Eddy viscosity modeling around curved boundaries through bifurcation approach and theory of rotating turbulence

Abstract

A novel approach to curvature effects based on the bifurcation theory and rotation turbulence energy spectrum is implemented to improve the sensitivity of the k−ϵ two-equation turbulence model (Jones-Launder form) to curved surfaces. This is done by accounting for the vorticity tensor, which becomes more significant in curved flows, something that the standard k−ϵ model does not originally consider. This new eddy viscosity model is based on the energy spectrum for a turbulent flow undergoing rotation and is then modeled on the bifurcation diagram in ϵ/Sk−η2/η1 phase space. The approach is demonstrated on three different test cases, 30° two-dimensional curved channel, 90° three-dimensional bend duct, and flow past cylinder, to test for the effects of convex and concave curvatures on turbulence. The results from these test cases are then contrasted against other existing eddy viscosity models as well as experimental data. The proposed approach provides better turbulence predictions along convex or concave surfaces, better memory effects, and are closer to the experimental results. For flow past cylinder, the new eddy viscosity model predicts drag coefficient that is closer to experiments with 8% difference, against 30% difference predicted by standard k−ϵ and Pettersson models.