A near-wall reynolds stress model for backward-facing step flows

A near-wall Reynolds stress model has been used in numerical computations for two-dimensional, incompressible turbulent flows over backward-facing steps. Numerical results are compared with Direct Numerical Simulation data as well as experimental data for flow quantities such as the skin friction, wall pressure,U-velocity and the Reynolds stress. Budgets of the transport equations for theU-velocity, turbulence kinetic energy,k and the Reynolds shear stress,— are also calculated and compared with the Direct Numerical Simulation data. The comparison reveals that the near-wall Reynolds stress model predicts the reattachment length fairly accurately. The near-wall Reynolds stress model also predicts the development of the boundary layer downstream of the reattachment point correctly when the Reynolds number is low. However, the model generally predicts a weak separation bubble and a slowly developing boundary layer when the Reynolds number is high.     

PIV measurements in a turbulent wall jet over a backward-facing step in a three-dimensional,non-confined channel

A study of a turbulent wall jet over a backward-facing step is especially of interest because it shows a rich phenomenon flow and a mechanism to alter the flow characteristics downstream of the step. However, studies on this flow configuration are rare. In this paper, we considered this flow configuration in a non-confined channel as the specific engineering applications of electrical rotating machines and alternator that can be found in modern wind generators of the power production industry and automobile engines. The turbulent wall jet over a backward-facing step in a non-confined wind tunnel had the jet Reynolds number of 24,100 and the step Reynolds number of 11,900. Particle image velocity (PIV) and stereoscopic PIV measurements were performed along the central plane and several cross-stream planes. Numerical simulation of the test configuration was conducted by solving the three-dimensional Reynolds Averaged Navier–Stokes (RANS) equations with the second-order closure Reynolds stress model (RSM). The mean flow fields and second-order statistical moments from the RSM simulation were compared to results that were obtained through the PIV and stereo-PIV experiments. The mean reattachment length obtained from the current configuration was much shorter than those from the backward-facing step in the plane channel. The stereo-PIV measurements in the cross-stream planes revealed a high three-dimensionality of the flow, a high population of streamwise vortice in the upper region, near the side walls and the corners formed by the side walls and the bottom wall. The obtained results also confirmed the presence of the wall-jet formation on the bottom wall.     

A numerical study of three-dimensional backward-facing step flow

The laminar and turbulent flow over a backward-facing step placed in a square duct was investigated numerically. The aspect ratio of the step (step width/step height) was 3 and the area expansion ratio was 2∶3. Three-dimensional effects were significant due to the small aspect ratio. To simulate turbulent flows, both a standardk-? model and a non-lineark-? model were employed and the results were compared. The non-linear model was found to yield better results. From the numerical results, the existence of the corner vortex and the flow field associated with it were clarified. The reattachment length of the three-dimensional flow was found to be considerably shorter than the corresponding two-dimensional flow. The evolution of longitudinal vortices was visualized. Surface flow patterns which clearly demonstrate three-dimensional aspects of the flow were presented. Based on various data available, topological flow pattern was also sketched. To support the findings explored in the present work, expeirmental data were compared with the numerical data where applicable.     

Numerical investigation of turbulent cavitating flow in an axial flow pump using a new transport-based model

Journal of Mechanical Science and Technology - With the aim to enhance the capability of predicting cavitating flows for conventional cavitation models, a developed alternative numerical model was...     

Numerical study on characteristics of turbulent two-phase gas-particle flow using multi-fluid model

The purpose of this research is to study numerically the turbulent gas-particle two-phase flow characteristics using the Eulerian-Eulerian method. A computer code is developed for the numerical study by using the k-ɛ-k _p two-phase turbulent model. The developed code is applied for particle-laden flows in which the particle volume fraction is between 10⁻⁵ and 10⁻² for the Stokes numbers smaller than unity. The gas and particle velocities and the particle volume fraction obtained by using this code are in good agreement with those obtained by a commercial code for the gas-particle jet flows within a rectangular enclosure. The gas-particle jet injected into a vertical rectangular 3D enclosure is numerically modeled to study the effect of the Stokes number, the particle volume fraction and the particle Reynolds numbers. The numerical results show that the Stokes number and the particle volume fraction are important parameters in turbulent gas-particle flows. A small Stokes number (St ≤ 0.07) implies that the particles are nearly at the velocity equilibrium with the gas phase, while a large Stokes number (St ≥ 0.07) implies that the slip velocity between the gas and particle phase increases and the particle velocity is less affected by the gas phase. A large particle volume fraction (α _p ≥ 0.0001) implies that the effect of the particles on the gas phase momentum increases, while a small particle volume fraction (α _p ≤ 0.0001) implies that the particles would have no or small effect on the gas flow field. For fixed Stokes number and particle volume fraction, an increase of the particle Reynolds number results in a decrease of the slip velocity between the gas and particle velocities.     

Numerical simulation of 2-D laminar flow subjected to the Lorentz force effect in a channel with backward-facing step

This paper presents the numerical solutions of a two-dimensional laminar flow over a backward-facing step in the presence of the Lorentz body force. The Navier-Stokes equations in a vorticity-stream function formulation are numerically solved using a uniform grid mesh of 2001 × 51 points. A second-order central difference approximation is used for spatial derivatives. The solutions progress in time with a fourth-order Runge-Kutta method. The unsteady backward-facing step flow solution is computed for Reynolds numbers 100 to 800. The size and genesis of the recirculating regions are dramatically affected by applying the Lorentz force. The results demonstrate that using an appropriate configuration for applying the Lorentz force can make it an essential tool for controlling the flow in channels with a backward-facing step.     

Numerical analysis of turbulent flow and heat transfer in a square sectioned U-bend duct by elliptic-blending second moment closure

A second moment turbulence closure using the elliptic-blending equation is introduced to analyze the turbulence and heat transfer in a square sectioned U-bend duct flow. The turbulent heat flux model based on the elliptic concept satisfies the near-wall balance between viscous diffusion, viscous dissipation and temperature-pressure gradient correlation, and also has the characteristics of approaching its respective conventional high Reynolds number model far away from the wall. Also, the traditional GGDH heat flux model is compared with the present elliptic concept-based heat flux model. The turbulent heat flux models are closely linked to the ellipticblending second moment closure which is used for the prediction of Reynolds stresses. The predicted results show their reasonable agreement with experimental data for a square sectioned U-bend duct flow field adopted in the present study.     

Flow visualization and transient behavior analysis of luminescent mini-tufts after a backward-facing step

Luminescent mini-tufts method has been used for surface flow visualization for a long time. One major challenging point of this method is quantitative analysis of transient flows and the dynamic structures. This study is focused on the application of luminescent mini-tufts method in transient flows. A backward-facing step (BFS) is used in this analysis, which is one classic model that consists both flow separation and re-attachment processes. In this study, the instantaneous mini-tufts recognition, image averaging and tuft inclination angle/tuft angle estimation processes are introduced for the analysis of luminescent mini-tufts for the first time on backward-facing step flow (Re_m = 2.0 × 10⁵–7.9 × 10⁵ and Re_h = 1.3 × 10⁴–5.3 × 10⁴). Detailed transient features and characterization process for the backward-facing step model are explained in this study. The combination of optical-oil flow and hot-wire anemometry methods with luminescent mini-tufts are also shown useful to give comprehensive flow field information, including the surface flow behaviors, boundary layer, re-attachment position identification, etc. In addition, the decomposition of the luminescent mini-tufts visualization data is also conducted to give the power spectral density (PSD) and characteristic frequencies for the mini-tufts behaviors under transient fluctuating flow conditions.     

Large-eddy simulation analysis of turbulent flow over a two-blade horizontal wind turbine rotor

Unsteady turbulent flow characteristics over a two-blade horizontal wind turbine rotor is analyzed using a large-eddy simulation technique. The wind turbine rotor corresponds to the configuration of the U.S. National Renewable Energy Laboratory (NREL) phase VI campaign. The filtered incompressible Navier-Stokes equations in a non-inertial reference frame fixed at the centroid of the rotor, are solved with centrifugal and Coriolis forces using an unstructured-grid finite-volume method. A systematic analysis of effects of grid resolution, computational domain size, and time-step size on simulation results, is carried out. Simulation results such as the surface pressure coefficient, thrust coefficient, torque coefficient, and normal and tangential force coefficients are found to agree favorably with experimental data. The simulation showed that pressure fluctuations, which produce broadband flow-induced noise and vibration of the blades, are especially significant in the mid-chord area of the suction side at around 70 to 95 percent spanwise locations. Large-scale vortices are found to be generated at the blade tip and the location connecting the blade with an airfoil cross section and the circular hub rod. These vortices propagate downstream with helical motions and are found to persist far downstream from the rotor.     

Comparison of two-equation model and reynolds stress models with experimental data for the three-dimensional turbulent boundary layer in a 30 degree bend

The objective of the present study is to investigate the pressure-strain correlation terms of the Reynolds stress models for the three dimensional turbulent boundary layer in a 30° bend tunnel. The numerical results obtained by models of Launder, Reece and Rodi (LRR), Fu and Speziale, Sarkar and Gatski (SSG) for the pressure-strain correlation terms are compared against experimental data and the calculated results from the standard k-ε model. The governing equations are discretized by the finite volume method and SIMPLE algorithm is used to calculate the presure field. The results show that the models of LRR and SSG predict the anisotropy of turbulent structure better than the standard k-ε model. Also, the results obtained from the LRR and SSG models are in better agreement with the experimental data than those of the Fu and standard k-ε models with regard to turbulent normal stresses. Nevertheless, LRR and SSG models do not effectively predict pressure-strain redistribution terms in the inner layer because the pressure-strain terms are based on the locally homogeneous approximation. Therefore, to give better predictions of the pressure-strain terms, non-local effects should be considered.     

Assessment of reynolds stress turbulence closures in the calculation of a transonic separated flow

In this study, the performances of various turbulence closure models are evaluated in the calculation of a transonic flow over axisymmetric bump. k-ε, explicit algebraic stress, and two Reynolds stress models, i. e., GL model proposed by Gibson & Launder and SSG model proposed by Speziale, Sarkar and Gatski, are chosen as turbulence closure models. SSG Reynolds stress model gives best predictions for pressure coefficients and the location of shock. The results with GL model also show quite accurate prediction of pressure coefficients downstream of shock wave. However, in the predictions of mean velocities and turbulent stresses, the results are not so satisfactory as in the prediction of pressure coefficients.     

Drag force control of flow over wavy cylinders at low reynolds number

Three-dimensional numerical simulations on the laminar flow around a circular cylinder with different diameter along the spanwise leading to a type of sinusoidal waviness, named wavy cylinder are performed at low Reynolds number. A series of wavy cylinders with different combinations of spanwise wavelength and wave amplitude are conducted at a Reynolds number of 100. The optimal range of wavelength and the effect of wave amplitude are obtained. The results show that the 3-D free shear layers from the cylinder are more difficult to roll up to vortex and hence the wake formation lengths of some typical wavy cylinders are larger than that of the circular cylinder and in some cases the free shear layers even do not roll up into vortex behind the cylinder. The mean drag coefficients of the typical wavy cylinders are less than that of a corresponding circular cylinder with the same mean diameter; also the fluctuating lift coefficients are reduced. The reduction of mean drag coefficient and fluctuating lift coefficient of wavy cylinder increases with the value of wavy amplitude. Furthermore, a typical wavy cylinder model at Re=150 is also simulated and found that the control of flow induced vibration by modifing the spanwise wavelength of cylinder has a relationship with the variation of Reynolds number.     

SK型静态混合器内的流动特性数值研究

基于微尺度流动特征的角度,研究SK型静态混合器内部湍流时的流动规律.利用计算流体力学专业软件并采用雷诺时均方程和标准的k-ε湍流模型对SK静态混合器内的湍流状态下的三维不可压缩流场进行数值模拟.数值计算和研究表明在含有多个SK型螺旋元件的静态混合器内,受元件衔接处的切割作用的流体将在其后的混合元件的3L/8处完成重新汇合;研究了SK型静态混合器的主要参数对流动阻力的影响,从而为静态混合器的优化设计提供了依据.     

Large eddy simulation of turbulent premixed combustion flows over backward facing step

Large eddy simulation (LES) of turbulent premixed combustion flows over backward facing step has been performed using a dynamic sub-grid G-equation flamelet model. A flamelet model for the premixed flame is combined with a dynamic sub-grid combustion model for the filtered propagation of flame speed. The objective of this study is to investigate the validity of the dynamic sub-grid G-equation model in a complex turbulent premixed combustion flow. For the purpose of validating the LES combustion model, the LES of isothermal and reacting shear layer formed at a backward facing step is carried out. The calculated results are compared with the experimental results, and a good agreement is obtained.     

Numerical simulation of turbulent flow in the suction chamber of a gearpump using deforming mesh and mesh replacement

The flow in the suction chamber of an external gearpump is numerically analysed. The evolution of the boundaries of the domain is very complex, and an arbitrary Lagrangian-Eulerian (ALE) formulation is used with mesh deformation and local remeshing. Nevertheless, a mesh replacement strategy is also adopted in order to avoid skewed meshes and allow for simulation of solid contact between gears. This process approximates a more realistic flow behaviour when the working pressure is larger than 10 bar, which is an important in fluid power systems where the pressure is usually greater than 100 bar.Aside from the laminar model, which fails as a result of the vortex configuration in the suction chamber, Standard k-ε, RNG k-ε, Realizable k-ε and Reynolds Stress Models (RSM) are tested. The numerical flow is compared with experimental data obtained with Time Resolved Particle Image Velocimetry. Although all of the models failed in some respect, the RSM and RNG k-ε were the best choice provided its behaviour close to the gearing zone and general shape of the vortex distribution.     

An analysis of turbulent flow around a NACA4412 airfoil by using a segregated finite element method

A turbulent flow around a NACA4412 airfoil is simulated by a segregated finite element method based on the SIMPLE algorithm and the low Reynolds numberk-ω turbulence model. The originalk-ω model and a modified version of thek-ω, model (shear stress transport model) are adopted, for which grid independent solutions are obtained, respectively. From the present numerical experiment, it has been shown that the segregated finite element method with thek-ω turbulence model can predict the turbulent flow leading to separation satisfactorily with apparently reduced memories compared with the mixed integrated formulation. It is also recommended that for the analysis of external flows a modifiedk-ω model should be used instead of the originalk-ω model, which combines the features of both the standardk-ε model and the originalk-ω model.     

TR-PIV measurement of separated and reattaching turbulent flow over a surface-mounted square cylinder

The separated and reattaching turbulent flow over a surface-mounted two-dimensional square cylinder was experimentally studied by using time-resolved particle image velocimetry (TR-PIV). A total of 61,440 instantaneous image frames were acquired at a framing rate of 125 Hz, yielding a reliable result of the statistical quantities. The time-averaged features of the separated and reattaching flow were analyzed in terms of distributions of the velocity vectors, vorticity, the streamwise velocity fluctuation intensity and shear stress. The association between the large-scale vortical structures and spatial variation of these time-averaged quantities were thoroughly discussed. The unsteady features of the flow were revealed from distributions of the reverse-flow intermittency, space-time contour plot of the fluctuating streamwise velocity, and cross-correlation of the streamwise velocity. Subsequently, a comprehensive understanding of the contribution of the flow structures into the fluctuating flow field was gained by using a snapshot proper orthogonal decomposition (POD) analysis. The results showed that the linear combination of the first five POD modes, which capture 57% of the fluctuation energy, was capable of representing the large-scale behaviors of the separated and reattaching turbulent flow in the senses of spectrum, instantaneous feature and spatial variation of the velocity fluctuation intensity.     

叶栅通道湍流流场的数值模拟方法的研究

采用标准k-ε湍流模型及壁面函数法对双圆弧平面叶栅通道进行数值模拟,开发了二维任意曲线坐标系下采用同位网格布局、能计算跨音速可压缩流动的SIMPLE方法计算程序.为提高精度,采用QUICK格式、CUI格式在不同的网格分布下计算,计算结果与文献和实验数据吻合较好.     

Numerical analysis of pulsating heat pipe based on separated flow model

The examination on the operating mechanism of a pulsating heat pipe (PHP) using visualization revealed that the working fluid in the PHP oscillated to the axial direction by the contraction and expansion of vapor plugs. This contraction and expansion is due to the formation and extinction of bubbles in the evaporating and condensing section, respectively. In this paper, a theoretical model of PHP was presented. The theoretical model was based on the separated flow model with two liquid slugs and three vapor plugs. The results show that the diameter, surface tension and charge ratio of working fluid have significant effects on the performance of the PHP. The following conclusions were obtained. The periodic oscillations of liquid slugs and vapor plugs were obtained under specified parameters. When the hydraulic diameter of the PHP was increased to d=3mm, the frequency of oscillation decreased. By increasing the charging ratio from 40 to 60 by volume ratio, the pressure difference between the evaporating section and condensing section increased, the amplitude of oscillation reduced, and the oscillation frequency decreased. The working fluid with higher surface tension resulted in an increase in the amplitude and frequency of oscillation. Also the average temperature of vapor plugs decreased.     

Numerical analysis of flow and pollutant dispersion over 2-d bell shaped hills

The numerical simulations of flow and pollutant particle dispersion are described for twodimensional bell shaped hills with various aspect ratios. The Reynolds-averaged incompressible Navier-Stokes equations with low Reynolds numberk-ɛ turbulent model are used to simulate the flowfield. The gradient diffusion equation is used to solve the pollutant dispersion field. The code was validated by comparison of velocity, turbulent kinetic energy, Reynolds shear stress, speed-up ratio, and ground level concentration with experimental and numerical data. Good agreement has been achieved and it has been found that the pollutant dispersion pattern and ground level concentration have been strongly influenced by the hill shape and aspect ratio, as well as the location and height of the source.