Author:
Nayfeh Ali Hasan,Saric William S.
Abstract
A non-linear analysis is presented for the stability of a liquid film adjacent to a compressible gas and under the influence of a body force directed either outward from or toward the liquid. The effects of the liquid's surface tension are taken into account. The non-linear Rayleigh–Taylor instability is included as a special case. The analysis considers the case of an inviscid liquid adjacent to a subsonic flow and the case of a very viscous liquid adjacent to a subsonic or a supersonic flow. For a subsonic external flow, it is found that the cut-off wave-number is amplitude dependent in the inviscid case whereas it is amplitude independent in the viscous case. It is found that the non-linear motion of the gas may be stabilizing or destabilizing, whereas the non-linear motion of the liquid is found to be stabilizing in the viscous case. For a supersonic external flow and a viscous liquid, the cut-off wave-number is amplitude dependent. Moreover, unstable disturbances with wave-numbers near the cut-off wave-number do not grow indefinitely with time but achieve a steady-state amplitude.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Reference26 articles.
1. Nayfeh, A. H. 1968 Forced oscillations of the van der Pol oscillator with delayed amplitude limiting IEEE Trans. on Circuit Theory,15,192.
2. Rayleigh, Lord 1883 Investigation of the character of an incompressible heavy fluid of variable density Proc. Roy. Soc. 14,170.
3. Willson, A. J. & Chang, I. D. 1967 Comments on ‘Stability of a liquid layer adjacent to a high-speed gas stream’.Phys. Fluids,10,2285.
4. Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics .New York:Academic.
5. Taylor, G. I. 1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their planes.Proc. Roy. Soc. A201,192.
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