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.     

HYDRAULIC PERFORMANCES OF SKIMMING FLOW OVER STEPPED SPILLWAY

Hydraulic performances of skimming flow over stepped spillway was studied by means of hydraulic model experiment. The stepped spillway is a modification of the WES (Waterways Experiment Station) standard spillway. The main objective of the experiment was to study the performances of skimming flow over stepped spillway, which include the skimming flow regime, the flow depth on the spillway , the effect of air en-trainment and the energy dissipation. Presented in this paper, the experimental results indicated that the stepped spillway is more effective at dissipating energy, the dissipation ratio decreases with increasing discharge, and the free surface air entrainment on stepped spillway occurs much more upstream than on smooth spillway.     

WEAKLY SWIRLING TURBULENT FLOW IN TURBID WATER HYDRAULIC SEPARATION DEVICE

This article deals with the characteristics of weakly swirling turbulent flow field in a Turbid Water Hydraulic Separation Device （TWHSD） through experimental and numerical researches. The flow field was measured by PIV, which provided streamlines, vortex structure, vorticity and velocity distribution in different test planes in the TWHSD. On the basis of the experimental results, the tangential and radial velocity distributions of the swirling flow field were obtained. Meanwhile, the numerical simulations were conducted with the RNG κ-ε and RSM turbulence models, respectively. According to the experimental and numerical results, the characteristics of the clear water flow field inside the TWHSD were determined. In view of simulation accuracy and time consumption, it is suggested to apply the RNG κ-ε model instead of the RSM model, which is more time consuming, to make further study on two-phases flow fields in the device.     

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.     

A NUMERICAL MODEL FOR 3-D FLOW IN OPEN CHANNELS

A 3-D model based on the Reynolds equations with closed k-ε turbulence model ispresented in this paper,which can be used to predict surface water flow in open channels.In-stead of the“rigid lid”approximation,the solution of the free surface equation is implemented inthe velocity-pressure iterative procedure on the basis of the conventional SIMPLE method.Thismodel was used to compute the flow in rectangular channels with trenches dredged across the bot-tom.The velocity,eddy viscosity coefficient,turbulent shear stress,turbulent kinetic energyand elevation of the free surface over the trenches dredged in the main channel,can be obtained.The computed results are in good agreement with existing experimentaing data.     

NUMERICAL SIMULATION OF TWO-DIMENSIONAL OVERTOPPING AGAINST SEAWALLS ARMORED WITH ARTIFICIAL UNITS IN REGULAR WAVES

A new mathematical model for the overtopping against seawalls armored with artificial units in regular waves was established. The 2-D numerical wave flume, based on the Reynolds Averaged Navier-Stokes (RANS) equations and the standard k-ε turbulence model, was developed to simulate the turbulent flows with the free surface, in which the Volume Of Fluid (VOF) method was used to handle the large deformation of the free surface and the relaxation approach of combined wave generation and absorbing was implemented. In order to consider the effects of energy dissipation due to the armors on a slope seawall, a porous media model was proposed and implemented in the numerical wave flume. A series of physical model experiments were carried out in the same condition of the numerical simulation to determine the drag coefficient in the porous media model in terms of the overtopping discharge. Compared the computational value of overtopping over the seawall with the experimental data, the values of the effective drag coefficient was calibrated for the layers of blocks at different locations along the seawalls.     

NUMERICAL SIMULATION OF 3-D TURBULENT FLOWS OF PLUNGE POOL AND ENERGY DISSIPATION ANALYSIS

A 3-D numerical model for simulating the complicated turbulent flows was developed and the code was made. A numerical calculation of the plunge pool of Laxiwa project in China was carried on. Those 3-D distributions of velocity,pressure on bottom wall,turbulence kinetic energy and turbulence energy dissipation rate are revealed in detail and the detailed flow patterns of plunge pool were shown. By studying on the characteristics of turbulent diffusion and energy dissipation,the calculated results show that the major turbulence and energy dissipation are taken place near the axis of water jet. The calculated results also indicated that the calculated maximum impact pressures on the bottom wall of the plunge pool have a good agreement with those obtained by physical hydraulic model test.     

Numerical models and theoretical analysis of supercritical bend flow

The flow pattern of supercritical flow in bend channels is complicated due to the shock wave phenomenon, which creates difficulties with regard to research and design of bend channels. Using the spillway of an actual project as an example, a three-dimensional numerical investigation was conducted to simulate the flow in a steep-slope bend based on the renormalization group(RNG) k-ε turbulence flow model and the volume of fluid(VOF) method. The validity of the numerical simulation was demonstrated by comparison between the results of numerical simulation and physical model tests. An optimal scheme of setting vertical vanes in the bend channel is presented. The results of numerical simulation and physical model tests are in agreement, which demonstrates the effectiveness of optimization of vertical vanes and the validity of the three-dimensional numerical simulation. Water depths along both bend walls were analyzed numerically and theoretically. The formula for calculating supercritical water depth along either bend wall was derived, and the critical condition of flow separation from the inner wall was determined.     

LARGE-EDDY AND DETACHED-EDDY SIMULATIONS OF THE SEPARATED FLOW AROUND A CIRCULAR CYLINDER

The separated turbulent flow around a circular cylinder is investigated using Large-Eddy Simulation (LES), Detached-Eddy Simulation (DES, or hybrid RANS/LES methods), and Unsteady Reynolds-Averaged Navier-Stokes (URANS). The purpose of this study is to examine some typical simulation approaches for the prediction of complex separated turbulent flow and to clarify the capability of applying these approaches to a typical case of the separated turbulent flow around a circular cylinder. Several turbulence models, i.e. dynamic Sub-grid Scale (SGS) model in LES, the DES-based Spalart-Allmaras (S-A) and k ? ω Shear-Stress-Transport (SST) models in DES, and the S-A and SST models in URANS, are used in the calculations. Some typical results, e.g., the mean pressure and drag coefficients, velocity profiles, Strouhal number, and Reynolds stresses, are obtained and compared with previous computational and experimental data. Based on our extensive calculations, we assess the capability and performance of these simulation approaches coupled with the relevant turbulence models to predict the separated turbulent flow.     

NUMERICAL ANALYSIS OF LEAKAGE FLOW THROUGH TWO LABYRINTH SEALS

The leakage flow through two labyrinth seals, e.g the interlocking seal and the stepped seal, was numerically investigated. Preliminary calculation of the seal-cavity averaged pressure by using the one-dimensional control volume method showed favorable agreement with the experimental measurements. Subsequently, in-depth understanding of the fluid flow through the labyrinth seals was obtained by employing Computational Fluid Dynamics (CFD) and k ?ε turbulence model, which resulted in a potential wealth of information like the streamline pattern, velocity vector field, and distribution of turbulent kinetic energy and static pressure. At the clearance of the seal the turbulent kinetic energy reached the peak value, while in the bulk region of the cavities it decayed fast. The static pressure rapidly dropped as the fluid flow went through the clearance; no distinct difference of the static pressure was inspected in the cavities. Also noted from the numerical results was that the stepped seal showed better sealing performance than the interlocking seal.     

THREE-DIMENSIONAL TURBULENCE NUMERICAL SIMULATION OF A STEPPED SPILLWAY OVERFLOW

1 .　ＩＮＴＲＯＤＵＣＴＩＯＮＴｈｅａｐｐｌｉｃａｔｉｏｎｏｆｔｈｅｓｔｅｐｐｅｄｓｐｉｌｌｗａｙｈａｓｈａｄａｌｏｎｇｈｉｓｔｏｒｙ .Ｔｈｅ ｐｈｙｓｉｃａｌｍｏｄｅｌｔｅｓｔｓｔｕｄｙｏｆｔｈｅｓｔｅｐｐｅｄｓｐｉｌｌｗａｙｈａｓｂｅｅｎ ｐｅｒｆｏｒｍ     

水沙两相浑水模型的紊流封闭及初步验证

一些学者采用两相浑水模型模拟挟沙水流运动,但其紊流封闭仍借用经验公式、单相紊流模型或双流体紊流模型,未形成两相浑水理论框架下的紊流模式。本文基于双流体紊流模型推导出固液两相浑水紊动能和紊动耗散的偏微分方程,给出固相偏移紊动能的渐近解,以表示固相紊动能与固液两相浑水紊动能的相对差,继而推导出固相紊动耗散的代数表达式,完成对固液两相浑水模型的紊流封闭。固液两相浑水紊流模型能够考虑相间作用和颗粒碰撞等物理机制,保留了双流体紊流模型能够分别计算固、液相各自紊动信息的特点,又将偏微分方程数量减少一半。采用河流动力学绝对含沙量分布的计算方法,并引入各向紊动强度分配系数进行修正后,利用实验资料对两相浑水紊流模型进行验证,计算结果同实测值符合较好,结果表明本文模型能反映出随着泥沙浓度增加,挟沙水流紊动抑制加剧的现象。     

用一种改进的κ—ε模型预测复杂湍流

Ｎａｇａｎｏ和Ｈｉｓｈｉｄａ提出了一个改进的κ－ε模型以计算壁湍流，并在简单流动的计算中得到验证，本文应用这一模型对突缩管内湍流，受限同轴射流和绕障碍物的二维渠道进行了数值预测，结果表明，引进流线曲率修正，该模型可以正确预测二维复杂流动的时均流速。     

A NEW DEPTH-AVERAGED ALGEBRAIC STRESS MODEL AND ITS VERIFICATION TEST

1.mThonvrmNTurbulencemodelshavefoundtheirwideapplicationsinscienceandtechnolOgyrelaedtofiuidflOw.UptonowvariouskindsOfturbulencemedelsaredeveloPedincludingtheone-equatbomodel(Bradshaw,P.etal.,1967),thetwo-equatbomedel(SPalding,l969),themuliple-equationmodel(Davidov,1961),thealgebraicstressmodl(Launder,etal.,1972)andsoon.Amongthesemodels,thetwo-equationkBmodeliswidelytestedandued.Thealgebraicstressmodelsareintermediatebetweensecond-ordercforuerschemesusingtranSPOrtequatbosfortheindividual…     

复杂剪切湍流场中湍流模型的研究

本文分析了双时间尺度湍流模型在复杂流场中的应用效果，并将双时间尺度概念和各向异性的Ｒｅｙｎｏｌｄｓ应力－应变关系相结合，对两个典型湍流场进行了数值模拟。结果表明，双时间尺度模型能较好地预测出复杂剪切流场中的平均物理量，较常规Ｋ－ε模型结果有很大改进。     

对二维翼空化流动的数值模拟

应用二维不可压缩N-S方程结合改进VOF空化模型模拟了NACA66二维翼的空化流动.数值计算中采用SST k-ω湍流模型计算了不同空泡数下定常稳态空化发生时水翼吸力面的压力分布,并与实验结果进行对比,发现空化末端压力梯度计算值明显大于实验值,而且压力有明显突增,通过修正空化模型中的经验参数较好地解决了这个问题.应用SST-SAS湍流模型及修正的经验参数较好地模拟了低空泡数时非定常云空泡的脱落现象,该数值方法对非稳态空化的发展,脱落过程及其频率的预报结果与实验结果吻合良好.     

ANALYSES OF TURBULENT MODELS WITH EXTREMUM LAW OF ENERGY DISSIPATION RATE

By introducing the extremum law of energy dissipation rate into the investigationof turbulent flow,the closure problem for the basic equations is briefly discussed in connectionwith a newly suggested semi-empirical turbulent flow model.As a result,several unknownfunctions which cannot be solved by the existed semi-empirical models are obtained in the presentpaper.It is shown that the turbulent flow models,as the constraints to the extremum problem,have direct influence on the final results of the primary parameters.     

非线性双时间尺度紊流模型的研究与应用

在双时间尺度紊流模型的基础上，对线性涡粘性模型进行了修正，建立了封闭的非线性双时间尺度紊流模型。采用交错网格系统和有限体积法，将修正后的模型应用于具有回流的突扩流的紊流模拟中，其计算结果比采用双时间尺度紊流模型的计算结果有进一步的改进；对泄洪洞进口三维流场的数值模拟的结果与试验结果也较为吻合。     

THREE-DIMENSIONAL NUMERICAL SIMULATION OF AERATED FLOWS DOWNSTREAM SUDDEN FALL AERATOR EXPANSION-IN A TUNNEL

Air entrainment is known to be one of efficient and inexpensive methods to prevent cavitation damages in hydropower projects.The shape of sudden expansion-fall is used as a common device for mitigating cavitation erosions.The complex flow patterns with cavitation are numerically simulated by using the realizable k-εturbulence model and the air-water mixture model.The calculated results are compared well with the experimental results as well as those obtained with the k-εturbulence model with the Volume Of Fluid(VOF)Model.The calculated results agree well with the experimental data for the aeration cavity and wall pressure.Moreover,the air concentration near sidewall is simulated by a mixture model.It is found that the mixture turbulence model is superior to the VOF turbulence model.     

应用K─ε湍流模型模拟空腔内热分层流动

本文应用常规Ｋ─ε湍流模型对空腔内的稳态和非稳态热分层流动进行了数值模拟，主要包括以下三方面的工作：１．空腔内恒温强迫对流流动的模拟；２．空腔内稳态热分层流动的模拟；３．空腔内非稳态热分层流动的模拟。计算结果和实验结果进行了比较，说明常规Ｋ─ε模型能较好地模拟热分层流动的平均温度分布，将对该模拟方法进一步应用于工程问题有重要的指导意义。