Prediction for Separation Flows Around a 6:1 Prolate Spheroid Using Hybrid RANS/LES Methods

Abstract

This paper presents some hybrid Reynolds-Averaged Navier-Stokes (RANS) and large-eddy-simulation (LES) methods for the separated flows at high angles of attack around 6:1 prolate spheroid. These hybrid RANS/LES methods including detached eddy simulation (DES) based on Spalart-Allmaras, Menter’s k-ω shear-stress-transport (SST) and k-ω with weakly nonlinear eddy viscosity formulation (Wilcox-Durbin+, WD+) models and zonal-RANS/LES methods based on SST and WD+ models through a flow-dependent blending function are implemented to switch smoothly from RANS near the wall to LES in the core flow region. All the hybrid methods are designed to have a RANS mode for the attached flows near the solid wall and have a LES behavior for the separated flows in the core flow region. The main objective of this paper is to apply the hybrid methods for high Reynolds separated flows around prolate spheroid at high-incidences. At the same time, fourth-order central scheme with particle 4 th -order artificial viscosity and fully implicit lower-upper symmetric-Gauss-Seidel with pseudo time sub-iteration are taken as the spatial and temporal methods, respectively. Comparison with measurement is carried out for pressure coefficients, skin friction, profiles of velocity and the surface flow patterns, etc. Reasonable agreement with the available measurements, accounting for the effect on grids and fundamental turbulence models, is obtained for these separation flows. I. Introduction lo air th ws around ships, submarines, torpedoes, hot balloons, ships and aircrafts are usually very complicated and entirely ree-dimensional (1-D). At high angle of attack (AOA), 3-D flow separation has been an interesting and challenging problem in fluid mechanics. Undesired effects such as loss of lift, increase of drag, amplification of unsteady fluctuations in the pressure fields and uncontrolled yawing moment caused by the asymmetric fore-body vortices always accompany when the 3-D separation takes place. 2-D separation flows are mainly dominated by the adverse pressure gradient, flow reversal, etc. In 3-D separation flows, the separation features can be sensitive to the body configuration, roughness of surface, AOA and Reynolds number, etc. In addition to the complex topology of the flow patterns, the 3-D separation flows strongly challenge experimental equipments, analytical and predictive tools. The prolate spheroid, with a 6:1 major-minor semi-axis ratio, has very simple configuration; however, the flows past it present almost all the fundamental transition and separation phenomena of a 3-D flows. The flow separating from the leeward side of the spheroid rolls up into a strong primary vortex on each side of the spheroid and reattaches at the symmetric plane. The primary vortex is always accompanied by one small secondary vortex, which separates and reattaches adjacent to the body. The flow transition includes not only the stream-wise Tollmien-Schilichting (T-S) wave instability but also cross-flow instability, which is lack of effective predictive tools with the transition models until now. The flows around prolate spheroid have been studied both experimentally 1,2,3 and computationally using Reynolds-Averaged Navier