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This document discusses an analytical treatment of the strong interaction problem in hypersonic viscous flow on a noninsulated flat plate is presented, using the method of similar solutions of the compressible boundary layer equations. Recent experimental data which confirm some of the theoretical results are also discussed.
The instability of hypersonic boundary-layer flows over flat plates is considered. The viscosity of the fluid is taken to be governed by Sutherland's law, which gives a much more accurate representation of the temperature dependence of fluid viscosity at hypersonic speeds than Chapmans's approximate linear law; although at lower speeds the temperature variation of the mean state is less pronounced so that the Chapman law can be used with some confidence. Attention is focussed on the so-called vorticity mode of instability of the viscous hypersonic boundary layer. The instability of the hypersonic boundary layer is non-interactive. The vorticity mode of instability of this flow operates on a significantly different lengthscale than that obtained if a Chapman viscosity law is assumed. The growth rate predicted by a linear viscosity law overestimates the size of the growth rate by O (M-sq). Next, the development of the vorticity mode as the wavenumber decreases is described, and it is shown that acoustic modes emerge when the wavenumber has decreased from it's O(1) initial value to O (M to the -3/2 power). (jhd).
Designed for advanced undergraduate and graduate courses in modern boundary-layer theory, this frequently cited work offers a self-contained treatment of theories for treating laminar and turbulent boundary layers of reacting gas mixtures. 1962 edition.
The interaction between the inviscid field and the large viscous boundary layer characteristic of hypersonic flow is analyzed from the continuum viewpoint. A variety of similarity parameters are derived to represent the viscous flow over slender bodies. The similitude is described by a binary collision scaling parameter, so that it is possible to apply a binary scaling that transforms density and length in inverse proportion at a fixed velocity and temperature. Experiments at a Mach number near 13 on a thermally controlled copper sharp plate were conducted to examine the wall temperature effects. Because of the wide range of test conditions covered in the experiments, the results provide some insight into viscous similarity when molecular effects begin to appear at the leading edge.
Theoretical inquiry is made into the high speed viscous flow past a sharp-edged flat plate whose surface is aligned with the oncoming flow. Basic information is sought concerning the fundamental nature of the flow field in regions near the leading edge. The role of upstream conditions is found to be fundamental. Study is made of the viscous layer region on the two-dimensional flat plate ahead of the strong interaction region. The Navier-Stokes equations are applied to the flow up to the point where continum treatments are no longer justifiable. Two initial velocity profiles were assumed in order to examine the details of the theory. Neither form proved to yield realistic flow fields in the light of experimental results. Computations from these two profile forms, however, did serve to bring out the sensitivity of the flow throughout the viscous layer region to initial conditions. It is concluded, in consequence, that the flow cannot be described by similar solutions or other solutions which ignore these initial values. (Author).
Calculation of drag coefficient of a flat semi-infinite heat-insulated plate in a hypersonic gas flow with slip is described. It is assumed that the region of flow between joined strong jumps of the packing and the plate consists of a non-viscous zone and laminar boundary layer. The strong interaction of the jump with the layer is considered. In calculation of the boundary layer the integral form of equation of pulses with linear profile of speed is used and taking into account the speed of slip. Parameters of flow on the external boundary of the boundary layer are calculated by the method of tangential wedges.