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Theoretical Investigations of Boundary Layer Stability

Report Number: AFFDL TR 64-184
Author(s): Gibbs S. Raetz; W. Byron Brown
Corporate Author: Northrop Corporation
Laboratory: Air Force Flight Dynamics Laboratory
Date of Publication: 1966-09
Pages: 142
Contract: AF 33(657)-11618
Project: 1366
Task: 136612
AD Number: AD0809388

The mathematical analysis underlying a Fortran program for calculating the proper solutions of the Orr-Sommerfeld system with sufficient accuracy and economy for applying the resonance theory of transition is described. This program covers spacewise growths, rather than timewise growths as in previous computations, of mainly two-dimensional Fourier components of the motion. It employs various innovations providing as much accuracy from efficient single-precision arithmetic as would be obtained from awkward multiple-precision arithmetic in previous calculation schemes. The source programs and some sample calculations, for the proncipal mode of oscillation of the Blasius boundary layer, are included. The Lees-Lin stability equation for compressible flow have been extended to include the terms involving the component of the mean boundary layer flow perpendicular to the flat plate. At Mach 5 this more than doubled the critical Reynolds number. Allowance was then made for the three-dimensional aspect of the disturbance velocity. The final result was to give good agreement with observed data in the lower branch of the neutral stability curve at Mach 2.2 and Mach 5, fair agreement with the upper branch at Mach 2.2 and large discrepancies with the data in the upper branch at Mach 5. Comparison of experimental determined neutral stability curves with those computed by simplified approximations have disagreed considerably at high Mach numbers on the upper branch, even when agreement was fairly good on the lower branch.

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