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A computer code for a turbulent, compressible boundary-layer method, capable of carrying out computations in a region of separated flow, is developed and tested. The procedure after separation is to specify either friction velocity or boundary-layer thickness as an independent variable and obtain external velocity as a dependent variable. This requires a trial and error alternation of the specified variable in order to match the desired experimental or computed external velocity. Satisfactorily results were obtained by this method in the analysis of certain specialized cases of separated flow. (Author).
Summary: Approximate formulas for the computation of the momentum thicknesses of turbulent boundary layers on two-dimensional bodies, on bodies of revolution at zero angle of attack, and on the inner surfaces of round channels all in compressible flow are given in the form of integrals that can be conveniently computed. The formulas involve the assumptions that the momentum thickness may be computed by use of a boundary-layer velocity profile which is fixed and that skin-friction formulas for flat plates may be used in the computation of boundary-layer thicknesses in flow with pressure gradients. The effect of density changes on the ration of the displacement thickness to the momentum thickness of the boundary layer is taken into account. Use is made of the experimental finding that the skin-friction coefficient for turbulent flow is independent of Mach number. The computations indicated that the effect of density changes on the momentum thickness in flows with pressure gradients is small for subsonic flows.
Analysis of Turbulent Boundary Layers focuses on turbulent flows meeting the requirements for the boundary-layer or thin-shear-layer approximations. Its approach is devising relatively fundamental, and often subtle, empirical engineering correlations, which are then introduced into various forms of describing equations for final solution. After introducing the topic on turbulence, the book examines the conservation equations for compressible turbulent flows, boundary-layer equations, and general behavior of turbulent boundary layers. The latter chapters describe the CS method for calculating two-dimensional and axisymmetric laminar and turbulent boundary layers. This book will be useful to readers who have advanced knowledge in fluid mechanics, especially to engineers who study the important problems of design.
The method predicts that a positive pressure gradient increases and a negative pressure gradient decreases the ratio of Stanton number to friction coefficient. The Crocco relation between the velocity and total enthalpy for a non-adiabatic surface and zero pressure gradient is generalized to non-zero pressure gradient. The relation between the velocity and the total enthalpy varies markedly from the flat plate Crocco relation as the pressure gradient departs from zero. The magnitude of the variation depends on the velocity profile shape parameter. (Author).