SUMMARYIn this paper a time-accurate, fully implicit method has been applied to solve a variety of steady and unsteady viscous ow problems. It uses a ÿnite volume cell-centred formulation on structured grids and employs central space discretization with artiÿcial dissipation for the residual computation. In order to obtain a second-order time-accurate implicit scheme, a Newton-like subiteration is performed in the original LU-SGS method to converge the calculations at each physical time step by means of a dualtime approach proposed by Jameson. The numerical experiments show that the present method is very e cient, reliable, and robust for steady and unsteady viscous ow simulations, especially for some low speed ow problems.
One of the emphases of this paper was the enhancement of drag prediction as well as the decomposition of drag into its physical components. The drag-prediction capability of the improved WBVS code for transonic ow about wing/body combinationwas veri ed by two approaches, code to code and code to experiment. The good agreements indicate that the wing body viscous has the capability to assess the aerodynamic performance in the supercritical wing design for civil transport aircraft. Another task of the present study was to redesign a supercritical wing for a new regional jet aircraft by employing the improved code as an analysis tool for wing/body combination. To accomplish this, a geometry-modifyingtechnique was employed to gradually improve the upper-and lower-surface shapes of wing sections.
NomenclatureC D = total drag coef cient C Di = induced drag coef cient C Dv = viscous drag coef cient C Dw = wave drag coef cient C Fb = friction drag coef cient of fuselage C L = lift coef cient C p = pressure coef cient c = local chord N c = mean aerodynamic chord M = Mach number n = unit vector normal to ¾ or 6 Re = Reynolds number based on mean aerodynamic chord S = wing area T = temperature .u; v; w/ = Cartesian velocity components V = velocity .x; y; z/ = Cartesian coordinates, x along streamwise and z spanwise 1s D s ¡ s 1 = speci c entropy produced by shock (1u, 1v, 1w/ = nondimensional perturbation velocity components ½ = density 6 = transverse surface downstream at a distance where there is no streamwise pressure gradient ¾ = surface of shock wave Subscripts n = component normal to shock 1 = conditions just upstream of shock 1 = freestream conditions
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