Prediction of turbulent separation over a backward-facing smooth ramp

Abstract

Large eddy simulation (LES) and Reynolds-averaged Navier–Stokes (RANS) calculations have been performed of the turbulent flow over a smoothly contoured ramp. The upstream conditions are obtained from a separate pre-computation of a flat-plate turbulent boundary layer. The flow in the primary calculation develops downstream, first experiencing an increase in the surface skin friction due to ramp curvature, then exhibiting a shallow separation with subsequent reattachment on a flat section downstream. The LES results provide a baseline for investigation of the flow and enable assessment of the RANS models, the specific closures applied being the Spalart–Allmaras one-equation model v ²−f, and a modified version of v ²−f. The wall layer is resolved in all of the calculations, the Reynolds number based on the boundary layer thickness at the inlet plane is 10 400. LES results show that the separation process is intermittent and exhibits a transition of turbulence structures, features that are challenging for the turbulence closures to model adequately. LES mean velocities return to the log law at about four ramp lengths downstream of the beginning of the curved section, whereas the turbulence quantities recover more slowly. The effect of separation is to increase the turbulence intensity away from the wall and decrease it in the vicinity of the wall. The recovery of the inner layer takes place through a rapid rebound process while that of the outer layer through a slow decay process. Both occur in a monotonic fashion. The steady RANS predictions upstream of separation for all the models are similar, with differences observed within and downstream of the separated region. RANS predictions of the skin friction following separation show a relatively slower recovery to the LES results. Spalart–Allmaras gives the closest agreement to LES on the size of the separation bubble. Downstream of separation, v ²−f yields a better agreement with LES than does its modified version, which exhibits a delayed reattachment and slower recovery. For the turbulence quantities, v ²−f yields a better agreement with LES than the other models. All the RANS models, however, fail to completely follow the dynamics of the inner layer in the rebound process revealed by LES.

Acknowledgment

This work was supported by the US Office of Naval Research (Grant Number N00014-98-1-0060; Program Officers Dr L. Patrick Purtell and Dr Ronald D. Joslin). The simulations were performed on the Cray J90 at the US Department of Defense High Performance Computing Major Shared Resource Centers (CEWES and NAVO).