Comparison of First and Second Order Turbulence Models for a Jet/3D Ramp Combination in Supersonic Flow

‡The full, unsteady three-dimensional Reynolds-Averaged Navier-Stokes Equations were used to perform a comparative evaluation of the performance of two first-order and of one second-order turbulence models. The flowfield chosen as the baseline test case is a Mach 4.0 turbulent flow over a three-dimensional compression ramp for which experimental data exists. In addition to this baseline ramp case, the turbulence models were also compared in the flowfield created by the interaction of the three-dimensional compression ramp and a sonic normal injection. The study aims at highlighting the relative shortcomings and advantages of first-order closure models compared to second-order models and, more specifically, the capability of state-of-the-art turbulence modeling as implemented in a commercial software, to produce results for complex flowfields. Both the pros and cons of eddy viscosity models were put in evidence and discussed when compared to Reynolds Stress models. The turbulence models selected for this study were the one-equation eddy viscosity model of Spalart-Allmaras, the two-equation eddy viscosity k- model of Wilcox and the second-order model proposed by Wilcox that, unlike most other Reynolds Stress models, use the turbulence frequency instead of the dissipation of turbulent kinetic energy, to compute the dissipation. The comparison of the turbulence models is intended as a general and partial guideline to the choice of turbulence models for those professionals in industry that use numerical codes with built-in turbulence models. For this reason the study made use of offthe-shelf commercial software rather than an in-house development code. The study showed the difficulty of converging the solution of a complex flowfield when using the Reynolds stress turbulence model and highlighted the usefulness for practical and design purposes of eddy-viscosity models.