APPLICATION OF ADVANCED REYNOLDS STRESS TRANSPORT MODELS TO HIGHLY SEPARATED FLOWS

Abstract

This paper considers the application of four Reynolds Averaged Navier Stokes (RANS) models to a range of progressively complex test cases, exhibiting both 2-D and 3-D flow separation. Two Eddy Viscosity Models (EVM) and two Reynolds Stress Transport Models (RSM) are employed, of which two (one in each category) are based on elliptic blending formulations. This study attempts to gain more insight into the importance of two modelling features for these flows; the usage of turbulence anisotropy resolving schemes and the near-wall limiting behaviour. As expected, there is no single best model, though some clear trend in performance is observed. INTRODUCTION The dramatic increase in available computational power in recent years has tended to draw turbulence research away from advanced Reynolds-Averaged Navier Stokes (RANS) closures, to focus instead on approaches that fully, or partially, resolve the turbulent structures. Since fully resolved approaches (Direct Numerical Simulation) remain impractical for industrially relevant cases, a series of progressively more significant approximations are usually adopted for such applications. While Large Eddy Simulation (LES) has been successfully applied to complex flows for moderately high Reynolds numbers, the formal application of this methodology also remains computationally prohibitive for the majority of industrial flows. In particular, the sufficient resolution of near-wall structures with LES requires extremely fine meshes. In response to the above limitations, a number of so called hybrid RANS-LES schemes have been developed across the community (see, for example Haase et al., 2009; Frohlich & von Terzi, 2008) in which the near-wall turbulence is modelled using a RANS approach, and LES employed for the outer flow regions. However, the majority of these hybrid methods retain rather simple (often linear) eddy-viscositybased RANS closures. These simple modelling schemes are known to perform poorly in flows with, amongst other features, complex separation, reattachment, impingement, and curvature (Haase et al., 2006). As such, it is relevant to question the impact of the RANSmodel on the hybrid solution, and the potential improvements one might gain by using a more complex scheme within such approaches. This paper therefore attempts to explore the performance of a number of advanced eddy-viscosity and Reynolds stress transport models in a range of flows involving challenging separation and reattachment features. The focus is on the use of such schemes within a purely RANS solution strategy, to illustrate their performance, although this will also allow some conclusions to be drawn regarding the expected performance if they were applied within the more computationally expensive hybrid approaches. A number of common 2-D flows are first examined, before two flows with 3-D effects are computed. DESCRIPTION OF THE MODELS Four models are compared in the present study, namely the k-! SST of Menter (1994), the SSG model of Speziale et al. (1991), the blended k− − v2/k (BL-v2/k ) model of Billard & Laurence (2011) and the Elliptic Blending RSM (EBRSM) of Manceau & Hanjalic (2002). The first two of these are fairly widely used and well validated models, thus serving as a reference against which to judge the performance of the more recent BL-v2/k and EBRSM schemes. The BL-v2/k and the EBRSM are, respectively, ellipticblending adaptations of the v2− f and the Ri j− fi j models of Durbin (1991) and Durbin (1993). Both models are designed to take at least some account of the correct near-wall asymptotic behaviour of the Reynolds stresses, without using traditional wall-reflection or other geometry-dependent terms, to simplify application to complex geometries. In both models, a non-dimensional parameter # is solved for using an elliptic equation of the form: