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.

COMPUTATION OF RECIRCULATING SWIRLING FLOW WITH THE GLM REYNOLDS STRESS CLOSURE

A Reynolds stress closure based on the generalized Langevin model (GLM), developed by Haworth and Pope, is applied to the flow calculation with swirl-induced recirculation. The purpose of the work is to assess the performance of this model under the complex flow conditions caused by the presence of strong swirl which gives rise to both unconventional recirculation in the vicinity of the symmetry axis and strong anisotropy in the turbulence field. Comparison of the computational results are made both with the experimental data of Roback and Johnson and the computational results obtained with the typical isotropization of production model (IPM) and the k-∈ type Boussinesq viscosity model.

Modeling and Numerical Simulation of Wings Effect on Turbulent Flow between two contra-rotating cylinders

Many industries in the world take part in the pollution of the environment. This pollution often comes from the reactions of combustion. To optimize these reactions and to minimize pollution, turbulence is a funda- mental tool. Several factors are at the origin of turbulence in the complex flows, among these factors, we can quote the effect of wings in the rotating flows. The interest of this work is to model and to simulate numeri- cally the effect of wings on the level of turbulence in the flow between two contra-rotating cylinders. We have fixed on these two cylinders eight wings uniformly distributed and we have varied the height of the wings to have six values from 2 mm to 20 mm by maintaining the same Reynolds number of rotation. The numerical tool is based on a statistical model in a point using the closing of the second order of the transport equations of the Reynolds stresses (Reynolds Stress Model: RSM). We have modelled wings effect on the flow by a source term added to the equation tangential speed. The results of the numerical simulation showed that all the average and fluctuating variables are affected the value of the kinetic energy of turbulence as those of Reynolds stresses increase with the height of the wings.

Modeling and Numerical Simulation of Wings Effect on Turbulent Flow between Two Contra-Rotating Discs

Turbulence is a fundamentally interesting physical phenomenon which is of fundamental interest. Indeed, it is at the origin of several industrial applications, the control of energy in these industrial applications pass by the comprehension and the modelling of turbulent flows. Several factors are at the origin of turbulence in the complex flows, among these factors, we can quote the effect of wings in the rotating flows. The interest of this work is to model and to simulate numerically the effect of wings on the level of turbulence in the flow between two contra-rotating discs. We have fixed on these two discs eight wings uniformly distributed and we have varied the height of the wings to have eleven values from 0 to 18 mm by maintaining the same Reynolds number of rotation. The numerical tool is based on a statistical model in a point using the closing of the second order of the transport equations of the Reynolds stresses （Reynolds Stress Model： RSM）. We have modelled wings effect on the flow by a source term added to the equation tangential speed. The results of the numerical simulation showed that all the average and fluctuating variables are affected the value of the kinetic energy of turbulence as those of Reynolds stresses increase with the height of the wings.

Extended intrinsic mean spin tensor for turbulence modelling in non-inertial frame of reference

We investigate the role of extended intrinsic mean spin tensor introduced in this work for turbulence modelling in a non-inertial frame of reference. It is described by the Euclidean group of transformations and, in particular, its significance and importance in the approach of the algebraic Reynolds stress modelling, such as in a nonlinear K-ε model. To this end and for illustration of the effect of extended intrinsic spin tensor on turbulence modelling, we examine several recently developed nonlinear K-ε models and compare their performance in predicting the homogeneous turbulent shear flow in a rotating frame of reference with LES data. Our results and analysis indicate that, only if the deficiencies of these models and the like be well understood and properly corrected, may in the near future, more sophisticated nonlinear K-ε models be developed to better predict complex turbulent flows in a non-inertial frame of reference.

MODELLING OF THE PRESSURE-VELOCITY CORRELATION IN TURBULENCE DIFFUSION

Most current computations of trubulent flows with second-moment closure adopt the diffusion mo- dels which neglect the effect of pressure-velocity correlation.ln the present paper the importance of this correlation effect is elucidated the neglect of this effect accounts for some major defects in the wide application of the se- cond-moment closures.Through the relation between and ,established by Lumley,we propose here a new turbulence diffusion model which takes into consideration the pressure effect.Applications of this new model in the computation of shearless turbulence mixing layer and plane-and round-jet flows show that the spreading rate of these flows can be satisfactorily captured.

Second-order modeling of non-premixed turbulent methane-air combustion

The main purpose of this research is the second-order modeling of flow and turbulent heat flux in nonpremixed methane-air combustion.A turbulent stream of non-premixed combustion in a stoichiometric condition,is numerically analyzed through the Reynolds averaged Navier-Stokes(RANS) equations.For modeling radiation and combustion,the discrete ordinates(DO) and eddy dissipation concept model have been applied.The Reynolds stress transport model(RSM) also was used for turbulence modeling.For THF in the energy equation,the GGDH model and high order algebraic model of HOGGDH with simple eddy diffusivity model have been applied.Comparing the numerical results of the SED model(with the turbulent Prandtl 0.85) and the second-order heat flux models with available experimental data follows that applying the second-order models significantly led to the modification of predicting temperature distribution and species mass fraction distribution in the combustion chamber.Calculation of turbulent Prandtl number in the combustion chamber shows that the assumption of Pr_(t) of 0.85 is far from reality and Pr_(t) in different areas varies from 0.4 to 1.2.

Simulation of Average Turbulent Pipe Flow: A Three-Equation Model

The aim of this study is to evaluate a three-equation turbulence model applied to pipe flow. Uncertainty is approximated by comparing with published direct numerical simulation results for fully-developed average pipe flow. The model is based on the Reynolds averaged Navier-Stokes equations. Boussinesq hypothesis is invoked for determining the Reynolds stresses. Three local length scales are solved, based on which the eddy viscosity is calculated. There are two parameters in the model;one accounts for surface roughness and the other is possibly attributed to the fluid. Error in the mean axial velocity and Reynolds stress is found to be negligible.

AN EXTENDED k-ε MODEL FOR NUMERICAL SIMULATION OF WIND FLOW AROUND BUILDINGS

It is assumed in this paper that for a high Reynolds number nearly homogeneouswind flow, the Reynolds stresses are uniquely related to the mean velocity gradientsand the two independent turbulent scaling parameters k and E. By applying dimensionalanalysis and owing to the Cayley-Hamilton theorem for tensors, a new turbulenceenclosure model so-called the axtended k-ε model has been developed. The coefficientsof the model expression were detemined by the wind tunnel experimental data ofhomogeneous shear turbulent flow. The model was compared with the standard k-εmodel in in composition and the prediction of the Reynold's normal Stresses. Using thenew model the numerical simulation of wind flow around a square cross-section tallbuilding was performed. The results show that the extended k-ε model improves theprediction of wind velocities around the building the building and wind pressures on the buildingenvelope.

气流强化末精煤溜槽脱水流场数值模拟

为提高选煤厂工业生产废能回收利用,将加压过滤机压风机运行过程产生的废热用于末精煤溜槽进一步脱水,在末精煤离心机出料溜槽设置矩形进风口(风刀),将废热引入溜槽中干燥精煤。通过SolidWorks建立模型并导入ICEM CFD中进行网格划分,然后导入Fluent中进行边界条件设置后进行数值模拟计算。系统研究了风刀位置、风刀数量、风刀角度和热风速度等因素对于溜槽内部流场的影响,结果表明:在双风刀、风速45 m/s、角度0°、高度600 mm条件下,可以明显优化气流在溜槽内的分布,中心平面Y轴右侧(靠近单风刀侧)距离200 mm处轴向未出现气流速度为0的区域,气流流场的作用较全面且均匀,为利用选煤厂废能提供了基础支撑。

Numerical simulation of fluid dynamics in the stirred tank by the SSG Reynolds Stress Model

The Speziale,Sarkar and Gatski Reynolds Stress Model(SSG RSM)is utilized to simulate the fluid dynamics in a full baffled stirred tank with a Rushton turbine impeller.Four levels of grid resolutions are chosen to determine an optimised number of grids for further simulations.CFD model data in terms of the flow field,trailing vortex,and the power number are compared with published experimental results.The comparison shows that the global fluid dynamics throughout the stirred tank and the local characteristics of trailing vortices near the blade tips can be captured by the SSG RSM.The predicted mean velocity components in axial,radial and tangential direction are also in good agreement with experiment data.The power number predicted is quite close to the designed value,which demonstrates that this model can accurately calculate the power number in the stirred tank.Therefore,the simulation by using a combination of SSG RSM and MRF impeller rotational model can accurately model turbulent fluid flow in the stirred tank,and it offers an alternative method for design and optimisation of stirred tanks.

Assessment of alternative scale-providing variables in a Reynolds-stress model using high-order methods

This paper is set in the high-order finite-difference discretization of the Reynolds-averaged Navier-Stokes(RANS)equations,which are coupled with the turbulence model equations.Three alternative scale-providing variables for the specific dissipation rate(o)are implemented in the framework of the Reynolds stress model(RSM)for improving its robustness.Specifically,g(=1/√ω)has natural boundary conditions and reduced spatial gradients,and a new numerical constraint is imposed on itω(=lnω)can preserve positivity and also has reduced spatial gradients;the eddy viscosity v,also has natural boundary conditions and its equation is improved in this work.The solution polynomials of the mean-flow and turbulence-model equations are both reconstructed by the weighted compact nonlinear scheme(WCNS).Moreover,several numerical techniques are introduced to improve the numerical stability of the equation system.A range of canonical as well as industrial turbulent flows are simulated to assess the accuracy and robustness of the scale-transformed models.Numerical results show that the scale-transformed models have significantly improved robustness compared to the w model and still keep the characteristics of RSM.Therefore,the high-order discretization of the RANS and RSM equations,which number 12 in total,can be successfully achieved.

High-order discretization of the Reynolds stress model with anε_(β)-adaptive algorithm

The Reynolds stress model(RSM)outperforms the eddy viscosity model(EVM)when simulating complex flows and has increased demand for high-order discretization.However,the complexity of the RSM equations results in poor numerical stability and weak convergence performance.One of the reasons is that the properties of Reynolds stresses are not fully considered in the design of the numerical scheme.In response to this issue,this study develops an adaptive algorithm to adjustε_(β)values(an empirical parameter in nonlinear weights)according to the magnitude and smoothness of the Reynolds stresses.This algorithm is introduced into the fifth-order weighted compact nonlinear scheme(WCNS)and is applied to the high-order discretization of the RSM.Three aeronautic test cases are simulated to investigate the performance of the algorithm.The numerical results show that,the adaptive algorithm can reduce the residual by up to 3 orders of magnitude and predict the correct weights for gradient reversals.These results confirm that the application of theε_(β)-adaptive algorithm to the high-order discretization of the RSM is beneficial both for enhancing convergence and improving resolution.

A theoretical model for Reynolds-stress and dissipation-rate budgets in near-wall region

A 3-D wave model for the turbulent coherent structures in near-wall region is proposed. The transport nature of the Reynolds stresses and dissipation rate of the turbulence kinetic energy are shown via computation based on the theoretical model. The mean velocity profile is also computed by using the same theoretical model. The theoretical results are in good agreement with those found from DNS, indicating that the theoretical model proposed can correctly describe the physical mechanism of turbulence in near wall region and it thus possibly opens a new way for turbulence modeling in this region.

A CONSTITUTIVE THEORY FOR THE REYNOLDS－STRESS CLOSURES IN TURBULENCE MODELLING

For the Reynolds-stress closures in turbulence modelling, a constitutive theory is developed based on the principle of frame indifference and the theory of invariants. The present study sheds light on existing closure models and is instructive to developing new closure relations.

旋流器流场的数值模拟及对流场特性的分析

旋流器内的流场对分离性能有很大的影响,由于受到各种因素的制约,各使用条件下的旋流器内部流场不可能完全由试验的方式来确定,因此采用数值模拟不失为一种有效的方法,在此液相采雷诺应力模型(RSM)和SIMPLEC算法,对水力旋流器内部流场进行了数值模拟计算,根据计算结果对旋流器内三维速度分布提出了一些新的认识,并分析了旋流器内出现速度缓变区原因,这将导致颗粒富集而出现高浓度区进而影响分离效率;此外,模拟结果显示除了进出口区域外,在分离主体部分的流场也存在着不对称性和不稳定性,这种不对称性和不稳定性受进口速度、进口结构布置以及旋流器锥角的影响;模拟结果还显示在空气柱中心处从底流口至溢流口方向上存在着压力梯度,这将是空气在空气柱内流动的推动力之一,以上的这些特性对进一步充分认识旋流器的分离机理提供了一些依据。

环流式旋风除尘器内流场的数值模拟

采用CFD模拟软件Fluent 6.2提供的雷诺应力模型(RSM)对环流式旋风除尘器内的流场进行了数值模拟研究。并与热线热膜风速仪实验测试结果进行了比较。模拟结果与实验结果基本吻合。结果表明:环流式旋风除尘器特殊的流路设计,避免了内外旋涡的相互干扰,增强了旋转速度,规整了流形,减小了强湍流对性能的影响,消除了旋风除尘器易产生的短路流和二次返混,提高了除尘效率,降低了设备的压降。通过对影响除尘器性能的局部涡进行分析,为进一步优化结构提供了参考依据。

TTU标模风压数值模拟及试验对比

以国际通用的低矮建筑标准模型TTU(德州理工大学)模型为考察对象,在同济大学TJ-2建筑风洞中进行了1∶50缩尺模型的风洞试验研究.通过风洞试验数据与原型场地实测数据的对比,以评估风洞模拟技术的可靠性;同时,基于国际商用软件Fluent的RSM(雷诺应力)模型和CFX的SST(剪切应力运输)模型,从数值模拟的角度研究了TTU实尺度模型的定常绕流场.将数值预测的压力场与实测结果及缩尺模型风洞试验数据进行了比较,分析了风洞试验与场地实测之间、数值模拟与试验之间的异同,得到一些有参考价值的结果.

基于雷诺应力模型的脱油旋流器流场特性研究

采用雷诺应力模型(RSM)对油水分离用水力旋流器进行了数值模拟,模拟出了循环流和短路流现象,得到了内部流场的轴向速度、径向速度和切向速度的分布规律;模拟结果与实验结果吻合较好,说明该湍流模型和计算方法的选取是正确的;另外,针对油相体积分数为2%,油滴粒径为40μm的混合介质进行分析,得出了油水二相的体积分数分布。在旋流器的轴心处油相体积分数最大,最大处混合介质中含油体积分数高达98.9%;在壁面附近体积分数很小,说明该水力旋流器的分离效果较好。通过数值模拟为进一步研究水力旋流器内部流场的分布和结构优化设计奠定了基础。

基于计算流体动力学的迷宫型灌水器流量预测

通过反求迷宫型灌水器注塑产品的实物结构,建立其流量数值预测的物理模型,分别采用层、紊流模型对40～150kPa压力下的灌水器流量进行数值计算,并相应开展该灌水器流量与压力关系的试验测试。试验结果验证了计算流体动力学(CFD)方法预测灌水器流量的可行性,同时对比发现紊流模型的计算值更接近于试验值。通过对迷宫流道内流场分布的研究表明,由于流道曲折度较大,其内流体流动状态的转折点大幅度提前,在雷诺数Re=250～300之间时,流动就开始过渡到紊流状态,从而导致灌水器内的流动在40～150kPa压力测试范围内均处于一种紊流状态。