On the compressible laminar boundary layer with suction

Abstract

The compressible laminar boundary layer in a pressure gradient with suction is analyzed on the basis of the momentum and thermal integral equations in conjunction with sixth and (for separation) seventh degree velocity, and seventh degree stagnation enthalpy profiles. For flow over a flat plate and for flows in a pressure gradient, straightforward and simple methods of calculating the boundary layer for a given Mach number, a given uniform wall temperature and a given suction distribution are shown. The results obtained by the present analysis agree well with available exact or purportedly accurate solutions for an impermeable or permeable wall, including the general asymptotic suction solutions for compressible flows with a pressure gradient and heat transfer. The asymptotic solutions imply that it should always be possible to entirely prevent separation in a given (finite) adverse pressure gradient by sufficient suction. A mathematically simple class of solutions in which the pressure gradient is arbitrarily prescribed, but the suction distribution is implicitly determined, is shown. Finally, the boundary layer with a linearly diminishing external velocity is calculated in detail. Of especial interest here is the delay and complete prevention of separation by suction, including determination of the minimum (homogeneous) suction parameter to entirely avoid separation. Effects of Mach number and wall temperature are shown.