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.     

Non-Equilibrium Mixing of Turbulence Scales Using a Continuous Hybrid RANS/LES Approach: Application to the Shearless Mixing Layer

A new subgrid-scale (SGS) model based on partially integrated transport method (PITM) is applied to the case of a turbulent spectral non-equilibrium flow created by the mixing of two turbulence fields of differing scales: the shearless mixing layer. The method can be viewed as a continuous hybrid RANS/LES approach. In this model the SGS length scale is no longer given by the size of the discretization step, but is dynamically estimated using an additional transport equation for the dissipation rate. The results are compared to those corresponding to the classical model of Smagorinsky and to the experimental data of Veeravalli and Warhaft. A method for creating an anisotropic analytical pseudo-random field for inflow conditions is also proposed. This approach based on subgrid-scale transport modelling combined with anisotropic inlet conditions gives better results for the prediction of the shearless mixing layer.     

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).     

A Priori Testing of Flamelet Generated Manifolds for Turbulent Partially Premixed Methane/Air Flames

To reduce high computational cost associated with simulations of reacting flows chemistry tabulation methods like the Flamelet Generated Manifold (FGM) method are commonly used. However, H₂, CO and OH predictions in RANS and LES simulations using the FGM (or a similar) method usually show a substantial deviation from measurements. The goal of this study is to assess the accuracy of low-dimensional FGM databases for the prediction of these species in turbulent, partially-premixed reacting flows. It will be examined to what extent turbulent, partially-premixed jet flames can be described by FGM databases based on premixed or counterflow diffusion flamelets and to what extent the chosen molecular transport model for the flamelet influences the accuracy of species mass fraction predictions in CFD-simulations. For LES and RANS applications a model that accounts for subgrid fluctuations has to be added introducing additional errors in numerical results. A priori analysis of FGM databases enables the exclusion of numerical errors (scheme accuracy, convergence) that occur in CFD simulations as well as the exclusion of errors originating from subgrid modeling assumptions in LES and RANS. Four different FGM databases are compared for H₂O, H₂, CO, CO₂ and OH predictions in Sandia Flames C to F. Species mass fractions will be compared to measurements directly and conditioned on mixture fraction. Special attention is paid to the representation of experimentally observed differential diffusion effects by FGM databases.     

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.     

The State of the Art of Hybrid RANS/LES Modeling for the Simulation of Turbulent Flows

This review presents the state of the art of hybrid RANS/LES modeling for the simulation of turbulent flows. After recalling the modeling used in RANS and LES methodologies, we propose in a first step a theoretical formalism developed in the spectral space that allows to unify the RANS and LES methods from a physical standpoint. In a second step, we discuss the principle of the hybrid RANS/LES methods capable of representing a RANS-type behavior in the vicinity of a solid boundary and an LES-type behavior far away from the wall boundary. Then, we analyze the principal hybrid RANS/LES methods usually used to perform numerical simulation of turbulent flows encountered in engineering applications. In particular, we investigate the very large eddy simulation (VLES), the detached eddy simulation (DES), the partially integrated transport modeling (PITM) method, the partially averaged Navier-Stokes (PANS) method, and the scale adaptive simulation (SAS) from a physical point of view. Finally, we establish the connection between these methods and more precisely, the link between PITM and PANS as well as DES and PITM showing that these methods that have been built by different ways, practical or theoretical manners have common points of comparison. It is the opinion of the author to consider that the most appropriate method for a particular application will depend on the expectations of the engineer and the computational resources the user is prepared to expend on the problem.     

An Attempt to Combine Large Eddy Simulation with the k-ε Model in a Channel-Flow Calculation

Large eddy simulation (LES) is combined with the Reynolds-averaged Navier–Stokes (RANS) equation in a turbulent channel-flow calculation. A one-equation subgrid-scale model is solved in a three-dimensional grid in the near-wall region whereas the standard k–ε model is solved in a one-dimensional grid in the outer region away from the wall. The two grid systems are overlapped to connect the two models smoothly. A turbulent channel flow is calculated at Reynolds numbers higher than typical LES and several statistical quantities are examined. The mean velocity profile is in good agreement with the logarithmic law. The profile of the turbulent kinetic energy in the near-wall region is smoothly connected with that of the turbulent energy for the k–ε model in the outer region. Turbulence statistics show that the solution in the near-wall region is as accurate as a usual LES. The present approach is different from wall modeling in LES that uses a RANS model near the wall. The former is not as efficient as the latter for calculating high-Reynolds-number flows. Nevertheless, the present method of combining the two models is expected to pave the way for constructing a unified turbulence model that is useful for many purposes including wall modeling. Received 11 June 1999 and accepted 15 December 2000     

Properties of the hybrid RANS/LES filter

One of the most important and challenging topics in the Large Eddy Simulation of turbulent flows is the connection of the LES technique to the well known and largely used RANS approach where the Navier–Stokes equations are Reynolds averaged. The hybridation of LES and RANS is not only important for its possible practical use, (a rational use of the computational means in different zones), but also from a theoretical point of view, and one possible procedure consists of blending RANS and LES models in the transition zone. In this paper a new filtering technique based on blending filters which transitions smoothly between LES and RANS is proposed and the associated universal model for the subgrid scale stresses is derived. PACS 47.27.Eq     

A hybrid dynamic Smagorinsky model for large eddy simulation

A hybrid dynamic subgrid-scale model (HDSM) pertaining to Large-eddy simulation (LES) has been developed. The coefficient obtained by German dynamic Smagorinsky model (DSM) was integrated with a new dynamic coefficient, based on the dynamic subgrid characteristic length and controlled by the subgrid-scale (SGS) motions. In HDSM, the characteristic wave number determining the characteristic length of the dynamic subgrid is calculated from a new energy weighted mean method when the subgrid scale turbulent kinetic energy and the dissipation wave number are known. The dissipation wave-number is derived from the SGS turbulent kinetic energy spectrum equation. The total dissipation rate spectrum equation is based on the Pao energy spectrum and local equilibrium assumption. The dynamic subgrid characteristic length could take into account the rapidly fluctuating small scale behaviours and the spatial variation of turbulent characteristics. HDSM was used to simulate the fully developed channel and turbulent flow past a circular cylinder, and to determine the impact of the dam-break flow on downstream structure. The HDSM is robust in respect to anisotropic mesh and is less sensitive to grid resolution, and would accurately describe the energy transfer from large-scale to SGS fluctuations and capture more fluctuations of turbulence with same meshes compared to the DSM.     

Passive Scalar Transport Modeling for Hybrid RANS/LES Simulation

A transport model for hybrid RANS/LES simulation of passive scalars is proposed. It invokes a dynamically computed subgrid Prandtl number. The method is based on computing test-filter fluxes. The formulation proves to be especially effective on coarse grids, as occur in DES. After testing it in a wall resolved LES, the present formulation is applied to the Adaptive DDES model of Yin et al. (Phys. Fluids 27, 025105 2015). It is validated by turbulent channel flow and turbulent boundary layer computations.     

Large-eddy structures of turbulent swirling flows and methane-air swirling diffusion combustion

Turbulent swirling flows and methane-air swirling diffusion combustion are studied by large-eddy simulation (LES) using a Smagorinsky-Lilly subgrid scale turbulence model and a second-order moment (SOM) SGS combustion model, and also by RANS modeling using the Reynolds Stress equation model with the IPCM+wall and IPCM pressure-strain models and SOM combustion model. The LES statistical results for swirling flows give good agreement with the experimental results, indicating that the adopted subgrid-scale turbulence model is suitable for swirling flows. The LES instantaneous results show the complex vortex shedding pattern in swirling flows. The initially formed large vortex structures soon break up in swirling flows. The LES statistical results of combustion modeling are near the experimental results and are as good as the RANS-SOM modeling results. The LES results show that the size and range of large vortex structures in swirling combustion are different from those of isothermal swirling flows, and the chemical reaction is intensified by the large-eddy vortex structures. The project supported by the Special Funds for Major State Basic Research (G-1999-0222-07). The English text was polished by Keren Wang.     

A von Neumann–Smagorinsky turbulent transport model for stratified shear flows

A simple subgrid turbulent diffusion model based on an analogy to the von Neumann–Richtmyer artificial viscosity is explored for use in modelling mixing in turbulent stratified shear flow. The model may be more generally applicable to multicomponent turbulent hydrodynamics and to subgrid turbulent transport of momentum, composition and energy. As in the case of the von Neumann artificial viscosity and many subgrid-scale models for large-eddy simulation, the turbulent diffusivity explicitly depends on the grid size and is not based on a quantitative model of the unresolved turbulence. In order to address the issue that it is often not known a priori when and where a flow will become turbulent, the turbulent diffusivity is set to zero when the flow is expected to be stable on the basis of a Richardson/Rayleigh–Taylor stability criterion, in analogy to setting the von Neumann artificial viscosity to zero in expanding flows. One-dimensional predictions of this model applied to a simple shear flow configuration are compared to those obtained using a K–ε model. The density and velocity profiles predicted by both models are shown to be very similar.     

An unsteady incompressible Navier–Stokes solver for large eddy simulation of turbulent flows

An unsteady incompressible Navier–Stokes solver that uses a dual time stepping method combined with spatially high‐order‐accurate finite differences, is developed for large eddy simulation (LES) of turbulent flows. The present solver uses a primitive variable formulation that is based on the artificial compressibility method and various convergence–acceleration techniques are incorporated to efficiently simulate unsteady flows. A localized dynamic subgrid model, which is formulated using the subgrid kinetic energy, is employed for subgrid turbulence modeling. To evaluate the accuracy and the efficiency of the new solver, a posteriori tests for various turbulent flows are carried out and the resulting turbulence statistics are compared with existing experimental and direct numerical simulation (DNS) data. Copyright © 1999 John Wiley & Sons, Ltd.     

An efficient very large eddy simulation model for simulation of turbulent flow

Among the various hybrid methodologies, Speziale's very large eddy simulation (VLES) is one that was proposed very early. It is a unified simulation approach that can change seamlessly from Reynolds Averaged Navier–Stokes (RANS) to direct numerical simulation (DNS) depending on the numerical resolution. The present study proposes a new improved variant of the original VLES model. The advantages are achieved in two ways: (i) RANS simulation can be recovered near the wall which is similar to the detached eddy simulation concept; (ii) a LES subgrid scale model can be reached by the introduction of a third length scale, that is, the integral turbulence length scale. Thus, the new model can provide a proper LES mode between the RANS and DNS limits. This new methodology is implemented in the standard k ? ? model. Applications are conducted for the turbulent channel flow at Reynolds number of Re_τ = 395, periodic hill flow at Re = 10,595, and turbulent flow past a square cylinder at Re = 22,000. In comparison with the available experimental data, DNS or LES, the new VLES model produces better predictions than the original VLES model. Furthermore, it is demonstrated that the new method is quite efficient in resolving the large flow structures and can give satisfactory predictions on a coarse mesh. Copyright © 2012 John Wiley & Sons, Ltd.     

Large-eddy simulation of circular cylinder flow at subcritical Reynolds number: Turbulent wake and sound radiation

The flows past a circular cylinder at Reynolds number 3900 are simulated using large-eddy simulation(LES) and the far-field sound is calculated from the LES results. A low dissipation energy-conserving finite volume scheme is used to discretize the incompressible Navier–Stokes equations. The dynamic global coefficient version of the Vreman's subgrid scale(SGS) model is used to compute the sub-grid stresses. Curle's integral of Lighthill's acoustic analogy is used to extract the sound radiated from the cylinder. The profiles of mean velocity and turbulent fluctuations obtained are consistent with the previous experimental and computational results. The sound radiation at far field exhibits the characteristic of a dipole and directivity. The sound spectra display the-5/3 power law. It is shown that Vreman's SGS model in company with dynamic procedure is suitable for LES of turbulence generated noise.     

Large eddy simulation using a dynamic mixing length subgrid‐scale model

A novel dynamic mixing length (DML) subgrid‐scale model for large eddy simulations is proposed in this work to improve the cutoff length of the Smagorinsky model. The characteristic mixing length (or the characteristic wave number) is dynamically estimated for the subgrid‐scale fluctuation of turbulence by the cutoff wave‐number, k_c, and the dissipation wave‐number, k_d. The dissipation wave number is derived from the kinetic energy spectrum equation and the dissipation spectrum equation. To prove the promise of the DML model, this model is used to simulate the lid‐driven cubical cavity with max‐velocity‐based Reynolds numbers 8850 and 12,000, the channel flows with friction‐velocity‐based Reynolds numbers 180, 395, 590, and 950, and the turbulent flow past a square cylinder at the higher Reynolds number 21,400, respectively, compared with the Smagorinsky model and Germano et al.'s dynamic Smagorinsky model. Different numerical experiments with different Reynolds numbers show that the DML model can be used in simulations of flows with a wide range of Reynolds numbers without the occurrence of singular values. The DML model can alleviate the dissipation of the Smagorinsky model without the loss of its robustness. The DML model shows some advantages over Germano et al.'s dynamic Smagorinsky model in its high stability and simplicity of calculation because the coefficient of the DML model always stays positive. The characteristic mixing length in the DML model reflects the subgrid‐scale fluctuation of turbulence in nature and thus the characteristic mixing length has a spatial and temporal distribution in turbulent flow. Copyright © 2011 John Wiley & Sons, Ltd.     

Hybrid LES–RANS technique based on a one-equation near-wall model

In order to reduce the high computational effort of wall-resolved large-eddy simulations (LES), the present paper suggests a hybrid LES–RANS approach which splits up the simulation into a near-wall RANS part and an outer LES part. Generally, RANS is adequate for attached boundary layers requiring reasonable CPU-time and memory, where LES can also be applied but demands extremely large resources. Contrarily, RANS often fails in flows with massive separation or large-scale vortical structures. Here, LES is without a doubt the best choice. The basic concept of hybrid methods is to combine the advantages of both approaches yielding a prediction method, which, on the one hand, assures reliable results for complex turbulent flows, including large-scale flow phenomena and massive separation, but, on the other hand, consumes much fewer resources than LES, especially for high Reynolds number flows encountered in technical applications. In the present study, a non-zonal hybrid technique is considered (according to the signification retained by the authors concerning the terms zonal and non-zonal), which leads to an approach where the suitable simulation technique is chosen more or less automatically. For this purpose the hybrid approach proposed relies on a unique modeling concept. In the LES mode a subgrid-scale model based on a one-equation model for the subgrid-scale turbulent kinetic energy is applied, where the length scale is defined by the filter width. For the viscosity-affected near-wall RANS mode the one-equation model proposed by Rodi et al. (J Fluids Eng 115:196–205, 1993) is used, which is based on the wall-normal velocity fluctuations as the velocity scale and algebraic relations for the length scales. Although the idea of combined LES–RANS methods is not new, a variety of open questions still has to be answered. This includes, in particular, the demand for appropriate coupling techniques between LES and RANS, adaptive control mechanisms, and proper subgrid-scale and RANS models. Here, in addition to the study on the behavior of the suggested hybrid LES–RANS approach, special emphasis is put on the investigation of suitable interface criteria and the adjustment of the RANS model. To investigate these issues, two different test cases are considered. Besides the standard plane channel flow test case, the flow over a periodic arrangement of hills is studied in detail. This test case includes a pressure-induced flow separation and subsequent reattachment. In comparison with a wall-resolved LES prediction encouraging results are achieved.      

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.     

LES-based filter-matrix lattice Boltzmann model for simulating fully developed turbulent channel flow

In this paper, a three-dimensional filter-matrix lattice Boltzmann (FMLB) model based on large eddy simulation (LES) was verified for simulating wall-bounded turbulent flows. The Vreman subgrid-scale model was employed in the present FMLB–LES framework, which had been proved to be capable of predicting turbulent near-wall region accurately. The fully developed turbulent channel flows were performed at a friction Reynolds number Re_τ of 180. The turbulence statistics computed from the present FMLB–LES simulations, including mean stream velocity profile, Reynolds stress profile and root-mean-square velocity fluctuations greed well with the LES results of multiple-relaxation-time (MRT) LB model, and some discrepancies in comparison with those direct numerical simulation (DNS) data of Kim et al. was also observed due to the relatively low grid resolution. Moreover, to investigate the influence of grid resolution on the present LES simulation, a DNS simulation on a finer gird was also implemented by present FMLB–D3Q19 model. Comparisons of detailed computed various turbulence statistics with available benchmark data of DNS showed quite well agreement.     

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