A hybrid RANS/LES simulation of high-Reynolds-number channel flow using additional filtering at the interface

A hybrid method combining large eddy simulation (LES) with the Reynolds-averaged Navier-Stokes (RANS) equation is used to simulate a turbulent channel flow at high Reynolds number. It is known that the mean velocity profile has a mismatch between the RANS and LES regions in hybrid simulations of a channel flow. The velocity mismatch is reproduced and its dependence on the location of the RANS/LES interface and on the type of RANS model is examined in order to better understand its properties. To remove the mismatch and to obtain better velocity profiles, additional filtering is applied to the velocity components in the wall-parallel planes near the interface. The additional filtering was previously introduced to simulate a channel flow at low Reynolds number. It is shown that the filtering is effective in reducing the mismatch even at high Reynolds number. Profiles of the velocity fluctuations of runs with and without the additional filtering are examined to help understand the reason for the mismatch. Due to the additional filtering, the wall-normal velocity fluctuation increases at the bottom of the LES region. The resulting velocity field creates the grid-scale shear stress more efficiently, and an overestimate of the velocity gradient is removed. The dependence of the velocity profile on the grid point number is also investigated. It is found that the velocity gradient in the core region is underestimated in the case of a coarse grid. Attention should be paid not only to the velocity mismatch near the interface but also to the velocity profile in the core region in hybrid simulations of a channel flow at high Reynolds number. PACS47.27.Eq; 47.27.Nz; 47.60.+i     

Non-zonal detached eddy simulation coupled with a steady RANS solver in the wall region

Xiao and Jenny (2012) proposed an interesting hybrid LES/RANS method in which they use two solvers and solve the RANS and LES equations in the entire computational domain. In the present work this method is simplified and used as a hybrid RANS-LES method, a wall-modeled LES. The two solvers are employed in the entire domain. Near the walls, the flow is governed by the steady RANS solver; drift terms are added to the DES equations to ensure that the time-averaged DES fields agree with the steady RANS field. Away from the walls, the flow is governed by the DES solver; in this region, the RANS field is set to the time-averaged LES field. The disadvantage of traditional DES models is that the RANS models in the near-wall region – which originally were developed and tuned for steady RANS – are used as URANS models where a large part of the turbulence is resolved. In the present method – where steady RANS is used in the near-wall region – the RANS turbulence models are used in a context for which they were developed. In standard DES methods, the near-wall accuracy can be degraded by the unsteady agitation coming from the LES region. It may in the present method be worth while to use an accurate, advanced RANS model. The EARSM model is used in the steady RANS solver. The new method is called NZ S-DES . It is found to substantially improve the predicting capability of the standard DES. A great advantage of the new model is that it is insensitive to the location of the RANS-LES interface.     

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.     

Scrutinizing URANS in Shedding Flows: The Case of Cylinder in Cross-Flow in the Subcritical Regime

To unravel the widespread perception that the RANS (Reynolds-averaged Navier-Stokes) concept is unreliable in predicting the dynamics of separated flows, we assessed the performance of two RANS closure levels, the linear eddy-viscosity (LEVM) and the second-moment (Reynolds stress, RSM) approaches in a massively separated generic flow over a bluff body. Considered is the canonical, zero-turbulence, cross-flow over an infinite cylinder with reference to our LES and the available DNS and experiments at two Reynolds numbers, Re = 3.9 × 10³ and 1.4 × 10⁵, both within the sub-critical regime with laminar separation. Both models capture successfully the vortex shedding frequency, but the low frequency modulations are detected only by the RSM. At high Reynolds numbers the RSM is markedly superior to the LEVM showing very good agreement with the LES and experimental data. The RSM, accounting naturally for the stress anisotropy and phase lag between the stress and strain eigenvectors, is especially successful in reproducing the growth rate of the turbulent kinetic energy in the initial shear layer which proved to be crucial for accurate prediction of the separation-induced transition. A scrutiny of the unsteady RANS (URANS) stress terms based on the conditional phase-averaged LES data shows a remarkable similarity of the normalized coherent and stochastic (modeled) stress components for the two Reynolds numbers considered. The mixed (cross) correlations, while non-negligible at the low Re number, diminish fast relative to the stochastic ones with increasing Reynolds number and, in the whole, are not significant to undermine the URANS concept and its applicability to high Re flows of industrial relevance.     

A Zonal RANS/LES Approach for Noise Sources Prediction

Hybrid CFD/CAA methods have generally to be used for the numerical simulation of trailing-edge noise (see [9, 20] for instance). This study focuses on the first step of such hybrid methods, which is to predict the unsteady aerodynamic sources by the mean of a 3D unsteady simulation of the flow. Such a simulation is however generally still away from the numerical capabilities of ‘usual’ supercomputers. This paper investigates the use of a zonal LES method (based on the NLDE – Non-Linear Disturbance Equations – technique) for the numerical prediction of the aerodynamic noise sources. This method makes it possible to perform only zonal LES close to the main elements responsible of sound generation, while the overall configuration is only treated by a RANS approach. Attention will be paid to the specific boundary treatment at the interface between the RANS and LES regions. More precisely, the problem of the generation of turbulent inflow conditions for the LES region will be carefully addressed. The method is first assessed in the simulation of a flat plate ended by a blunted trailing-edge, and then applied to the simulation of the flow over a NACA0012 airfoil with blunted trailing-edge.     

Hybrid RANS/LES of flow and heat transfer in round impinging jets

Fluid flow and convective heat transfer predictions are presented of round impinging jets for several combinations of nozzle-plate distances H/D = 2, 6 and 13.5 (where D is the nozzle diameter) and Reynolds numbers Re = 5000, 23,000 and 70,000 with the newest version of the k-ω model of Wilcox (2008) and three hybrid RANS/LES models. In the RANS mode of the hybrid RANS/LES models, the k-ω model is recovered. Three formulations are considered to activate the LES mode. The first model is similar to the hybrid models of Davidson and Peng (2003) and Kok et al. (2004). The turbulent length scale is replaced by the grid size in the destruction term of the k-equation and in the definition of the RANS eddy viscosity. As grid size, a maximum measure of the hexahedral grid cell is used. The second model has the same k-equation, but the eddy viscosity is the minimum of the k-ω eddy viscosity and the Smagorinsky eddy viscosity, following a proposal by Batten et al. (2004). The Smagorinsky eddy viscosity is formed with the cube root of the cell volume. The third model has, again, the same k-equation, but has an eddy viscosity which is an intermediate between the eddy viscosities of the first and second models. This is reached by using the cube root of the cell volume in the eddy viscosity formula of the first model.The simulation results are compared with experimental data for the high Reynolds number cases Re = 23,000 and Re = 70,000 and LES data for the low-Reynolds number case Re = 5000. The Reynolds numbers are defined with the nozzle diameter and the bulk velocity at nozzle outlet. At low nozzle-plate distance (the impingement plate is in the core of the jet), turbulent kinetic energy is overpredicted by RANS in the stagnation flow region. This leads to overprediction of the heat transfer rate along the impingement plate in the impact zone. At high nozzle-plate distance (the impingement plate is in the mixed-out region of the jet), the turbulence mixing is underpredicted by RANS in the shear layer of the jet which gives a too high length of the jet core. This also results in overprediction of the heat transfer rate in the impingement zone caused by too big temperature gradients at impingement.All hybrid RANS/LES models are able to correct the heat transfer overprediction of the RANS model. For good predictions at low nozzle-plate distance, it is necessary to sufficiently resolve the formation and development of the near-wall vortices in the jet impingement region. At high nozzle-plate distance, the essence is to capture the evolution and breakup of the flow unsteadiness in the shear layer of the jet, so that accurate mean and fluctuating velocity profiles are obtained in the impingement region. Although the models have a quite different theoretical justification and generate a quite different eddy viscosity in some flow regions, their overall results are very comparable. The reason is that in zones that are crucial for the results, the models behave similarly.     

A Rapid and Accurate Switch from RANS to LES in Boundary Layers Using an Overlap Region

An efficient recycling algorithm is developed for injecting resolved turbulent content in a boundary layer as it switches from a Reynolds Averaged Navier-Stokes (RANS) type treatment to a Large Eddy Simulation (LES) type treatment inside a generalized Detached-Eddy Simulation (DES). The motivation is to use RANS in the thinnest boundary-layer area, following the original argument in favour of DES, and LES in the thicker boundary-layer areas especially approaching separation, to improve accuracy and possibly obtain unsteady outputs. The algorithm relies on an overlap of the RANS and LES domains and, therefore, the availability of both RANS and LES solutions in the recycling region, which is about 5 boundary-layer thicknesses long. This permits a smooth transfer of the turbulent stresses from this section to the LES inflow. The continuity of the skin-friction distribution is very good, reflecting the excellent viability of the resolved turbulence. The approach is validated in a flat-plate boundary layer and an airfoil near stall, with mild pressure gradient near the interface, and then applied to the compressible flow over an idealized airliner windshield wiper. The pressure fluctuations at reattachment are 12dB more intense than under a simple boundary layer at the same speed, and the output contains all the quantities needed to calculate the transmission of sound through the glass.     

Prediction of separation flows around a 6：1 prolate spheroid using RANS/LES hybrid approaches

This paper presents hybrid Reynolds-averaged Navier–Stokes (RANS) and large-eddy-simulation (LES) methods for the separated flows at high angles of attack around a 6:1 prolate spheroid. The RANS/LES hybrid methods studied in this work include the detached eddy simulation (DES) based on Spalart–Allmaras (S–A), Menter’s k–ω shear-stress-transport (SST) and k–ω with weakly nonlinear eddy viscosity formulation (Wilcox–Durbin+, WD+) models and the zonal-RANS/LES methods based on the SST and WD+ models. The switch from RANS near the wall to LES in the core flow region is smooth through the implementation of a flow-dependent blending function for the zonal hybrid method. All the hybrid methods are designed to have a RANS mode for the attached flows and have a LES behavior for the separated flows. The main objective of this paper is to apply the hybrid methods for the high Reynolds number separated flows around prolate spheroid at high-incidences. A fourth-order central scheme with fourth-order artificial viscosity is applied for spatial differencing. The fully implicit lower–upper symmetric-Gauss–Seidel with pseudo time sub-iteration is taken as the temporal differentiation. Comparisons with available measurements are carried out for pressure distribution, skin friction, and profiles of velocity, etc. Reasonable agreement with the experiments, accounting for the effect on grids and fundamental turbulence models, is obtained for the separation flows. The project supported by the National Natural Science Foundation of China (10502030 and 90505005).     

Log-layer mismatch and commutation error in hybrid RANS/LES simulation of channel flow

Hybrid approach combining large eddy simulation (LES) with the Reynolds-averaged Navier–Stokes equation (RANS) is expected to accurately simulate wall-bounded turbulent flows at high Reynolds numbers. As an important issue in developing hybrid methods, it is known that the log layers in the RANS and LES regions are not lined up in hybrid RANS/LES simulations of channel flow. Although several methods including additional filtering near the RANS/LES interface have been proposed to eliminate the log-layer mismatch, there is no obvious physical justification for the methods and some ad hoc tuning is necessary. In this work, the commutation error terms in the filtered velocity equations are investigated to justify the method of additional filtering. It is shown that the additional filtering can be considered as a finite difference approximation to extra terms due to the non-commutivity between the hybrid filter and the spatial derivative. Moreover, an expression determining the filter width and its location for the additional filtering is obtained. To validate the expression, a hybrid simulation of channel flow is carried out. The additional filtering with the filter width derived is shown to be effective in eliminating the log-layer mismatch and improving the mean velocity profile.     

Performances of LES and RANS Models for Simulation of Complex Flows in a Coaxial Jet Mixer

Flow and mixing processes in a classical coaxial jet mixer have been investigated numerically. Calculations have been performed using three Large Eddy Simulation models and three unsteady RANS models. The time averaged mixture fraction and axial velocity, their rms values and energy spectra are compared with LIF and LDA measurements for both j- and r-modes of the jet mixer flow. A special attention is paid to the ability of different models to reproduce unsteady effects. The analysis demonstrates the superiority of the LES method with the dynamic mixed SGS model (DMM) with respect to other RANS and LES models.     

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     

Computational analysis of impinging shock-wave boundary layer interaction under conditions of incipient separation

The interaction of an oblique shock wave with a turbulent boundary layer under conditions of incipient separation is analyzed by means of large-eddy simulation (LES) and Reynolds-averaged Navier–Stokes (RANS) turbulence models, with the objective to explore their predictive capabilities, in particular with respect to the unsteady features of the interaction. Consistent with earlier direct numerical simulations, we have found that the flow dynamics in the interaction zone is characterized by strong intermittency associated with the formation of scattered spots of flow reversal near the nominal position of the reflected shock. Comparison with experimental results (at much larger Reynolds number) show that the qualitative features of the interaction are predicted reasonably well by both LES and RANS models. RANS models supplemented with a semi-empirical closure are also found to provide reasonable estimate of the fluctuating pressure loads at the wall.     

An advanced switching parameter for a hybrid LES/RANS model considering the characteristics of near-wall turbulent length scales

In this study, we proposed an idea for an advanced switching parameter used in a hybrid approach connecting large eddy simulation (LES) with Reynolds-averaged Navier–Stokes modeling [the hybrid LES/RANS (HLR) model]. Although the HLR model is promising way to predict engineering turbulent flows, an important problem is that RANS is always adopted in the near-wall region, even if the grid resolution is fine enough for LES. To overcome this difficulty, the switching parameter proposed here introduced knowledge of the Kolmogorov microscale that is thought to be reasonable for representing the near-wall turbulence. This parameter enabled the present HLR model to be smoothly replaced by a full LES if a grid resolution was fine enough in the near-wall region. To confirm model performance, the present HLR model was applied to numerical simulations of a periodic hill flow as well as fundamental plane channel flows. The model generally provided reasonable predictions for these test cases that include complex turbulence with massive flow separation.     

Experimental and Computational Investigations of Flow and Mixing in a Single-Annular Combustor Configuration

A complementary experimental and computational study of the flow and mixing in a single annular gas turbine combustor has been carried out. The object of the investigation is a generic mixing chamber model, representing an unfolded segment of a simplified Rich-Quick-Lean (RQL) combustion chamber operating under isothermal, non-reacting conditions at ambient pressure. Two configurations without and with secondary air injection were considered. To provide an appropriate reference database several planar optical measurement techniques (time-resolved flow visualisation, PIV, QLS) were used. The PIV measurements have been performed providing profiles of all velocity and Reynolds-stress components at selected locations within the combustor. Application of a two-layer hybrid LES/RANS (HLR) method coupling a near-wall k − ε RANS model with conventional LES in the core flow was the focus of the computational work. In addition to the direct comparison with the experimental results, the HLR performance is comparatively assessed with the results obtained by using conventional LES using the same (coarser) grid as HLR and two eddy-viscosity-based RANS models. The HLR model reproduced all important flow features, in particular with regard to the penetrating behaviour of the secondary air jets, their interaction with the swirled main flow, swirl-induced free recirculation zone evolution and associated precessing-vortex core phenomenon in good agreement with experimental findings.     

Reconstruction of turbulent fluctuations for hybrid RANS/LES simulations using a Synthetic-Eddy Method

A coupling methodology between an upstream Reynolds Averaged Navier–Stokes (RANS) simulation and a Large Eddy Simulation (LES) further downstream is presented. The focus of this work is on the RANS-to-LES interface inside an attached turbulent boundary layer, where an unsteady LES content has to be explicitly generated from a steady RANS solution. The performance of the Synthetic-Eddy Method (SEM), which generates realistic synthetic eddies at the inflow of the LES, is investigated on a wide variety of turbulent flows, from simple channel and square duct flows to the flow over an airfoil trailing edge. The SEM is compared to other existing methods of generation of synthetic turbulence for LES, and is shown to reduce substantially the distance required to develop realistic turbulence downstream of the inlet.     

超声速燃烧火焰稳定凹腔质量交换特性的数值研究

对超声速冷流条件下用于超燃冲压发动机的凹腔火焰稳定器的质量交换特性进行研 究. 采用混合RANS/LES方法对非定常流场进行数值模拟，考虑了凹腔的长深比和后缘角度两 个关键参数. 计算得到了凹腔剪切层拟序结构的演化过程. 对凹腔压力振荡历程进行幅频分 析，所得到的频率和理论分析结果及一些计算结果十分吻合. 结果表明，凹腔的长深比和后 缘倾角对凹腔质量交换过程都有较大的影响. 凹腔驻留时间随着长深比的增加而增加. 随着 后缘倾角减小，长深比较小的凹腔的驻留时间增加，长深比较大的凹腔则完全相反. 该计算 结果为凹腔设计提供了新认识.     

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).     

Feedback-controlled forcing in hybrid LES/RANS

The computational cost of large eddy simulation (LES) increases rapidly with the Reynolds number when applied to attached boundary layers. This problem can be avoided by use of a Reynolds-averaged Navier–Stokes (RANS) model in the inner part of the boundary layer, which reduces the computational cost drastically. Such hybrid LES/RANS methods yield accurate results in general, but suffer from an artificial buffer layer and a shift in the velocity profile around the modeling interface. This velocity shift can be removed by use of additional forcing, but the results are very sensitive to the forcing amplitude.

The present paper proposes a feedback algorithm which efficiently finds the appropriate amplitude and thus yields accurate flow statistics. The feedback algorithm is relatively robust, both in that it is insensitive to the values of the parameters involved and that it yields accurate results with different forcing fields and for different Reynolds numbers. It is argued that the feedback algorithm is consistent with the underlying assumptions of hybrid LES/RANS and that it does not introduce additional empiricism into the method.     

Dynamic Evaluation of Mesh Resolution and Its Application in Hybrid LES/RANS Methods

In this work, we investigate a resolution evaluation criterion based on the ratio between turbulent length-scales and grid spacing within the context of dynamic resolution evaluation in hybrid LES/RANS simulations. A modified version of the commonly used length-scale criterion is adopted. The modified length-scale criterion is evaluated for a plane channel flow and compared to the criterion based on two-point correlations. Simulation results show qualitative agreement between the two criteria and physical predictions from both resolution indicators. These observations are confirmed by simulations of flows over periodic hills. It is further demonstrated that the length-scale based criterion is relatively less sensitive on variation of model parameters compared to criteria based on resolved percentage of turbulent quantities. The improved resolution criterion is applied in a dual-mesh hybrid LES/RANS solver. Numerical simulations with the hybrid solver suggest that the interactions between the length-scale resolution indicator and the solution are moderate, and that favorable comparisons with benchmark results are obtained. In summary, we demonstrate that the modified length-scale based resolution indicator performs satisfactorily in both pure LES and hybrid simulations. Therefore, it is selected as a promising candidate to provide reliable predictions of resolution adequacy for individual cells in hybrid LES/RANS simulations.     

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.