Des, Hybrid Rans/les and Pans Models for Unsteady Separated Turbulent Flow Simulations

This paper presents computational results for two DES (Detached Eddy Simulation), one hybrid RANS (Reynolds Averaged Navier-Stokes)/ LES (Large Eddy Simulation) and some preliminary results from PANS (Partially Averaged Navier-Stokes) turbulence for simulation of unsteady separated turbulent flows. The models are implemented in a full 3-D Navier Stokes solver and are based on the twoequation k-ε model. The formulations of each model are presented and results are analyzed for subsonic flow over a Backward Facing Step (BFS). Simulations are carried out using a 3 order Roe scheme. A comparative assessment is made between the predictions from the DES, hybrid and PANS models. The predicted results are compared with the available experimental data for skin-friction coefficient, and different turbulent quantities. The three-dimensionality of the flow field and the separated fine scale structures are presented through the Q iso-surfaces. INTRODUCTION Most of the numerical simulations for engineering applications at high Reynolds numbers are obtained using the RANS turbulence models. While RANS models yield prediction of useful accuracy in attached flows; they fail to accurately capture the complex flow structures in regimes substantially different from the thin shear and attached boundary layers. Simulation strategies such as LES are attractive as an alternative for prediction of flow fields where RANS is deficient but carry a prohibitive computational cost for resolving boundary layer turbulence at high Reynolds numbers. This in turn provides a strong incentive for the merging of these two techniques in DES, hybrid RANS-LES and PANS approaches. DES [1,2,3] is a recently developed and the one of the most widely used hybridization technique for realistic simulations of high speed turbulent flows with massive separation. DES models were developed to combine the fine tuned RANS methodology in the attached boundary layers with the power of LES in the shear layers and separated flow regions at realistic Reynolds numbers [4,5]. It is a unified approach based on the adoption of a single turbulence model that function as a sub-grid scale LES model in the separated flow regions where the grid is nearly isotropic and as a RANS model in attached boundary layers regions. It retains the essential features of LES type method as well as employs a computationally cheaper RANS method in regions where it is appropriate. This technique was originally designed to simulate massively separated flows and it provides better insight into the three-dimensional and time dependent flow features in comparison to the RANS models [6]. Spalart et al. [4] first proposed the concept of DES based on the original formulation of the Spalart-Allmaras (S-A) one-equation RANS model [7]. Subsequently, Strelets [5], Bush et al. [8], Batten et al. [9], Nichols et al. [10] proposed parallel concepts of DES based on two-equation turbulence models. Applications of the DES models for a wide variety of problems [11-15] involving separated flow configurations have shown certain degree of success relative to the RANS predictions. While DES is based on the adoption of a single turbulence model that functions as two different models (LES and RANS) in different regions, another class of hybridization technique relies on using two distinct turbulent models in the RANS and LES regions and is commonly known as the hybrid RANS/LES method. Georgiadis et al. [16] initiated the concept of explicit hybrid RANS/LES models by dividing the computational domain into RANS and LES regions. Baurle et al. [17] proposed another concept of hybrid technique that is based on a k-ω RANS and a sub-grid scale turbulent kinetic energy (SGS TKE) model. It relies on modifying the RANS TKE equations to a form that is consistent with the SGS TKE equation based on a blending function. Basu et al. [18] developed DES and hybrid models and applied them to transonic cavity flow and acoustic field simulations. They found that both the DES and hybrid models predicted the flow and acoustic fields in a similar fashion and increasing dissipation rate (ε) or decreasing turbulent kinetic energy (k) results in the same level of eddy viscosity in the DES formulations. Recently, Girimaji et al. [19] developed PANS (Partially Averaged Navier Stokes) based on the unresolvedto-total ratios of kinetic energy and dissipation. They have applied the PANS model for flow over a square cylinder, a