Two-dimensional viscous flow past a flat plate

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Abstract
Using the Navier-Stokes equations of the vorticity-stream function form in body-fitted orthogonal coordinates, the flow past a flat plate at various angles of incidence has been numerically investigated for Reynolds number up to 30. By treating the singularity at the tip analytically, in that the near-tip behavior is expanded in powers of the local variables and matched to the outer finite-difference solution, the calculation procedure can be made very accurate, robust and efficient. It is shown that the singular behavior of the vorticity and pressure are well captured, and the analytic pressure distribution around the tip enables one to calculate the forces acting on the plate accurately. The results are seen to be in good agreement with those reported earlier for the flow past a normal flat plate. The flow pattern at other angles of incidence is discussed, and a detailed flow map along with the drag and lift coefficients with respect to the angle of incidence and Re is presented.