A modified transition model is given based on the shear stress transport (SST) turbulence model and an intermittency transport equation. The energy gradient term in the original model is replaced by flow strain rate to saving computational costs. The model employs local variables only, and then it can be conveniently implemented in modern computational fluid dynamics codes. The fifth-order weighted compact nonlinear scheme and the fourth-order staggered scheme are applied to discrete the governing equations for the purpose of minimizing discretization errors, so as to mitigate the confusion between numerical errors and transition model errors. The high-order package is compared with a second-order TVD method on simulating the transitional flow of a flat plate. Numerical results indicate that the high-order package give better grid convergence property than that of the second-order method. Validation of the transition model is performed for transitional flows ranging from low speed to hypersonic speed.
The Spalart-Allmaras （S-A） turbulence model, the shear-stress transport （SST） turbulence model and their compressibility corrections are revaluated for hypersonic compression comer flows by using high-order difference schemes. The compressibility effect of density gradient, pressure dilatation and turbulent Mach number is accounted. In order to reduce confusions between model uncertainties and discretization errors, the formally fifth-order explicit weighted compact nonlinear scheme （WCNS-E-5） is adopted for convection terms, and a fourth-order staggered central difference scheme is applied for viscous terms. The 15° and 34° compression comers at Mach number 9.22 are investigated. Numerical results show that the original SST model is superior to the original S-A model in the resolution of separated regions and predictions of wall pressures and wall heat-flux rates. The capability of the S-A model can be largely improved by blending Catris＇ and Shur＇s compressibility corrections. Among the three corrections of the SST model listed in the present paper, Catris＇ modification brings the best results. However, the dissipation and pressure dilatation corrections result in much larger separated regions than that of the experiment, and are much worse than the original SST model as well as the other two corrections. The correction of turbulent Mach number makes the separated region slightly smaller than that of the original SST model. Some results of low-order schemes are also presented. When compared to the results of the high-order schemes, the separated regions are smaller, and the peak wall pressures and peak heat-flux rates are lower in the region of the reattachment points.
The purpose of this article is to summarize our recent progress in high-order and high accurate CFD methods for flow problems with complex grids as well as to discuss the engineering prospects in using these methods.Despite the rapid development of high-order algorithms in CFD,the applications of high-order and high accurate methods on complex configurations are still limited.One of the main reasons which hinder the widely applications of thesemethods is the complexity of grids.Many aspects which can be neglected for low-order schemes must be treated carefully for high-order ones when the configurations are complex.In order to implement highorder finite difference schemes on complex multi-block grids,the geometric conservation lawand block-interface conditions are discussed.A conservativemetricmethod is applied to calculate the grid derivatives,and a characteristic-based interface condition is employed to fulfil high-order multi-block computing.The fifth-order WCNS-E-5 proposed by Deng[9,10]is applied to simulate flows with complex grids,including a double-delta wing,a transonic airplane configuration,and a hypersonic X-38 configuration.The results in this paper and the references show pleasant prospects in engineering-oriented applications of high-order schemes.
