Numerical research on flow and thermal transport in cooling pool of electrical power station using three depth-averaged turbulence models

This paper describes a numerical simulation of thermal discharge in the cooling pool of an electrical power station, aiming to develop general-purpose computational programs for grid generation and flow/pollutant transport in the complex domains of natural and artificial waterways. Three depth-averaged two-equation closure turbulence models, k - ε , k - w , and k - ω , were used to close the quasi three-dimensional hydrodynamic model. The k -ω model was recently established by the authors and is still in th...     

A TVD Scheme for Incompressible Flow Coupled With Different Turbulence Modles on A Ground-Mounted Square-RIB Flow

A finite-difference Total Variation Diminishing (TVD) numerical simulation model for coupling the Reynolds Averaged Navier-Stokes (RANS) equations, pressure-relative continuity equation and various k-ε turbulence models was developed to solve the incompressible flow based on the pseudo-compressibility method. The hyperbolicity of all these equations was studied and the discretization of the fully coupling equations with all the primal variables and source terms were made in this article. Numerical simulation for modeling the flow around a ground-mounted square rib was implemented and validated by comparing with the published wind tunnel experimental data. It is shown that such a numerical simulation method with a proper turbulence model has a very good accuracy to simulate the flow around a surface-mounted rib. It is concluded that the Renormalization Group (RNG) and Chen-Kim k-ε turbulence models have much better ability to predict the characteristics of the vortex structure and flow separation than the standard k-ε model.     

A TVD SCHEME FOR INCOMPRESSIBLE FLOW COUPLED WITH DIFFERENT TURBULENCE MODLES ON A GROUND-MOUNTED SQUARE-RIB FLOW

A finite-difference Total Variation Diminishing (TVD) numerical simulation model for coupling the Reynolds Averaged Navier-Stokes (RANS) equations, pressure-relative continuity equation and various k-εturbulence models was developed to solve the incompressible flow based on the pseudo-compressibility method. The hyperbolicity of all these equations was studied and the discretization of the fully coupling equations with all the primal variables and source terms were made in this article. Numerical simulation for modeling the flow around a ground-mounted square rib was implemented and validated by comparing with the published wind tunnel experimental data. It is shown that such a numerical simulation method with a proper turbulence model has a very good accuracy to simulate the flow around a surface-mounted rib. It is concluded that the Renormalization Group (RNG) and Chen-Kim k-εturbulence models have much better ability to predict the characteristics of the vortex structure and flow separation than the standard k-εmodel.     

THE NUMERICAL COMPUTATION OF TURBULENT FLOW IN TEE-JUNCTION

A numerical model for calculating the turbulent flow in tee-junction is given in thispaper.The calculations are performed using a finite-difference procedure,and turbulence is ac-counted for by using a two-equation k-ε model of turbulence.Results,consisting of mean veloci-ty profiles and pressure losses due to the junction,have been obtained,and show that the flowsituation in tee-junction is very complex.The computed results agree closely with the experimen-tal data and validate that the present model is reasonable and the numerical calculations are suc-cessful.     

SIMULATION OF STRONG TURBULENCE FLOW WITH FREE SURFACE INCLUDING THE EFFECTS OF STREAMLINE CURVATURE

This paper is concerned with a mathematical model for two-dimensional strong turbulence flow with free surface including the effects of streamline curvature in orthogonal curvilinear coordinate system, with which the characteristics of the turbulence flow field on the ogee spillway was numerical simulated. In the numerical simulation, the flow control equations in orthogonal curvilinear coordinate system were discretized by the finite volume method, the physical parameters（ P, U,V,K,ε,γt , etc. ） were arranged on a staggered grid, the discretized equations were solved with the SIMPLEC method, and the complex free surface was dealt with VOF method. The computed results show that the velocity fields, pressure field, shear stress distribution and kinetic energy of turbulent flow on the ogee spillway are in agreement with experimental data. This confirms that the model can be used for numerieal simulation of the turbulence flow on ogee spillway.     

THE NUMERICAL SIMULATION OF TWO-DIMENSIONAL OPEN CHANNEL TURBULENCE

A numerical simulation on 2-D open channel turbulence using the two-equationturbulent model(k-e model) is made.The diseretization equations of depth-averaged 2-D differ-ential equation are obtained by the control-volume formulation.Some examples including theflows in straight open channel,symmetry sudden expansion and one-side sudden expansion arecalculated by using the SIMPLE algorithm.The distributions of the flow velocity u,the kineticturbulent energy k,and the turbulent viscosity μ,etc.are obtained.The numerical calculationsindicate a good agreement with experimental data and other turbulent models calulations.     

THREE-DIMENSIONAL SIMULATION OF MEANDERING RIVER BASED ON 3-D RNG κ-ε TURBULENCE MODEL

A 3-D numerical model for calculating flow in non-curvilinear coordinates was established in this article. The flow was simulated by solving the full Reynolds-averaged Navier-Stokes equations with the RNG κ-ε turbulence model. In the horizontal x-y-plane, a boundary-fitted curvilinear co-ordinate system was adopted, while in the vertical direction, a σ co-ordinate transformation was used to represent the free surface and bed topography. The water level was determined by solving the 2-D Poisson equation derived from 2-D depth averaged momentum equations. The finite-volume method was used to discretize the equations and the SIMPLEC algorithm was applied to acquire the coupling of velocity and pressure. This model was applied to simulate the meandering channels and natural rivers, and the water levels and the velocities for all sections were given. By contrasting and analyzing, the agreement with measurements is generally good. The feasibility studies of simulating flow of the natural fiver have been conducted to demonstrate its applicability to hydraulic engineering research.     

Numerical simulation of turbulent flow around a forced moving circular cylinder on cut cells

Fixed and forced moving circular cylinders in turbulent flows are studied by using the Large Eddy Simulation （LES） and two-equation based Detached Eddy Simulation （DES） turbulence models. The Cartesian cut cell approach is adopted to track the body surface across a stationary background grid covering the whole computational domain. A cell-centered finite volume method of second-order accuracy in both time and space is developed to solve the flow field in fluid cells, which is also modified accordingly in cut cells and merged cells. In order to compare different turbulence models, the current flow past a fixed circular cylinder at a moderate Reynolds number, Re = 3 900, is tested first. The model is also applied to the simulation of a forced oscillating circular cylinder in the turbulent flow, and the influences of different oscillation amplitudes, frequencies and free stream velocities are discussed. The numerical results indicate that the present numerical model based on the Cartesian cut cell approach is capable of solving the turbulent flow around a body undergoing motions, which is a foundation for the possible future study on wake induced oscillation and vortex induced vibration.     

Numerical simulation unsteady cloud cavitating flow with a filter-based density correction model简

In this paper, various turbulence closure models for unsteady cavitating flows are investigated. The filter-based model （FBM） and the density correction model （DCM） were proposed to reduce the turbulent eddy viscosities in a turbulent cavitating flow based on the local meshing resolution and the local fluid density, respectively. The effects of the resolution control parameters in the FBM and DCM models are discussed. It is shown that the eddy viscosity near the cavity closure region can significantly influence the cavity shapes and the unsteady shedding pattern of the cavitating flows. To improve the predictions, a Filter-Based Density Cor-rection model （FBDCM） is proposed, which blends the FBM and DCM models according to the local fluid density. The new FBDCM model can effectively represent the eddy viscosity, according to the multi-phase characteristics of the unsteady cavitating flows. The experimental validations regarding the force analysis and the unsteady cavity visualization show that good agreements with experimental visualizations and measurements are obtained by the FBDCM model. For the FBDCM model, the attached cavity length and the resulting hydrodynamic characteristics are subsequently affected by the detail turbulence modeling parameters, and the model is shown to be effective in improving the overall predictive capability.     

Application of CLEAR-VOF method to wave and flow simulations

A two-dimensional numerical model based on the Navier-Stokes equations and computational Lagrangian-Eulerian advection remap-volume of fluid (CLEAR-VOF) method was developed to simulate wave and flow problems. The Navier-Stokes equations were discretized with a three-step finite element method that has a third-order accuracy. In the CLEAR-VOF method, the VOF function F was calculated in the Lagrangian manner and allowed the complicated free surface to be accurately captured. The propagation of regular waves and solitary waves over a flat bottom, and shoaling and breaking of solitary waves on two different slopes were simulated with this model, and the numerical results agreed with experimental data and theoretical solutions. A benchmark test of dam-collapse flow was also simulated with an unstructured mesh, and the capability of the present model for wave and flow simulations with unstructured meshes, was verified. The results show that the model is effective for numerical simulation of wave and flow problems with both structured and unstructured meshes.     

虹吸式出水流道水力性能数值计算湍流模型适用性

为寻求适用于大型低扬程泵站虹吸式出水流道水力性能数值计算的湍流模型,首先采用透明流道模型对某低扬程泵站虹吸式出水流道进行了试验研究,测试了流道水头损失并分析了流道内流态; 在网格无关性分析的基础上,选择常用的一方程湍流模型(S-A湍流模型)、二方程湍流模型(k-ε湍流模型、k-ω湍流模型)及Reynolds Stress湍流模型分别对该虹吸式出水流道水力性能进行了三维湍流流动数值计算,并将计算结果与模型试验结果进行比较。结果表明:与一方程湍流模型和Reynolds Stress湍流模型相比,二方程湍流模型在虹吸式出水流道水头损失的计算中更具优越性,采用Standard k-ε,Realizable k-ε和SST k-ω等3种二方程湍流模型计算得到的流道水头损失相对误差小于3%,其中,Standard k-ε湍流模型计算得到的流场与模型试验结果最吻合。     

随机波浪边界层的数值模拟与分析

该文基于雷诺平均的Navier-Stokes方程和k-ω两方程紊流模型建立了随机波浪边界层数学模型,模拟了粗糙底床上方的随机波浪边界层流速、床面剪切应力和紊动能量分布,计算结果与实测数据吻合良好。探讨了随机波浪边界层水动力特性,发现随机波浪时间序列中各个子波的紊动能量近似随该子波均方根自由振荡速度平方的增大而线性增大,但各个子波的紊动能量还受到上一个子波紊动能量传递的影响,体现了随机波浪与规则波浪的区别。整个随机波浪时间序列的有效摩阻系数和单个子波的摩阻系数均与前人实验数据和经验公式较为一致。     

辐流式沉淀池液固两相流力学特性三维数值模拟

采用两相流混合模型,选取RNG k-ε湍流模型封闭两相流时均方程,对辐流式二次沉淀池液固两相流力学特性进行三维数值模拟。采用有限体积法求解微分方程;紊动能、紊流耗散均采用Quick离散格式;速度与压力耦合求解时使用了压力隐式算子分裂PISO(Pressure-Implicit with Splitting of Operators)算法。通过模拟获得了速度场、紊动能和污泥质量浓度等参量在空间的分布规律,对沉淀池的设计有一定的参考价值。     

Unsteady shallow meandering flows in rectangular reservoirs: A modal analysis of URANS modelling

Shallow flows are common in natural and human-made environments. Even for simple rectangular shallow reservoirs, recent laboratory experiments show that the developing flow fields are particularly complex, involving large-scale turbulent structures. For specific combinations of reservoir size and hydraulic conditions, a meandering jet can be observed. While some aspects of this pseudo-2D flow pattern can be reproduced using a 2D numerical model, new 3D simulations, based on the unsteady Reynolds-Averaged Navier-Stokes equations, show consistent advantages as presented herein. A Proper Orthogonal Decomposition was used to characterize the four most energetic modes of the meandering jet at the free surface level, allowing comparison against experimental data and 2D (depth-averaged) numerical results. Three different isotropic eddy viscosity models (RNG k-ε, k-ε, k-ω) were tested. The 3D models accurately predicted the frequency of the modes, whereas the amplitudes of the modes and associated energy were damped for the friction-dominant cases and augmented for non-frictional ones. The performance of the three turbulence models remained essentially similar, with slightly better predictions by RNG k-ε model in the case with the highest Reynolds number. Finally, the Q-criterion was used to identify vortices and study their dynamics, assisting on the identification of the differences between: i) the three-dimensional phenomenon (here reproduced), ii) its two-dimensional footprint in the free surface (experimental observations) and iii) the depth-averaged case (represented by 2D models).     

Comparison of depth-averaged concentration and bed load flux sediment transport models of dam-break flow

This paper presents numerical simulations of dam-break flow over a movable bed. Two different mathematical models were compared: a fully coupled formulation of shallow water equations with erosion and deposition terms (a depth-averaged concentration flux model), and shallow water equations with a fully coupled Exner equation (a bed load flux model). Both models were discretized using the cell-centered finite volume method, and a second-order Godunov-type scheme was used to solve the equations. The numerical flux was calculated using a Harten, Lax, and van Leer approximate Riemann solver with the contact wave restored (HLLC). A novel slope source term treatment that considers the density change was introduced to the depth-averaged concentration flux model to obtain higher-order accuracy. A source term that accounts for the sediment flux was added to the bed load flux model to reflect the influence of sediment movement on the momentum of the water. In a one-dimensional test case, a sensitivity study on different model parameters was carried out. For the depth-averaged concentration flux model, Manning's coefficient and sediment porosity values showed an almost linear relationship with the bottom change, and for the bed load flux model, the sediment porosity was identified as the most sensitive parameter. The capabilities and limitations of both model concepts are demonstrated in a benchmark experimental test case dealing with dam-break flow over variable bed topography.     

Simulation of flow in compound open-channel using a discontinuous Galerkin finite-element method with Smagorinsky turbulence closure

The small-scale spatial variability of eddy viscosity which is characteristic for the turbulent shear stress in compound open-channel flows was studied and investigated in this paper. Different options including a constant value, zero-equation, one-equation, two-equation, and Smagorinsky turbulence models for parameterizing the eddy viscosity were developed in the framework of the discontinuous Galerkin finite-element SLIM model and applied for presenting the complex velocity profile in two different experimental data sets of laboratory flumes. A very good qualitative agreement was achieved between numerical results and measurement data for both velocity and flow depth of all experimental data sets in general. In addition, the calculation results showed that the turbulent Smagorinsky empiricism allowed a better presentation of non-uniform velocity in the floodplain and transition regions between plain and main channels than the others in all calculated cases. This empiricism predicted a very close variation of eddy viscosity in comparison with the results calculated by the depth-averaged Reynolds' stress and the lateral gradient of longitudinal velocity. The eddy viscosity varies significantly in the channel section; in particular the small values often occurred around the middle location of floodplains and the central location of the main channel while the large values appeared in the transition regions, presenting different minimum and maximum values of eddy viscosity in each flow region. The effects of eddy viscosity variation on lateral distribution of velocity profile were also investigated and discussed.     

FST2DH模型在水流计算中的应用实例

河道水流模拟和河床冲淤计算是河流模拟中经常遇到的问题。FST2DH模型是比较适用于水动力和泥沙计算的二维模型，对局部水工构筑物附近水流和泥沙运动的模拟更具优势，河流桥墩附近的水流模拟实例也说明该模型是方便和有效的。     

NUMERICAL STUDY OF TURBULENT JETS CONFINED BETWEEN TWO CONCENTRIC SPHERES

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