Computing the development of disturbances in the Blasius boundary layer due to localized unsteady two-dimensional wall injection

Citation

Doan, Phuc The (1981) Computing the development of disturbances in the Blasius boundary layer due to localized unsteady two-dimensional wall injection. Engineer's thesis, California Institute of Technology. doi:10.7907/bt7y-zn32. https://resolver.caltech.edu/CaltechETD:etd-10052006-115727

Abstract

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The localized unsteady two-dimensional wall injection of fluid into the Blasius boundary layer was mathematically modeled as a mixed initial-value boundary-value problem. Here the magnitude of the initial disturbance was sufficiently small so that the problem was linear. For the case of parallel mean flow, detailed formulation was discussed, and then, as an illustration, the problem of instantaneous blowing through a narrow slit in the wall was specifically analyzed and computed at a Reynolds number based on displacement thickness of 750 with the result showing a wave packet traveling at .44 times the speed of the freestream, amplifying like [...], spreading like 0.1x, where x is the distance from the slit, and eventually containing only frequencies whose imaginary parts lie between 0.009 and -0.010. To account for the effect of the boundary layer growth on the evolution of the disturbance, a perturbation method based on the idea of multiple scales was presented.

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