UNSTEADY VISCOUS THIN AIRFOIL THEORY.

The concept of viscous thin airfoil theory introduced previously by the author is formulated for unsteady incompressible flow. The theory is developed in detail for a flat plate airfoil with no thickness boundary layer. It is shown that the viscous pressure-downwash kernel function has a logarithmic singularity in contrast to the Cauchy singularity of inviscid theory. There is no eigensolution and no need for a Kutta condition to obtain a unique solution. It is shown by direct numerical solution that for Reynolds number greater than 1000, the viscous and inviscid results are virtually the same except in the immediate vicinity of the trailing edge. There, the pressure loading is greater than inviscid theory would indicate and the phase of the complex loading is less than inviscid theory. The effect of edge bluntness is illustrated for the case of steady flow.