Towards a Unified Turbulence Simulation Approach for Wall-Bounded Flows

A hybrid Reynolds-averaged Navier–Stokes/Large-Eddy Simulation (RANS/LES) methodology has received considerable attention in recent years, especially in its application to wall-bounded flows at high-Reynolds numbers. In the conventional zonal hybrid approach, eddy-viscosity-type RANS and subgrid scale models are applied in the RANS and LES zones, respectively. In contrast, the non-zonal hybrid approach uses only a generalized turbulence model, which provides a unified simulation approach that spans the continuous spectrum of modeling/simulation schemes from RANS to LES. A particular realization of the non-zonal approach, known as partially resolved numerical simulation (PRNS), uses a generalized turbulence model obtained from a rescaling of a conventional RANS model through the introduction of a resolution control function F _R , where F _R is used to characterize the degree of modeling required to represent the unresolved scales of turbulent motion. A new generalized functional form for F _R in PRNS is proposed in this study, and its performance is compared with unsteady RANS (URANS) and LES computations for attached and separated wall-bounded turbulent flows. It is demonstrated that PRNS behaves similarly to LES, but outperforms URANS in general.     

Application of the PITM Method Using Inlet Synthetic Turbulence Generation for the Simulation of the Turbulent Flow in a Small Axisymmetric Contraction

We investigate the turbulence modeling of second moment closure used both in RANS and PITM methodologies from a fundamental point of view and its capacity to predict the flow in a low turbulence wind tunnel of small axisymmetric contraction designed by Uberoi and Wallis. This flow presents a complex phenomenon in physics of fluid turbulence. The anisotropy ratio of the turbulent stresses τ ₁₁/τ ₂₂ initially close to 1.4 returns to unity through the contraction, but surprisingly, this ratio gradually increases to its pre-contraction value in the uniform section downstream the contraction. This point constitutes the interesting paradox of the Uberoi and Wallis experiment. We perform numerical simulations of the turbulent flow in this wind tunnel using both a Reynolds stress model developed in RANS modeling and a subfilter scale stress model derived from the partially integrated transport modeling method. With the aim of reproducing the experimental grid turbulence resulting from the effects of the square-mesh biplane grid on the uniform wind tunnel stream, we develop a new analytical spectral method of generation of pseudo-random velocity fields in a cubic box. These velocity fields are then introduced in the channel using a matching numerical technique. Both RANS and PITM simulations are performed on several meshes to study the effects of the contraction on the mean velocity and turbulence. As a result, it is found that the RANS computation using the Reynolds stress model fails to reproduce the increase of anisotropy in the centerline of the channel after passing the contraction. In the contrary, the PITM simulation predicts fairly well this turbulent flow according to the experimental data, and especially, the “return to anisotropy” in the straight section of the channel downstream the contraction. This work shows that the PITM method used in conjunction with an analytical synthetic turbulence generation as inflow is well suited for simulating this flow, while allowing a drastic reduction of the computational resources.     

Joint RANS/LES Approach to Premixed Flame Modelling in the Context of the TFC Combustion Model

We present an original timesaving joint RANS/LES approach to simulate turbulent premixed combustion. It is intended mainly for industrial applications where LES may not be practical. It is based on successive RANS/LES numerical modelling, where turbulent characteristics determined from RANS simulations are used in LES equations for estimation of the subgrid chemical source and viscosity. This approach has been developed using our TFC premixed combustion model, which is based on a generalization of the Kolmogorov’s ideas. We assume existence of small-scale statistically equilibrium structures not only of turbulence but also of the reaction zones. At the same time, non-equilibrium large-scale structures of reaction sheets and turbulent eddies are described statistically by model combustion and turbulence equations in RANS simulations or follow directly without modelling in LES. Assumption of small-scale equilibrium gives an opportunity to express the mean combustion rate (controlled by small-scale coupling of turbulence and chemistry) in the RANS and LES sub-problems in terms of integral or subgrid parameters of turbulence and the chemical time, i.e. the definition of the reaction rate is similar to that of the mean dissipation rate in turbulence models where it is expressed in terms of integral or subgrid turbulent parameters. Our approach therefore renders compatible the combustion and turbulent parts of the RANS and LES sub-problems and yields reasonable agreement between the RANS and averaged LES results. Combining RANS simulations of averaged fields with LES method (and especially coupled and acoustic codes) for simulation of corresponding nonstationary process (and unsteady combustion regimes) is a promising strategy for industrial applications. In this work we present results of simulations carried out employing the joint RANS/LES approach for three examples: High velocity premixed combustion in a channel, combustion in the shear flow behind an obstacle and the impinging flame (a premixed flame attached to an obstacle).     

基于Navier-Stokes方程残差的隐式大涡模拟有限元模型

对应于湍流的大尺度与小尺度流场信息, 本文在有限元的框架下, 假设Navier-Stokes方程的解的形函数由大尺度和不可解尺度形函数叠加组成, 引入对应的权函数, 将Navier-Stokes方程的有限元变分形式分解为大尺度和不可解尺度系统. 根据不可解尺度系统, 构建基于Navier-Stokes大尺度方程残差的不可解尺度模型, 将其代入Navier-Stokes方程的大尺度系统, 进而数值求解大尺度系统得到Navier-Stokes方程的大尺度解. 该方法无需像传统的大涡模拟方法那样对方程的解进行过滤, 通过对形函数进行尺度分解实现解的尺度分解. 本文使用该方法的自编程序代码开展了槽道湍流的数值模拟. 通过与有限差分大涡模拟、DNS计算结果的比较, 发现在使用较少网格情况下该方法预测的平均流向速度在近壁区与DNS数据吻合, 在黏性外层略偏高; 该方法对雷诺应力预测偏低导致从流向向垂向方向上湍动能输运略偏低. 流向速度等值面图显示该方法有效捕捉到了大尺度旋涡结构; 同时在近壁区可以观察到明显的低速条带结构.      

基于基因表达式编程的数据驱动湍流建模

计算流体动力学是湍流研究的重要手段, 其中雷诺平均模拟在航空航天等实际工程中得到了广泛应用. 雷诺平均模拟的结果很大程度上依赖于湍流模型的预测精度, 而实际工程应用中常用的模型往往精度有限. 近年来, 数据驱动的湍流建模方法得到越来越多的关注. 本文介绍了基于基因表达式编程 (gene-expression programming, GEP) 方法的湍流建模相关进展. 本文首先讨论基因表达式编程应用于湍流建模的具体方法, 包括基本算法、显式代数应力模型和湍流传热两种建模框架、模型测试方法以及损失函数设置等. 在此基础上, 基因表达式编程方法被应用于涡轮叶栅尾流混合、竖直平板间自然对流、三维横向流中的射流等问题. 结果表明, GEP可以有效提升常用模型对于尾流混合损失、壁面热通量等关键参数的预测精度. 基因表达式编程方法可以显式给出模型方程, 因此模型具有可解释性强等特点. 基于双向耦合方法得到的模型还被证明具有较好的后验测试精度和鲁棒性. 基因表达式编程方法还被初步应用于大涡模拟亚格子应力和边界层转捩等问题的建模, 在不同湍流建模领域表现出很大的潜力.      

Simulation of wing-body junction flows with hybrid RANS/LES methods

In this paper, flows past two wing-body junctions, the Rood at zero angle of attack and NASA TN D-712 at 12.5° angle of attack, are investigated with two Reynolds-Averaged Navier-Stokes (RANS) and large eddy simulation (LES) hybrid methods. One is detached eddy simulation (DES) and the other is delayed-DES, both are based on a weakly nonlinear two-equation k–ω model. While the RANS method can predict the mean flow behaviours reasonably accurately, its performance for the turbulent kinetic energy and shear stress, as compared with available experimental data, is not satisfactory. DES, through introducing a length scale in the dissipation terms of the turbulent kinetic energy equation, delivers flow separation, a vortex or the onset of vortex breakdown too early. DDES, with its delayed effect, shows a great improvement in flow structures and turbulence characteristics, and agrees well with measurements.     

A RESIDUAL-BASED UNRESOLVED-SCALE FINITE ELEMENT MODELLING FOR IMPLICT LARGE EDDY SIMULATION 1)

对应于湍流的大尺度与小尺度流场信息, 本文在有限元的框架下, 假设Navier-Stokes方程的解的形函数由大尺度和不可解尺度形函数叠加组成, 引入对应的权函数, 将Navier-Stokes方程的有限元变分形式分解为大尺度和不可解尺度系统. 根据不可解尺度系统, 构建基于Navier-Stokes大尺度方程残差的不可解尺度模型, 将其代入Navier-Stokes方程的大尺度系统, 进而数值求解大尺度系统得到Navier-Stokes方程的大尺度解. 该方法无需像传统的大涡模拟方法那样对方程的解进行过滤, 通过对形函数进行尺度分解实现解的尺度分解. 本文使用该方法的自编程序代码开展了槽道湍流的数值模拟. 通过与有限差分大涡模拟、DNS计算结果的比较, 发现在使用较少网格情况下该方法预测的平均流向速度在近壁区与DNS数据吻合, 在黏性外层略偏高; 该方法对雷诺应力预测偏低导致从流向向垂向方向上湍动能输运略偏低. 流向速度等值面图显示该方法有效捕捉到了大尺度旋涡结构; 同时在近壁区可以观察到明显的低速条带结构.     

速度估计模型在大涡模拟中的应用

介绍了速度估计模型的基本思想及其在物理空间的实现。速度估计模型依靠湍流大尺度的非线性作用估计出小尺度,从而可直接求解亚格子应力项而不需要额外的模型。本文采用该模型对不同雷诺数下的各向同性衰减湍流进行了模拟,并与直接数值模拟、理论分析和其他亚格子模型的大涡模拟结果进行了比较。也初步考察了网格分辨率、不同精度的紧致格式对大涡模拟结果的影响。     

On the simulation of the flow around a circular cylinder at Re=140,000

The flow around a circular cylinder at Reynolds number of 1.4 × 10⁵ is examined with Reynolds-Averaged Navier–Stokes equations (RANS) and Scale-Resolving Simulation (SRS) methods. Such problem is in the upper limit of the flow regime where turbulent transition occurs in the free shear-layers and so the flow dynamics is dominated by the spatial development of vortex-shedding structure, and in particular by the Kelvin–Helmholtz rollers and turbulence onset. The objectives of this investigation are threefold: (i) determine the aptitude of distinct RANS and SRS models to simulate the correct flow regime; (ii) compare the predictions of selected methods with available experimental measurements; and (iii) examine key modelling and flow features that contribute to the observed results. The evaluated models range from RANS supplemented with linear, transition, and non-linear turbulent viscosity closures, to hybrid and bridging SRS methods. Bridging computations are conducted at various constant degrees of physical resolution (range of resolved scales). The results illustrate the complexity of predicting the present flow problem. It is shown that RANS and SRS formulations modelling turbulence in boundary-layers with the selected linear turbulent viscosity closures lead to a premature onset of turbulence which alters the flow regime of the simulations. Although the transition and non-linear RANS closures can predict the correct flow regime, the outcome of this study indicates that solely the bridging model at constant physical resolution is able to achieve an accurate and physics-based prediction of the flow dynamics. Nonetheless, the necessary degree of physical resolution makes the numerical requisites of such computations demanding.     

A Hybrid RANS/LES Simulation of Turbulent Channel Flow

Hybrid models combining large eddy simulation (LES) with Reynolds-averaged Navier–Stokes (RANS) simulation are expected to be useful for wall modeling in the LES of high Reynolds number flows. Some hybrid simulations of turbulent channel flow have a common defect; the mean velocity profile has a mismatch between the RANS and LES regions due to a steep velocity gradient at the interface. This mismatch is reproduced and examined using a simple hybrid model; the Smagorinsky model is switched to a RANS model increasing the filter width. It is suggested that a rapid spatial variation in the eddy viscosity is responsible for an underestimate of the grid-scale shear stress and for the steep velocity gradient. To reduce the mean velocity mismatch a new scheme is proposed; additional filtering is introduced to define two kinds of velocity components at the interface between the two regions. The two components are used to remove inconsistency in the velocity equations due to a rapid variation in the filter width. Using the new scheme, simulations of channel flow are carried out with the simple hybrid model. It is shown that the grid-scale shear stress becomes large enough and most of the mean velocity mismatch is removed. Simulations for higher Reynolds numbers are carried out with the k–ε model and the one-equation subgrid-scale model. Although it is necessary to improve the turbulence models and the treatment of the buffer region, the new scheme is shown to be effective for reducing the mismatch and to be useful for developing better hybrid simulations. Received 5 April 2002 and accepted 8 January 2003 Published online 25 March 2003 Communicated by M.Y. Hussaini     

A reformulated synthetic turbulence generation method for a zonal RANS–LES method and its application to zero-pressure gradient boundary layers

A synthetic turbulence generation (STG) method for subsonic and supersonic flows at low and moderate Reynolds numbers to provide inflow distributions of zonal Reynolds-averaged Navier–Stokes (RANS) – large-eddy simulation (LES) methods is presented. The STG method splits the LES inflow region into three planes where a local velocity signal is decomposed from the turbulent flow properties of the upstream RANS solution. Based on the wall-normal position and the local flow Reynolds number, specific length and velocity scales with different vorticity content are imposed at the inlet plane of the boundary layer. The quality of the STG method for incompressible and compressible zero-pressure gradient boundary layers is shown by comparing the zonal RANS–LES data with pure LES, pure RANS, and direct numerical simulation (DNS) solutions. The distributions of the time and spanwise wall-shear stress, Reynolds stress distributions, and two point correlations of the zonal RANS–LES simulations are smooth in the transition region and in good agreement with the pure LES and reference DNS findings. The STG approach reduces the RANS-to-LES transition length to less than four boundary-layer thicknesses.     

Numerical study of an oscillatory turbulent flow over a flat plate

Oscillatory turbulent flow over a flat plate is studied using large eddy simulation (LES) and Reynolds-average Navier-Stokes (RANS) methods. A dynamic subgrid-scale model is employed in LES and Saffman's turbulence model is used in RANS. The flow behaviors are discussed for the accelerating and decelerating phases during the oscillating cycle. The friction force on the wall and its phase shift from laminar to turbulent regime are also investigated for different Reynolds numbers. The project supported by the Youngster Funding of Academia Sinica and by the National Natural Science Foundation of China     

On the performance of WENO/TENO schemes to resolve turbulence in DNS/LES of high‐speed compressible flows

High‐speed compressible turbulent flows typically contain discontinuities and have been widely modeled using Weighted Essentially Non‐Oscillatory (WENO) schemes due to their high‐order accuracy and sharp shock capturing capability. However, such schemes may damp the small scales of turbulence and result in inaccurate solutions in the context of turbulence‐resolving simulations. In this connection, the recently developed Targeted Essentially Non‐Oscillatory (TENO) schemes, including adaptive variants, may offer significant improvements. The present study aims to quantify the potential of these new schemes for a fully turbulent supersonic flow. Specifically, DNS of a compressible turbulent channel flow with M = 1.5 and Re_τ = 222 is conducted using OpenSBLI, a high‐order finite difference computational fluid dynamics framework. This flow configuration is chosen to decouple the effect of flow discontinuities and turbulence and focus on the capability of the aforementioned high‐order schemes to resolve turbulent structures. The effect of the spatial resolution in different directions and coarse grid implicit LES are also evaluated against the WALE LES model. The TENO schemes are found to exhibit significant performance improvements over the WENO schemes in terms of the accuracy of the statistics and the resolution of the three‐dimensional vortical structures. The sixth‐order adaptive TENO scheme is found to produce comparable results to those obtained with nondissipative fourth‐ and sixth‐order central schemes and reference data obtained with spectral methods. Although the most computationally expensive scheme, it is shown that this adaptive scheme can produce satisfactory results if used as an implicit LES model.     

High-order Large Eddy Simulations of Confined Rotor-Stator Flows

In many engineering and industrial applications, the investigation of rotating turbulent flow is of great interest. In rotor-stator cavities, the centrifugal and Coriolis forces have a strong influence on the turbulence by producing a secondary flow in the meridian plane composed of two thin boundary layers along the disks separated by a non-viscous geostrophic core. Most numerical simulations have been performed using RANS and URANS modelling, and very few investigations have been performed using LES. This paper reports on quantitative comparisons of two high-order LES methods to predict a turbulent rotor-stator flow at the rotational Reynolds number Re(=?Ωb ²/ν)?=4 × 10⁵. The classical dynamic Smagorinsky model for the subgrid-scale stress (Germano et al., Phys Fluids A 3(7):1760–1765, 1991) is compared to a spectral vanishing viscosity technique (Séverac & Serre, J Comp Phys 226(2):1234–1255, 2007). Numerical results include both instantaneous data and post-processed statistics. The results show that both LES methods are able to accurately describe the unsteady flow structures and to satisfactorily predict mean velocities as well as Reynolds stress tensor components. A slight advantage is given to the spectral SVV approach in terms of accuracy and CPU cost. The strong improvements obtained in the present results with respect to RANS results confirm that LES is the appropriate level of modelling for flows in which fully turbulent and transition regimes are involved.     

CFD ANALYSIS OF TURBULENT FLOW PAST SQUARE CYLINDER USING DYNAMIC LES

Computational fluid dynamics (CFD) analysis of turbulent flow past a square cylinder is conducted using large eddy simulation (LES). In the first part of the paper, the implementation of the three-dimensional (3-D) LES computation based on the conventional standard Smagorinsky model (S model) shows a good prediction capability compared with that of turbulence models based on Reynolds-averaged Navier-Stokes equations (RANS models). Next, the computation using the dynamic Smagorinsky model (DS model) is carried out, and the improvement by the use of DS model is described. Lastly, the Lagrangian dynamic Smagorinsky model (LDS model) is introduced to overcome the disadvantages of DS model, e.g., calculation instability. Results obtained from the various SGS models are compared with those from experiments.     

VLES Modeling of Flow Over Walls with Variably-shaped Roughness by Reference to Complementary DNS

Turbulent flow over variably-shaped rough walls, characterized by either a regular or a random arrangement of axisymmetric roughness elements in an open channel flow configuration, is investigated computationally within a VLES (Very Large Eddy Simulation) framework by utilizing a volumetric forcing-based roughness model. The prime objective of the present work is to assess the roughness model’s capability to predict mean velocities and turbulent intensities in conjunction with this recently formulated hybrid LES/RANS (Reynolds-Averaged Navier-Stokes) model. The friction velocity-based Reynolds number is in the range Re_τ =?460 ? 500. A non-dimensional drag function accounting for the shape of the roughness elements is introduced and evaluated based on the results of complementary direct numerical simulations (DNS). The dynamics of the residual motion of the presently adopted VLES methodology is described by an appropriately modified elliptic-relaxation-based ζ ? f (\(\zeta =\overline {v^{2}}/k\)) RANS model.     

A dynamic two-equation Sub Grid Scale model

In this paper we demonstrate that the transport equation of the generalised subgrid scale (SGS) turbulent stress tensor is form-invariant but not frame-indifferent under Euclidean transformations of the frame. A new closure equation between the generalized SGS turbulent stress tensor and the resolved kinematic quantities is proposed. The closure equation at the basis of the proposed model (Two-Equation Model, TEM): a) respects the principle of the turbulence frame indifference [1]; b) takes into account both the anisotropy of the turbulence velocity scales and turbulence length scales; c) removes any balance assumption between the production and dissipation of SGS turbulent kinetic energy; d) assumes scale similarity in the definition of the second-order tensor representing the turbulent velocity scales. In the proposed model: a) the closure coefficient C which appears in the constitutive equation is uniquely determined without using Germanos dynamic procedure [2]; b) the generalized SGS turbulent stress tensor is related exclusively to the generalized SGS turbulent kinetic energy (which is calculated by means of its balance equation) and the modified Leonard tensor; c) the viscous dissipation of the generalized SGS turbulent kinetic energy is calculated by solving the balance equation. The proposed model is tested for a turbulent channel flow at Reynolds numbers (based on friction velocity and channel half-width) ranging from 180 to 2340.Received: 11 February 2004, Accepted: 20 August 2004, Published online: 22 February 2005PACS: 02.60.Cb, 47.27.Eq, 47.11. + j Correspondence to: F. Gallerano     

Unified turbulence models for LES and RANS,FDF and PDF simulations

A review of existing basic turbulence modeling approaches reveals the need for the development of unified turbulence models which can be used continuously as filter density function (FDF) or probability density function (PDF) methods, large eddy simulation (LES) or Reynolds-averaged Navier–Stokes (RANS) methods. It is then shown that such unified stochastic and deterministic turbulence models can be constructed by explaining the dependence of the characteristic time scale of velocity fluctuations on the scale considered. The unified stochastic model obtained generalizes usually applied FDF and PDF models. The unified deterministic turbulence model that is implied by the stochastic model recovers and extends well-known linear and nonlinear LES and RANS models for the subgrid-scale and Reynolds stress tensor.