Assessment of Numerical and Modeling Errors of RANS based Transition Models for Low-Reynolds Number 2-D Flows

Abstract

In this paper we report the outcome of several workshops organized in the NATO Applied Vehicle Technology (AVT)-313 activity {\it Incompressible Laminar-to-Turbulent Flow Transition Study} that focused on assessing the numerical and modeling accuracy of the $\gamma-Re_{\theta}$ and $\gamma$ transition models coupled to the $k-\omega$ Shear-Stress Transport (SST) two-equation eddy-viscosity model. Three test cases were selected: flow over a flat plate with two different levels of turbulence intensity at the inlet; flow around the Eppler 387 foil at a Reynolds number of $3 \times 10^5$ and angles of attack of 1$^\circ$ and $7^\circ$; flow around the NACA 0015 foil at a Reynolds number of $1.8 \times 10^5$ and angles of attack of 5$^\circ$ and $10^\circ$. The flat plate flow conditions correspond to natural and bypass transition, whereas the other two test cases include laminar separation bubbles that lead to separation-induced transition. For each test case, the selected quantities of interest include integral and local flow quantities. Sets of geometrically similar grids with a wide range of grid refinement ratios were generated for each of the test cases to allow the estimation of numerical uncertainties for all quantities of interest selected for this study. Several RANS flow solvers were used, employing common grids with the same boundary conditions and mathematical models. Therefore, it is possible to analyze the consistency of the results, i.e., to check if the intervals defined by the different numerical solutions with their respective uncertainties overlap with each other. Modeling errors can also be addressed for the selected flow quantities that have experimental data available. However, the experimental information available in these cases is not sufficient to guarantee that experiments and simulations are performed with the same settings. Nonetheless, the available experimental data is sufficient to guarantee that modeling errors are significantly reduced with the use of the transition models when compared to simulations performed using only the $k-\omega$ SST model.