Investigation of the sensitivity of turbulent closures and coupling of hybrid RANS‐LES models for predicting flow fields with separation and reattachment

Hybrid models have found widespread applications for simulation of wall‐bounded flows at high Reynolds numbers. Typically, these models employ Reynolds‐averaged Navier–Stokes (RANS) and large eddy simulation (LES) in the near‐body and off‐body regions, respectively. A number of coupling strategies between the RANS and LES regions have been proposed, tested, and applied in the literature with varying degree of success. Linear eddy‐viscosity models (LEVM) are often used for the closure of turbulent stress tensor in RANS and LES regions. LEVM incorrectly predicts the anisotropy of Reynolds normal stress at the RANS‐LES interface region. To overcome this issue, use of non‐linear eddy‐viscosity models (NLEVM) have started receiving attention. In this study, a generic non‐linear blended modeling framework for performing hybrid simulations is proposed. Flow over the periodic hills is used as the test case for model evaluation. This case is chosen due to complex flow physics with simplified geometry. Analysis of the simulations suggests that the non‐linear hybrid models show a better performance than linear hybrid models. It is also observed that the non‐linear closures are less sensitive to the RANS‐LES coupling and grid resolution. Copyright © 2016 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.      

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.     

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.     

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.     

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.     

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     

A multiscale approach to hybrid RANS/LES wall modeling within a high-order discontinuous Galerkin scheme using function enrichment

We present a novel approach to hybrid Reynolds-averaged Navier-Stokes (RANS)/ large eddy simulation (LES) wall modeling based on function enrichment, which overcomes the common problem of the RANS-LES transition and enables coarse meshes near the boundary. While the concept of function enrichment as an efficient discretization technique for turbulent boundary layers has been proposed in an earlier article by Krank & Wall (A new approach to wall modeling in LES of incompressible flow via function enrichment. J Comput Phys. 2016;316:94-116), the contribution of this work is a rigorous derivation of a new multiscale turbulence modeling approach and a corresponding discontinuous Galerkin discretization scheme. In the near-wall area, the Navier-Stokes equations are explicitly solved for an LES and a RANS component in one single equation. This is done by providing the Galerkin method with an independent set of shape functions for each of these two methods; the standard high-order polynomial basis resolves turbulent eddies, where the mesh is sufficiently fine and the enrichment automatically computes the ensemble-averaged flow if the LES mesh is too coarse. As a result of the derivation, the RANS model is applied solely to the RANS degrees of freedom, which effectively prevents the typical issue of a log-layer mismatch in attached boundary layers. As the full Navier-Stokes equations are solved in the boundary layer, spatial refinement gradually yields wall-resolved LES with exact boundary conditions. Numerical tests show the outstanding characteristics of the wall model regarding grid independence, superiority compared to equilibrium wall models in separated flows, and achieve a speed-up by two orders of magnitude compared to wall-resolved LES.     

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).     

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.     

用基于M-SST模型的DES数值模拟喷流流场

脱体涡数值模拟方法(dettached eddy simulation,DES)是把雷诺平均Navier-Stokes方程(RANS)方法及大涡模拟方法(LES)结合起来模拟有脱体涡的湍流流场的数值模拟方法,其主要思想是在物面附近解雷诺平均Navier-Stokes方程、在其他区域采用Smagorinski大涡模拟方法。本文在剪切应力传输(SST)湍流模型的基础上用DES及混合非结构网格数值模拟具有横向喷流的湍流流场,算法采用Osher逆风格式,利用该套程序(包括网格生成及算法),对导弹在不同马赫数下的喷流流场进行了数值模拟,并与同时开展的实验研究的结果进行了对比,结果表明用该方法处理这类问题是较准确的。     

Studies of the unsteady supersonic base flows around three afterbodies

Unsteady supersonic base flows around three afterbodies, cylindrical （Cy）, boattailed （BT） and three-step （MS）, are investigated in this paper. Reynolds-averaged Navier-Stokes （RANS） and two RANS/LES （large-eddy simulation） hybrid methods, detached eddy simulation （DES） and delayed-DES （DDES）, are used to predict the base flow characteristics around the baseline Cy afterbody. All the RANS and hybrid methods are based on the two-equation SST （shear-stress transport） model with compressible corrections （CC）. According to the comparison of measurements, both DES and DDES can produce more satisfactory results than RANS. RANS can only present the ＂stable＂ flow pat- terns, while the hybrid methods can demonstrate unsteady flow structures. DDES and DES results are little different from one another although the latter exhibits better agreement with the experiment. DES is taken to investigate the 5° BT and three-step afterbodies. The mean flow data and the instantaneous turbulent coherent structures are compared against available measurements.     

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.     

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.     

Vortical structures and pressure pulsations in draft tube of a Francis-99 turbine at part load: RANS and hybrid RANS/LES analysis

Recognizing the limitations of the conventional linear-eddy-viscosity (LEVM) Reynolds-averaged Navier–Stokes (RANS) models to reproduce complex three-dimensional unsteady flows in hydraulic machinery, we performed a comparative assessment of a second-moment (Re-stress model, RSM) RANS closure and a hybrid RANS/LES method in capturing the flow and vortical structures in the draft tube of a Francis hydroturbine at off-design conditions. Considered is a case of part load (PL) at a flow rate of only 35% of the best efficiency point (BEP) characterised by multiple unsteady vortex systems. Despite some remaining uncertainties in generating the inflow conditions, both approaches reproduced reasonably well the measured mean velocity and the rms of its fluctuations, as well as the pressure spectrum with peaks detecting the precessing vortex core. In contrast to the common LEVMs, the Re-stress closure showed sufficient receptivity to intrinsic unsteadiness and reproduced well the overall flow and vortical patterns as well as the associated pressure pulsations in accord with the experiments. The hybrid RANS/LES method gave similar predictions as the RSM, but resolving a wider range of scales, which however, showed no significant effect on the dynamics of the dominant processing vortex core and the pressure pulsations.     

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.     

Numerical prediction of turbulent flows using Reynolds‐averaged Navier–Stokes and large‐eddy simulation with uncertain inflow conditions

Numerous comparisons between Reynolds‐averaged Navier–Stokes (RANS) and large‐eddy simulation (LES) modeling have already been performed for a large variety of turbulent flows in the context of fully deterministic flows, that is, with fixed flow and model parameters. More recently, RANS and LES have been separately assessed in conjunction with stochastic flow and/or model parameters. The present paper performs a comparison of the RANS k ? ε model and the LES dynamic Smagorinsky model for turbulent flow in a pipe geometry subject to uncertain inflow conditions. The influence of the experimental uncertainties on the computed flow is analyzed using a non‐intrusive polynomial chaos approach for two flow configurations (with or without swirl). Measured quantities including an estimation of the measurement error are then compared with the statistical representation (mean value and variance) of their RANS and LES numerical approximations in order to check whether experiment/simulation discrepancies can be explained within the uncertainty inherent to the studied configuration. The statistics of the RANS prediction are found in poor agreement with experimental results when the flow is characterized by a strong swirl, whereas the computationally more expensive LES prediction remains statistically well inside the measurement intervals for the key flow quantities.Copyright © 2012 John Wiley & Sons, Ltd.     

Large eddy simulation of fuel injection and mixing process in a diesel engine

The large eddy simulation(LES) approach implemented in the KIVA-3V code and based on one-equation sub-grid turbulent kinetic energy model are employed for numerical computation of diesel sprays in a constant volume vessel and in a Caterpillar 3400 series diesel engine.Computational results are compared with those obtained by an RANS(RNG k-ε) model as well as with experimental data.The sensitivity of the LES results to mesh resolution is also discussed.The results show that LES generally provides flow and spray characteristics in better agreement with experimental data than RANS;and that small-scale random vortical structures of the in-cylinder turbulent spray field can be captured by LES.Furthermore,the penetrations of fuel droplets and vapors calculated by LES are larger than the RANS result,and the sub-grid turbulent kinetic energy and sub-grid turbulent viscosity provided by the LES model are evidently less than those calculated by the RANS model.Finally,it is found that the initial swirl significantly affects the spray penetration and the distribution of fuel vapor within the combustion chamber.     

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