Intensive injection of fluid into a hypersonic stream from the surface of a finite length plate
Intensive uniform injection of an incompressible fluid from the surface of a plane plate into a parallel hypersonic flow of perfect gas is discussed using a thin layer approximation to calculate the flow near the plate. To describe the surrounding hypersonic flow the so called tangent wedge method and Newton's formula, respectively, are applied. The introduction of dimensionless variables of order unity into the thin layer equations leads to a description of the contour of the contact surface between the gas and the fluid or the thin layer thickness respectively. Finally one gets a linear integral equation for the pressure distribution along the plate. The governing parameter is the pressure at the trailing edge of the plate. Great parts of the paper are concerned with the analytic solution of the integral equation. This succeeds in the application of Laplace transforms and some other transformations combined with the introduction of several mathematical functions such as the gamma function and the Riemann zeta function. As a result the pressure distribution at the plate is expressed by series expansions connected with these functions.
scientific article; zbMATH DE number 3709814