Davies, Christopher (1995) Evolution of Tollmien-Schlichting waves over a compliant panel. PhD thesis, University of Warwick.

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Abstract

The adaptation of Tollmien-Schlichting waves as they propagate over the leading and trailing edges of finite-length compliant panels is investigated by means of numerical simulation. The behaviour so determined is pertinent to the application of compliant walls for transition delay. We consider a model problem where the compliant panels form a section in the walls bounding a plane channel fluid flow. The results obtained are encouraging. They indicate that compliant panels with lengths comparable to the Tollmien-Schlichting wavelength can have a significant stabilising effect. In some instances, the passage of a Tollmien-Schlichting wave over the edges of a compliant panel leads to the excitation of stable flow-induced surface waves. The presence of such additional waves does not appear to be associated with any adverse effect upon the stability of the Tollmien-Schlichting wave.

The numerical scheme used for the simulations derives from a mixed finite-difference/spectral discretisation of the linearised two-dimensional Navier-Stokes equations, which were taken in a vorticity-velocity formulation. Numerical stability problems were overcome by treating the inertia of the compliant wall and the fluid together when imposing the boundary conditions. This allowed the interactively coupled fluid and the wall motion to be computed without any prior restriction on the form taken by the disturbances.

An investigation was also carried out into the linear stability of plane channel flow bounded by compliant walls throughout. In the case of the Tollmien-Schlichting mode this relied, for the most part, on the determination of numerical solutions to the Orr-Sommerfeld equation. Flow-induced surface waves could be studied more readily using an approximate analytic theory. Good agreement was achieved between the predictions of the analytic theory and numerical results obtained directly from the Orr-Sommerfeld equation, particularly for travelling wave flutter. The linear stability results for the wholly compliant-walled channel were used to analyse the behaviour displayed by Tollmien-Schlichting waves in the numerical simulations that were conducted with finite-length compliant panels

Item Type:	Thesis (PhD)
Subjects:	T Technology > TA Engineering (General). Civil engineering (General)
Library of Congress Subject Headings (LCSH):	Fluid dynamics, Drag (Aerodynamics), Transition flow, Waves -- Mathematical models, Water waves -- Mathematical models, Channels (Hydraulic engineering)
Official Date:	January 1995
Dates:	Date Event January 1995 Submitted
Institution:	University of Warwick
Theses Department:	Department of Engineering
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Carpenter, P. W. (Peter William), 1942-
Sponsors:	Science and Engineering Research Council (Great Britain) ; Marine Technology Directorate Limited
Format of File:	pdf
Extent:	viii, 262 leaves : charts
Language:	eng

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