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Resonant instability of ducted free supersonic mixing layers induced by periodic Mach waves

Published online by Cambridge University Press:  26 April 2006

Christopher K. W. Tam  and
Fang Q. Hu
Christopher K. W. Tam
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, FL 32306–3027, USA
Fang Q. Hu
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, FL 32306–3027, USA
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Abstract

It is known that the mixing or spreading rate of free mixing layers decreases with an increase in the convective Mach number of the flow. At supersonic convective Mach number the natural rate of mixing of the shear layers is very small. It is believed that the decrease in mixing rate is directly related to the decrease in the rate of growth of the instabilities of these flows. In an earlier study (Tarn & Hu 1989) it was found that inside a rectangular channel supersonic free shear layers can support two families of instability waves and two families of acoustic wave modes. In this paper the possibility of driving these normal acoustic wave modes into resonant instability by using a periodic Mach wave system is investigated. The Mach waves can be generated by wavy walls. By properly choosing the wavelength of the periodic Mach wave system mutual secular excitation of two selected acoustic wave modes can be achieved. In undergoing resonant instability, the acoustic modes are locked into mutual simultaneous forcing. The periodic Mach waves serve as a catalyst without actually being involved in energy transfer. The resonant instability process is analysed by the method of multiple scales. Numerical results indicate that by using wavy walls with an amplitude-to-wavelength ratio of 1½% it is possible to obtain a total spatial growth of e9 folds over a distance of ten channel heights. This offers reasonable promise for mixing enhancement. The results of a parametric study of the effects of flow Mach numbers, temperature ratio, shear-layer thickness, modal numbers as well as three-dimensional effects on the spatial growth rate of the resonant instability are reported and examined so as to provide basic information needed for future feasibility analysis.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 229 , August 1991 , pp. 65 - 85
Copyright
© 1991 Cambridge University Press

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