Asymptotic solution of incompressible boundary layer equations with negative pressure gradient and large injection rates

During entry of bodies into the Earth's atmosphere with high velocities, the mass removal from the body surface as a result of the large convective and primarily radiation fluxes may become arbitrarily large, i. e., the injection rate into the boundary layer may approach infinity. The present article presents a solution of the Prandtl equations for the incompressible boundary layer with negative pressure gradient (dp/dx<0) for large injection rates. The existence of a solution of the boundary layer equations with arbitrary injection rate under the condition dp/dx<0 was shown in Oleinik's work [1].The asymptotic solution obtained agrees with the exact numerical solution for those values of the injection rate for which the boundary layer approximation still remains valid. An analogous solution for the self-similar equations in the vicinity of the stagnation point was previously obtained in [2]. The use of the asymptotic solution makes it possible to find an expression for the friction coefficient which is convenient for concrete calculations in the case of arbitrary negative pressure gradients.In conclusion the author wishes to thank G. A. Tirskii for guidance in the work and I. Gershbein for permitting the use of the numerical solution.