Laminar, steady and unsteady flow over inclined plates in two and three dimensions

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Virginia Tech


The problem studied is the laminar flow over inclined, finite flat plates for moderately high Reynolds numbers in two and three dimensions. There are only few prior analyses, mainly for two dimensional flow, for this problem, and thus it was decided that it was worthwhile to study it now in great detail. The full Navier-Stokes equations were solved using a weak Galerkin formulation for the Finite Element Method with the pressure determined by a penalty approach. The influence of grid resolution, boundary conditions and size of the domain was studied. The true nature of the flow for different Reynolds numbers was also examined through steady and unsteady simulations of the two dimensional cases for 6600 â ¤ ReL â ¤18000. Results for the three dimensional flow over square plates at two angles of attack, a = 3.0 and 8.0 degrees for ReL = 100 are presented. The results are given in terms of skin friction and pressure coefficient variations along with flowfield visualization. Comparison between the two dimensional and three dimensional flow indicates the influence of the third coordinate to the flow. The analysis indicated that the two dimensional flow over a finite thick plate at 3.0 degrees angle of attack is steady up to Re = 12000. The solution for the upper surface is strongly influenced by the presence of a recirculation bubble at the leading edge. The slope of the lift curve for the 2D viscous flow is less than 2Ï , the result predicted by the thin wing theory. The solution for the three dimensional flow is strongly influenced by the the existence of the tip vortices. The slope of the lift curve for the 3D viscous flow is less than the one corresponding to the 2D flow. In addition, the effect of the aspect ratio on the lift does not agree with the inviscid lifting line theory prediction.