The effect of heating/ cooling on the upper-branch stability of boundary layer flows over a compliant boundary

Sandile S. Motsa; Precious Sibanda; Jitesh S.B. Gajjar

Sandile S. Motsa University of Zimbabwe
Precious Sibanda University of Zimbabwe
Jitesh S.B. Gajjar University of Manchester

Abstract

We investigate the evolution of Tollmien- Schlichting waves in boundary layers in the presence of moderate buoyancy arising from the heating or cooling of a compliant wall. We exploit the multi-deck structure of the flow in the limit of large Reynolds numbers to make an asymptotic analysis of the pertubed flow, along the upper-branch of the neutral stability curve, to derive linear neutral results. These results are discussed and are compared to rigid wall results. Also, a brief parametric study, based on the linear neutral results, is presented and the results are discussed.

Keywords

linear stability, heating and cooling, compliant surface,

References

[1] P.W. Carpenter, J .S.B. Gajjar. A general theory for two and three dimensional wall-mode instabilities in boundary layers over isotropic and anisotropic compliant walls. Theoret. Comput. Fluid Dynamics, 1: 349- 378, 1990.
[2] P.W. Carpenter, A.D. Garrad. The hydrodynamic stability of flow over Kramer type compliant surfaces. Part 1. Tollmien- Schlichting instabilities. J. Fluid Mech., 155: 465- 510, 1985.
[3] P.W. Carpenter, A.D. Garrad. The hydrodynamic stability of flow over Kramer type compliant surfaces. Part 2. Flow-induced surface instabilities. J. Fluid Mech., 170: 199- 232, 1986.
[4] P.W. Carpenter, P.J. Morris. Effect of anisotropic wall compliance on boundary layer stability and transition. J. Fluid Mech., 218: 171- 223, 1990.
[5] C. Davies, P.W. Carpenter. Instabilities in plane channel flow between compliant walls. J. Fluid Mech., 352: 201- 243, 1997.

The effect of heating/ cooling on the upper-branch stability of boundary layer flows over a compliant boundary

Abstract

Keywords

References

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