Axially Symmetric Laminar Compressible Boundary Layers with Pressure Gradient

Citation

Imster, Harry Frederick and Lesko, James Steven (1948) Axially Symmetric Laminar Compressible Boundary Layers with Pressure Gradient. Engineer's thesis, California Institute of Technology. doi:10.7907/HFMY-CY49. https://resolver.caltech.edu/CaltechETD:etd-12192008-074849

Abstract

Previous work on the subject of laminar compressible boundary layers has considered the flat plate without a pressure gradient (Karmen, Emmons and Brainerd), the flat plate with a pressure gradient (Illingworth), and the cone without pressure gradient (Hantzsche and Wendt). It is the purpose of this investigation to determine the effect of pressure gradient on the boundary layer thickness and skin friction for a figure of revolution in compressible flow. The basic momentum, continuity, and energy equations of viscous, compressible flow are reduced to an approximate form in the neighborhood of the surface of a figure of revolution by the usual boundary layer assumptions and the particular assumptions that no heat is transferred between the figure of revolution and the fluid and that the Prandtl number is equal to unity. An integral relation is then developed for the approximate equations and is subsequently reduced to a differential equation in which the boundary layer thickness is the dependent variable. In addition to considering the case of compressible flow with a pressure gradient, three other cases are examined in order to aid in the interpretation of the results. These are: compressible flow with no pressure gradient, and incompressible flow with and without pressure gradient. The equations are then applied to a figure of revolution over which pressure distributions have been experimentally determined at two Mach numbers and two Reynolds numbers. The resulting boundary layer thickness distributions are then used to determine the skin friction drag for the various cases. The effects of boundary layer velocity profile relation on skin friction drag coefficient are considered in some detail. The results of the investigation indicate that the usual practice of applying flat plate laminar skin friction drag coefficients (either compressible or incompressible) to figures of revolution in supersonic flow may be unconservative by a considerable margin. It is also shown that resulting drag values are considerably dependent on the boundary conditions used to obtain the boundary layer velocity profile.

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