Calculation Method for Three-Dimensional Rotationally Symmetrical Laminar Boundary Layers with Arbitrary Free-Stream Velocity and Arbitrary Wall-Temperature Variation

Abstract

A calculation method is presented enabling a rapid prediction of the distribution of the local skin-friction and heat-transfer coefficients to be made for rotationally symmetrical bodies having arbitrarily specified free-stream velocity distributions and surface-temperature variations for constant-property, incompressible, laminar boundary-layer flows. The method utilizes the Mangier transformation as a basis, thus enabling the results calculated by Hartree and Levy for the two-dimensional case to be used directly in the determination of boundary-layer quantities for the three-dimensional case. Example results using the proposed method are presented in the form of the boundary-layer momentum and displacement thicknesses, the skin-friction coefficients, and the heat-transfer coefficients for a three-dimensional half-body with constant surface temperature. These results, utilizing the Hartree velocity profiles, are compared with similar results obtained by Scholkemeier utilizing the Pohlhausen P-4 velocity profiles. The skin-friction coefficient for stagnation-point flow as obtained by the approximate method is compared with the exact solution for this region given by Homann to show excellent agreement.