Compressibility and pressure-gradient correction assessment for turbulent hypersonic flows

Abstract

NOWLEDGE of the flow development in hypersonic windtunnel nozzles is of primary importance to the design of such nozzles as well as to the characterization of the flowfield in the test section. In the perfect-gas regime, reliable numerical methods have been developed for both of the design work and the flow analysis, but there still exist some deficiencies in predicting the turbulent hypersonic nozzle wall boundary layers. This problem is believed to be a consequence of the deficiencies in the compressible eddy-viscosity turbulence models currently adopted in engineering applications. Specifically, to improve the accuracy of such calculations, the importance of compressibility and pressure-gradient effects should be investigated, since the hypersonic wind-tunnel nozzle flow is characterized by the existence of an increasing main flow Mach number and a varying pressure gradient in the streamwise direction. A numerical study of that nature is presented in this work. Several explicit compressibility and pressure-gradient corrections are introduced to two widely used eddy-viscosity turbulence models for the calculations of hypersonic wind-tunnel nozzle flows. The results are compared with those obtained with the standard models to evaluate the effects of the corrections, and are compared with measurements to verify the accuracy of the calculations and to see the improvements gained. Numerical Modeling The study was carried out by solving three-dimensional Reynolds-averaged Navier-Stokes equations. They are the transport equations to describe the conservation of mass, momentum, and energy with the assumption of a perfect gas. When two-equation turbulence models are employed, the system has two more equations for the turbulent kinetic energy k and its dissipation rate €. In the present work the turbulence is closed by four alternative eddy-viscosity models, among which the Baldwin-Lomax algebraic model1 and the k-€ model of Chien 2 are chosen as the baseline models for the purpose of evaluating the compressibility and pressure-gradient corrections. The other two are their modified versions, respectively, with the modifications outlined below.