Assessing Numerical Aspects of Transitional Flow Simulations Using the RANS Equations

Abstract

This paper addresses the influence of the scheme used in the convective terms of turbulence and transition transport equations on the numerical accuracy of transitional flow simulations. Three transition models are combined with the k−ω Shear Stress Transport turbulence model: the γ−Reθ model, the γ model and the Amplification Factor Transport model. Two airfoils and a 6:1 prolate spheroid are used as test cases. Using first-order upwind in the convective terms of the k and ω transport equations has a weak effect on the numerical accuracy of the simulations when there is no transition model. However, when combined with the transition models, there is a significant improvement if second-order schemes are used. The iterative convergence obtained for the first-order approach was similar to that observed with the second-order schemes. Therefore, common ‘rules of thumb’ from RANS simulations at high Reynolds numbers may fail when transition models are included.