Simplified Method for Calculation of Compressible Laminar Boundary Layer With Arbitrary Free-Stream Pressure Gradient

The Karman-Pohlhausen integral method, as applied to compressible laminar boundary layers, was simplified by an analysis similar to the incompressible Holstein-Bohlen method. Although this simplification is helpful for many calculations, it is of greatest value when conditions at the edge of the boundary layer are known from experimental measurements. The analysis was conducted under the assumptions of a Prandtl number of 1, zero heat transfer, and a linear viscosity-temperature relation velocity profiles are approximated by a fourth-degree polynomial. Results are presented so that velocity and temperature profiles, momentum and displacement thicknesses, and wall shear stress can be calculated for flows over two-dimensional bodies with arbitrary free-stream velocity distributions. The results are also applicable to flows over three-dimensional bodies with axial symmetry through the use of Manglers transformation.