Turbulence modelling for supercritical flows including examples with passive shock control

The aerodynamic performance of supercritical aerofoils at transonic speeds is strongly influenced by the shock wave-boundary-layer interaction. Passiv e shock control is one of the techniques used for controlling the undesirab le effects of strong shock wave-boundary-layer interaction leading to exten sive separation. Using passive shock control, the stall margin is increased and the onset of buffeting is delayed. Passive shock control is modelled b y introducing a closed plenum chamber underneath a perforated surface at th e foot of the shock wave where a combination of blowing and suction is gene rated. As a result, a strong normal shock wave is changed into a series of weak shock waves with lambda shape. Since the Baldwin-Lomax turbulence mode l has been used extensively for passive shock control modelling, which exhi bits poor predictability for separated flows, an attempt has been made to m odify the Reynolds normal stresses for this model so as to improve the accu racy of numerical results for flows with separation. Further modification t o the Baldwin-Lomax model has been employed so that the mass transpiration effects are taken into account for the passive shock control computations. In this paper, a brief description on an implicit finite-volume TVD scheme in general coordinates is given and the details of the Balwin-Lomax turbule nce model and its modifications are presented. The validated numerical resu lts for several RAE 2822 aerofoil problems plus corresponding results for t he modelled methods are presented and compared with some experimental data and other numerical results.