The Lag RST Turbulence Model Applied to a Vortex Flow

Abstract

A turbulent line vortex, also known as a q-vortex, is computed using the Reynoldsaveraged Navier-Stokes (RANS) equations and a slightly modified version of the lag Reynolds stress transport (RST) turbulence model proposed by Olsen and Coakley. The lag RST model is based on Wilcox’s k-ω two-equation equilibrium turbulence model. However, it attempts to model the behavior of non-equilibrium turbulence with the addition of a “lag” or “relaxation” equation for the Reynolds stress tensor. The results are compared to the direct numerical simulation (DNS) data of Qin and additional results obtained using other turbulence models. The results show that the lag RST model captures the misalignment between the principal axes of the Reynolds stress tensor and those of the strain rate tensor, which is seen in Qin’s DNS data. This misalignment is a result of the Reynolds stresses requiring time to react to changes in the mean flow. However, the lagging feature of the lag RST model comes at the expense of underpredicting Reynolds stress peak magnitudes. The model also does not predict the transition of peak turbulent kinetic energy from the vortex core edge to the vortex centerline when turbulence begins to decay as observed in the DNS. Although there are problems with the lag RST model in predicting this turbulent vortex flow, it does capture the non-equilibrium lag effect that linear eddy-viscosity models cannot.