Solution of the wedge entry problem by numerical conformal mapping

Abstract

An accurate quasi-analytic method of solution is presented for the classical hydrodynamics problem of the constant-velocity entry of a prismatic wedge into a weightless incompressible inviscid fluid. The method uses the Wagner function W, which reduces the problem to the determination of a mapping function Λ = [Lscr ](W) for the hodograph. [Lscr ](W) is constructed by using the hodograph for an unsymmetric diamond together with a modifying or ‘preparatory’ trans-formation. A computer method of conformal mapping is developed and is used to obtain this latter transformation. Results are presented for the case of a 90° wedge and show that the solution is both more accurate than previous solutions, having an error of less than 1 %, and more complete, as it portrays the entire flow field and furnishes information about the functional dependence among the variables.