10 cm drop
Effect of drop implementation on separation zone dimensions.
The combined effect of drop and roughness is shown in Figure 7. According to this figure, by installing a drop structure at the entrance of the intake, the dimensions of the separation zone scales down in any desired roughness coefficient. Results indicated that by increasing the roughness coefficient or drop implementation individually, the separation zone area decreases up to 38 and 25% respectively. However, employing both techniques simultaneously can reduce the separation zone area up to 63% (Table 4). The reason for the reduction of the dimensions of the separation zone area by drop implementation can be attributed to the increase of discharge ratio. This reduces the dimensions of the separation zone area.Table 4
Reduction in percentage of combined effect of roughness and 10 cm drop
Combined effect of roughness and drop on separation zone dimensions.
This method increases the discharge ratio (ratio of turnout to main channel discharge). The results are compatible with the literature. Some other researchers reported that increasing the discharge ratio can scale down the separation zone dimensions (Karami Moghaddam & Keshavarzi 2007; Ramamurthy et al. 2007). However, these researchers employed other methods to enhance the discharge ratio. Drop implementation is simple and applicable in practice, since there is normally an elevation difference between the main and lateral canal in irrigation networks to ensure gravity flow occurance.
Table 4 depicts the decrease in percentage of the separation zone compared to base line conditions in different arrangements of the combined tests.Figure 8VIEW LARGEDOWNLOAD SLIDE
Velocity profiles for various roughness coefficients along turnout width.
A comparison between the proposed methods introduced in this paper and traditional methods such as installation of submerged vanes, and changing the inlet geometry (angle, radius) was performed. Figure 8 shows the comparison of the results. The comparison shows that the new techniques can be highly influential and still practical. In this research, with no change in structural geometry (enhancement of roughness coefficient) or minor changes with respect to drop implementation, the dimensions of the separation zone are decreased noticeably. The velocity values were also recorded by a one-dimensional velocity meter at 15 cm distance from the turnout entrance and in a transverse direction (perpendicular to the flow direction). The results are shown in Figure 9.Figure 9VIEW LARGEDOWNLOAD SLIDE
Effect of roughness on separation zone dimensions in numerical study.
This study examined the flow patterns around the entrance of a diversion channel due to various wall roughnesses in the diversion channel. Results indicated that increasing the discharge ratio in the main channel and diversion channel reduces the area of the separation zone in the diversion channel.Figure 10VIEW LARGEDOWNLOAD SLIDE
Comparision of the vortex area (software output) for three roughnesses (0.009, 0.023 and 0.032).A laboratory and numerical error rate of 0.2605 was calculated from the following formula,
where Uexp is the experimental result, Unum is the numerical result, and N is the number of data.
Figure 9 shows the effect of roughness on separation zone dimensions in numerical study. Figure 10 compares the vortex area (software output) for three roughnesses, 0.009, 0.023 and 0.032 and Figure 11 shows the flow lines (tecplot output) that indicate the effect of roughness on flow in the separation zone. Numerical analysis shows that by increasing the roughness coefficient, the dimensions of the separation zone area decrease, as shown in Figure 10 where the separation zone area at n=0.032 is less than the separation zone area at n=0.009.Figure 11VIEW LARGEDOWNLOAD SLIDE
Comparison of vortex area in 3D mode (tecplot output) with two roughnesses (a) 0.009 and (b) 0.032.Figure 12VIEW LARGEDOWNLOAD SLIDE
Velocity vector for flow condition Q1/422 l/s, near surface.
The velocities intensified moving midway toward the turnout showing that the effective area is scaled down. The velocity values were almost equal to zero near the side walls as expected. As shown in Figure 12 the approach vortex area velocity decreases. Experimental and numerical measured velocity at x=0.15 m of the diversion channel compared in Figure 13 shows that away from the separation zone area, the velocity increases. All longitudinal velocity contours near the vortex area are distinctly different between different roughnesses. The separation zone is larger at less roughness both in length and width.Figure 13VIEW LARGEDOWNLOAD SLIDE
This study introduces practical and feasible methods for enhancing turnout efficiency by reducing the separation zone dimensions. Increasing the roughness coefficient and implementation of inlet drop were considered as remedies for reduction of separation zone dimensions. A data set has been compiled that fully describes the complex, 3D flow conditions present in a 90 degree turnout channel for selected flow conditions. The aim of this numerical model was to compare the results of a laboratory model in the area of the separation zone and velocity. Results showed that enhancing roughness coefficient reduce the separation zone dimensions up to 38% while the drop implementation effect can scale down this area differently based on roughness coefficient used. Combining both methods can reduce the separation zone dimensions up to 63%. Further research is proposed to investigate the effect of roughness and drop implementation on sedimentation pattern at lateral turnouts. The dimensions of the separation zone decreases with the increase of the non-dimensional parameter, due to the reduction ratio of turnout discharge increasing in all the experiments.
This method increases the discharge ratio (ratio of turnout to main channel discharge). The results are compatible with the literature. Other researchers have reported that intensifying the discharge ratio can scale down the separation zone dimensions (Karami Moghaddam & Keshavarzi 2007; Ramamurthy et al. 2007). However, they employed other methods to enhance the discharge ratio. Employing both techniques simultaneously can decrease the separation zone dimensions up to 63%. A comparison between the new methods introduced in this paper and traditional methods such as installation of submerged vanes, and changing the inlet geometry (angle, radius) was performed. The comparison shows that the new techniques can be highly influential and still practical. The numerical and laboratory models are in good agreement and show that the method used in this study has been effective in reducing the separation area. This method is simple, economical and can prevent sediment deposition in the intake canal. Results show that CFD prediction of the fluid through the separation zone at the canal intake can be predicted reasonably well and the RNG model offers the best results in terms of predictability.
A 3D numerical model of heat transfer and fluid flow of molten pool in the process of laser wire deposition was presented by computational fluid dynamics technique. The simulation results of the deposition morphology were also compared with the experimental results under the condition of liquid bridge transfer mode. Moreover, they showed a good agreement. Considering the effect of recoil pressure, the morphology of the deposit metal obtained by the simulation was similar to the experiment result. Molten metal at the wire tip was peeled off and flowed into the molten pool, and then spread to both sides of the deposition layer under the recoil pressure. In addition, the results of simulation and high-speed charge-coupled device presented that a wedge transition zone, with a length of ∼6 mm, was formed behind the keyhole in the liquid bridge transfer process, where the height of deposited metal decreased gradually. After solidification, metal in the transition zone retained the original melt morphology, resulting in a decrease in the height of the tail of the deposition layer.
LWD, CFD, liquid bridge transfer, fluid dynamics, wedge transition zone
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1 Civil Enigneering Department, Lahijan Branch.Islamic Azad University.Lahijan.Iran
2 Department of Civil Engnieering, University of Qom,Qom,Iran
3 Civil Engineering Department, Lahijan Branch,Islamic Azad Univeristy,Lahijan,Iran
홍수와 그 위험을 통제해야 할 필요성은 누구에게도 숨겨져 있지 않습니다. 또한 이 현상으로 인해 다양한 경제, 사회 및 환경 문제가 영향을 받습니다. 홍수 제어 방법의 설계 및 최적 관리의 첫 번째 단계는 홍수 중 하천 거동을 올바르게 식별하는 것입니다.
홍수 경로 지정, 하상 및 하천 면적 결정 등과 같은 대부분의 하천 엔지니어링 프로젝트에서 하천 단면의 수리학적 매개변수의 평균값을 계산하는 것으로 충분합니다. 오늘날 유체 환경 연구에서 수치 및 분석 방법의 사용이 성장하고 발전했습니다.
신뢰할 수 있는 결과 생성으로 인해 물리적 모델에 대한 좋은 대안이 될 수 있었습니다. 오늘날 수치 모델의 급속한 발전과 컴퓨터 계산 속도의 증가로 인해 3D 수치 모델의 사용이 선호되며 또한 강의 속도 분포 및 전단 응력을 측정하는 데 시간이 많이 걸리고 비용이 많이 들기 때문에 결과 3D 수치 모델의 가치가 있을 것입니다.
한편, 본 연구에서는 복합단면에 대해 FLOW-3D 모델을 이용한 종합적인 수치연구가 이루어지지 않았음을 보여주고 있어 적절한 연구기반을 제공하고 있습니다.
따라서 본 연구의 혁신은 발산 및 수렴 범람원을 동반하는 비 각형 복합 단면에서 흐름의 상태 및 수리 성능에 대한 거칠기와 같은 매개 변수의 영향에 대한 수치 연구입니다.
수치해석 결과를 검증하기 위해 Younesi(2013) 연구를 이용하였습니다. 이 실험에서는 먼저 고정층이 있는 복합 프리즘 및 비 프리즘 단면의 수리 흐름을 조사한 다음 조건을 유지하면서 프리즘 및 비 프리즘 모드에서 퇴적물 이동 실험을 수행했습니다.
실험은 15미터 길이의 연구 채널에서 수행되었습니다. 이 운하는 초당 250리터의 시스템에서 재순환을 위해 제공될 수 있는 유속과 0.0088 000의 종경사를 가진 폭 400mm의 두 개의 대칭 범람원이 있는 합성 운하입니다. 범람원의 가장자리는 0.18미터와 같고 주요 운하의 너비는 0.4미터와 같습니다(그림 1).
본수로의 바닥과 벽을 거칠게 하기 위해 평균직경 0.65mm의 퇴적물을 사용하였으며, 각 단계에서 범람원의 벽과 바닥은 평균직경 0.65, 1.3, 1.78의 퇴적물로 거칠게 하였습다. (mm). 삼각형 오버플로는 운하 상류에서 운하로의 유입량을 측정하는 데 사용됩니다.
상대깊이 0.15와 0.25, 직경 14mm의 마이크로몰리나 실험과 상대깊이 0.35의 실험에서는 유속을 측정하기 위해 3차원 속도계(ADV)를 사용하였습니다. 수위는 0.1mm의 정확도로 깊이 게이지로 측정 되었습니다.
본 연구에서는 수면 프로파일의 수치적 모델을 검증하기 위해 실험 0.25-2에서 발산대의 시작, 중간 및 끝에서 세 단면의 평균 깊이 속도 분포 및 경계 전단 응력) -11.3-NP 및 0.25-2-5.7-NP 및 또한 각형 복합 단면의 0.25-2-2 P 테스트가 평가되었습니다.
각형 합성 단면의 P.20-2-2-P 테스트와 관련된 RMSE 및 NRMSE 지수 값 및 표 (2) 실험 11.3에서 RMSE 및 NRMSE 지수 값 -2-0.25-NP 및 -0.25. 2-5.7-NP가 제공됩니다. 실험 0.25-2-5.7-NP-11.3-2-0.25, NP 및 P.2.0-2-2-P의 평균 깊이 속도의 검증과 관련된 결과가 표시됩니다. 0.25-2-5.7-NP 실험에서 초, 중, 기말 NRMSE의 양은 각각 5.7, 11.8, 10.3%로 계산되었으며, 이는 초급이 우수, 중급이 양호, 최종 성적. 배치. 보시다시피, RMSE 값은 각각 0.026, 0.037 및 0.026으로 계산됩니다.
실험 11.3-2-0.25, NP에서 초급, 중급 및 최종 수준의 NRMSE 값은 각각 7, 11.2 및 15.4%로 계산되었으며, 이는 초급에서 우수 범주 및 우수 범주에서 중간 및 최종 수준. 가져 가다. 보시다시피, RMSE 값은 각각 0.032, 0.038, 0.04로 계산됩니다. 0.25-2-P 실험에서 NRMSE 값은 1.7%로 계산되어 우수 범주에 속한다. 보시다시피 RMSE 값도 0.004로 계산됩니다. 중간 깊이의 속도 분포와 관련하여 수치 모델은 실험실 결과에 적합하며 접합 영역에 작은 오류만 입력되었다고 말할 수 있습니다. 이는 2차 전지의 이동 결과로 간주될 수 있습니다. 모서리를 향해. 결론: 본 연구에서는 3차원 유동 해석이 가능한 Flow 3D 소프트웨어를 사용하여 각형 및 비각형 단면이 복합된 수로의 유동 패턴을 조사했습니다. 3개의 다른 상대 거칠기(1, 2 및 2.74)와 3개의 상대 깊이(0.15, 0.25 및 0.35) 및 5.7 및 11.3도의 발산 각도에 대해 속도의 세로 성분 변화, 평균 깊이 속도 분포, 경계 범람원에 의해 전달되는 유속뿐만 아니라 전단 응력 분포를 조사했습니다.
결과는 수로를 따라 범람원의 폭이 증가함에 따라 유속량이 감소함을 보여주었다. 또한 조도가 유동패턴에 미치는 영향에 대한 연구는 일반적으로 벽의 거칠기에 따라 모든 구간에서 유속량이 감소하는 것으로 나타났으며, 또한 본관과 범람원의 교차점에서의 유동패턴은 벽의 거칠기 영향을 더 많이 받는 것으로 나타났습니다. 결과는 또한 상대 깊이가 증가하거나 상대 거칠기가 감소함에 따라 주 수로와 범람원 사이의 속도 구배가 감소함을 보여주었습니다.
Intrpduction: The need to control floods and their dangers is not hidden from anyone. In addition, a wide range of economic, social and environmental issues are affected by this phenomenon. The first step in the design and optimal management of flood control methods is the correct identification of river behavior during floods. In most river engineering projects such as flood routing, determining the bed and river area, etc., calculating the average values of hydraulic parameters of the river section is sufficient. Today, the use of numerical and analytical methods in the study of fluid environment have grown and developed. Due to the production of reliable results, they have been able to be a good alternative to physical models. Today, with the rapid development of numerical models and increasing the speed of computer calculations, the use of 3D numerical models is preferred and also due to the fact that measuring the velocity distribution and shear stress in rivers is very time consuming and expensive, the results of 3D numerical models It will be valuable. On the other hand, the present studies show that comprehensive numerical research using FLOW-3D model has not been performed on composite sections, so a suitable ground for research is provided. Therefore, the innovation of the present study is the numerical study of the effects of parameters such as roughness on the status and hydraulic performance of the flow in non-prismatic composite sections, which are accompanied by divergent and convergent floodplains, which have received less attention numerically.
Methodology: Younesi (2013) research has been used to validate the results of numerical simulation. In these experiments, first the hydraulic flow in composite prismatic and non-prismatic sections with fixed bed was examined and then, while maintaining the conditions, sediment transfer experiments were performed in prismatic and non-prismatic mode. The experiments were performed in a research channel 15 meters long. This canal is a composite canal with two symmetrical floodplains with a width of 400 mm with a flow rate that can be provided for recirculation in the system of 250 liters per second and a longitudinal slope of 0.0088 000. The depth of the main canal to the edge of the floodplain is equal to 0.18 meters and the width of the main canal is equal to 0.4 meters (Figure 1). In order to roughen the bed and walls of the main canal, sediments with an average diameter of 0.65 mm have been used and at each stage, the walls and bed of floodplains have been roughened by sediments with an average diameter of 0.65, 1.3 and 1.78 (mm). A triangular overflow is used to measure the inflow to the canal, upstream of the canal. In order to measure the flow velocity in experiments with relative depth of 0.15 and 0.25, a micromolina with a diameter of 14 mm and in experiments with relative depth of 0.35, a three-dimensional speedometer (ADV) was used. The water level was also taken by depth gauges with an accuracy of 0.1 mm. Result and Diccussion: In the present study, in order to validate the numerical model of water surface profile, average depth velocity distribution and boundary shear stress in the three sections at the beginning, middle and end of the divergence zone) in experiments 0.25-2-11.3-NP and 0.25-2-5.7-NP and Also, the 0.25-2-2 P test of the prismatic composite section has been evaluated. In Table (1) the values of RMSE and NRMSE indices related to the P.20-2-2-P test of the prismatic composite section, and also in Table (2) the values of the RMSE and NRMSE indices in the experiments 11.3-2-0.25-NP and -0.25. 2-5.7-NP is provided. The results related to the validation of the average depth velocity of the experiments 0.25-2-5.7- NP-11.3-2-0.25, NP and P.2.0-2-2-P are shown. In 0.25-2-5.7-NP experiment, the amount of NRMSE in elementary, middle and final grades was calculated to be 5.7, 11.8 and 10.3%, respectively, which is in the excellent grade in the elementary grade and good in the middle and final grades. Placed. As can be seen, the RMSE values are calculated as 0.026, 0.037 and 0.026, respectively. In the experiment 11.3-2-0.25, NP, the NRMSE values in the primary, middle and final levels were calculated as 7, 11.2 and 15.4%, respectively, which are in the excellent category in the primary level and in the good category in the middle and final levels. Take. As can be seen, the RMSE values are calculated as 0.032, 0.038 and 0.04, respectively. In the 0.25-2-P experiment, the NRMSE value was calculated to be 1.7%, which is in the excellent category. As can be seen, the RMSE value is also calculated to be 0.004. Regarding the medium-depth velocity distribution, it can be said that the numerical model has an acceptable compliance with the laboratory results and only a small error has been entered in the junction area, which can be considered as a result of the movement of secondary cells towards the corners. Conclusion: in this research The flow pattern in waterways with composite prismatic and non-prismatic sections was investigated using Flow 3D software that is capable of three-dimensional flow analysis. For three different relative roughnesses (1, 2 and 2.74) as well as three relative depths (0.15, 0.25 and 0.35) and divergence angles of 5.7 and 11.3 degrees, changes in the longitudinal component of velocity, The average depth velocity distribution, the boundary shear stress distribution as well as the flow rate transmitted by the floodplains were investigated. The results showed that with increasing the width of floodplains along the canal, the amount of velocity decreases. Also, the study of the effect of roughness on the flow pattern showed that in general, with wall roughness, the amount of velocity has decreased in all sections and also the flow pattern at the junction of the main canal and floodplain is more affected by wall roughness. The results also showed that with increasing relative depth or decreasing relative roughness, the velocity gradient between the main channel and floodplains decreases
Parshall Flumes의 효율성 향상을 위한 수치 및 실험 모델링의 적용: 최신 기술 검토
Mehdi Heyrani 1,* , Abdolmajid Mohammadian 1, Ioan Nistor 1 and Omerul Faruk Dursun 2
열린 채널에서 흐름을 관리하는 기본 단계 중 하나는 속성을 결정하는 것입니다. 개방 수로의 흐름에 관한 추가 정보를 제공하기 위해 경험적 방정식이 개발되었습니다. 이러한 실험 방정식을 얻는 것은 비용과 시간이 많이 소요됩니다. 따라서 대체 솔루션이 모색되었습니다.
지난 세기 동안 움직이는 부분이 없는 정적 측정 장치인 Parshall 수로가 개방 수로의 흐름을 측정하는 데 중요한 역할을 했습니다. 많은 연구자들이 관개 및 폐수 관리와 같은 다양한 분야에서 Parshall 수로의 적용을 연구하는 데 관심을 집중해 왔습니다.
여러 학자들이 실험 결과를 사용하여 Parshall 수로의 등급 방정식을 향상시켰지만 다른 학자들은 수치 시뮬레이션을 사용하여 높이-방전 관계 방정식을 재보정하기 위해 대체 데이터 소스를 사용했습니다. 컴퓨팅 하드웨어가 지난 수십 년 동안 크게 발전하여 과거에 경험했던 제한된 해상도를 뛰어넘는 것이 가능해짐에 따라 CFD(Computational Fluid Dynamic) 소프트웨어가 오늘날 대중화되고 있습니다.
여러 CFD 모델은 가용성에 따라 오픈 소스 또는 상업적으로 허가되어 수위 결과를 생성하기 위해 다양한 구성의 수로, 특히 Parshall 수로에 대한 수치 시뮬레이션을 수행하는 데 사용되었습니다.
FLOW-3D, Ansys Fluent, OpenFOAM 등 지금까지 사용되어 온 다양한 CFD 도구에 대해 실험 데이터로 정밀 교정한 결과, 출력이 안정적이고 실제 시나리오에 구현할 수 있음이 확인되었습니다.
결과를 생성하기 위해 이 기술을 사용하는 이점은 필요한 경우 유속 또는 구조적 형상과 같은 초기 조건을 조정하는 CFD 접근 방식의 능력입니다. 수로 크기와 수로가 위치한 부지의 조건과 관련하여 상황에 적합한 특정 Parshall 수로로 선택이 좁혀집니다.
표준 Parshall 수로를 선택하는 것이 항상 가능한 것은 아닙니다. 따라서 엔지니어는 가장 가까운 수로 크기에 약간의 수정을 제공하고 정확한 유량을 생성하기 위해 새로운 등급 곡선을 제공합니다.
이 검토는 기존 등급 방정식을 향상시키거나 구조의 기하학에 대한 추가 수정을 제안하기 위해 Parshall 수로에서 수치 시뮬레이션 및 물리적 실험 데이터의 적용을 목표로 하는 여러 학자의 작업에 대해 수행되었습니다.
One of the primary steps in managing the flow in an open channel is determining its properties. Empirical equations are developed to provide further information regarding the flow in open channels. Obtaining such experimental equations is expensive and time consuming; therefore, alternative solutions have been sought. Over the last century, the Parshall flume, a static measuring device with no moving parts, has played a significant role in measuring the flow in open channels. Many researchers have focused their interest on studying the application of Parshall flumes in various fields like irrigation and wastewater management. Although various scholars used experimental results to enhance the rating equation of the Parshall flume, others used an alternative source of data to recalibrate the height–discharge relation equation using numerical simulation. Computational Fluid Dynamic (CFD) software is becoming popular nowadays as computing hardware has advanced significantly within the last few decades, making it possible to go beyond the limited resolution that was experienced in the past. Multiple CFD models, depending on their availability, either open-source or commercially licensed, have been used to perform numerical simulations on different configurations of flumes, especially Parshall flumes, to produce water level results. Regarding various CFD tools that have been used, i.e., FLOW-3D, Ansys Fluent, or OpenFOAM, after precise calibration with experimental data, it has been determined that the output is reliable and can be implemented to the actual scenarios. The benefit of using this technique to produce results is the ability of the CFD approach to adjust the initial conditions, like flow velocity or structural geometry, where necessary. With respect to channel size and the condition of the site where the flume is located, the choices are narrowed to the specific Parshall flume suitable to the situation. It is not always possible to select the standard Parshall flume; therefore, engineers provide some modification to the closest flume size and provide a new rating curve to produce accurate flowrates. This review has been performed on the works of a number of scholars who targeted the application of numerical simulation and physical experimental data in Parshall flumes to either enhance the existing rating equation or propose further modification to the structure’s geometry.
Parshall flume; CFD; OpenFOAM; FLOW-3D; numerical simulation; turbulence model
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계단식 여수로는 댐의 여수로 위로 흐르는 큰 물의 에너지를 분산시키는 비용 효율적인 유압 구조입니다. 이 연구에서는 삼각주형 요소(TPE)가 계단식 배수로의 수력 성능에 미치는 영향에 초점을 맞췄습니다. 9개의 계단식 배수로 모델이 TPE의 다양한 모양과 레이아웃으로 실험 및 수치적으로 조사되었습니다. 적절한 난류 모델을 채택하려면 RNG k – ε 및 표준 k – ε모델을 활용했습니다. 계산 모델 결과는 계단 표면의 속도 분포 및 압력 프로파일을 포함하여 실험 사례의 계단 여수로에 대한 복잡한 흐름을 만족스럽게 시뮬레이션했습니다. 결과는 계단식 여수로에 TPE를 설치하는 것이 캐비테이션 효과를 줄이는 효과적인 방법이 될 수 있음을 나타냅니다. 계단식 여수로에 TPE를 설치하면 에너지 소실률이 최대 54% 증가했습니다. 계단식 배수로의 성능은 TPE가 더 가깝게 배치되었을 때 개선되었습니다. 또한, 실험 데이터를 이용하여 거칠기 계수( f )와 임계 깊이 대 단차 거칠기( yc / k )의 비율 사이의 관계를 높은 정확도로 얻었다.
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Maryam Bagheria, Seyed M. Ali Zomorodianb, Masih Zolghadrc, H. MD. Azamathulla d,* and C. Venkata Siva Rama Prasade a Hydraulic Structures, Department of Water Engineering, Shiraz University, Shiraz, Iran b Department of Water Engineering, College of Agriculture, Shiraz University, Shiraz, Iran c Department of Water Sciences Engineering, College of Agriculture, Jahrom University, Jahrom, Iran dCivil & Environmental Engineering, The University of the West Indies, St. Augustine Campus, Port of Spain, Trinidad eDepartment of Civil Engineering, St. Peters Engineering College, Hyderabad, India *Corresponding author. E-mail: firstname.lastname@example.org
Flow separation at the upstream side of the lateral turnouts (intakes) is a critical issue causing eddy currents at the turn-out entrance. It reduces the effective width of flow, turn-out capacity and efficiency.
Therefore, it is essential to identify the dimensions of the separation zone and propose remedies to reduce its dimensions. Installation of 7 types of roughening elements at the turn-out entrance and 3 different bed level inverts, with 4 different discharges (total of 84 experiments) were examined in this study as a method to reduce the dimensions of the separation zone.
Additionally, a 3-D Computational Fluid Dynamic (CFD) model was utilized to evaluate the flow pattern and dimensions of the separation zone. Results showed that enhancing the roughness coefficient can reduce the separation zone dimensions up to 38% while the drop implementation effect can scale down this area differently based on the roughness coefficient used. Combining both methods can reduce the separation zone dimensions up to 63%.
측면 분기기(흡입구)의 상류 측에서 흐름 분리는 분기기 입구에서 와류를 일으키는 중요한 문제입니다. 이는 흐름의 유효 폭, 턴아웃 용량 및 효율성을 감소시킵니다. 따라서 분리지대의 크기를 파악하고 크기를 줄이기 위한 방안을 제시하는 것이 필수적이다.
이 연구에서는 분리 구역의 치수를 줄이기 위한 방법으로 4가지 다른 배출(총 84개 실험)과 함께 7가지 유형의 조면화 요소를 출구 입구에 설치하고 3가지 서로 다른 베드 레벨 반전 장치를 조사했습니다.
또한 3D CFD(Computational Fluid Dynamics) 모델을 사용하여 분리 영역의 흐름 패턴과 치수를 평가했습니다. 결과는 거칠기 계수를 향상시키면 분리 영역 치수를 최대 38%까지 줄일 수 있는 반면 드롭 구현 효과는 사용된 거칠기 계수를 기반으로 이 영역을 다르게 축소할 수 있음을 보여주었습니다.
두 가지 방법을 결합하면 분리 영역 치수를 최대 63%까지 줄일 수 있습니다.
discharge ratio, flow separation zone, intake, three dimensional simulation
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본 연구에서는 LW(Labyrinth Weir)와 PKW(Piano Key Weir)가 결합된 T자형 웨어(TSW)라는 새로운 비선형 웨어를 도입하여 수압 성능을 비교하였다.
PKW. 입구 키, 출구 키 또는 두 키 모두에서 수직 벽의 존재에 따라 TSW 위어는 각각 A, B 또는 C 유형 웨어로 분류되었습니다. 다른 TSW 사례의 흐름 패턴을 분석하고 배출 계수 곡선을 제공했습니다. 또한 테스트된 둑의 유체역학을 정확하게 연구하기 위해 FLOW-3D 소프트웨어를 사용하여 3D 수치 시뮬레이션을 수행했습니다.
결과는 출구 키(C-TSW 유형)의 상류에 수직 벽을 삽입하는 것이 PKW의 유압 성능에 미미한 영향을 미치는 것으로 나타났습니다. B-TSW의 토출계수는 PKW 대비 최대 16% 증가하였으며, Ht/p 0.45까지 수직벽의 성능향상 효과 증가 B-TSW는 유지되었습니다.
실험적 및 수치적 실험을 통해 가장 높은 방전 용량을 갖는 B-TSW에서 수직벽의 최적 높이비(Pd/P)는 0.4로 결정되었다.
In the present study, a new nonlinear weir called the T-shaped weir (TSW), which is a combination of the labyrinth weir (LW) and the piano key weir (PKW), was introduced, and its hydraulic performance was compared with the PKW. Based on the presence of the vertical walls at the inlet key, outlet key, or both keys, the TSW weirs were classified as type A, B, or C weirs, respectively. The flow pattern of different TSW cases was analyzed, and the discharge coefficient curves were provided. Furthermore, to accurately study the hydrodynamics of the tested weirs, 3D numerical simulations were performed using the FLOW-3D software. The results showed that inserting a vertical wall at the upstream of the outlet keys (C-TSW type) has a negligible effect on the hydraulic performance of the PKW. A maximum increase of 16% occurred in the discharge coefficient of the B-TSW in comparison to the PKW, and up to a head to height ratio (Ht/p) of 0.45, the effect of the vertical wall on increasing the performance of the B-TSW was maintained. Based on the experimental and numerical tests, the optimal height ratio of the vertical wall (Pd/P) in B-TSW with highest discharge capacity was determined to be equal to 0.4.
Bremer F. L. & Oertel M. 2017 Numerical investigation of wall thickness influence on Piano key Weir discharge coefficients: A preliminary study. In Labyrinth and Piano Key Weirs III – PKW 2017. CRC Press, London, UK, pp. 101–108.
Cicero G. M., Delisle J. R., Lefebvre V. & Vermeulen J. 2013 Experimental and Numerical Study of the Hydraulic Performance of A Trapezoidal PKW. In Labyrinths and Piano Key Weirs PKW 2013. CRC Press, Boca Raton, FL, pp. 265–272.
Lefebvre V., Vermeulen J. & Blancher B. 2013 Influence of Geometrical Parameters on PK-Weirs Discharge with 3D Numerical Analysis. In: Labyrinth and Piano key Weirs II – PKW 2013. CRC Press, London, pp. 49–56.
Lempérière F. & Ouamane A. 2003 The piano keys weir: a new cost-effective solution for spillways. International Journal on Hydropower & Dams 10 (5), 144–149.
Machiels O., Erpicum S., Archambeau P., Dewals B. J. & Pirotton M. 2011 Influence of piano key weir height on its discharge capacity. In Proc. Int. Conf. Labyrinth and Piano Key Weirs Liège B, pp. 59–66.
Pralong J., Vermeulen J., Blancher B., Laugier F., Erpicum S., Machiels O., Pirotton M., Boillat J.-L., Leite Ribeiro M. & Schleiss A. 2011a A naming convention for the Piano Key Weirs geometrical parameters. In Labyrinth and Piano key Weirs – PKW 2011. CRC Press, London, pp. 271–278.
Pralong J., Montarros F., Blancher B. & Laugier F. 2011b A sensitivity analysis of Piano Key Weirs geometrical parameters based on 3D numerical modelling. In Labyrinth and Piano key Weirs – PKW 2011. CRC Press, London, pp. 133–139.
Ribeiro M. L., Bieri M., Boillat J. L., Schleiss A., Delorme F. & Laugier F. 2009 Hydraulic capacity improvement of existing spillways–design of a piano key weir. In Proceedings (on CD) of the 23rd Congress of the Int. Commission on Large Dams CIGB-ICOLD, Brasilia, Vol. 2, No. CONF, pp. 100–118.
1 Department of Civil Engineering, Faculty of Engineering, University of Maragheh, Iran
2 Water Engineering Department, University of Tabriz, Tabriz, Iran
3 M.Sc. Student, Department of Civil Engineering, Faculty of Engineering, University of Maragheh, Maragheh, Iran
The importance of water control and distribution in irrigation and behind dams requires the use of practical and modern methods. The presence of sill under sluice gate is one of the solutions to control the flow rate. Therefore, this study was conducted to numerically investigate the discharge coefficient (Cd) of sluice gate with different heights and widths of sills in free flow conditions. The simulations were performed using FLOW-3D software and finite volume method. The results of numerical study showed that the gate opening has a good effect on the Cd with sill and non-sill condition. In both cases, the gate opening is inversely related to the Cd. This means that the Cd increases as the gate opening decreases. Results showed that reducing the gate opening from 5 cm to 2 cm increases the Cd in the gate with sill by 9% compared to the non-sill gate. The results also indicate that the height of the sill is one of the parameters affecting the Cd. The minimum and maximum discharge coefficients in gate with sill compared to the non-sill condition were estimated at 1.5% and 18%, respectively. Examination of sill width changes showed that decreasing the width reduces the discharge coefficient by reducing the amount of velocity and flow pressure along the sill sides. The effect of three parameters of gate opening, sill height and sill width were compared. The results showed that increasing the sill width compared to the two mentioned parameters has the maximum increase in the Cd
관개 및 댐 뒤에서 물 관리 및 분배의 중요성은 실용적이고 현대적인 방법의 사용을 요구합니다. 수문 아래 문턱의 존재는 유량을 제어하는 솔루션 중 하나입니다.
따라서 본 연구는 자유유동 조건에서 문턱의 높이와 너비가 다른 수문의 토출계수(Cd)를 수치적으로 조사하기 위해 수행되었습니다. 시뮬레이션은 FLOW-3D 소프트웨어와 유한 체적 방법을 사용하여 수행되었습니다.
수치 연구의 결과는 게이트 개방이 sill 및 non-sill 조건에서 Cd에 좋은 영향을 미치는 것으로 나타났습니다. 두 경우 모두 게이트 개방은 Cd와 반비례합니다. 이것은 게이트 개방이 감소함에 따라 Cd가 증가한다는 것을 의미합니다.
결과에 따르면 게이트 개구부를 5cm에서 2cm로 줄이면 비문이 있는 게이트에 비해 씰이 있는 게이트의 Cd가 9% 증가합니다. 결과는 또한 문턱의 높이가 Cd에 영향을 미치는 매개변수 중 하나임을 나타냅니다.
문턱이 없는 문에 비해 문턱이 있는 문에서 최소 및 최대 배출 계수는 각각 1.5% 및 18%로 추정되었습니다. 문턱 너비 변화를 조사하면 너비를 줄이면 문턱 측면을 따라 유속과 흐름 압력의 양이 감소하여 배출 계수가 감소하는 것으로 나타났습니다.
게이트 개방, 문턱 높이 및 문턱 너비의 세 가지 매개변수의 효과를 비교했습니다. 결과는 언급된 두 매개변수에 비해 씰 너비를 늘리면 Cd가 최대로 증가한다는 것을 보여주었습니다.
결과는 또한 문턱의 높이가 Cd에 영향을 미치는 매개변수 중 하나임을 나타냅니다. 문턱이 없는 문에 비해 문턱이 있는 문에서 최소 및 최대 배출 계수는 각각 1.5% 및 18%로 추정되었습니다. 문턱 너비 변화를 조사하면 너비를 줄이면 문턱 측면을 따라 유속과 흐름 압력의 양이 감소하여 배출 계수가 감소하는 것으로 나타났습니다.
게이트 개방, 문턱 높이 및 문턱 너비의 세 가지 매개변수의 효과를 비교했습니다. 결과는 언급된 두 매개변수와 비교하여 문턱 너비를 늘리면 Cd가 최대로 증가한다는 것을 보여주었습니다.
결과는 또한 문턱의 높이가 Cd에 영향을 미치는 매개변수 중 하나임을 나타냅니다. 문턱이 없는 문에 비해 문턱이 있는 문에서 최소 및 최대 배출 계수는 각각 1.5% 및 18%로 추정되었습니다.
문턱 너비 변화를 조사하면 너비를 줄이면 문턱 측면을 따라 유속과 흐름 압력의 양이 감소하여 배출 계수가 감소하는 것으로 나타났습니다. 게이트 개방, 문턱 높이 및 문턱 너비의 세 가지 매개변수의 효과를 비교했습니다. 결과는 언급된 두 매개변수에 비해 씰 너비를 늘리면 Cd가 최대로 증가한다는 것을 보여주었습니다. 문턱 너비 변화를 조사하면 너비를 줄이면 문턱 측면을 따라 유속과 흐름 압력의 양이 감소하여 배출 계수가 감소하는 것으로 나타났습니다.
게이트 개방, 문턱 높이 및 문턱 너비의 세 가지 매개변수의 효과를 비교했습니다. 결과는 언급된 두 매개변수에 비해 씰 너비를 늘리면 Cd가 최대로 증가한다는 것을 보여주었습니다. 문턱 너비 변화를 조사하면 너비를 줄이면 문턱 측면을 따라 유속과 흐름 압력의 양이 감소하여 배출 계수가 감소하는 것으로 나타났습니다.
게이트 개방, 문턱 높이 및 문턱 너비의 세 가지 매개변수의 효과를 비교했습니다. 결과는 언급된 두 매개변수와 비교하여 문턱 너비를 늘리면 Cd가 최대로 증가한다는 것을 보여주었습니다.
많은 계단식 배수로 지오메트리 설계 지침이 평평한 단계를 위해 개발되었지만 통합 단계를 설계하는 것이 더 효율적으로 작동하는 배수로에 대한 적절한 대안이 될 수 있습니다.
이 논문은 POOL의 다른 높이에서 공기 연행과 보이드 비율의 시작점을 다루는 것을 목표로 합니다. 그 후, FLOW-3D 소프트웨어를 사용하여 POOL과 경사면의 높이를 다르게 하여 폭기된 지역과 폭기되지 않은 지역에서 압력 분포를 평가했습니다.
얻어진 수치 결과와 실험 결과의 비교는 본 연구에 사용된 모든 방류에 대해 잘 일치했습니다. POOL 높이는 시작 지점 위치에 미미한 영향을 미쳤습니다. 공극률의 값은 높은 방류에 비해 낮은 방전에서 더 많은 영향을 받았습니다.
여수로의 마루(통기되지 않은 지역)에서는 음압이 나타나지 않았으며 각 방류에서 마루를 따라 높이가 15cm인 수영장에서 최대 압력 값이 얻어졌습니다.
모든 사면에서 웅덩이 및 평평한 계단형 여수로의 계단층 부근에서는 음압이 형성되지 않았습니다. 그러나 평단식 여수로에 비해 평단식 여수로의 수직면 부근에서 음압이 더 많이 형성되어 평단식 슈트에서 캐비테이션 현상이 발생할 확률이 증가하였습니다.
Study of inception point, void fraction and pressure over pooled stWhile many stepped spillways geometry design guidelines were developed for flat steps, designing pooled steps might be an appropriate alternative to spillways working more efficiency. This paper aims to deal with the inception point of air-entrainment and void fraction in the different height of the pools. Following that, pressure distribution was evaluated in aerated and non-aerated regions under the effect of different heights of the pools and slopes through the use of the FLOW-3D software. Comparison of obtained numerical results with experimental ones was in good agreement for all discharges used in this study. Pools height had the insignificant effect on the inception point location. The value of void fraction was more affected in lower discharges in comparison with higher ones. Negative pressure was not seen over the crest of spillway (non-aerated region), and the maximum pressure values were obtained for pools with 15 cm height along the crest in each discharge. In all slopes, negative pressure was not formed near the step bed in the pooled and flat stepped spillways. However, negative pressure was formed in more area near the vertical face in the flat stepped spillway compared with the pooled stepped spillway which increases the probability of cavitation phenomenon in the flat stepped chute.
압력, 공극률 및 시작점을 평가하기 위해 POOL된 계단식 여수로가 사용되었습니다. 또한 POOL의 다른 높이가 사용되었습니다. 이 연구의 수치 시뮬레이션은 Flow-3D 소프트웨어를 통해 수행되었습니다. 얻어진 결과는 풀이 압력, 공극률 및 시작점을 포함한 2상 유동 특성에 영향을 미칠 수 있음을 나타냅니다.
마루 위에는 음압이 보이지 않았습니다. 압력 값은 사용된 모든 높이와 15cm 높이에서 얻은 최대 값에 대해 다릅니다. 또한, 풀링 스텝은 플랫 케이스에 비해 음압점 감소에 더 효과적인 역할을 하였습니다. 시작 지점 위치는 특히 9 및 15cm 높이에 대해 스키밍 흐름 영역과 비교하여 낮잠 및 전환 흐름 영역에서 더 많은 영향을 받았습니다.
본 연구에서는 자유표면을 모사하기 위해 VOF 방법과 k -ε (RNG) 난류 모델을 활용하여 FLOW-3D 소프트웨어를 사용하였고, 계단식 배수로의 유동을 모사하기 위한 목적으로 난류 특성을 모사하였다. 얻은 결과는 수치 모델이 시작점 위치, 보이드 비율 및 압력을 적절하게 시뮬레이션했음을 나타냅니다. 풀의 높이는 공기 유입 위치에 미미한 영향을 미치므로 얻은 결과는 이 문서에서 제시된 상관 관계와 잘 일치했습니다. 즉, 사용 가능한 상관 관계를 서로 다른 풀 높이에 사용할 수 있습니다. 공극률의 결과는 스텝 풀 근처의 나프 유동 영역에서 공극율 값이 다른 배출보다 더 큰 것으로 나타났다. 더욱이 고방출량 .0 113m3/s에서 수영장 높이를 변경해도 수영장 표면 근처의 공극률 값에는 영향을 미치지 않았습니다.
낮잠 및 전환 체제의 압력 분포에 대한 0 및 3cm 높이의 수영장 효과는 많은 지점에서 대부분 유사했습니다. 더욱이 조사된 모든 높이에서 여수로의 마루를 따라 부압이 없었습니다. 여수로 끝단의 바닥 부근의 압력 결과는 평평하고 고인 경우 부압이 발생하지 않았음을 나타냅니다. 수직면 부근의 음압은 웅덩이에 비해 평평한 계단형 여수로의 깊이(w=0 cm)의 대부분에서 발생하였다. 또한 더 큰 사면에 대한 풀링 케이스에서 음압이 제거되었습니다. 평단식 여수로에서는 계단의 수직면에 인접한 더 넓은 지역에서 음압이 발생하였기 때문에 이 여수로에서는 고형단식여수로보다 캐비테이션 현상이 발생할 가능성이 더 큽니다.
In this study, the FLOW-3D software was used through utilizing the VOF method and k −ε (RNG) turbulence model in order to simulate free surface, and turbulence characteristics for the purpose of simulating flow over pooled stepped spillway. The results obtained indicated that the numerical model properly simulated the inception point location, void fraction, and pressure. The height of the pools has the insignificant effect on the location of air entrainment, so that obtained results were in good agreement with the correlations presented in this paper. In other words, available correlations can be used for different pool heights. The results of void fraction showed that the void fraction values in nappe flow regime near the step pool were more than the other discharges. Furthermore in high discharge, 0.113m3/s, altering pool height had no effect on the value of void fraction near the pool surface.
The effect of the pools with 0 and 3 cm heights over the pressure distribution in nappe and transition regimes was mostly similar in many points. Furthermore, in all examined heights there was no negative pressure along the crest of the spillway. The pressure results near the bed of the step at the end of the spillway indicated that negative pressure did not occur in the flat and pooled cases. Negative pressure near the vertical face occurred in the most part of the depth in the flat stepped spillway (w=0 cm) in comparison with the pooled case. Also, the negative pressure was eliminated in the pooled case for the larger slopes. Since negative pressure occurred in a larger area adjacent the vertical face of the steps in the flat stepped spillways, it is more likely that cavitation phenomenon occurs in this spillway rather than the pooled stepped spillways.
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1 Civil Engineering,Enginnering Faculty,,Univeristy of Qom.Qom.Iran 2 Civil Engineering Department,Engineering Faculty,Islamic Azad University of Lahijan,Iran
교각이 물의 흐름 앞에 위치하면 소용돌이가 형성되고 그 활동으로 교각 주변의 하상 재료가 침식되고 세굴 구멍이 생성됩니다. 기초 깊이와 교각 말뚝이 충분하지 않으면 교량은 실패합니다.
말뚝 캡의 다른 레벨링에서 유동층의 총 전단 응력 연구는 말뚝 캡 위치가 동일할 때 가장 높은 전단 응력이 생성됨을 보여줍니다. 강바닥과 같은 수준; 강바닥보다 낮은 위치에 파일 캡을 설치하여 최대 전단 응력을 감소시킵니다.
이 경우에 해당하기 때문일 수 있습니다. 교각 그룹 사이의 거리가 증가하고 두 번째 교각의 존재는 교각 그룹의 유량을 감소시키고 한 교각 그룹의 다른 교각은 흐름 패턴 형성에서 두 개의 독립적인 교각으로 작용합니다.
파일 캡의 다른 레벨링에서 세굴의 최종 길이 방향 단면을 비교함으로써 세굴 깊이의 가장 큰 감소는 에어로포일 모양의 파일 캡에서 발생하며 더 날카로운 노즈와 더 나은 공기 역학적 모양을 가진 파일 캡이 제어하기에 좋은 옵션이라는 결론을 내렸습니다. 말굽 와류를 제거하고 경사 교각 그룹 주변의 세굴 깊이를 줄입니다.
When the bridge piers are located in front of the water flow, vortices are formed against it and due to their activity, the materials of the river bed are eroded around the bridge piers and the scouring hole is created. If the foundation depth and bridge pier piles are insufficient, the bridge will fail.The study of total shear stress in the flow bed at different leveling of the pile caps shows that the highest shear stress is created when the pile cap position is at the same level as the river bed; by installing the pile cap at a lower level than the river bed, the maximum shear stress decreases. This may be due to the fact that in this case, the distance between the pier group increases and the presence of the second pier decreases the flow rate in the pier group and different pier in the one pier group acts as the two independent piers in the formation of the flow pattern. By comparing the final longitudinal sections of the scouring at different leveling of the pile cap, it is concluded that the largest reduction in scouring depth occurs in aerofoil-shaped pile caps and pile caps with the sharper nose and better aerodynamic shapes are good options to control the horseshoe vortices and will reduce the scouring depth around the inclined pier group.
Study on the effect of morphological changes of bridge piers on water movement properties
Xianqi Zhanga,b,c, Tao Wanga,* and Bingsen Duana a Water Conservancy College, North china University of Water Resources and Electric Power, Zhengzhou 450046, China b Collaborative Innovation Center of Water Resources Efficient Utilization and Protection Engineering, Zhengzhou 450046, China c Technology Research Center of Water Conservancy and Marine Tra
하천을 가로지르는 교각의 다른 형태는 하천의 유동에 큰 영향을 미치며, 교각의 형태 변화가 물의 유동 특성에 미치는 영향에 대한 연구는 교량 설계 및 하천 범람에 큰 가치가 있습니다.
유체 역학 모델은 하천 흐름 패턴의 변화를 효과적으로 시뮬레이션하고 예측할 수 있으므로 하천 관리에 대한 과학적 데이터 지원을 제공할 수 있습니다.
본 논문은 Mike21을 기반으로 유체역학 모델을 구축하고 이를 황하 하류의 하천 유체역학 수치해석에 적용하고, 타원 교각을 예로 들어 교각 형태 변화가 유속에 미치는 영향을 모사한다. 강의 수위와 흐름장. 결과는 하천의 흐름 특성에 대한 타원형 교각 형태의 영향이 중요하다는 것을 보여줍니다.
동일한 유량에서 최대 축 비율에서 교각의 혼잡 값은 최소 축 비율의 1.65배이며 축 비율이 클수록 혼잡이 심각합니다. 최대 축 비율에서 유속의 차이는 최소 축 비율의 2.33배에 달할 수 있습니다.
The different shapes of bridge piers across rivers have a great influence on the river water movement, and the study of the influence of pier morphology changes on the water movement characteristics is of great value for bridge design and river flooding. The hydrodynamic model can effectively simulate and predict the changes of river flow patterns, which can provide scientific data support for river management. This paper constructs a hydrodynamic model based on Mike21 and applies it to the numerical simulation of river hydrodynamics in the lower reaches of the Yellow River, taking elliptical piers as an example, and simulates the effect of the change of pier morphology on the flow velocity, water level and flow field of the river. The results show that the effect of elliptical pier morphology on the flow characteristics of the river channel is significant; under the same flow rate, the congestion value of the pier at the maximum axis ratio is 1.65 times of the minimum axis ratio, and the larger the axis ratio, the more serious the congestion; the difference in flow velocity at the maximum axis ratio can reach 2.33 times of the minimum axis ratio.
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A comparative performance analysis of the CFD platforms OpenFOAM and FLOW-3D is presented, focusing on a 3D swirling turbulent flow: a steady hydraulic jump at low Reynolds number. Turbulence is treated using RANS approach RNG k-ε. A Volume Of Fluid (VOF) method is used to track the air–water interface, consequently aeration is modeled using an Eulerian–Eulerian approach. Structured meshes of cubic elements are used to discretize the channel geometry. The numerical model accuracy is assessed comparing representative hydraulic jump variables (sequent depth ratio, roller length, mean velocity profiles, velocity decay or free surface profile) to experimental data. The model results are also compared to previous studies to broaden the result validation. Both codes reproduced the phenomenon under study concurring with experimental data, although special care must be taken when swirling flows occur. Both models can be used to reproduce the hydraulic performance of energy dissipation structures at low Reynolds numbers.
CFD 플랫폼 OpenFOAM 및 FLOW-3D의 비교 성능 분석이 3D 소용돌이치는 난류인 낮은 레이놀즈 수에서 안정적인 유압 점프에 초점을 맞춰 제시됩니다. 난류는 RANS 접근법 RNG k-ε을 사용하여 처리됩니다.
VOF(Volume Of Fluid) 방법은 공기-물 계면을 추적하는 데 사용되며 결과적으로 Eulerian-Eulerian 접근 방식을 사용하여 폭기가 모델링됩니다. 입방체 요소의 구조화된 메쉬는 채널 형상을 이산화하는 데 사용됩니다. 수치 모델 정확도는 대표적인 유압 점프 변수(연속 깊이 비율, 롤러 길이, 평균 속도 프로파일, 속도 감쇠 또는 자유 표면 프로파일)를 실험 데이터와 비교하여 평가됩니다.
모델 결과는 또한 결과 검증을 확장하기 위해 이전 연구와 비교됩니다. 소용돌이 흐름이 발생할 때 특별한 주의가 필요하지만 두 코드 모두 실험 데이터와 일치하는 연구 중인 현상을 재현했습니다. 두 모델 모두 낮은 레이놀즈 수에서 에너지 소산 구조의 수리 성능을 재현하는 데 사용할 수 있습니다.
CFDRANS, OpenFOAM, FLOW-3D ,Hydraulic jump, Air–water flow, Low Reynolds number
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Triangular Macroroughnesses 대한 잠긴 수압 점프의 유동장 수치 시뮬레이션
by Amir Ghaderi 1,2,Mehdi Dasineh 3,Francesco Aristodemo 2 andCostanza Aricò 4,*1Department of Civil Engineering, Faculty of Engineering, University of Zanjan, Zanjan 537138791, Iran2Department of Civil Engineering, University of Calabria, Arcavacata, 87036 Rende, Italy3Department of Civil Engineering, Faculty of Engineering, University of Maragheh, Maragheh 8311155181, Iran4Department of Engineering, University of Palermo, Viale delle Scienze, 90128 Palermo, Italy*Author to whom correspondence should be addressed.Academic Editor: Anis YounesWater2021, 13(5), 674; https://doi.org/10.3390/w13050674
The submerged hydraulic jump is a sudden change from the supercritical to subcritical flow, specified by strong turbulence, air entrainment and energy loss. Despite recent studies, hydraulic jump characteristics in smooth and rough beds, the turbulence, the mean velocity and the flow patterns in the cavity region of a submerged hydraulic jump in the rough beds, especially in the case of triangular macroroughnesses, are not completely understood. The objective of this paper was to numerically investigate via the FLOW-3D model the effects of triangular macroroughnesses on the characteristics of submerged jump, including the longitudinal profile of streamlines, flow patterns in the cavity region, horizontal velocity profiles, streamwise velocity distribution, thickness of the inner layer, bed shear stress coefficient, Turbulent Kinetic Energy (TKE) and energy loss, in different macroroughness arrangements and various inlet Froude numbers (1.7 < Fr1 < 9.3). To verify the accuracy and reliability of the present numerical simulations, literature experimental data were considered.
수중 유압 점프는 강한 난류, 공기 동반 및 에너지 손실로 지정된 초임계에서 아임계 흐름으로의 급격한 변화입니다. 최근 연구에도 불구하고, 특히 삼각형 거시적 거칠기의 경우, 평활 및 거친 베드에서의 수압 점프 특성, 거친 베드에서 잠긴 수압 점프의 공동 영역에서 난류, 평균 속도 및 유동 패턴이 완전히 이해되지 않았습니다.
이 논문의 목적은 유선의 종방향 프로파일, 캐비티 영역의 유동 패턴, 수평 속도 프로파일, 스트림 방향 속도 분포, 두께를 포함하여 서브머지드 점프의 특성에 대한 삼각형 거시 거칠기의 영향을 FLOW-3D 모델을 통해 수치적으로 조사하는 것이었습니다.
내부 층의 층 전단 응력 계수, 난류 운동 에너지(TKE) 및 에너지 손실, 다양한 거시 거칠기 배열 및 다양한 입구 Froude 수(1.7 < Fr1 < 9.3). 현재 수치 시뮬레이션의 정확성과 신뢰성을 검증하기 위해 문헌 실험 데이터를 고려했습니다.
격렬한 난류 혼합과 기포 동반이 있는 수압 점프는 초임계에서 아임계 흐름으로의 변화 과정으로 간주됩니다. 자유 및 수중 유압 점프는 일반적으로 게이트, 배수로 및 둑과 같은 수력 구조 아래의 에너지 손실에 적합합니다. 매끄러운 베드에서 유압 점프의 특성은 널리 연구되었습니다[2,3,4,5,6,7,8,9].
베드의 거칠기 요소가 매끄러운 베드와 비교하여 수압 점프의 특성에 어떻게 영향을 미치는지 예측하기 위해 거시적 거칠기에 대한 자유 및 수중 수력 점프에 대해 여러 실험 및 수치 연구가 수행되었습니다. Ead와 Rajaratnam은 사인파 거대 거칠기에 대한 수리학적 점프의 특성을 조사하고 무차원 분석을 통해 수면 프로파일과 배출을 정규화했습니다.
Tokyayet al. 은 두 사인 곡선 거대 거칠기에 대한 점프 길이 비율과 에너지 손실이 매끄러운 베드보다 각각 35% 더 작고 6% 더 높다는 것을 관찰했습니다. Abbaspur et al. 는 6개의 사인파형 거대 거칠기에 대한 수력학적 점프의 특성을 연구했습니다. 그 결과, 꼬리수심과 점프길이는 평상보다 낮았고 Froude 수는 점프길이에 큰 영향을 미쳤습니다.
Shafai-Bejestan과 Neisi는 수압 점프에 대한 마름모꼴 거대 거칠기의 영향을 조사했습니다. 결과는 마름모꼴 거시 거칠기를 사용하면 매끄러운 침대와 비교하여 꼬리 수심과 점프 길이를 감소시키는 것으로 나타났습니다. Izadjoo와 Shafai-Bejestan은 다양한 사다리꼴 거시 거칠기에 대한 수압 점프를 연구했습니다.
그들은 전단응력계수가 평활층보다 10배 이상 크고 점프길이가 50% 감소하는 것을 관찰하였습니다. Nikmehr과 Aminpour는 Flow-3D 모델 버전 11.2를 사용하여 사다리꼴 블록이 있는 거시적 거칠기에 대한 수력학적 점프의 특성을 조사했습니다. 결과는 거시 거칠기의 높이와 거리가 증가할수록 전단 응력 계수뿐만 아니라 베드 근처에서 속도가 감소하는 것으로 나타났습니다.
Ghaderi et al. 은 다양한 형태의 거시 거칠기(삼각형, 정사각형 및 반 타원형)에 대한 자유 및 수중 수력 점프 특성을 연구했습니다. 결과는 Froude 수의 증가에 따라 자유 및 수중 점프에서 전단 응력 계수, 에너지 손실, 수중 깊이, 미수 깊이 및 상대 점프 길이가 증가함을 나타냅니다.
자유 및 수중 점프에서 가장 높은 전단 응력과 에너지 손실은 삼각형의 거시 거칠기가 존재할 때 발생했습니다. Elsebaie와 Shabayek은 5가지 형태의 거시적 거칠기(삼각형, 사다리꼴, 2개의 측면 경사 및 직사각형이 있는 정현파)에 대한 수력학적 점프의 특성을 연구했습니다. 결과는 모든 거시적 거칠기에 대한 에너지 손실이 매끄러운 베드에서보다 15배 이상이라는 것을 보여주었습니다.
Samadi-Boroujeni et al. 는 다양한 각도의 6개의 삼각형 거시 거칠기에 대한 수력 점프를 조사한 결과 삼각형 거시 거칠기가 평활 베드에 비해 점프 길이를 줄이고 에너지 손실과 베드 전단 응력 계수를 증가시키는 것으로 나타났습니다.
Ahmed et al. 은 매끄러운 베드와 삼각형 거시 거칠기에서 수중 수력 점프 특성을 조사했습니다. 결과는 부드러운 침대와 비교할 때 잠긴 깊이와 점프 길이가 감소했다고 밝혔습니다. 표 1은 다른 연구자들이 제시한 과거의 유압 점프에 대한 실험 및 수치 연구의 세부 사항을 나열합니다.
Table 1. Main characteristics of some past experimental and numerical studies on hydraulic jumps.
-Smooth and rough beds-Rectangular channel-Free and submerged jump
CL = 4.50 CW = 0.75 CH = 0.70
-Triangular, square and semi-oval macroroughnesses (RH = 40 and distance of roughness of I = 40, 80, 120, 160 and 200)
-Horizontal velocity distributions-Bed shear stress coefficient-Sequent depth ratio and submerged depth ratio-Jump length-Energy loss
Rectangular channel Smooth and rough beds Submerged jump
CL = 4.50 CW = 0.75 CH = 0.70
-Triangular macroroughnesses (RH = 40 and distance of roughness of I = 40, 80, 120, 160 and 200)
-Longitudinal profile of streamlines-Flow patterns in the cavity region-Horizontal velocity profiles-Streamwise velocity distribution-Bed shear stress coefficient-TKE-Thickness of the inner layer-Energy loss
이전에 논의된 조사의 주요 부분은 실험실 접근 방식을 기반으로 하며 사인파, 마름모꼴, 사다리꼴, 정사각형, 직사각형 및 삼각형 매크로 거칠기가 공액 깊이, 잠긴 깊이, 점프 길이, 에너지 손실과 같은 일부 자유 및 수중 유압 점프 특성에 어떻게 영향을 미치는지 조사합니다.
베드 및 전단 응력 계수. 더욱이, 저자에 의해 다양한 형태의 거시적 거칠기에 대한 수력학적 점프에 대한 이전 발표된 논문을 참조하면, 삼각형의 거대조도는 가장 높은 층 전단 응력 계수 및 에너지 손실을 가지며 또한 가장 낮은 잠긴 깊이, tailwater를 갖는 것으로 관찰되었습니다.
다른 거친 모양, 즉 정사각형 및 반 타원형과 부드러운 침대에 비해 깊이와 점프 길이. 따라서 본 논문에서는 삼각형 매크로 거칠기를 사용하여(일정한 거칠기 높이가 T = 4cm이고 삼각형 거칠기의 거리가 I = 4, 8, 12, 16 및 20cm인 다른 T/I 비율에 대해), 특정 캐비티 영역의 유동 패턴, 난류 운동 에너지(TKE) 및 흐름 방향 속도 분포와 같은 연구가 필요합니다.
CFD(Computational Fluid Dynamics) 방법은 자유 및 수중 유압 점프와 같은 복잡한 흐름의 모델링 프로세스를 수행하는 중요한 도구로 등장하며 수중 유압 점프의 특성은 CFD 시뮬레이션을 사용하여 정확하게 예측할 수 있습니다 [22,23 ].
본 논문은 초기에 수중 유압 점프의 주요 특성, 수치 모델에 대한 입력 매개변수 및 Ahmed et al.의 참조 실험 조사를 제시합니다. , 검증 목적으로 보고되었습니다. 또한, 본 연구에서는 유선의 종방향 프로파일, 캐비티 영역의 유동 패턴, 수평 속도 프로파일, 내부 층의 두께, 베드 전단 응력 계수, TKE 및 에너지 손실과 같은 특성을 조사할 것입니다.
Table 2. Effective parameters in the numerical model.
4, 8, 12, 16, 20
Table 3. Main flow variables for the numerical and physical models (Ahmed et al. ).
Numerical and Physical
T/I = 0.5
T/I = 0.25
Table 4. Characteristics of the computational grids.
Nested Block Cell Size (cm)
Containing Block Cell Size (cm)
Table 5. The numerical results of mesh convergence analysis.
본 논문에서는 유선의 종방향 프로파일, 공동 영역의 유동 패턴, 수평 속도 프로파일, 스트림 방향 속도 분포, 내부 층의 두께, 베드 전단 응력 계수, 난류 운동 에너지(TKE)를 포함하는 수중 유압 점프의 특성을 제시하고 논의했습니다. ) 및 삼각형 거시적 거칠기에 대한 에너지 손실. 이러한 특성은 FLOW-3D® 모델을 사용하여 수치적으로 조사되었습니다. 자유 표면을 시뮬레이션하기 위한 VOF(Volume of Fluid) 방법과 난류 RNG k-ε 모델이 구현됩니다. 본 모델을 검증하기 위해 평활층과 삼각형 거시 거칠기에 대해 수치 시뮬레이션과 실험 결과를 비교했습니다. 본 연구의 다음과 같은 결과를 도출할 수 있다.
개발 및 개발 지역의 삼각형 거시 거칠기의 흐름 패턴은 수중 유압 점프 조건의 매끄러운 바닥과 비교하여 더 작은 영역에서 동일합니다. 삼각형의 거대 거칠기는 거대 거칠기 사이의 공동 영역에서 또 다른 시계 방향 와류의 형성으로 이어집니다.
T/I = 1, 0.5 및 0.33과 같은 거리에 대해 속도 벡터 분포는 캐비티 영역에서 시계 방향 소용돌이를 표시하며, 여기서 속도의 크기는 평균 유속보다 훨씬 작습니다. 삼각형 거대 거칠기(T/I = 0.25 및 0.2) 사이의 거리를 늘리면 캐비티 영역에 크기가 다른 두 개의 소용돌이가 형성됩니다.
삼각형 거시조도 사이의 거리가 충분히 길면 흐름이 다음 조도에 도달할 때까지 속도 분포가 회복됩니다. 그러나 짧은 거리에서 흐름은 속도 분포의 적절한 회복 없이 다음 거칠기에 도달합니다. 따라서 거시 거칠기 사이의 거리가 감소함에 따라 마찰 계수의 증가율이 감소합니다.
삼각형의 거시적 거칠기에서, 잠수 점프의 지정된 섹션에서 최대 속도는 자유 점프보다 높은 값으로 이어집니다. 또한, 수중 점프에서 두 가지 유형의 베드(부드러움 및 거친 베드)에 대해 깊이 및 와류 증가로 인해 베드로부터의 최대 속도 거리는 감소합니다. 잠수 점프에서 경계층 두께는 자유 점프보다 얇습니다.
매끄러운 베드의 난류 영역은 게이트로부터의 거리에 따라 생성되고 자유 표면 롤러 영역 근처에서 발생하는 반면, 거시적 거칠기에서는 난류가 게이트 근처에서 시작되어 더 큰 강도와 제한된 스위프 영역으로 시작됩니다. 이는 반시계 방향 순환의 결과입니다. 거시 거칠기 사이의 공간에서 자유 표면 롤러 및 시계 방향 와류.
삼각 거시 거칠기에서 침지 점프의 베드 전단 응력 계수와 에너지 손실은 유입구 Froude 수의 증가에 따라 증가하는 매끄러운 베드에서 발견된 것보다 더 큽니다. T/I = 0.50 및 0.20에서 최고 및 최저 베드 전단 응력 계수 및 에너지 손실이 평활 베드에 비해 거칠기 요소의 거리가 증가함에 따라 발생합니다.
거의 거칠기 요소가 있는 삼각형 매크로 거칠기의 존재에 의해 주어지는 점프 길이와 잠긴 수심 및 꼬리 수심의 감소는 결과적으로 크기, 즉 길이 및 높이가 감소하는 정수조 설계에 사용될 수 있습니다.
일반적으로 CFD 모델은 다양한 수력 조건 및 기하학적 배열을 고려하여 잠수 점프의 특성 예측을 시뮬레이션할 수 있습니다. 캐비티 영역의 흐름 패턴, 흐름 방향 및 수평 속도 분포, 베드 전단 응력 계수, TKE 및 유압 점프의 에너지 손실은 수치적 방법으로 시뮬레이션할 수 있습니다. 그러나 거시적 차원과 유동장 및 공동 유동의 변화에 대한 다양한 배열에 대한 연구는 향후 과제로 남아 있다.
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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.
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.
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이 연구에서는 비드 운동과 유체 흐름에 미치는 영향에 대한 자세한 분석을 제공하기 위해 연속 흐름 마이크로 채널 내부의 비드 자기 영동에 대한 수치 흐름 중심 연구를 보고합니다.
수치 모델은 Lagrangian 접근 방식을 포함하며 영구 자석에 의해 생성 된 자기장의 적용에 의해 혈액에서 비드 분리 및 유동 버퍼로의 수집을 예측합니다.
다음 시나리오가 모델링됩니다. (i) 운동량이 유체에서 점 입자로 처리되는 비드로 전달되는 단방향 커플 링, (ii) 비드가 점 입자로 처리되고 운동량이 다음으로부터 전달되는 양방향 결합 비드를 유체로 또는 그 반대로, (iii) 유체 변위에서 비드 체적의 영향을 고려한 양방향 커플 링.
결과는 세 가지 시나리오에서 비드 궤적에 약간의 차이가 있지만 특히 높은 자기력이 비드에 적용될 때 유동장에 상당한 변화가 있음을 나타냅니다.
따라서 높은 자기력을 사용할 때 비드 운동과 유동장의 체적 효과를 고려한 정확한 전체 유동 중심 모델을 해결해야 합니다. 그럼에도 불구하고 비드가 중간 또는 낮은 자기력을 받을 때 계산적으로 저렴한 모델을 안전하게 사용하여 자기 영동을 모델링 할 수 있습니다.
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Department of Chemical and Biomolecular Engineering, ETSIIT, University of Cantabria, Avda. Los Castros s/n, 39005, Santander, SpainJenifer Gómez-Pastora, Eugenio Bringas & Inmaculada Ortiz
Flow Science, Inc, Santa Fe, New Mexico, 87505, USAIoannis H. Karampelas
Department of Chemical and Biological Engineering, University at Buffalo (SUNY), Buffalo, New York, 14260, USAEdward P. Furlani
Department of Electrical Engineering, University at Buffalo (SUNY), Buffalo, New York, 14260, USAEdward P. Furlani
This paper demonstrates that the Volume of Fluid (TruVOF) method in FLOW-3D (a general purpose CFD software) is an effective tool for studying droplet dynamics and mixing in microfluidic devices. The first example studied is a T-junction where flow patterns for both droplet generation and passive mixing are analyzed. The second example studied is a co-flowing device where the formation and breakup of bubbles is simulated. The effect of viscosity on bubble formation is also analyzed. For a T-junction the bubble size is corroborated with experimental data. Both the bubble size and frequency are studied and corroborated with experimental data for a co-flowing device. The third example studied is the electrowetting phenomenon observed in a small water droplet resting on a dielectric material. The steady-state contact angle is plotted against the voltage applied. The results are compared with both the Young-Lippmann curve and experimental results.
이 논문은 FLOW-3D (범용 CFD 소프트웨어)의 유체 부피 (TruVOF) 방법이 미세 유체 장치에서 액적 역학 및 혼합을 연구하는데 효과적인 도구임을 보여줍니다.
연구된 첫 번째 예는 액적 생성 및 수동 혼합에 대한 흐름 패턴이 분석되는 T- 접합입니다. 연구된 두 번째 예는 기포의 형성 및 분해가 시뮬레이션 되는 동시 유동 장치입니다.
기포 형성에 대한 점도의 영향도 분석됩니다. T 접합의 경우 기포 크기는 실험 데이터로 확증됩니다. 기포 크기와 빈도 모두 공동 유동 장치에 대한 실험 데이터로 연구되고 확증됩니다.
연구된 세 번째 예는 유전 물질 위에 놓인 작은 물방울에서 관찰 된 전기 습윤 현상입니다. 정상 상태 접촉각은 적용된 전압에 대해 플롯됩니다. 결과는 Young-Lippmann 곡선 및 실험 결과와 비교됩니다.
Junichi Saeki and Tsutomu Kono Production Engineering Research Laboratory, Hitachi Ltd. 292, Y shida-cho, Totsuka-ku, Yokohama, 244-0817 Japan
Thermosetting molding compounds are widely used for encapsulating semiconductor devices and electronic modules. In recent years, the number of electronic parts encapsulated in an electronic module has increased, in order to meet the requirements for high performance. As a result, the configuration of inserted parts during molding has become very complicated. Meanwhile, package thickness has been reduced in response to consumer demands for miniaturization. These trends have led to complicated flow patterns of molten compounds in a mold cavity, increasing the difficulty of predicting the occurrence of void formation or gold-wire deformation.
A method of three-dimensional (3-D) flow analysis of thermosetting compounds has been developed with the objective of minimizing the trial term before mass production and of enhancing the quality of molded products. A constitutive equation model was developed to describe isothermal viscosity changes as a function of time and temperature. This isothermal model was used for predicting non-isothermal viscosity changes. In addition, an empirical model was developed for calculating the amount of wire deformation as a function of viscosity, wire configuration, and other parameters. These models were integrated with FLOW-3D® software, which is used for multipurpose 3-D flow analysis.
The mold-filling dynamics of an epoxy compound were analyzed using the newly developed modeling software during transfer molding of an actual high performance electronic module. The changes in the 3-D distributions of parameters such as temperature, viscosity, velocity, and pressure were compared with the flow front patterns. The predicted results of cavity filling behavior corresponded well with actual short shot data. As well, the predicted amount of gold-wire deformation at each LSI chip with a substrate connection also corresponded well with observed data obtained by X-ray inspection of the molded product.
열경화성 몰딩 컴파운드는 반도체 장치 및 전자 모듈을 캡슐화하는 데 널리 사용됩니다. 최근에는 고성능에 대한 요구 사항을 충족시키기 위해 전자 모듈에 캡슐화되는 전자 부품의 수가 증가하고 있습니다.
그 결과 성형시 삽입 부품의 구성이 매우 복잡해졌습니다. 한편, 소비자의 소형화 요구에 부응하여 패키지 두께를 줄였다. 이러한 경향은 몰드 캐비티에서 용융된 화합물의 복잡한 흐름 패턴을 야기하여 보이드 형성 또는 금선 변형의 발생을 예측하기 어렵게합니다.
열경화성 화합물의 3 차원 (3-D) 유동 분석 방법은 대량 생산 전에 시험 기간을 최소화하고 성형 제품의 품질을 향상시킬 목적으로 개발되었습니다. 시간과 온도의 함수로서 등온 점도 변화를 설명하기 위해 구성 방정식 모델이 개발되었습니다. 이 등온 모델은 비등 온 점도 변화를 예측하는 데 사용되었습니다.
또한 점도, 와이어 구성 및 기타 매개 변수의 함수로 와이어 변형량을 계산하기위한 경험적 모델이 개발되었습니다. 이 모델은 다목적 3D 흐름 분석에 사용되는 FLOW-3D® 소프트웨어와 통합되었습니다.
실제 고성능 전자 모듈의 트랜스퍼 몰딩 과정에서 새로 개발 된 모델링 소프트웨어를 사용하여 에폭시 화합물의 몰드 충전 역학을 분석했습니다. 온도, 점도, 속도 및 압력과 같은 매개 변수의 3D 분포 변화를 유동 선단 패턴과 비교했습니다.
캐비티 충전 거동의 예측 결과는 실제 미 성형 데이터와 잘 일치했습니다. 또한, 기판 연결이 있는 각 LSI 칩에서 예상되는 금선 변형량은 성형품의 X-ray 검사에서 얻은 관찰 데이터와도 잘 일치했습니다.
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S. Noruzi1 and J. Ahadiyan2* 1– M.Sc. Student, Faculty of Water Sciences Engineering, Shahid Chamran University of Ahvaz, Iran. 2*-Corresponding Author, Associate Professor, Faculty of Water Sciences Engineering, Shahid Chamran University of Ahvaz, Iran.
The discharge coefficient of morning glory spillway is decreased with eddies created by vortex at the inlet part of weir. However, a series of specific blades can reduce vortices which result in the spillway efficiency is increased. Hence, in this research numerical modeling of installed breaker blade on morning glory spillway was evaluated using Flow-3D model. To achieve these purposes, morning glory spillway was modeled without and with blades 3, 4 and 6 blades at 45 degree angle. To simulate the turbulence fluctuations, the modified k-e model (RNG k-e) was used and its results were compared to the experimental data. Results showed that by installing blades, the discharge coefficient increases up to 42 percent with 25 percent decreasing in the upstream water level. Moreover, among the three different arrangements of blades, the six-blade model was found to have more satisfactory results than other models. In comparison to control model, for H/D between 0 to 0.1 and 0.1 to 0.2 the discharge coefficient has been increased 40 and 57 percent for six-blade arrangement, respectively.
모닝 글로리의 방류계수는 위어 입구 부분의 와류에 의해 생성된 소용돌이로 감소합니다. 그러나 일련의 특정 블레이드는 와류를 줄여 여수로 효율성을 높일 수 있습니다. 따라서 본 연구에서는 모닝 글로리 여수로에 설치된 브레이커 블레이드의 수치 모델링을 FLOW-3D 모델을 사용하여 평가했습니다. 이러한 목적을 달성하기 위해 모닝 글로리 여수로는 45도 각도로 블레이드 3, 4 및 6 블레이드 있는 모델과 없는 모델로 모델링되었습니다. 난류 변동을 시뮬레이션하기 위해 수정된 k-e 모델 (RNG k-e)을 사용하고 그 결과를 실험 데이터와 비교했습니다. 결과에 따르면 블레이드를 설치하면 상류 수위가 25 % 감소하면서 배출 계수가 42 %까지 증가합니다. 또한 3 개의 서로다른 블레이드 배열 중 6 개 블레이드 모델이 다른 모델보다 더 만족스러운 결과를 나타냈다. 기본 모델과 비교하여 H / D가 0 ~ 0.1 및 0.1 ~ 0.2 인 경우, 6개 블레이드 배열에서 방류계수가 각각 40 % 및 57 % 증가했습니다.
1 -حیدری ارجلو، س.، موسوی جهرمی، س. ح. و ادیب، ا. 1386 .بررسی تاثیر شیب بر تعداد بهینه پلکانها در سرریزهای پلکانی، مجله علوم و مهندسی .)123-136 :)2(33 ،كشاورزی علمی )آبیاری 2 -حاجیپور، گ. 1363 .بررسی آزمایشگاهی تأثیر تیغههای گردابشکن بر هیدرولیک جریان سرریز نیلوفری. پایاننامه كارشناسی ارشد رشته سازههای آبی، دانشکده مهندسی علوم آب، دانشگاه شهید چمران اهواز. 3 -رنجبر ملکشاه، م.، 1363 .بررسی رفتار سرریز نیلوفری با پایین دست تاج پلکانی بوسیله مدلسازی رایانهای، پایاننامه كارشناسی ارشد مهندسی عمران، دانشکده مهندسی عمران، دانشگاه خواجه نصیر طوسی. 4 -رمضانی، س. كاویانپور، م ر. و ع. حسنی نژاد. 1362 .بررسی پارامترهای مؤثر بر آبگذری سرریزهای نیلوفری. هفتمین كنگره ملی مهندسی عمران، دانشکده مهندسی شهید نیکبخت، زاهدان. 1 -سامانی، م. 1331 .طراحی سازههای هیدرولیکی. انتشارات شركت مهندسی مشاور دز آب اهواز 1 -قاسمزاده، ف. 1362 .شبیه سازی مسائل هیدرولیکی در 3D-FLOW .تهران، نوآور. 3 -كمانبدست، 1 ،.موسوی، س.ر. 1361 .مطالعه آزمایشگاهی تأثیر تعداد و زاویه گرداب شکن بر مشخصات جریان در سرریز نیلوفری مربعی، نشریه علوم آب و خاک )غعلوم و فنون كشاورزی و منابع طبیعی(، سال بیستم، شماره 38 ،صفحه 182-131 . 8 -نظری پوركیانی، ع ا. 1363 .بررسی فشار و سرعت جریان در سرریز نیلوفری سد البرز با استفاده از نرمافزار 3D-FLOW .اولین كنفرانس سراسری توسعه محوری مهندسی عمران، معماری، برق و مکانیک ایران. 6 -نوحانی، ا.، جمالی امام قیس، ر. 1364 .بررسی آزمایشگاهی تأثیرشکل تیغه های ضد گرداب برراندمان تخلیهی سرریزهای نیلوفری، نشریه آبیاری و زهکشی ایران، جلد 6 ،شماره 1 ،صفحه 346-341 . 10-Akbari, A A., Nohani, E and A. Afrous. 2015. Numerical study of the effect of anti-vortex plates on the inflow pattern in shaft spillways. Indian Journal of Fundamental and Applied Life Sciences, 5(S1): 3819-3826. 11-Anonymous, 1965. Design of Small Dams. Water Resources Technical publication, U.S Department of the interior Bureau of Reclamation. 12-Bagheri, A., Shafai Bajestan, M., Mousavi Jahromi, H., Kashkuli, H. and H. Sedghi. 2010. Hydraulic evaluation of the flow over polyhedral morning glory spillways. Word Applied Sciences Journal, 9(7): 712-717. 13- Fattor, C. A. and J. D. Bacchiega. 2003. Analysis of instabilities in the charge of regime in morning glory spillways. Journal of Hydraulic Research, 40(4): 114-123. 14- Khatsuria, R. M. 2005. Hydraulics of spillways and energy dissipaters. Marcel Dekker. Department of Civil and Environmental Engineering Georgia, Institute of Technology Atlanta, Newyork, USA. 15-Mousavi. S. R., Kamanbedast, A.A., and H. Fathian. 2013. Experimental investigation of the effect of number of anti-vortex piers on submergence threshold in morning glory spillway with square inlet. Technical Journal of Engineering and Applied Sciences, 3(24): 3534-3540. 16- Novak, P. 2007. Hydraulic Structures, Fourth edition published by Taylor and Francis. University of New Castle upon, Tyne, UK, Landon and Network. 17-Tavana, M H., Mousavi Jahromi, H., Shafai Bajestan, M., Masjedi, A. R. and H. Sedghi. 2011. Optimization of number and direction of vortex breakers in the morning glory spillway using physical model. Economy, Environmental and Conservation Journal, 17(2): 435-440. 18-Vresteeg. H. K and W. Malalasekera. 1995. An introduction to computational fluid dynamics. Longman Scientific and Technical. New York. 19-Yakhot. V and L. M. Smith. 1992. The renormalization group. The e-expansion and of turbulence models. Journal of Computing, 7(1): 35-61.
1 MS Student, Department of Water Structures, Faculty of Water and Environmental Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
2 Professor, Department of Water Structures, Faculty of Water and Environmental Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
3 shahid chamran university
Due to the crisis of water scarcity, water resources management has become inevitable in Iran. Dam reservoirs are among the most important used water resources. Construction of a dam on a river reduces the flow velocity in the reservoir, finally resulting in the deposit of sediments in it. The depositing of sediments in the dam reservoir reduces its useful volume and disturbs the dam’s performance in terms of water storage. Therefore, solutions have always been proposed to manage and discharge sediments in the reservoir during the service period. In this regard, pressurized flushing is a common solution for eliminating sediments. In this method, by opening the bottom gates, the upstream water pressure discharges the sediments through the orifice. The volume of the exited sediments is a function of factors, such as gate diameter, sediments type and size, water height upstream the gate, and outflow discharge. Numerous studies have been conducted on the effect of the mentioned factors on the volume of sediments exited from an orifice. Shahmirzadi et al. (2010) experimentally evaluated the effect of the diameter of bottom dischargers on the dimensions of the flushing cone. Powell and Khan (2015) conducted tests to investigate the flow pattern upstream of a dam orifice under the fixed bed and equilibrium scour (mobile bed) conditions. Their results demonstrated that the velocity’s horizontal component was almost equal for both fixed and equilibrium scour conditions. The same conditions were also the case for the vertical component of the velocity.
Spillways are constructed to evacuate flood discharge safely so that a flood wave does not overtop the dam body. There are different types of spillways, with the ogee type being the conventional one. A stepped spillway is an example of a nonconventional spillway. The turbulent flow over a stepped spillway was studied numerically by using the Flow-3D package. Different fluid flow characteristics such as longitudinal flow velocity, temperature distribution, density and chemical concentration can be well simulated by Flow-3D. In this study, the influence of slope changes on flow characteristics such as air entrainment, velocity distribution and dynamic pressures distribution over a stepped spillway was modelled by Flow-3D. The results from the numerical model were compared with an experimental study done by others in the literature. Two models of a stepped spillway with different discharge for each model were simulated. The turbulent flow in the experimental model was simulated by the Renormalized Group (RNG) turbulence scheme in the numerical model. A good agreement was achieved between the numerical results and the observed ones, which are exhibited in terms of graphics and statistical tables.
배수로는 홍수가 댐 몸체 위로 넘치지 않도록 안전하게 홍수를 피할 수 있도록 건설되었습니다. 다른 유형의 배수로가 있으며, ogee 유형이 기존 유형입니다. 계단식 배수로는 비 전통적인 배수로의 예입니다. 계단식 배수로 위의 난류는 Flow-3D 패키지를 사용하여 수치적으로 연구되었습니다.
세로 유속, 온도 분포, 밀도 및 화학 농도와 같은 다양한 유체 흐름 특성은 Flow-3D로 잘 시뮬레이션 할 수 있습니다. 이 연구에서는 계단식 배수로에 대한 공기 혼입, 속도 분포 및 동적 압력 분포와 같은 유동 특성에 대한 경사 변화의 영향을 Flow-3D로 모델링 했습니다.
수치 모델의 결과는 문헌에서 다른 사람들이 수행한 실험 연구와 비교되었습니다. 각 모델에 대해 서로 다른 배출이 있는 계단식 배수로의 두 모델이 시뮬레이션되었습니다. 실험 모델의 난류 흐름은 수치 모델의 Renormalized Group (RNG) 난류 계획에 의해 시뮬레이션되었습니다. 수치 결과와 관찰 된 결과 사이에 좋은 일치가 이루어졌으며, 이는 그래픽 및 통계 테이블로 표시됩니다.
댐 구조는 물 보호가 생활의 핵심이기 때문에 물을 저장하거나 물을 운반하는 전 세계에서 가장 중요한 프로젝트입니다. 그리고 여수로는 댐의 가장 중요한 부분 중 하나로 분류됩니다. 홍수로 인한 파괴 나 피해로부터 댐을 보호하기 위해 여수로가 건설됩니다.
수력 발전, 항해, 레크리에이션 및 어업의 중요성을 감안할 때 댐 건설 및 홍수 통제는 전 세계적으로 매우 중요한 문제로 간주 될 수 있습니다. 많은 유형의 배수로가 있지만 가장 일반적인 유형은 다음과 같습니다 : ogee 배수로, 자유 낙하 배수로, 사이펀 배수로, 슈트 배수로, 측면 채널 배수로, 터널 배수로, 샤프트 배수로 및 계단식 배수로.
그리고 모든 여수로는 입구 채널, 제어 구조, 배출 캐리어 및 출구 채널의 네 가지 필수 구성 요소로 구성됩니다. 특히 롤러 압축 콘크리트 (RCC) 댐 건설 기술과 더 쉽고 빠르며 저렴한 건설 기술로 분류 된 계단식 배수로 건설과 관련하여 최근 수십 년 동안 많은 계단식 배수로가 건설되었습니다 (Chanson 2002; Felder & Chanson 2011).
계단식 배수로 구조는 캐비테이션 위험을 감소시키는 에너지 소산 속도를 증가시킵니다 (Boes & Hager 2003b). 계단식 배수로는 다양한 조건에서 더 매력적으로 만드는 장점이 있습니다.
계단식 배수로의 흐름 거동은 일반적으로 낮잠, 천이 및 스키밍 흐름 체제의 세 가지 다른 영역으로 분류됩니다 (Chanson 2002). 유속이 낮을 때 nappe 흐름 체제가 발생하고 자유 낙하하는 낮잠의 시퀀스로 특징 지워지는 반면, 스키밍 흐름 체제에서는 물이 외부 계단 가장자리 위의 유사 바닥에서 일관된 흐름으로 계단 위로 흐릅니다.
또한 주요 흐름에서 3 차원 재순환 소용돌이가 발생한다는 것도 분명합니다 (예 : Chanson 2002; Gonzalez & Chanson 2008). 계단 가장자리 근처의 의사 바닥에서 흐름의 방향은 가상 바닥과 가상으로 정렬됩니다. Takahashi & Ohtsu (2012)에 따르면, 스키밍 흐름 체제에서 주어진 유속에 대해 흐름은 계단 가장자리 근처의 수평 계단면에 영향을 미치고 슈트 경사가 감소하면 충돌 영역의 면적이 증가합니다. 전이 흐름 체제는 나페 흐름과 스키밍 흐름 체제 사이에서 발생합니다. 계단식 배수로를 설계 할 때 스키밍 흐름 체계를 고려해야합니다 (예 : Chanson 1994, Matos 2000, Chanson 2002, Boes & Hager 2003a).
CFD (Computational Fluid Dynamics), 즉 수력 공학의 수치 모델은 일반적으로 물리적 모델에 소요되는 총 비용과 시간을 줄여줍니다. 따라서 수치 모델은 실험 모델보다 빠르고 저렴한 것으로 분류되며 동시에 하나 이상의 목적으로 사용될 수도 있습니다. 사용 가능한 많은 CFD 소프트웨어 패키지가 있지만 가장 널리 사용되는 것은 FLOW-3D입니다. 이 연구에서는 Flow 3D 소프트웨어를 사용하여 유량이 서로 다른 두 모델에 대해 계단식 배수로에서 공기 농도, 속도 분포 및 동적 압력 분포를 시뮬레이션합니다.
Roshan et al. (2010)은 서로 다른 수의 계단 및 배출을 가진 계단식 배수로의 두 가지 물리적 모델에 대한 흐름 체제 및 에너지 소산 조사를 연구했습니다. 실험 모델의 기울기는 각각 19.2 %, 12 단계와 23 단계의 수입니다. 결과는 23 단계 물리적 모델에서 관찰 된 흐름 영역이 12 단계 모델보다 더 수용 가능한 것으로 간주되었음을 보여줍니다. 그러나 12 단계 모델의 에너지 손실은 23 단계 모델보다 더 많았습니다. 그리고 실험은 스키밍 흐름 체제에서 23 단계 모델의 에너지 소산이 12 단계 모델보다 약 12 % 더 적다는 것을 관찰했습니다.
Ghaderi et al. (2020a)는 계단 크기와 유속이 다른 정련 매개 변수의 영향을 조사하기 위해 계단식 배수로에 대한 실험 연구를 수행했습니다. 그 결과, 흐름 체계가 냅페 흐름 체계에서 발생하는 최소 scouring 깊이와 같은 scouring 구멍 치수에 영향을 미친다는 것을 보여주었습니다. 또한 테일 워터 깊이와 계단 크기는 최대 scouring깊이에 대한 실제 매개 변수입니다. 테일 워터의 깊이를 6.31cm에서 8.54 및 11.82cm로 늘림으로써 수세 깊이가 각각 18.56 % 및 11.42 % 증가했습니다. 또한 이 증가하는 테일 워터 깊이는 scouring 길이를 각각 31.43 % 및 16.55 % 감소 시킵니다. 또한 유속을 높이면 Froude 수가 증가하고 흐름의 운동량이 증가하면 scouring이 촉진됩니다. 또한 결과는 중간의 scouring이 횡단면의 측벽보다 적다는 것을 나타냅니다. 계단식 배수로 하류의 최대 scouring 깊이를 예측 한 후 실험 결과와 비교하기 위한 실험식이 제안 되었습니다. 그리고 비교 결과 제안 된 공식은 각각 3.86 %와 9.31 %의 상대 오차와 최대 오차 내에서 scouring 깊이를 예측할 수 있음을 보여주었습니다.
Ghaderi et al. (2020b)는 사다리꼴 미로 모양 (TLS) 단계의 수치 조사를 했습니다. 결과는 이러한 유형의 배수로가 확대 비율 LT / Wt (LT는 총 가장자리 길이, Wt는 배수로의 폭)를 증가시키기 때문에 더 나은 성능을 갖는 것으로 관찰되었습니다. 또한 사다리꼴 미로 모양의 계단식 배수로는 더 큰 마찰 계수와 더 낮은 잔류 수두를 가지고 있습니다. 마찰 계수는 다양한 배율에 대해 0.79에서 1.33까지 다르며 평평한 계단식 배수로의 경우 대략 0.66과 같습니다. 또한 TLS 계단식 배수로에서 잔류 수두의 비율 (Hres / dc)은 약 2.89이고 평평한 계단식 배수로의 경우 약 4.32와 같습니다.
Shahheydari et al. (2015)는 Flow-3D 소프트웨어, RNG k-ε 모델 및 VOF (Volume of Fluid) 방법을 사용하여 배출 계수 및 에너지 소산과 같은 자유 표면 흐름의 프로파일을 연구하여 스키밍 흐름 체제에서 계단식 배수로에 대한 흐름을 조사했습니다. 실험 결과와 비교했습니다. 결과는 에너지 소산 율과 방전 계수율의 관계가 역으로 실험 모델의 결과와 잘 일치 함을 보여 주었다.
Mohammad Rezapour Tabari & Tavakoli (2016)는 계단 높이 (h), 계단 길이 (L), 계단 수 (Ns) 및 단위 폭의 방전 (q)과 같은 다양한 매개 변수가 계단식 에너지 소산에 미치는 영향을 조사했습니다. 방수로. 그들은 해석에 FLOW-3D 소프트웨어를 사용하여 계단식 배수로에서 에너지 손실과 임계 흐름 깊이 사이의 관계를 평가했습니다. 또한 유동 난류에 사용되는 방정식과 표준 k-ɛ 모델을 풀기 위해 유한 체적 방법을 적용했습니다. 결과에 따르면 스텝 수가 증가하고 유량 배출량이 증가하면 에너지 손실이 감소합니다. 얻은 결과를 다른 연구와 비교하고 경험적, 수학적 조사를 수행하여 결국 합격 가능한 결과를 얻었습니다.
ListenReadSpeaker webReader: ListenFor all numerical models the basic principle is very similar: a set of partial differential equations (PDE) present the physical problems. The flow of fluids (gas and liquid) are governed by the conservation laws of mass, momentum and energy. For Computational Fluid Dynamics (CFD), the PDE system is substituted by a set of algebraic equations which can be worked out by using numerical methods (Versteeg & Malalasekera 2007). Flow-3D uses the finite volume approach to solve the Reynolds Averaged Navier-Stokes (RANS) equation, by applying the technique of Fractional Area/Volume Obstacle Representation (FAVOR) to define an obstacle (Flow Science Inc. 2012). Equations (1) and (2) are RANS and continuity equations with FAVOR variables that are applied for incompressible flows.
(2)where is the velocity in xi direction, t is the time, is the fractional area open to flow in the subscript directions, is the volume fraction of fluid in each cell, p is the hydrostatic pressure, is the density, is the gravitational force in subscript directions and is the Reynolds stresses.
Turbulence modelling is one of three key elements in CFD (Gunal 1996). There are many types of turbulence models, but the most common are Zero-equation models, One-equation models, Two-equation models, Reynolds Stress/Flux models and Algebraic Stress/Flux models. In FLOW-3D software, five turbulence models are available. The formulation used in the FLOW-3D software differs slightly from other formulations that includes the influence of the fractional areas/volumes of the FAVORTM method and generalizes the turbulence production (or decay) associated with buoyancy forces. The latter generalization, for example, includes buoyancy effects associated with non-inertial accelerations.
The available turbulence models in Flow-3D software are the Prandtl Mixing Length Model, the One-Equation Turbulent Energy Model, the Two-Equation Standard Model, the Two-Equation Renormalization-Group (RNG) Model and large Eddy Simulation Model (Flow Science Inc. 2012).In this research the RNG model was selected because this model is more commonly used than other models in dealing with particles; moreover, it is more accurate to work with air entrainment and other particles. In general, the RNG model is classified as a more widely-used application than the standard k-ɛ model. And in particular, the RNG model is more accurate in flows that have strong shear regions than the standard k-ɛ model and it is defined to describe low intensity turbulent flows. For the turbulent dissipation it solves an additional transport equation:
(3)where CDIS1, CDIS2, and CDIS3 are dimensionless parameters and the user can modify them. The diffusion of dissipation, Diff ɛ, is
(4)where u, v and w are the x, y and z coordinates of the fluid velocity; , , and , are FLOW-3D’s FAVORTM defined terms; and are turbulence due to shearing and buoyancy effects, respectively. R and are related to the cylindrical coordinate system. The default values of RMTKE, CDIS1 and CNU differ, being 1.39, 1.42 and 0.085 respectively. And CDIS2 is calculated from turbulent production () and turbulent kinetic energy ().The kinematic turbulent viscosity is the same in all turbulence transport models and is calculated from
(5)where : is the turbulent kinematic viscosity. is defined as the numerical challenge between the RNG and the two-equation k-ɛ models, found in the equation below. To avoid an unphysically large result for in Equation (3), since this equation could produce a value for very close to zero and also because the physical value of may approach to zero in such cases, the value of is calculated from the following equation:
(6)where : the turbulent length scale.
VOF and FAVOR are classifications of volume-fraction methods. In these two methods, firstly the area should be subdivided into a control volume grid or a small element. Each flow parameter like velocity, temperature and pressure values within the element are computed for each element containing liquids. Generally, these values represent the volumetric average of values in the elements.Numerous methods have been used recently to solve free infinite boundaries in the various numerical simulations. VOF is an easy and powerful method created based on the concept of a fractional intensity of fluid. A significant number of studies have confirmed that this method is more flexible and efficient than others dealing with the configurations of a complex free boundary. By using VOF technology the Flow-3D free surface was modelled and first declared in Hirt & Nichols (1981). In the VOF method there are three ingredients: a planner to define the surface, an algorithm for tracking the surface as a net mediator moving over a computational grid, and application of the boundary conditions to the surface. Configurations of the fluids are defined in terms of VOF function, F (x, y, z, t) (Hirt & Nichols 1981). And this VOF function shows the volume of flow per unit volume
(9)where is the density of the fluid, is a turbulent diffusion term,