A Nonlinear Eddy-Viscosity Model for Near-Wall Turbulence

Abstract

In this work the original V2F model of Durbin (Theor. Comput. Fluid Dyn. 3:1–13, 1991) and the nonlinear V2F model of Pettersson Reif (Flow Turbul. Combust. 76:241–256, 2006) have been assessed for several adverse pressure gradient (APG) turbulent boundary layer flows, designed as benchmark cases within the WALLTURB consortium. The APG flows have been created by putting curved surfaces (bumps) on walls of otherwise plane channels. On the diverging side of the bumps the flows either separate or are close to separation. We have found that even though the NLV2F model accounts for the Reynolds-stress anisotropy, this does not seem to significantly improve the model predictions. It is in fact very interesting to note that without the effect of curvature, the two models respond almost identical to the imposed adverse pressure-gradient. When the flow gets close to separation the differences between the models are on the other hand significant and the models generally perform worse. All in all, the results seem to reveal that it is not the lack of turbulence anisotropy information per se that is the primary source for the long standing problem related to the prediction of adverse pressure-gradient turbulent boundary layers. This is our primary motivation for our long term objective to include turbulence structure information alongside improved turbulence anisotropy predictions in an attempt to improve the modeling of the turbulence time scale (k/ε).