Numerically Determined Empirical Relationships for a Transitional Turbulence Model

Abstract

Turbulence models in computational fluid dynamics (CFD) aim to capture a complex phenomenon through simplified mathematical models. The models themselves range in terms of application, complexity and methodology. This work looked at a transitional model for Reynolds averaged Navier Stokes equations. In particular the focus was on the correlation based intermittency and momentum thickness Reynolds number (γ - R̃eθt) model. The original model has high order correlations, that were determined and calibrated from flat plate tests of various pressure gradients. In this work the correlations were simplified to reduce the number of calibration coefficients and help in understanding the effect of each parameter. Flat plate test data, from the European Research Community on Flow, Turbulence and Combustion (ERCOFTAC) T3A series, were used to verify the lower order approximations through OpenFOAM simulations. The open source CFD package OpenFOAM was used for its easy access to the base code. The reduced order model was then applied to a National Advisory Committee for Aeronautics (NACA) 0012 foil at a transitional Reynolds number of 360 000 as a means of validation. The reduced order, the original γ - R̃eθt and the fully turbulent k - omega shear stress transport (k − ω SST) turbulence models are compared over a range of angles of attack to highlight the difference between models. The proposed model reduced the runtime of simulation by approximately 6%. The reduction in model coefficients meant a step by step adjustment could be implemented to increase model accuracy. In addition the adjusted model increased the accuracy of drag prediction on a NACA0012 airfoil, while maintaining a similar lift prediction as the original.

Keywords

• Transitional turbulence model; Optimization; NACA foil; OpenFOAM; Flat plate.