An iterative data-driven turbulence modeling framework based on Reynolds stress representation

Data-driven turbulence modeling studies have reached such a stage that the basic framework is settled,but several essential issues remain that strongly affect the performance.Two problems are studied in the current research:(1)the processing of the Reynolds stress tensor and(2)the coupling method between the machine learning model and flow solver.For the Reynolds stress processing issue,we perform the theoretical derivation to extend the relevant tensor arguments of Reynolds stress.Then,the tensor representation theorem is employed to give the complete irreducible invariants and integrity basis.An adaptive regularization term is employed to enhance the representation performance.For the coupling issue,an iterative coupling framework with consistent convergence is proposed and then applied to a canonical separated flow.The results have high consistency with the direct numerical simulation true values,which proves the validity of the current approach.

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.

用RSM模拟旋风分离器内的三维湍流流场

为了选择更适合于旋风分离器流场数值模拟的湍流模型,采用多种湍流模型对旋风分离器的内流场进行数值模拟,并将计算值与试验值进行比较.结果显示:采用RSM(雷诺应力模型)得到的结果比采用标准k-ε模型的更贴近实验值,更适合用于强旋流流场的数值模拟,揭示了强旋流所具有的涡结构及各向异性的特点;采用雷诺应力模型及曲线坐标系下的SIMPLEC算法可以计算湍流各向异性的复杂三维流场.

RSM与LES模拟旋风分离器流场动态特性的对比分析

为评价雷诺应力模型(RSM)与大涡模拟(LES)两种方法计算旋风分离器动态流场的精度,利用FLUENT14对旋风分离器内气相动态流场特性进行数值模拟及分析,考察了两种方法计算得到的瞬时切向速度分布、切向速度脉动强度及切向速度频谱特性。计算结果与热线风速仪(HWA,Hot-wire anemometer)测量的切向速度数据进行无量纲对比表明,在时均切向速度上,LES的模拟结果比RSM的准确性高;在瞬时切向速度上,LES预测的瞬时切向速度可以反映旋流摆动造成的切向速度的波动特性,呈现出接近实验测量值的高频速度脉动变化;而RSM难以预测瞬时切向速度的波动变化,仅给出低频小幅值的波动。因此采用LES预测旋风分离器流场能够捕捉动态信息,揭示流场的动态特性。

使用RSM模型对旋风除尘器内湍流各向异性的数值模拟

旋风除尘器内三维湍流流场具有典型的各项异性,本文采用雷诺应力模型求解该流场得到了三维湍流流场的详细数据,得出了雷诺应力6个分量的分布图,揭示了这类强旋流流场湍流各向异性的特征。典型的几个算例的实践表明:采用雷诺应力模型求解这类流场非常必要,它能较好地反映这类流场的真实物理流动;与相关实验数据的比较表明吻合性较好,显示了本文算法的可行性;计算中发现,发展非结构网格更有利于模拟壁面附近的流动,并节省计算机内存。

一种DRSM湍流模型在导弹绕流模拟中的应用研究

基于平均N-S方程,采用微分雷诺应力湍流模型,非结构混合网格技术,对十字翼导弹绕流流场进行数值模拟。微分雷诺应力模型需要求解雷诺应力张量的每个分量的偏微分方程组,采用压力-应变速率和三阶速度相关项使方程封闭。理论上,微分雷诺应力模型更能反映物理实际。本文研究了十字翼导弹非结构网格的网格收敛性,重点分析了中等大攻角的导弹的压力分布和绕流流场,并将DRSM湍流模型的预测结果与实验数据及SST湍流模型结果进行了对比,数值计算结果和实验数据吻合良好,验证了该种湍流模型对导弹湍流流场的预测能力。

Application of deep learning method to Reynolds stress models of channel flow based on reduced-order modeling of DNS data

Recently,the methodology of deep learning is used to improve the calculation accuracy of the Reynolds-averaged Navier-Stokes (RANS) model.In this paper,a neural network is designed to predict the Reynolds stress of a channel flow of different Reynolds numbers.The rationality and the high efficiency of the neural network is validated by comparing with the results of the direct numerical simulation (DNS),the large eddy simulation (LES),and the deep neural network (DNN) of other studies.To further enhance the prediction accuracy,three methods are developed by using several algorithms and simplified models in the neural network.In the method 1.the regularization is introduced and it is found that the oscillation and the overfitting of the results are eflectively prevented.In the method 2,y^+ is embedded in the input variable while the combination of the invariants is simplified in the method 3.From the predicted results,it can be seen that by using the first two methods,the errors are reduced.Moreover,the method 3 shows considerable advantages in the DNS trend and the smoothness of a curve.Consequently,it is concluded that the DNNs can predict effectively the anisotropic Reynolds stress and is a promising technique of the computational fluid dynamics.

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.

Experimental investigation of Reynolds stress complex eddy viscosity model for coherent structure dynamics

Time sequence signals of streamwise and normal velocity components,as well as velocity strain rate,at different vertical locations in the turbulent boundary layer over a smooth flat plate in a wind tunnel have been finely examined by the use of double-sensor hot-wire anemometry.The local module maximum for wavelet coefficient of longitudinal velocity component,as a detecting index,is employed to educe the ejection and sweep process of the coherent structure burst in the turbulent boundary layer from the random fluctuating background.The coherent waveforms of Reynolds stress residual contribution term for random fluctuations to coherent structure,as well as the velocity strain rate of coherent structure,are extracted by the conditional phase average technique.Based on the theoretical analysis of eddy viscosity coefficient in complex eddy viscosity model for coherent structure,the macro-relaxation effect between Reynolds stress residual contribution term of random fluctuations to coherent structure and the velocity strain rate of coherent structure is studied and the variations of the phase difference between them across the turbulent boundary layer are investigated experimentally.The rationality of complex eddy viscosity model for coherent structure is confirmed through the investigation.

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.

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.

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.

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.

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.

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.

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.

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.

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.