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.     

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).     

A New Version of Detached-eddy Simulation, Resistant to Ambiguous Grid Densities

Detached-eddy simulation (DES) is well understood in thin boundary layers, with the turbulence model in its Reynolds-averaged Navier–Stokes (RANS) mode and flattened grid cells, and in regions of massive separation, with the turbulence model in its large-eddy simulation (LES) mode and grid cells close to isotropic. However its initial formulation, denoted DES97 from here on, can exhibit an incorrect behavior in thick boundary layers and shallow separation regions. This behavior begins when the grid spacing parallel to the wall Δ_∥ becomes less than the boundary-layer thickness δ, either through grid refinement or boundary-layer thickening. The grid spacing is then fine enough for the DES length scale to follow the LES branch (and therefore lower the eddy viscosity below the RANS level), but resolved Reynolds stresses deriving from velocity fluctuations (“LES content”) have not replaced the modeled Reynolds stresses. LES content may be lacking because the resolution is not fine enough to fully support it, and/or because of delays in its generation by instabilities. The depleted stresses reduce the skin friction, which can lead to premature separation.For some research studies in small domains, Δ_∥ is made much smaller than δ, and LES content is generated intentionally. However for natural DES applications in useful domains, it is preferable to over-ride the DES limiter and maintain RANS behavior in boundary layers, independent of Δ_∥ relative to δ. For this purpose, a new version of the technique – referred to as DDES, for Delayed DES – is presented which is based on a simple modification to DES97, similar to one proposed by Menter and Kuntz for the shear–stress transport (SST) model, but applicable to other models. Tests in boundary layers, on a single and a multi-element airfoil, a cylinder, and a backward-facing step demonstrate that RANS function is indeed maintained in thick boundary layers, without preventing LES function after massive separation. The new formulation better fulfills the intent of DES. Two other issues are discussed: the use of DES as a wall model in LES of attached flows, in which the known log-layer mismatch is not resolved by DDES; and a correction that is helpful at low cell Reynolds numbers.     

Detached eddy simulation of flow around two wall-mounted cubes in tandem

We investigate the performance of unsteady Reynolds-averaged Navier–Stokes (URANS) computation and various versions of detached eddy simulation (DES) in resolving coherent structures in turbulent flow around two cubes mounted in tandem on a flat plate at Reynolds number (Re) of 22,000 and for a thin incoming boundary layer. Calculations are carried out using four different coherent structure resolving turbulence models: (1) URANS with the Spalart–Allmaras model; (2) the standard DES [Spalart, P.R., Jou, W.H., Strelets, M., Allmaras, S.R., 1997. Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach. In: Liu, C., Liu, Z., (Eds.), Advances in DNS/LES. Greyden Press, Columbus, OH]; (3) the Delayed DES (DDES); and (4) the DES with a low-Re modification (DES-LR) [Spalart, P., Deck, S., Shur, M., Squires, K., Strelets, M., Travin, A., 2006. A new version of detached eddy simulation, resistant to ambiguous grid densities. Theor. Comput. Fluid Dyn. 20 (3), 181–195]. The grid sensitivity of the computed solutions is examined by carrying out simulations on two successively refined grids. The computed results for all cases are compared with the experimental measurements of Martinuzzi and Havel [Martinuzzi, R., Havel, B., 2000. Turbulent flow around two interfering surface-mounted cubic obstacles in tandem arrangement. ASME J. Fluids Eng. 122, 24–31] for two different cube spacings. All turbulence models reproduce essentially identical separation of the approach thin boundary layer and yield an unsteady horseshoe vortex system consisting of multiple vortices in the leading edge region of the upstream cube. Significant discrepancies between the URANS and all DES solutions are observed, however, in other regions of interest such as the shear layers emanating from the cubes, the inter-cube gap and the downstream wake. Regardless of the grid refinement, URANS fails to capture key features of the mean flow, including the second horseshoe vortex in the upstream junction and recirculating flow on the top surface of the downstream cube for the large cube spacing, and underestimates significantly turbulence statistics in most regions of the flow for both cases. On the coarse mesh, all three DES approaches appear to yield very similar results and fail to reproduce the second horseshoe vortex. The standard DES and DDES solutions obtained on the fine meshes are essentially identical and both suffer from premature switching to unresolved DNS, due to the mis-interpretation of grid refinement as wall proximity, which leads to spurious vortices in the inter-cube region. Numerical solutions show that the low-Re modification (DES-LR) is critical prerequisite in DES on the ambiguously fine – not fine enough for full LES – mesh to prevent excessive nonlinear drop of the subgrid eddy viscosity in low cell-Re regions like in the inter-obstacle gap. Mean flow quantities and turbulence statistics obtained with DES-LR on the fine mesh are in good overall agreement with the measurements in most regions of interest for both cases.     

Applications of scale-adaptive simulation technique based on one-equation turbulence model

A modified scale-adaptive simulation (SAS) technique based on the Spalart-Allmaras (SA) model is proposed. To clarify its capability in prediction of the complex turbulent flow, two typical cases are carried out, i.e., the subcritical flow past a circular cylinder and the transonic flow over a hemisphere cylinder. For comparison, the same cases are calculated by the detached-eddy simulation (DES), the delayed-detached eddy simulation (DDES), and the XY-SAS approaches. Some typical results including the mean pressure coefficient, velocity, and Reynolds stress profiles are obtained and compared with the experiments. Extensive calculations show that the proposed SAS technique can give better prediction of the massively separated flow and shock/turbulent-boundary-layer interaction than the DES and DDES methods. Furthermore, by the comparison of the XY-SAS model with the present SAS model, some improvements can be obtained.     

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.      

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。     

High‐order detached eddy simulation,zonal LES and URANS of cavity and labyrinth seal flows

Hybrid numerical large eddy simulation (NLES), detached eddy simulation (DES) and URANS methods are assessed on a cavity and a labyrinth seal geometry. A high sixth‐order discretization scheme is used and is validated using the test case of a two‐dimensional vortex. The hybrid approach adopts a new blending function. For the URANS simulations, the flow within the cavity remains steady, and the results show significant variation between models. Surprisingly, low levels of resolved turbulence are observed in the cavity for the DES simulation, and the cavity shear layer remains two dimensional. The hybrid RANS–NLES approach does not suffer from this trait. For the labyrinth seal, both the URANS and DES approaches give low levels of resolved turbulence. The zonal Hamilton–Jacobi approach on the other had given significantly more resolved content. Both DES and hybrid RANS–NLES give good agreement with the experimentally measured velocity profiles. Again, there is significant variation between the URANS models, and swirl velocities are overpredicted. Copyright © 2013 John Wiley & Sons, Ltd.     

Investigation of large-scale structures of annular swirling jet in a non-premixed burner using delayed detached eddy simulation

Delayed detached eddy simulation (DDES) is accompanied with Stereo-PIV measurements to study the non-reacting flow field of a non-premixed swirl burner in this paper. Comparisons of experimental and numerical data show that the DDES results are capable of predicting the mean swirling flow features adequately. The instantaneous flow field is found to be strongly affected by the Kelvin–Helmholtz instability. The flow near the injector involves a complex behavior including a recirculation zone. The 3D flow structure at the burner exit, visualized by the iso-surface of Q-criterion, displays four instability types. The dominant instabilities are vortex ring structures induced by the Kelvin–Helmholtz instability, and finger structures induced by the swirling instability. Pressure fluctuation signal recorded in the swirling jet region show that the computational flow passes through transition instants from RANS to DDES equations. After that, the swirling jet becomes fully developed with an oscillation frequency of 222 Hz.     

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.     

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.     

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.     

Development of DDES and IDDES Formulations for the k-ω Shear Stress Transport Model

Modifications are proposed of two recently developed hybrid CFD strategies, Delayed Detached Eddy Simulation (DDES) and DDES with Improved wall-modeling capability (IDDES). The modifications are aimed at fine-tuning of these approaches to the k-ω SST background RANS model. The first one includes recalibrated empirical constants in the shielding function of the SA-based DDES model which are shown to be suboptimal (not providing the needed level of elimination of the Model Stress Depletion (MSD)) for the SST-based DDES model. For the SST-IDDES variant, in addition to that, a simplification of the original SA–based formulation is proposed, which does not cause any visible degradation of the model performance. Both modifications are extensively tested on a range of attached and separated flows (developed channel, backward-facing step, periodic hills, wall-mounted hump, and hydrofoil with trailing edge separation).     

A hybrid RANS/LES approach with scale-adaptive capabilities for highly separated flows

A new hybrid RANS/LES approach with scale-adaptive capabilities is developed. The blending function in the SST model is adopted to prevent the invasion of the von Karman length scale to the RANS region, and the compressibility correction proposed by Wilcox is incorporated to produce a realistic shear layer development in compressible flows. The new model is validated for a subcritical flow past a circular cylinder and a supersonic base flow. Time-averaged turbulent statistics predicted by the new model show fairly good agreement with the experimental data, slight improvements over DES simulations, and are much better than SAS results. The main advantage of the new model over the DES method is that the distribution of the blending function reflects local vortex structures instead of grid spacing in the turbulent wake. The sequence of the effect intensity of the compressibility correction from strong to weak is SAS, the new model and DES.     

Delayed detached eddy simulation of the end-effect regime and side-loads in an overexpanded nozzle flow

The separated flow in an overexpanded nozzle featuring a restricted shock separation is investigated numerically using delayed detached eddy simulation and compared with the experimental data of Nguyen et al. (Int J Flow Turbul Combust 71(1):161–181, 2003). First, the enormous cost of a Large Eddy Simulation for such a nozzle flow is assessed before being performed to motivate the practical need for using an hybrid RANS/LES method. The calculation is then used to investigate the “end-effect” regime which involves a strong global unsteadiness with very large amplitude fluctuations of about 15–20% of nozzle divergent length. The flow regime is characterized by high wall pressure fluctuations which are hopefully nearly axisymmetric. The main properties (rms levels, amplitude of displacement of the separation) of the motion are rather well reproduced by DDES compared to the experiment. However, a major difference lies in the frequency of the computed motion which is higher than in the experiment. This major discrepancy is currently not explained by the author. The properties of the side-loads are also briefly discussed.      

Recent improvements in the Zonal Detached Eddy Simulation (ZDES) formulation

An efficient generalized Zonal Detached Eddy Simulation method (ZDES) is presented, which aims at performing hybrid Reynolds Averaged Numerical Simulation (RANS)/Large Eddy Simulation (LES) calculations for both internal and external aerodynamics problems. It is based on a zonal formulation of the hybrid length scale that allows to combine the zonal approach with the best features of Delayed Detached Eddy Simulation (DDES) (Spalart et?al. Theor Comput Fluid Dyn 20:181–195, 2006). In other words, the presumed weak point of a zonal approach, namely that the location of separation has to be known in advance, is now overcome. What is more, the problem of slow LES content development in mixing layers when they are treated neither in RANS nor in LES mode is investigated. It is argued that the subgrid length scale Δ_max?=?max(Δx, Δy, Δz) entering DDES is physically justified to shield the boundary layer but is definitely not a good subgrid length scale in LES mode. Remedies are proposed based on new zonal subgrid length scales that depend not only on the grid spacing but also on the flow solution and especially on the local vorticity vector. The method is validated on a spatially developing mixing layer as well as in a backward facing step flow and then applied to a three-element airfoil. It is argued in this latter case that a precise control of the RANS mode thanks to a zonal approach is essential. More generally, in all simulated cases in this study, ZDES has proven to be very efficient as regards the behavior in LES mode while retaining the strongest asset of DDES, namely the treatment of the attached boundary layer in RANS mode. The issue of zonal or non-zonal treatment of turbulent flows is also briefly discussed.     

Hybrid URANS/LES Turbulence Simulation of Vortex Shedding Behind a Triangular Flameholder

In this study a detached eddy simulation (DES) model, which belongs to the group of hybrid URANS/LES turbulence models, is used for the simulation of vortex shedding behind a triangular obstacle. In the near wall region or in regions where the grid resolution is not sufficiently fine to resolve smaller structures, the two-equation RANS shear-stress transport (SST) model is used. In the other regions with higher grid resolution a LES model, which uses a transport equation for the turbulent subgrid energy, is applied. The DES model is first investigated for two standard test cases, namely decaying homogeneous isotropic turbulence and the backward facing step, respectively. For the decaying homogeneous isotropic turbulence test case the evolution of the energy spectra in wavenumber space for different times are studied for both the DES and a Smagorinsky type LES model. Different grid resolutions are analyzed with a special emphasis on the modeling constant connecting the filter length scale to the grid size. The results are compared to experimental data. The backward facing step test case is used to study the model behavior for a case with a transition region between a RANS modeling approach close to the wall and LES based modeling in the intense shear flow region. The final application is the simulation of the vortex shedding behind a triangular obstacle. First, the influence of the inlet condition formulation is studied in detail as they can have a significant influence especially for LES based models. Detailed comparisons between simulation and experiment for the flow structure past the obstacle and statistical quantities such as the shedding frequency are shown. Finally the additional temporal and spatial information provided by the DES model is used to show the predicted anisotropy of turbulence.     

Investigation of Alternative Length Scale Substitutions in Detached-Eddy Simulation

The objective of this work is the comparison of three different DES-style hybrid RANS/LES implementations based on the Wilcox k– model. The three variants are designed to investigate alternative methods of substitution of the DES length scale within the background Reynolds Averaged Navier-Stokes (RANS) model. Basis for comparison is provided by both the idealised case of the decay of isotropic turbulence (DIT) as well as the practical case of the massively separated, turbulent flow around an airfoil at high angle of attack. The results of the investigations are discussed in detail, the outcome of which is an emphasis of the importance of DIT as a method for calibration, as well as of the relative freedom with which alternative DES-inspired approaches can be implemented for flows of practical relevance.     

Experiences with two detached eddy simulation approaches through use of a high-order finite volume solver

In the present study, two advanced detached eddy simulation (DES) approaches, shear-layer-adapted delayed DES and zonal DES in mode II, which are known to help transition from RANS to LES mode, are employed in various flow problems in conjunction with a high-order finite volume solver. The numerical scheme, being only applicable on structured grids, has low-dissipation and low-dispersion features. Such features benefit mostly in the LES mode, minimizing the interference of numerical diffusion with subgrid eddy viscosity. First, corresponding subgrid models are validated via decaying homogeneous turbulence benchmark case. Then, a channel flow problem is chosen to examine these models in attached flow situations. Finally, flow around an airfoil at low Reynolds number is solved using the shear-layer-adapted delayed DES approach only, in an aim to obtain trailing-edge noise spectrum at an observer location. Despite some log-layer mismatch over turbulent boundary layers, which is typical of most DES methods, the combined application of high-resolution numerical method and advanced DES approaches, which are implemented on a stabilized Spalart-Allmaras turbulence model, shows merit in resolution of turbulence in regions of interest.     

Assessment of Delayed DES and Improved Delayed DES Combined with a Shear-Layer-Adapted Subgrid Length-Scale in Separated Flows

A comparative study is conducted between the original versions of Delayed Detached-Eddy Simulation (DDES) and Improved DDES (IDDES) and these approaches combined with a new (shear layer adapted) definition of the subgrid length-scale recently proposed in Shur et al. (Flow Turbul. Combust. 95(4), 709–737, 2015). This definition is aimed at accelerating the transition to resolved turbulence in separated shear-layers, which significant delay is typical of the non-zonal hybrid RANS-LES models, in general, and DES-like approaches, in particular. An objective of the study is widening the validation database of the new solutions-dependent definition of the length-scale compared to that employed in the original work of Shur et al. In order to reach this, three different complex separated flows with well-understood flow physics were considered, which all are widely used for the validation of different CFD approaches. These flows are: a flow with non-fixed pressure-induced separation and reattachment (wall-mounted hump), a massively separated flow (NACA 0021 airfoil beyond stall), and a supersonic separated flow (wake behind a cylindrical forebody). The results of simulations suggest that the DDES and IDDES models combined with the shear-layer adapted subgrid length-scale perform according to their design (no unforeseen interactions of the shear-layer adapted length-scale with the empirical functions involved in the DDES and IDDES formulations are observed) and considerably mitigate the delay of transition from fully modeled to partially resolved turbulence in the separated shear layers compared to the standard DES definition of the length-scale (maximum local grid-spacing).