Hypersonic flow past a rectangular profile through which gas is blown strongly (Q794519)

The hypersonic flow past a rectangular profile and past the end of a cylinder with strong uniformly distributed subsonic blowing of inviscid gas at the front face of the body is discussed. Main interest is drawn on the form of the contact surface separating the blowing region from the exterior flow and on the pressure distribution at the body front face. The so called modified Newton formula is used and flow functions are established for two flow regimes, namely that near the center of the front face and that near the edge located sidewards. Series expansion with respect to the thickness of the thin blowing layer are established. With the help of the boundary conditions at the body one gets an integral equation for the pressure. The solutions of the integral equation for the two-dimensional as well as for the axisymmetric flow are discussed in detail by the use of power series expansions including asymptotic expansions. Among others Laplace transformations and descriptions using the hodograph plane of the velocity are employed. The obtained exterior and interior solutions are matched to get the pressure at the front face of the body. The physical meanings of the different parts of the solutions are discussed in view of the drag of the body in connection with the blowing rate.