APPROXIMATE ANALYSIS OF THE SLOT INJECTION OF A GAS IN LAMINAR FLOW

Abstract

The laminar diffusion and combustion of a gas injected into a high-speed uniform stream by means of a wall slot are considered. The Dorodnitzin-Howarth transformation is employed to reduce the boundary layer equations to incompressible form; the nonsimilar flow field is treated by a modified Oseen approximation in conjunction with the integral method. Thermal boundary conditions corresponding to an adiabatic wall and to constant wall enthalpy are discussed. The injection of homogeneous, heterogeneous, nonreactive, and reactive gases is treated. For the latter case, the models usually employed for chemical behavior, namely, frozen and equilibrium flow, are considered. The analysis is applicable to a wide variety of laminar flows, e.g., those involving cooling, thermal protection, skin-friction reduction, and supersonic deflagration. A numerical example of practical interest in connection with the venting of gaseous hydrogen boiloff from a rocket booster is presented.