Abstract
The objective is to develop a high-resolution numerical scheme for calculating turbulent transonicows past airfoils. The numerical scheme essentially combines a multigrid explicit ® nite volume time-marching scheme with a convective upwind split pressure (CUSP) scheme for controlling arti® cial dissipation, and convergence rate is further enhanced by using local time stepping and implicit residual smoothing. One- and two-equation turbulence models areincorporated into thenumerical scheme to assess the ability of various turbulencemodels in the prediction of turbulent transonicow over airfoils within the framework of the CUSP formulation of arti® cial dissipation.Animplicit,factored,upwind-biasednumericalschemeisusedfortheintegrationoftheturbulence® eld equations. Transonic viscousows around the RAE-2822 airfoil are computed using this scheme. The results show reasonably good agreement with existing experimental data and an improved resolution of transonicviscousows. HE structure of turbulent transonicow around an airfoil is complex because of the presence of shock waves and vis- cous layers. When one computes thisow® eld numerically, it is important to establish a high-resolution algorithm for the solution of turbulent transonicows so as to improve the numerical pre- diction capabilities of the algorithm. Whereas a variety of ef® cient numerical solution procedures have been proposed for the solution of Navier± Stokes equations, the focus of this work is on explicit ® nite volume numerical schemes that require an explicit addition of arti® cial dissipative terms to ensure numerical stability and to resolve discontinuities and shear layers in theow® eld. The intro- duction of numerical dissipation could lead to the contamination of the physical dissipation and excessive smearing of shock waves. All oftheseaffecttheaccuracyofthesolutionofviscousowproblems. Hence, there is a need to control the amount of arti® cial dissipation without affecting numerical stability. One approach is to reduce the arti® cial dissipation through the use ofthe velocity scaling ofthe ar- ti® cial dissipation such as Kunz 1 and Varma and Caughey 2 orofthe matrix-value dissipation of Turkel and Vatsa. 3 Although the matrix- valued dissipation produces better resolution ofow features than
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