Turbulent flow around a wall-mounted cube: A direct numerical simulation

An immersed-boundary method was employed to perform a direct numerical simulation (DNS) of flow around a wall-mounted cube in a fully developed turbulent channel for a Reynolds number Re = 5610, based on the bulk velocity and the channel height. Instantaneous results of the DNS of a plain channel flow were used as a fully developed inflow condition for the main channel. The results confirm the unsteadiness of the considered flow caused by the unstable interaction of a horseshoe vortex formed in front of the cube and on both its sides with an arch-type vortex behind the cube. The time-averaged data of the turbulence mean-square intensities, Reynolds shear stresses, kinetic energy and dissipation rate are presented. The negative turbulence production is predicted in the region in front of the cube where the main horseshoe vortex originates.     

基于雷诺应力模型的平衡大气边界层模拟

基于雷诺应力湍流模型（简称RSM模型）,研究了平衡大气边界层风场数值模拟问题．假设流体不可压,且不计雷诺应力输运方程中的对流项、浮力产生项、系统旋转产生项和扩散项,在准各向同性的条件下,推导出RSM模型湍动能k的表达式是标准k-ε模型k常数表达式的0.893倍．考虑k沿高度变化的修正,根据在标准k-ε模型中满足水平均匀性的湍流来流边界条件,提出在RSM模型中产生平衡大气边界层的湍流来流边界条件．基于空风洞的数值模拟结果表明,与工程上常用的湍流来流边界条件相比,基于本文提出的湍流来流边界条件得到的风场水平均匀性更优,且在整个流域内,得到的雷诺应力剖面更合适．从而验证了该湍流来流边界条件的适用性．     

Three-dimensional particle-tracking velocimetry measurement of turbulence statistics and energy budget in a backward-facing step flow

Using a three-dimensional (3-D) particle-tracking velocimeter, detailed turbulent flow measurements were made in a plane channel with a one-sided 50% abrupt expansion, which acted as a backward-facing step. The turbulent channel flow reached a fully developed state well upstream of the step. The Reynolds number based on the upstream centerline velocity and the step height H was 5540. With the mean reattachment point located at 6.51H downstream of the step, the measurement region ranged from −2H upstream to 12H downstream of the step. Various turbulent statistics and the energy budget were calculated from numerous instantaneous vector distributions. As in previous experimental investigations, the Reynolds normal and shear stresses had maximum values upstream of the reattachment. The stress anisotropy tensor revealed a peculiar phenomenon near the reattachment wall, wherein the spanwise normal stress was the largest among the three normal stresses. The triple velocity correlations indicated large values in the separating shear layer, and hence the turbulent diffusion was a major term in the energy budget. Comparison was made between the present results and those of the direct numerical simulation (DNS) of Le et al. (1993), and it was found that the mean and fluctuating velocities, the Reynolds shear stress, and the turbulent energy budget were in excellent agreement, although there was a considerable difference in the inflow conditions.     

Generation of turbulent inflow and initial conditions based on multi‐correlated random fields

Direct or large eddy simulation of a turbulent flow field is strongly influenced by its initial or inflow boundary condition. This paper presents a new stochastic approach to generate an artificial turbulent velocity field for initial or inflow boundary condition based on digital filtering. Each velocity component of the artificial turbulent velocity field is generated by linear combination of individual uncorrelated random fields. These uncorrelated random fields are obtained by filtering random white‐noise fields. Using common elements in these linear combinations results in multi‐correlation among different velocity components. The generated velocity field reproduces locally desired Reynolds stress components and integral length scales including cross‐integral length scales. The method appears to be simple, flexible and more accurate in comparison with previously developed methods. The accuracy and performance of the method are demonstrated by numerical simulation of a homogeneous turbulent shear flow with high and low shear rates. To assess the accuracy and performance of the method, simulation results are compared with a reference simulation. Copyright © 2007 John Wiley & Sons, Ltd.     

含污染物的弱弯曲明渠弯道湍流数值模拟

建立了可模拟弯道中含污染物湍流的三维部分抛物型代数应力模型。针对左右两岸分别泄放污染物的环流非充分发展弯道流进行了计算。分析了水流结构及污染物浓度分布的特点。     

Derivation of a second-order model for Reynolds stress using renormalization group analysis and the two-scale expansion technique

With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Yakhot-Orszag renormalization group method to analyze the fluctuating field,the Reynolds-average terms in the Reynolds stress transport equation,such as the convective term,the pressure-gradient-velocity correlation term and the dissipation term,are modeled.Two numerical examples:turbulent flow past a backward-facing step and the fully developed flow in a rotating channel,are presented for testing the efficiency of the proposed second-order model.For these two numerical examples,the proposed model performs as well as the Gibson-Launder (GL) model,giving better prediction than the standard k-ε model,especially in the abilities to calculate the secondary flow in the backward-facing step flow and to capture the asymmetric turbulent structure caused by frame rotation.     

Influence of curvature on drag reduction by opposition control in turbulent flow along a thin cylinder

Opposition controlled fully developed turbulent flow along a thin cylinder is analyzed by means of direct numerical simulations. The influence of cylinder curvature on the skin-friction drag reduction effect by the classical opposition control (i.e., the radial velocity control) is investigated. The curvature of the cylinder affects the uncontrolled flow statistics; for instance, skin-friction coefficient increases while Reynolds shear stress (RSS) and turbulent intensity decrease. However, the control effect in the case of a small curvature is similar to that in channel flow. When the curvature is large, the maximum drag reduction rate decreased. However, the optimal location of the detection plane is the same as that in a flat plate. Further, the drag reduction effect is achieved even on a high detection plane where the drag increases in the flat plate. Although a difference in the drag reduction effect can be observed with a change in the curvature, its mechanism considered in this analysis based on the transport of the Reynolds stress is similar to that of the flat plate.     

Numerical simulation of a low-Reynolds-number turbulent wake behind a flat plate

A numerical simulation of a plane turbulent wake at a very low Reynolds number has been performed using finite volume methods. The wake was produced by allowing two turbulent boundary layers, simulated separately in advance, to interact downstream of the trailing edge of a thin flat plate. A number of innovative numerical techniques were required in the simulation, such as the provision of fully turbulent time-dependent inflow data from a separate simulation, advective outflow boundary conditions and the approximate representation of an internal solid surface by a method which is computationally efficient. The resulting simulation successfully reproduced many of the statistical properties of the turbulent near-wake flow at low Reynolds number.     

Experiments in Turbulent Pipe Flow with Polymer Additives at Maximum Drag Reduction

In this paper we report on (two-component) LDV experiments in a fully developed turbulent pipe flow with a drag-reducing polymer (partially hydrolyzed polyacrylamide) dissolved in water. The Reynolds number based on the mean velocity, the pipe diameter and the local viscosity at the wall is approximately 10000. We have used polymer solutions with three different concentrations which have been chosen such that maximum drag reduction occurs. The amount of drag reduction found is 60–70%. Our experimental results are compared with results obtained with water and with a very dilute solution which exhibits only a small amount of drag reduction. We have focused on the observation of turbulence statistics (mean velocities and turbulence intensities) and on the various contributions to the total shear stress. The latter consists of a turbulent, a solvent (viscous) and a polymeric part. The polymers are found to contribute significantly to the total stress. With respect to the mean velocity profile we find a thickening of the buffer layer and an increase in the slope of the logarithmic profile. With respect to the turbulence statistics we find for the streamwise velocity fluctuations an increase of the root mean square at low polymer concentration but a return to values comparable to those for water at higher concentrations. The root mean square of the normal velocity fluctuations shows a strong decrease. Also the Reynolds (turbulent) shear stress and the correlation coefficient between the stream wise and the normal components are drastically reduced over the entire pipe diameter. In all cases the Reynolds stress stays definitely non-zero at maximum drag reduction. The consequence of the drop of the Reynolds stress is a large polymer stress, which can be 60% of the total stress. The kinetic-energy balance of the mean flow shows a large transfer of energy directly to the polymers instead of the route by turbulence. The kinetic energy of the turbulence suggests a possibly negative polymeric dissipation of turbulent energy. This revised version was published online in July 2006 with corrections to the Cover Date.     

Numerical analysis of turbulent structure in compound meandering open channel by algebraic Reynolds stress model

The turbulent flow in a compound meandering channel with a rectangular cross section is one of the most complicated turbulent flows, because the flow behaviour is influenced by several kinds of forces, including centrifugal forces, pressure‐driven forces and shear stresses generated by momentum transfer between the main channel and the flood plain. Numerical analysis has been performed for the fully developed turbulent flow in a compound meandering open‐channel flow using an algebraic Reynolds stress model. The boundary‐fitted coordinate system is introduced as a method for coordinate transformation in order to set the boundary conditions along the complicated shape of the meandering open channel. The turbulence model consists of transport equations for turbulent energy and dissipation, in conjunction with an algebraic stress model based on the Reynolds stress transport equations. With reference to the pressure–strain term, we have made use of a modified pressure–strain term. The boundary condition of the fluctuating vertical velocity is set to zero not only for the free surface, but also for computational grid points next to the free surface, because experimental results have shown that the fluctuating vertical velocity approaches zero near the free surface. In order to examine the validity of the present numerical method and the turbulent model, the calculated results are compared with experimental data measured by laser Doppler anemometer. In addition, the compound meandering open channel is clarified somewhat based on the calculated results. As a result of the analysis, the present algebraic Reynolds stress model is shown to be able to reasonably predict the turbulent flow in a compound meandering open channel. Copyright © 2005 John Wiley & Sons, Ltd.     

On the effect of Reynolds number on von Kármán’s constant

Fully developed turbulence measurements in pipe flow were made in the Reynolds number ranging from 10×10³ to 350×10³ with a hot-wire anemometer and a Pitot tube. Comparisons were made with the experimental results of previous work. The mean velocity profile and the turbulent intensity in the experiments indicate that for the mean velocity profile, in the fully developed turbulent pipe flow, von Kármán's constant κ is a function of Reynolds number, i.e. κ increases slowly with the Reynolds number. The empirical relationships could not be considered to be accurate enough to describe the fully developed turbulence over the whole Reynolds number range in pipe flow. The project supported by the Deutscher Akademische Austauschdienst (DAAD)     

可压缩均匀剪切湍流的二阶矩模拟

基于对可压缩湍流中脉动压力场和脉动速度场特征的理论分析以及ＤＮＳ结果,建立了可均匀剪切湍流中压力－变形率关联的压缩性修正模式,应用这个模式,加上Ｓａｒｋａｒ等建立的脉动体胀率项（ｄｉｌａｔａｔｉｏｎａｌ ｔｅｒｍｓ）的模式,预测可压缩均匀剪切湍流随时间的发展,所得雷诺应力各是性张量的平衡值与Ｂｌａｉｓｄｅｌｌ等的ＤＮＳ数据非常一致。这个模式准确地预测出均匀剪切湍流中压缩性导致的雷诺应力结构的“流向     

Observations on the predictions of fully developed rotating pipe flow using differential and explicit algebraic Reynolds stress models

The differences between two differential Reynolds stress models (DRSM) and their corresponding explicit algebraic Reynolds stress models (EARSM) are investigated by studying fully developed axially rotating turbulent pipe flow. The mean flow and the turbulence quantities are strongly influenced by the imposed rotation, and is well captured by the differential models as well as their algebraic truncations. All the tested models give mean velocity profiles that are in good qualitative agreement with the experimental data. It is demonstrated that the predicted turbulence kinetic energy levels vary dramatically depending on the diffusion model used, and that this is closely related to the model for the evolution of the length-scale determining quantity. Furthermore, the effect of the weak equilibrium assumption, underlying the EARSMs, and the approximation imposed for 3D mean flows on the turbulence levels are investigated. In general the predictions obtained with the EARSMs rather closely follow those of the corresponding DRSMs.     

Large eddy simulation of a developing turbulent boundary layer at a low Reynolds number

A spectral code has been used to simulate a developing turbulent boundary layer at low Reynolds number Re_θ (based on free stream velocity and momentum thickness) between 353 and 576. The starting field was generated by allowing a step change of temperature to diffuse outwards from one wall in a fully developed channel flow. The thermal boundary layer so created was conditionally sampled to convert it into a momentum boundary layer with an irrotational free stream region, a process which is justified by appeal to experiments. This initial field was allowed to develop until the momentum boundary layer thickness δ₉₉₅ had grown to about 1·5 times its original thickness. The results of the simulation have been compared with a wide range of experimental data. The outcome of this comparison is generally very satisfactory; the main trends of the experiments are well reproduced and our simulation supplements and extends the existing sets of experimental data. The simulation also gives pressure statistics which cannot be obtained experimentally. In particular, it gives the contribution of pressure diffusion to the balance equations for the Reynolds stress and indicates the error produced by omitting this term.     

DNS of backward‐facing step flow with fully turbulent inflow

Direct numerical simulation (DNS) has been performed to study the channel flow over a backward‐facing step at a Reynolds number Re_b=5600 based on the step height h and the inflow bulk velocity U_b. A dynamic method has been used in order to generate realistic turbulent inflow conditions. The results upstream of the step compared well with the fully developed channel flow. Downstream of the step our results show excellent agreement with experimental data. Copyright © 2009 John Wiley & Sons, Ltd.     

Numerical simulation and visualization of fiber suspension in a turbulent round jet

The turbulent properties of the fiber suspension in a turbulent round jet are numerically simulated and visualized, and some of the results are compared with the experimental data. The effects of the Reynolds number, fiber volume fraction, and aspect ratio are analyzed. The results show that the fiber injection in the flow has a delay effect on the streamwise velocity decay along the jet axis, and such an effect becomes more obvious with the increases in the fiber volume fraction and aspect ratio and the decrease in the Reynolds number. The flow with fibers shows an increase in the streamwise velocity along the radial direction, and the increase magnitude is directly proportional to the fiber volume fraction and aspect ratio and inversely proportional to the Reynolds number. The presence of fibers makes the turbulent kinetic energy and Reynolds stress increase, and the extent increases with the fiber volume fraction, Reynolds number, and fiber aspect ratio.     

Direct numerical simulation of turbulence over resolved and modeled rough walls with irregularly distributed roughness

To simulate turbulent flow over a rough wall without resolving complicated rough geometries, a macroscopic rough wall model is developed based on spatial (plane) averaging theory. The plane-averaged drag force term, which arises through averaging the Navier–Stokes equations in a plane parallel to a rough wall, can be modeled using a plane porosity and a plane hydraulic diameter. To evaluate the developed model, direct and macroscopic model simulations for turbulence over irregularly distributed semi-spheres at Reynolds number of 300 are carried out using the D3Q27 multiple-relaxation time lattice Boltzmann method. The results show that the developed model can be used to predict rough wall skin friction. The results agree quantitatively with standard turbulence statistics such as mean velocity and Reynolds stress profiles with the fully resolved DNS data. Since velocity dispersion occurs inside the rough wall and is found to contribute to turbulence energy dissipation, which the developed model cannot account for, the developed model fails to reproduce dispersion-related turbulence energy dissipation. However, it is found that the plane-averaged drag force term can successfully recover the deficiency of dispersion-related turbulence energy dissipation.     

Inflow boundary condition for DNS of turbulent boundary layers on supersonic blunt cones

For direct numerical simulation (DNS) of turbulent boundary layers, gen- eration of an appropriate inflow condition needs to be considered. This paper proposes a method, with which the inflow condition for spatial-mode DNS of turbulent boundary layers on supersonic blunt cones with different Mach numbers, Reynolds numbers and wall temperature conditions can be generated. This is based only on a given instant flow field obtained by a temporal-mode DNS of a turbulent boundary layer on a flat plate. Effectiveness of the method is shown in three typical examples by comparing the results with those obtained by other methods.     

Self-preservation of rough-wall turbulent boundary layers

It is proposed that all fully rough-wall boundary layers should satisfy self-preservation more closely than a smooth-wall boundary layer. Previous work has shown that the self-preserving forms of the momentum and turbulent kinetic energy equations for a zero pressure gradient turbulent boundary layer, at sufficiently high Reynolds number, require that the wall shear stress is constant with x, and the layer thickness increases linearly with x. Measurements in two rough wall boundary layers suggest these conditions are met without assuming a form for the mean velocity distribution, and are more likely to exist in a fully rough wall layer than a smooth wall layer.     

防风网透流风空气动力学特性大涡数值模拟研究

基于有限体积法建立不可压缩粘性流体运动的大涡模拟模型,采用Smagorinsky-Lilly亚格子模型,并引入浸入边界法(IBM)实现无滑移固壁边界条件,对雷诺数30~30000之间防风网透流风进行模拟研究。基于模拟结果,提出蝶型防风网透流风存在4个典型分区结构,流场中存在由蝶型形态引起的大尺度分层剪切流动,加强流体动能耗散。透流风在雷诺数300时发生层流至湍流的转捩,而在雷诺数增长至3000以上时,湍流充分发展,纵向流速脉动强度可达70%。防风网整体空气阻力远大于单个孔口射流阻力的线性叠加,射流间的相互作用以及大尺度的分层剪切结构大大增加流体阻力损失,这为通过优化孔口布置和网板形态来节省材料提供了科学依据。