Study of the Boundary Layer at Supersonic Speeds in Turbulent Flow: Case of Flow along a Flat Plate*

The flow of a gaseous fluid past a rigid, smooth half-plane, parallel to the asymptotic velocity of the stream, is studied. The edge of the half-plane (leading edge) is assumed to be orthogonal to the stream, and, in addition, it is assumed that the flow is everywhere "turbulent". The motion within the boundary layer is investigated in an attempt to clarify many of the assumed and conjectured facts relating to the turbulent layer within a supersonic stream. For instance, it is found for supersonic flow, within the range of Mach numbers examined, that a drag law holds which is formally identical with the one which is true for incompressible fluids, and, moreover, that the thickness of the boundary layer also obeys a law which is formally analogous to the one describing the growth of the layer in the incompressible fluid case. In addition, such relationships as those concerned with the velocity and temperature distributions within the layer, and the transfer of heat from the stream to the constraining plate at various Reynolds and Mach numbers are deduced from clearly set forth premises. Analogies and extensions are presented for full understanding of the phenomena described. In presenting the results of this study of the motion within the turbulent layer it is found necessary to obtain the solution as an asymptotic one, i.e., one which is rigorously valid at a sufficient distance from the leading edge. The formulas obtained contain a parameter, the determination of which must be left to experiment. A plausible value of it, based upon the results obtained by Frossel1 from his investigation on suband supersonic streams in pipes, will be given.