AASCIT Journal of Physics 2015; 1(4): 236-245 Published online July 10, 2015 (http://www.aascit.org/journal/physics) Keywords Cebeci and Smith Model, Jones and Launder Model, Coakley Model, Granville Model, Favre-Averaged Navier-Stokes Equations, Van Leer Algorithm, First Order Scheme Received: June 5, 2015 Revised: June 16, 2015 Accepted: June 17, 2015 Comparison of Several Turbulence Models as Applied to Hypersonic Flows in 2D – Part I Edisson Sávio de Góes Maciel Aeronautical Engineering Division (IEA), Aeronautical Technological Institute (ITA), SP, Brasil Email address edisavio@edissonsavio.eng.br Citation Edisson Sávio de Góes Maciel. Comparison of Several Turbulence Models as Applied to Hypersonic Flows in 2D – Part I. AASCIT Journal of Physics. Vol. 1, No. 4, 2015, pp. 236-245. Abstract In the present work, the Van Leer flux vector splitting scheme is implemented to solve the two-dimensional Favre-averaged Navier-Stokes equations. The Cebeci and Smith and Granville algebraic models and the Jones and Launder and Coakley two-equation models are used in order to close the problem. The physical problem under study is the “cold gas” hypersonic flow around a reentry capsule configuration. The results have demonstrated that the aerodynamic coefficient of lift is better predicted by the Coakley turbulence model; However, the stagnation pressure ahead of the reentry capsule configuration is better predicted by the Granville turbulence model. 1. Introduction Conventional non-upwind algorithms have been used extensively to solve a wide variety of problems ([1]). Conventional algorithms are somewhat unreliable in the sense that for every different problem (and sometimes, every different case in the same class of problems) artificial dissipation terms must be specially tuned and judicially chosen for convergence. Also, complex problems with shocks and steep compression and expansion gradients may defy solution altogether. First order upwind schemes are in general more robust but are also more involved in their derivation and application. Some upwind schemes that have been applied to the Euler equations are, for example, [2-3]. Some comments about these methods are reported below: [2] suggested an upwind scheme based on the flux vector splitting concept. This scheme considered the fact that the convective flux vector components could be written as flow Mach number polynomial functions, as main characteristic. Such polynomials presented the particularity of having the minor possible degree and the scheme had to satisfy seven basic properties to form such polynomials. This scheme was presented to the Euler equations in Cartesian coordinates and three-dimensions. [3] emphasized that the [4] scheme had low computational complexity and low numerical diffusion when compared to other methods. They also mentioned that the original method had several deficiencies. It yielded pressure oscillations in the proximity of shock waves. Problems with adverse mesh and with flow alignment were also reported. [3] proposed a hybrid flux vector splitting approach which alternated between the [4] scheme and the [2] scheme, at the shock-wave regions. This strategy assured that strength shock resolution was clearly and well defined. There is a practical necessity in the aeronautical industry and in other fields of the capability of calculating separated turbulent compressible flows. With the available numerical methods, researches seem able to analyze several separated flows, three-dimensional in general, if an appropriated turbulence model is employed.