Critical Assessment of Hybrid RANS-LES Modeling for Attached and Separated Flows

Critical Assessment of Hybrid RANS-LES Modeling for Attached and Separated Flows

Introduction

Turbulent shear flows, including attached boundary layers and separated shear layers, are important application test cases for computational fluid dynamics prediction since they are observed for a wide array of engineering processes and systems. In particular, turbulence modeling for these systems is an important aspect of the simulation that is often responsible for predictive error. Reynolds-averaged Navier-Stokes (RANS) models are known to perform relatively well for turbulent boundary layer flow [1] due to the somewhat universal nature of wall-bounded turbulence. RANS models typically do not perform as well in regions of separated flow due to the presence of adverse pressure gradients, strong three-dimensionality, shear layer reattachment, and large-scale unsteadiness [2–8]. Large eddy simulation (LES) models theoretically provide greater accuracy than RANS approaches in these regions, but their application to attached wall-bounded flows suffers from significantly increased computational expense relative to RANS. As a consequence, the LES approach is still not widely used for industrial analysis and design for high Reynolds number flows, especially those with attached boundary layers [9]. Hybrid RANS/LES (HRL) [1] approaches offer a potentially attractive alternative to RANS or LES, since they attempt to combine the advantages of both RANS and LES modeling in an optimized manner that resolves both attached and separated flows effectively. Specifically, HRL models have the potential for greater accuracy than RANS and less expense than LES. Interest in HRL methods has, therefore, grown substantially over the past several years.

Hybrid RANS-LES models are categorized as either zonal or nonzonal. For zonal models, the RANS and LES models are separately employed in selected regions of the computational domain which are determined a priori. Development of effective methods for coupling the two model types at their interface remains a challenge and is an ongoing area of research. Nonzonal methods are generally simpler to implement and do not require the user to decide where LES or RANS is used in a particular simulation. In a nonzonal model, the eddy viscosity adopts a value representative of a RANS model in the near-wall region and a value representative of an LES subgrid stress (SGS) model in separated regions. Detached-eddy simulation (DES) is probably the most commonly used nonzonal modeling methodology. Blending between RANS and LES model types in the original DES formulation is a function of the local grid size and has been shown to suffer from inaccuracy in attached boundary layers. While several ad hoc modifications have been implemented to address these limitations, the modifications often only mitigate weaknesses while not completely resolving them. For example, to address the problem of reduced levels of eddy viscosity in attached boundary layers due to premature switching to LES mode, Spalart et al. introduced a modified version of the baseline DES model denoted as Delayed DES (DDES). DDES adopts a definition for length scale different from that in the original baseline DES model, as a function of local mean flow and turbulence model variables. Shur et al. introduced a DES version with an additional modification—improved delayed DES (IDDES)—in an attempt to eliminate the well known “log layer mismatch” issue that arises in classical DES and wall-modeled LES (WM-LES). The IDDES model behaves similar to DDES except that it replicates a WM-LES type model in boundary layer regions when resolved turbulent fluctuations are present.

The key challenge for nonzonal HRL modeling is that of effectively specifying the transition between RANS and LES modes in the simulation. Typically, such a transition is defined based on the value of the eddy viscosity that varies between the Reynolds stress model and the SGS value. Significantly, the Reynolds stress and subgrid stress are mathematically distinct and physically different; therefore, any method that switches between the two using a single parameter (i.e., eddy viscosity) is not straightforward. This is because the Reynolds stress is based on an ensemble averaging of all turbulent scales present in the flow field, while the subgrid stress is based on (typically spatial) filtering of all turbulence scales that are not directly resolved in the simulation for a given mesh size. The difficulty in defining zonal transition using a single variable for eddy viscosity has been identified as a major weakness for commonly used HRL models. Additionally, many of the currently used HRL models incorporate the local grid size directly as a model variable. This necessitates that great care is taken when constructing grids for HRL modeling. For the best performance, the grid should be built with foreknowledge of the expected model behavior and design of the specific grid used as the method of forcing RANS-to-LES transition in the desired locations of the domain.

The transition from a purely modeled RANS stress to a resolved dominating LES stress has been recognized as a major concern. The problem is exacerbated if separation occurs at a clearly defined location such as a sharp point (e.g., a backward-facing step) and the separating boundary layer lacks any initial level of fluctuating turbulence content. Paterson and Peltier studied the issues for RANS-to-LES transition for cases where no geometrically imposed separation point exists. The authors note that a delay in the development of resolved fluctuations stress terms is present in the RANS-to-LES transition region upstream of the separation location; therefore, the (SGS) turbulent viscosity values obtain dominance over the RANS eddy viscosity values prematurely. This effect is the well known “modeled-stress depletion” described by Spalart et al. Nitikin et al. also demonstrated the difficulties inherent in calculating the appropriate level of grid resolution for the “gray region” that lies between the RANS and LES modes, particularly for RANS-to-LES transition that occurs in the wall normal direction in boundary layer flows.

Previous researchers have attempted to resolve the RANS-to-LES transition issue including efforts discussed above. Menter et al. introduced the concept of scale-adaptive simulation (SAS), which is significant as it provides the potential to develop turbulence models that are applicable in both RANS and LES modes without including any explicit grid-dependence. Hamba proposed that rapid variation of the filter width near the interface of the RANS and LES zones is the primary reason for the log-layer mismatch in channel flow simulations and that the problem can be resolved by using an additional filtering operation. Piomelli et al. have proposed the use of a pseudo-random forcing function as a backscatter model in the interface region as a means of resolving the underlying issues of the a transition layer between RANS and LES. It is important to note that most of these prior attempts should be viewed as ad hoc modifications rather than fundamental changes to the basic modeling approach. Celik, in a review paper, proposes that entirely new criteria are needed in order to effectively address the RANS-to-LES transition issue in HRL models in a more fundamental way.

The dynamic hybrid RANS-LES (DHRL) modeling methodology presented in this paper was specifically developed as an attempt to resolve the aforementioned weaknesses, including explicit grid dependence, that have been documented for most previous HRL models. Furthermore, it is assumed that these issues are fundamental in nature and unlikely to be effectively addressed using ad hoc modifications. The novel features of the DHRL modeling framework are that (1) it is a general framework which allows coupling of any particular RANS model with any particular LES model; (2) it does not include mesh size as a variable in the model formulation; (3) the blending between RANS and LES modes is enforced through the assumption of continuity in total turbulence energy production; and (4) it exactly reduces to the underlying RANS model in flow regions that exhibit numerically steady-state results.

In the present paper, a detailed investigation of the DHRL model is presented using the finite-volume based commercial CFD software Ansys FLUENT^®. The DHRL model was implemented into FLUENT using the user-defined function (UDF) capability available with that solver. For the present cases, the DHRL framework was used to integrate Menter’s SST k-ω model as the RANS component, with monotonically integrated LES (MILES) as the LES model component. To evaluate the performance of the DHRL model in both attached and separated flow regions, the test cases considered were turbulent channel flow matching the DNS case of Hoyas and Jimenez and backward-facing step flow matching the experimental case of Driver and Seegmiller. Simulation results using the DHRL model are compared with the corresponding DNS and experimental data, and with the results of companion simulations using other RANS and HRL turbulence models available in FLUENT.