NUMERICAL SIMULATION OF TURBULENT FREE SURFACE FLOW OVER OBSTRUCTION

A two-dimensional hybrid numerical model, FEM-LES-VOF, for free surface flows is proposed in this study, which is a combination of three-step Taylor-Galerkin finite element method, large eddy simulation with the Smagorinsky sub-grid model and Computational Lagrangian-Eulerian Advection Remap Volume of Fluid （CLEAR-VOF） method. The present FEM-LES-VOF model allows the fluid flows involving violent free surface and turbulence subject to complex boundary configuration to be simulated in a straightforward manner with unstructured grids in the context of finite element method. Numerical simulation of a benchmark problem of dam breaking is conducted to verify the present model. Comparisons with experimental data show that the proposed model works well and is capable of producing reliable predictions for free surface flows. Using the FEM-LES-VOF model, the free surface flow over a semi-circular obstruction is investigated. The simulation results are compared with available experimental and numerical results. Good performance of the FEM-LES-VOF model is demonstrated again. Moreover, the numerical studies show that the turbulence plays an important role in the evolution of free surface when the reflected wave propagates upstream during the fluid flow passing the submerged obstacle.     

NUMERICAL CALCULATION OF TURBULENT FLOW WITH FREE SURFACE

The problem of free surface is one of main difficulties in the numerical calculation of turbulent flow. This pa-per presents the concept of "elastic-lid" for the first time, which is used to calculate the steady turbulent flow do-mains with complex free surfaces. This method can be combined with the existing steady turbulence models. Com-pared with MAC and other unsteady methods, it is simpler and can give us the parameters related to turbulentflow. The method is supported by the techniques of "block-off" and "elastic-grid". which can be selected for dif-ferent problems. Finally, three examples are given to show the application of the "elastic-lid" method. The calcu-lated results are in good agreement with the measured.     

Improved conservative level set method for free surface flow simulation

By coupling the standard and the conservative level set methods, an improved conservative level set method is proposed to capture the free surface smoothly with excellent mass conservation properties. The improvement lies in the fact that the surface normal is computed from a signed distance function instead of the Heaviside function. Comparing with the conservative level set method, the inevitable numerical discretization errors to point the surface normal in arbitrary directions could be eliminated, and the instability of the numerical solution could be improved efficiently. The advantage is clear in the straightforward combination of the standard level set and the conservative level set and a little effort is taken in coding compared with other coupled methods. The present method is validated with several well-known benchmark problems, including the 2-D Zalesak＇s disk rotating, the 3-D sphere stretching in deformation vortex and the dam break flow simulation. The results are shown to be in good agreement with the published experimental data and numerical results.     

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.     

Tracking methods for free surface and simulation of a liquid droplet impacting on a solid surface based on SPH

With some popular tracking methods for free surface, simulations of several typical examples are carried out under various flow field conditions.The results show that the Smoothed Particle Hydrodynamics (SPH) method is very suitable in simulating the flow problems with a free surface.A viscous liquid droplet with an initial velocity impacting on a solid surface is simulated based on the SPH method, and the surface tension is considered by searching the free surface particles, the initial impact effect is co...     

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.     

A Three-Dimensional Desingularized High Order Panel Method Based on Nurbs

A desingularized high order panel method based on Non-Uniform Rational B-Spline （NURBS） was developed to deal with three-dimensional potential flow problems. A NURBS surface was used to precisely represent the body geometry. Velocity potential on the body surface was described by the B-spline after the source density distribution on the body surface had been solved. The collocation approach was employed to satisfy the Neurnann boundary condition and Gaussian quadrature points were chosen as both the collocation points and the source points. The singularity was removed by a combined method, so the process of the numerical computation was non-singular. In order to verify the method proposed, the unbounded flow problems of sphere and ellipsoid, the wave-making problem of a submerged ellipsoid were chosen as computational examples. It is shown that the numerical results are in good agreement with analytical solutions and other numerical results in all cases, and sufficient accuracy of numerical solution can be reached with a small number of panels.     

3-D simulation of transient flow patterns in a corridor-shaped air-cushion surge chamber based on computational fluid dynamics

The 3-D characteristics of the water-air flow patterns in a corridor-shaped air-cushion surge chamber during hydraulic transients need to be considered in the shape optimization. To verify the reliability of the water-air two-phase model, namely, the volume of fluid model, the process of charging water into a closed air chamber is successfully simulated. Using the model, the 3-D flow characteristics under the load rejection and acceptance conditions within the air-cushion surge chamber of a specific hydropower station are studied. The free surface waves, the flow patterns, and the pressure changes during the surge wave process are analyzed in detail. The longitudinal flow of water in the long corridor-shaped surge chamber is similar to the open channel flow with respect to the wave propagation, reflection and superposition characteristics. The lumped parameters of the 3-D numerical simulation agree with the results of a 1-D calculation of hydraulic transients in the whole water conveying system, which validates the 3-D method. The 3-D flow structures obtained can be applied to the shape optimization of the chamber.     

A NUMERICAL METHOD FOR CALCULATING THE EFFECTS OF INLET FLOW ON HYDRODYNAMIC CHARACTERISTICS OF A HYDROFOIL-STRUT-POD CONFIGURATION

A numerical method based on the doublet distribution for calculating theeffects of inlet flow on hydrodynamic characteristics of a hydrofoil-strut-pod configurationunder the linearized free water surface condition is presented in this paper.Inlet flow con-dition is represented by a control section S,in the inlet tube on which the axial velocity is u-niform and determined by a given flowrate.The numerical results for some typical casesare compared with corresponding experimental data.It is found that good agreement be-tween computational and experimental results can be achieved.This numerical methodmay be applied to the prediction of foilborne performance characteristics of a waterjet pro-pelled hydrofoil craft and to optimization of integrated hydrofoil waterjet propulsion sys-tem.     

Unstructured finite volume method for water impact on a rigid body

A new method is presented for the water impact simulation, in which the air-water two phase flow is solved using the pressure-based computational fluid dynamics method. Theoretically, the air effects can be taken into account in the water structure interaction. The key point of this method is the air-water interface capture, which is treated as a physical discontinuity and can be captured by a well-designed high order scheme. According to a normalized variable diagram, a high order discrete scheme on unstructured grids is realised, so a numerical method for the free surface flow on a fixed grid can be established. This method is implemented using an in-house code, the General Transport Equation Analyzer, which is an unstructured grid finite volume solver. The method is verified with the wedge water and structure interaction problem.     

Time domain simulations of radiation and diffraction by a Rankine panel method

The radiation and the diffraction of a ship with a forward speed are studied by using a time domain Rankine panel method. The free surface conditions are linearized onto an undisturbed free surface based on the double body flow. The linearized body boundary condition is applied on the mean wetted hull surface. The fluid domain boundary is discretized by a collection of quadric panels. The unknown quantities, including the free surface elevation, the normal flux over the free surface and the potential on the fluid domain boundary, are determined at each time step. The numerical results are compared with experimental data and other numerical solutions, showing satisfactory agreements.     

九龙峡水电站溢流堰三维数值模拟

 利用 FLUNET 软件,以 k-ε湍流模型封闭 Reynods 方程,采用 VOF 法追踪自由水面,对九龙峡水电站表孔溢流堰的水流按定常流动进行了三维数值模拟。结果表明：溢流堰的泄流能力、水面线、压力分布和流速分布等计算结果与模型试验实测结果吻合良好,说明数值模拟计算可以用于一些水工建筑物泄流计算和设计     

基于光滑粒子流体动力学方法的溃坝水流模拟

受全球气候变暖的影响,由极端天气引发的类似溃坝等问题发生的概率大大增加,深入研究溃坝水流的水动力特性势在必行。在分析光滑粒子流体动力学基本原理的基础上,提出了一种改进的边界处理方法,即将接近壁面的流体视为层流,在耦合动力边界附近引入层流黏性近似边界层理论。采用该方法对溃坝水流进行数值模拟,将SPH数值模拟得到的外轮廓、自由液面高度以及压力与实验结果进行了比较和分析。结果表明：改进的边界处理方法较完整地得到了水流与壁面相互作用而产生的多种复杂的物理现象,其外部轮廓与实验非常吻合;自由表面融合过程中液面间冲击的能量耗散会导致融合后的液面高度存在一些差异;不同监测点处压力随时间的变化基本落在置信区间之内。数值模拟结果与实验结果吻合度较高,验证了改进方案的可靠性和计算结果的准确性。     

Numerical simulation of hydro-elastic problems with smoothed particle hydrodynamics method

Violent free surface flows with strong fluid-solid interactions can produce a tremendous pressure load on structures, resu-lting in elastic and even plastic deformations. Modeling hydro-elastic problem...     

工程中液面波动的数值模拟

本文研究数值模拟含有自由表面的三维非定常流动的表面波动情况。运用部分单元法的概念成功地 各种复杂形状的边界以及复杂的边界条件和流场内部的障碍物，运用ＶＯＦ方法踪自由液面。     

Study of fluid resonance between two side-by-side floating barges

The hydrodynamic interaction between two vessels in a side-by-side configuration attracted research attentions in recent years. However, because the conventional potential flow theory does not consider the fluid viscosity, in the hydrodynamic results, the wave elevations were overestimated in the narrow gap under resonance conditions. To overcome this limitation and investigate the complex fluid flow around multiple bodies in detail, this study examines the fluid resonance between two identical floating barges using a viscous flow analysis program FLOW-3D. The volume of fluid method is implemented for tracking the free surface, and a porous media model is used near the outflow boundary to enhance the wave absorption. A three-dimensional numerical wave basin is established and validated by comparison with the waves generated using theoretical values. On this basis, a computational fluid dynamics(CFD) simulation of the two barges in a resonance wave period is performed, and the wave elevations, the fluid flow around the barges, and the motions of the barges are discussed. The numerical simulation is verified by comparison with results of corresponding experimental data.     

大藤峡水利枢纽船闸中间渠道非恒定流三维数值模拟研究

采用两相流模型,辅以RNGk-ε湍流模型来模拟双级船闸中间渠道的水力特性,对于自由水面的模拟采用了VOF法.通过对中间渠道中非恒定流的三维数值模拟,主要针对波速、振荡波高、局部水面比降、渠道流速等水力要素进行分析,给出了上、下级船闸不同运转方式下的水力特性,为工程设计提供依据,且可为今后类似工程提供参考和借鉴.     

Turbulence characteristics in free-surface flow over two-dimensional dunes

The turbulent structure of open-channel flows over two-dimensional dunes is investigated numerically using large-eddy simulation (LES), in order to improve our understanding of the interaction between the dune-generated turbulence and the free surface dynamics. The filtered Navier–Stokes equations in the LES model have been discretised using the finite volume method, with a dynamic sub-grid model being employed for the unresolved scales of turbulence. The partial cell treatment has been implemented in a Cartesian grid form to deal with the dune topography. Both the volume of fluid method and rigid lid approach have been employed in the numerical framework to investigate the effects of the free surface treatment on the flow characteristics. The numerical model predicted mean flow velocities, turbulence intensities and Reynolds stresses have been compared with experimental measurements published in the literature, with a detailed analysis being undertaken to assess the accuracy of the model results and the effects of the free surface treatment on the velocity and turbulence predictions. The instantaneous flow structure has been investigated, with emphasis being focused on the free surface dynamics and coherent structures.