A Reynolds stress closure description of separation control with vortex generators in a plane asymmetric diffuser

Abstract

A way to model the effects of streamwise vortices in a turbulent flow with one homogeneous direction is presented. The Reynolds averaged Navier-Stokes equations are solved with a differential Reynolds stress turbulence model. Assuming that the vortices can be approximated with the Lamb-Oseen model, wall-normal Reynolds stress distributions are calculated, corresponding to the spanwise variances of the estimated velocity distribution downstream of the vortex generators. The Reynolds stress contributions that are due to the vortex generators are added to the Reynolds stresses from the turbulence model so as to mimic the increased mixing due to the vortex generators. Volume forces are applied also in the mean momentum equations to account for the drag of the vortex generators. The model is tested and compared with experimental data from a plane asymmetric diffuser flow which is separating without vortex generators. The results indicate that the model is able to mimic the major features of vortex generator flow control and that the flow case in question is susceptible to separation control. The model results show that the pressure recovery of the diffuser could be increased by almost 10% by applying vortex generators and that, if keeping the shape of the vortex generators fixed, their optimal position is close to the diffuser inlet. Computations also indicated that the time to re-establish the separation zone when the control suddenly is turned off is substantially longer than the time it takes to remove the separation after the control is turned on again. Some work on adapting a differential Reynolds stress turbulence model was necessary in order to make it capable of realistic predictions of the asymmetric diffuser flow in which the vortex generator model is tested. However, the main focus of the article is on the modelling of vortex generator effects.