Numerical simulation of flow separation over a backward-facing step with high Reynolds number

Large eddy simulation (LES) explicitly calculates the large-scale vortex field and parameterizes the small-scale vortices.In this study,LES and κ-ε models were developed for a specific geometrical configuration of backward-facing step (BFS).The simulation results were validated with particle image velocimetry (PIV) measurements and direct numerical simulation (DNS).This LES simulation was carried out with a Reynolds number of 9000 in a pressurized water tunnel with an expansion ratio of 2.00.The results indicate that the LES model can reveal largescale vortex motion although with a larger grid-cell size.However,the LES model tends to overestimate the top wall separation and the Reynolds stress components for the BFS flow simulation without a sufficiently fine grid.Overall,LES is a potential tool for simulating separated flow controlled by large-scale vortices.

Response of turbulent fluctuations to the periodic perturbations in a flow over a backward facing step

The flow structures in a separated shear layer actuated by a synthetic jet actuator were studied using experimental methods. When forced at a frequency much lower than the natural shedding frequency （fH/U = 0.042 orfXr/U = 0.24）, the vertical flapping motion of the shear layer downstream of the separation point became prominent. The size of the peak in the pressure spectra at the forcing frequency （Sta = fAH//U） measured near the separation point （x/H = 1） increased linearly with the forcing ampli- tude （u＇/U） suggesting a linear response of the pressure fluctuations to the forcing by the synthetic jet. The linear response did not hold for the pressure fluctuations away from the jet exit as the magnitude of the peak for StA measured at x/H = 3 soon saturated when the forcing amplitude became larger than 0.3.

EXPERIMENTAL INVESTIGATION ON THE TURBULENT COHERENT STRUCTURES OF LAMINAR SEPARATION FLOW OVER A BACKWARD FACING STEP

The experimental investigation is conducted with LDV and hydrogen bubble technique in water flow. The shear layer thickness. the vorticity thickness. the maximulll value of turbulence intensities. the turbulent coherent structure. the variations of wall shear stress and the boundary layer shape factor are obtained. In the redevelopment region. the detailed analysis is first made for the streak structures in the near wall region and the turbulent boundary layer is formed at (x-xr) / h = 20.

Effect of Richardson number on entropy generation over backward facing step

The flow over a backward facing step （BFS） has been taken as a useful proto- type to investigate intrinsic mechanisms of separated flow with heat transfer. However, to date, the open literature on the effect of Richardson number on entropy generation over the BFS is absent yet, although the flow pattern and heat transfer characteristic both will receive significant influence caused by the variation of Richardson number in many prac- tical applications, such as in microelectromechanical systems and aerocrafts. The effect of Richardson number on entropy generation in the BFS flow is reported in this paper for the first time. The entropy generation analysis is conducted through numerically solving the entropy generation equation. The velocity and temperature, which are the inputs of the entropy generation equation, are evaluated by the lattice Boltzmann method. It is found that the distributions of local entropy generation number and Bejan number are significantly influenced by the variation of Richardson number. The total entropy gen- eration number is a monotonic decreasing function of Richardson number, whereas the average Bejan number is a monotonic increasing function of Richardson number.

Effects of Baffle on Entropy Generation in Separated Convection Flow Adjacent to Inclined Backward-Facing Step

Numerical simulations of a two-dimensional laminar forced convection flow adjacent to inclined backward-facing step in a rectangular duct are presented to examine effects of baffle on flow, heat transfer and entropy generation distributions. The main aim of using baffles is to enhance the value of convection coefficient on the bottom wall. But the useful energy can be destroyed due to intrinsic irreversibilities in the flow by the baffle. In the present work, the amount of energy loss is estimated by the computation of entropy generation. The values of velocity and temperature which are the inputs of the entropy generation equation are obtained by the numerical solution of momentum and energy equations with blocked-off method using computational fluid dynamic technique. Discretized forms of the governing equations in the (x, y) plane are obtained by the control volume method and solved using the SIMPLE algorithm. Numerical expressions, in terms of Nusselt number, entropy generation number, Bejan number and coefficient of friction are derived in dimensionless form. Results show that although a baffle mounted onto the upper wall increases the magnitude of Nusselts number on the bottom wall, but a considerable increase in the amount of entropy generation number takes place because of this technique. For validation, the numerical results for the Nusselt number and entropy generation number are compared with theoretical findings by other investigators and reasonable agreement is found.

Analysis of Combined Radiation and Forced Convection Heat Transfer in 3D Laminar Flow over an Inclined Forward Facing Step

In the current study, a numerical investigation of three-dimensional combined convection-radiation heat transfer over an inclined forward facing step (FFS) in a horizontal rectangular duct is presented. The fluid is treated as a gray, absorbing, emitting and scattering medium. To simulate the incline surface of FFS, the blocked-off method is employed in this study. The set of governing equations for gas flow are solved numerically using the CFD technique to obtain the temperature and velocity fields. Since the gas is considered as a radiating medium, all of the convection, conduction and radiation heat transfer mechanisms are presented in the energy equation. For computation of radiative term in energy equation, the radiative transfer equation (RTE) is solved numerically by the discrete ordinates method (DOM) to find the divergence of radiative heat flux distribution inside the radiating medium. The effects of optical thickness, radiation-conduction parameter and albedo coefficient on heat transfer behavior of the system are carried out.

Numerical application of k-ε turbulence model to the flow over a backward-facing step

A model that uses the operator splitting technique based on Eulerian-Lagrangian method and embeds the k-ε turbulence mode is developed. The model is used to simulate a two dimensional flow over a backward-facing step with triangular mesh discrete flow field. The convection operator is solved with the characteristic method and the diffusion operator and pressure-Poisson equation are solved by finite element method. The results from the example showed that numerical results are well agreed with the experimental data,and that the method can be adapted to simulate complex turbulent flow with strong non-linear convection. The treatment of boundary conditions is also studied in the paper.

Analysis of flow over backward facing step with transition

The present study deals with the study of the velocity distribution and the separation phenomenon of flow of air over a two dimensional backward facing step. The flow of air over a backward facing step has been investigated numerically using FLUENT. Flow simulation has been carried out in a backward facing step having an expansion ratio （ratio of the height before and after the step） of 1：1.94 and the results obtained are compared with the published experimental results. Comparison of flow characteristics between steps with three different transitions is made. The variation ofreattachment length for all the three cases are analyzed for wide range of Reynolds number ranging from 100 to 7000 which covers the laminar, transition and turbulent flow of air. Simulation of the flow over steps with expansion ratios of 1：1.24, 1：1.38, 1：1.47, 1：1.53, 1：1.94, 1：2.20 are also carried out to examine the effect of different expansion ratios on the reattachment length. It is found that the primary reattachment length increases with increase in the expansion ratio. The primary reattachment length at the bottom wall downstream of the step is minimum for the step with round edged transition and maximum for the step with a vertical drop transition.

Large Eddy Simulation of a dilute particleladen turbulent flow over a backwardfacing step

Dilute gas-particle turbulent flows over a backward-facing step are numerically simulated by Large Eddy Simulation (LES) for the continuous phase and Lagran- gian particle trajectory method for the particle phase. Predicted results of mean velocities and fluctuating velocities of both phases agree well with the experimental data, and demonstrate that the main characteristics of the flow are accurately captured by the simulations. Characteristics of separation and reattachments as well as essential features of the coherent structure are obtained, in which the processes of vortex roll up, growth, pairing and breaking up are shown in details. Particle dispersions are then investigated through particles’ instantaneous distri- butions in coherent structure as well as the mean and fluctuating properties of particle number density (PND). The predicted mean PND agree well with experiment results. For small particles, the instantaneous distributions show much preferential concentration, while their mean PND shows more uniform distribution in down- stream region. On the contrary, for large particles, their instantaneous distributions are much uniform (without clear preferential concentration) due to less effect of large eddy coherent, while their mean PND across the section is not uniform for more particles are distributed in the main flow region. The preferential concentra- tion of particles by the large-scale eddies can lead to a high fluctuating PND.

An experimental study on fine structures of supersonic laminar/turbulent flow over a backward-facing step based on NPLS

Fine structures of supersonic flow over a 5 mm high backward facing step(BFS),including expansion wave fan,reattachment shock,supersonic boundary layer were measured in a Ma=3.0 low-noise indraft wind tunnel.By varying the superficial roughness of the wall upstream from the step,supersonic laminar flow and supersonic turbulent flow could be formed over a BFS.Measurements on the spatiotemporal features of the holistic flow field and the fine structures in four typical regions were carried out using NPLS(nano-based planar laser scattering).Flow structures,including expansion wave fan,reattachment shock,supersonic boundary layer and its separation,reattachment and redevelopment are revealed by measuring the holistic structure of the transient flow field.Comparing the two time-averaged flow fields with each other,it is apparent that supersonic turbulent flow over a BFS(STF-BFS) has a larger expansion angle and a shorter recirculation region,and its redeveloped boundary layer increases at a smaller obliquity while the angle of reattachment shock is the same for the supersonic laminar flow over a BFS(SLF-BFS).With regard to time-evolution features,the K-H vortices in the SLF-BFS suffers from shearing,expansion,reattachment and three-dimensional effects while in the STF-BFS large-scale structures are affected by the incline and distortion at the reattachment point due to expansion,viscosity and reverse-pressure.Studies on local regions indicate that in the SLF-BFS,the emergence of compression waves which distinctly converge into a reattachment shock is due to the local convective Mach number and the inducement of K-H vortices in the free shear layer.Nevertheless,in the STF-BFS,compression waves and K-H vortices are barely evident,and the formation of a reattachment shock is related to the wall compressive effect.

SIMULTANEOUS FLOW VISUALIZATION AND WALL-PRESSURE MEASUR EMENT OF THE TURBULENT SEPARATED AND REATTACHING FLOW OVER A BACKWARD-FACING STEP

Unsteady behaviors of the large-scale vortical structure superimposed in the turbulent separated and reattaching flow over a backward-facing step were convincingly delineated by performing simultaneous measurements of the wall pressure fluctuations and visualizations of the flow. Toward this end, a synchronized instrumentation system integrated with the microphone array and the high-speed camera was established. The smoke-wire technique was employed to visualize the unsteady events. A thorough analysis based on the wall pressure fluctuations disclosed that the large-scale vortical structure shedding at the frequency of fH/Uo = 0.064 gave a primary contribution to the wall pressure fluctuations, and consequently dominated unsteady behaviors of the turbulent shear layer. The convection velocity of the large-scale vortical structure was determined as Uc =0.55 U0. The instantaneous flow visualizations and wall pressure were compared in a straightforward manner. Below the separation bubble and the reattachment zone, the negative peak of the time-varying wall pressure was in phase with passage of the local large-scale vortical structure. In the redeveloping turbulent boundary layer, the decaying large-scale vortical structure was clearly revealed.

Probability of Sediment Incipient Motion Under Complex Flows

Presented in this paper is a mathematical model to calculate the probability of the sediment incipient motion, in which the effects of the fluctuating pressure and the seepage are considered. The instantaneous bed shear velocity and the pressure gradient on the bed downstream of the backward-facing step flow are obtained according to the PIV measurements. It is found that the instantaneous pressure gradient on the bed obeys normal distribution. The probability of the sediment incipient motion on the bed downstream of the backward-facing step flow is given by the mathematical model. The predicted results agree well with the experiment in the region downstream of the reattachment point while a large discrepancy between the theory and experiment is seen in the region near the reattachment point. The possible reasons for this discrepancy are discussed.

WALL PRESSURE FLUCTUATIONS OF TURBULENT FLOW OVER BACKWARD-FACING STEP WITH AND WITHOUT ENTRAINMENT: MICROPHONE ARRAY MEASUREMENT

Wall pressure fluctuations in turbulent boundary layer flow over backward-facing step with and without entrainment were investigated. Digital array pressure sensors and multi-arrayed microphones were employed to acquire the time-averaged static pressure and fluctuating pressure, respectively. The differences of two flows were scrutinized in terms of static pressure characteristics, pressure fluctuations, cross-correlation and coherence of wall pressure. Introduction of the entrainment increased scale of large-scale vortical structure and reduced its convection velocity. However, shedding frequency of large-scale vortical structures was found to be the same for both flows.

Turbulent Forced Convection of Radiative Gas Flow in a Duct with Separation

In the present work, a numerical solution is described for turbulent forced convection flow of an absorbing, emitting, scattering and gray fluid over a two-dimensional backward facing step in a horizontal duct. The AKN low-Reynolds-number model is employed to predict turbulent flows with separation and heat transfer, while the radiation part of the problem is modeled by the discrete ordinate method (DOM). Discretized forms of the governing equations for fluid flow are obtained by finite volume approach and solved using SIMPLE algorithm. Results are presented for the distributions of Nusselt numbers as a function of the controlling parameters like radiation-conduction parameter (RC) and optical thickness.

Large Eddy Simulation of Particle-Laden Turbulent Flow over a Backward-Facing Step

Particle diffusion in large eddy structures with various Stokes number was analyzed numerically for the two-dimensional gas-particle turbulent flow over a backward-facing step. The continuous phase simulation was analyzed using the large eddy simulation (LES) method while the particle phase was analyzed by the Lagrangian method. The spatial and temporal results were used to analyze the evolution of the large eddy coherent structures and the vortex-particle interactions. The effect of the particle Stokes number on the in-stantaneous particle concentration distributions was also discussed. The simulations of the single-phase flow reproduced the character of the separation and reattachment flow and the essential features of the coherent structures. Numerous and complex vortex structures appeared at the high Reynolds number. Furthermore, the simulation shows that the Stokes number plays an important role in the particle dispersion and the instanta-neous particle distribution. The continuous phase time-averaged results and the particle phase time-averaged results obtained from the LES analysis agree well with previous experimental data.

EXPERIMENT STUDY ON SEDIMENT INCIPIENCE IN BACKWARD-FACING STEP FLOW

Flow over a backward-facing step was studied to investigate the effect of large-scale vortex structures on sediment incipience. The transient flow velocity field at the downstream of the backward-facing step was obtained using the technique of Particle Tracking Velocimetry （PTV）. The optical amplification technique was employed to measure the instantaneous flow velocities near the bed and the instantaneous bed shear stress was given. The experimental observations revealed a new insight into the oscillation of the large-scale structure and the three-dimensional characteristics of the flow. In particular, very high turbulence intensity, instantaneous horizontal velocity near the bed and the bed shear stress near the reattachment point were observed. The sediment incipient probability obtained from the sequent images of sediment particles near the bed indicates that the critical instantaneous shear stress of the sediment incipience is independent of flow conditions.

考虑双向耦合效应的格子Boltzmann气固两相湍流模型

在流体粒子概率密度函数输运方程中考虑颗粒对流体的反作用力,发展了考虑双向耦合效应的LB气固两相流模型,引入Smagorinsky亚格子模型模拟高雷诺数气相流场.对经典后台阶气固两相流动进行模拟,气相和颗粒相速度分布与实验结果进行比较,发现考虑双向耦合效应的LB气固两相流模型结果明显优于单向耦合结果.进一步研究不同惯性颗粒在流场中的弥散特性,小颗粒(St～O(0.1))对流体的跟随性较好,在流场中分布较为均匀;而St～O(1)的颗粒难被流场涡卷吸进入涡内,呈现倾向性弥散现象;大颗粒(St～O(10))由于自身惯性进入流场涡,在流场中分布较为均匀.

不可压缩二维流动Navier-Stokes方程的有限元解

对不可压缩流体沿二维后台阶流动的Ｎ－Ｓ方程的流函数－涡量式用有限元方法加以求解，固壁上的涡量用时间迭代法加以确定。分别计算Ｒｅ＝２００，４００，８００和１０００时流动区域的流函数和涡量值，并在Ｒｅ＝８００时与有关文献的结果相比较，基本吻合。且在此基础上讨论了出口条件对计算结果的影响。本文的方法对分析流经液压阀口等流动问题具有借鉴意义。

后台阶流动的非均匀格子Boltzmann方法模拟

使用非均匀格子Boltzmann方法对后台阶流动进行了数值模拟。将流体流动区域划分为不同的子区域:对于每个子区域内部,分布函数使用均匀网格计算;对于区域边界,分布函数采用嵌套网格方法进行处理。数值计算结果与其它实验、数值结果相吻合。

Richardson数对后台阶流动熵产的影响

后台阶流动是研究伴随有传热现象的分离流动的常用模型.虽然Richardson数的改变会明显影响分离流动的流动和传热特性,但是迄今为止关于Richardson数对后台阶流动熵产影响的研究依然很少.基于求解熵产方程,第一次系统研究Richardson数对后台阶流动熵产的影响.对于求解熵产方程所需的速度和温度等变量,通过格子Boltzmann方法来得到.通过上述工作可以发现,后台阶流动中熵产和Bejan数的分布随Richardson数变化显著.总熵产数是Richardson数的单调减函数而平均Bejan数是Richardson数的单调增函数.