Estimation of Discretization Uncertainty Using the γ−Reθ Transition Model for Transitional Flows on 6:1 Spheroid

Abstract

This paper aims to estimate the surface mesh size related discretization uncertainties using the γ−Reθ transition model combined with the shear stress transport (SST) k–ω turbulence model. For comparison, this work employs an available experimental study performed with a 6:1 prolate spheroid. The grid convergence index (GCI) study is performed for axial force, surface skin friction, and pressure coefficients with three levels of meshes. The transition model estimates the axial force coefficients (CX), approximately half of which are obtained using fully turbulent calculations with higher GCI values. The GCI values around the axial force coefficients for the level-2 mesh are less than 1% based on fully turbulent calculations. However, with the transition model, these values for the same mesh level increase to 10%. While the GCI values of surface pressure coefficients are very small based on both fully turbulent and transition model calculations, these coefficients show differences at the trailing part of the spheroid. Significant differences are also observed in the surface friction coefficients. While the model captures drastic changes in terms of transition in the surface friction coefficients at the suction side of the spheroid, such drastic change is not observed in fully turbulent calculations. On the other hand, there is no sign of any transition phenomenon at the pressure side, contrary to the observations of experimental measurements. The transition model is not able to estimate the transition front geometry correctly. The GCI values of the surface friction coefficients increase dramatically, up to 765% around the transition regions.