Comparison between the two-equation turbulence models of Jones and Launder and of Wilcox and Rubesin applied to aerospace problems

Abstract

In the present work, the Van Leer flux vector splitting scheme is implemented on a finite-volume context. The two-dimensional Favre-averaged Navier-Stokes equations are solved using an upwind discretization on a structured mesh. The Jones and Launder and the Wilcox and Rubesin two-equation models are used in order to close the problem. The physical problems under studies are the low supersonic flow along a ramp and the moderate supersonic flow around a blunt body configuration. The implemented scheme uses a MUSCL (Monotone Upstream-centered Schemes for Conservation Laws) procedure to reach second order accuracy in space. The time integration uses a Runge-Kutta method of five stages and is second order accurate. The algorithm is accelerated to the steady state solution using a spatially variable time step. This technique has proved excellent gains in terms of convergence rate as reported in Maciel. The results have demonstrated that the Wilcox and Rubesin model has yielded more critical pressure fields than the ones due to Jones and Launder. The shock angle of the oblique shock wave in the ramp problem and the stagnation pressure ahead of the blunt body configuration are better predicted by the Wilcox and Rubesin turbulence model. Key words: Van Leer algorithm, Jones and Launder turbulence model, Wilcox and Rubesin turbulence model, finite volumes and structured discretization, Navier-Stokes equations.