The Effect of Yield Stress on the Performance of Viscosity Regularization

Abstract

—In this study we investigate the effect of yield stress on the performance of viscosity regularization models in predicting unsteady flow of yield stress fluids. Viscosity regularization is popular for its simplicity of implementation into CFD codes and relatively low computational cost; however, the discussion on the limitations of this method in predicting the flow behavior has remained qualitative. We present a quantitative comparison between regularization and exact rheology in predicting natural convection of the Bingham fluids in a square cavity with differen- tially heated sidewalls. We consider a range of Bingham numbers and compare viscosity regularization results with augmented Lagrangian solutions. We show that the accuracy of viscosity regularization declines as the Bingham number increases. We also show that for high yield stress values the computational cost of viscosity regularization increases significantly.