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The stability of two-phase flow over a swept wing

Published online by Cambridge University Press:  26 April 2006

Adrian V. Coward  and
Philip Hall
Adrian V. Coward
Affiliation:
Department of Mathematics, University of Manchester, Manchester M13 9PL, UK
Philip Hall
Affiliation:
Department of Mathematics, University of Manchester, Manchester M13 9PL, UK
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Abstract

We use numerical and asymptotic techniques to study the stability of a two-phase air/water flow above a flat porous plate. This flow is a model of the boundary layer which forms on a yawed cylinder and can be used as a useful approximation to the air flow over swept wings. The air and water form an immiscible interface which can destabilize the flow, leading to travelling wave disturbances which move along the attachment line. This instability occurs for lower Reynolds numbers than is the case in the absence of a water layer. The two-fluid flow can be used as a crude model of the effect of heavy rain on the leading edge of a swept wing.

We also investigate the instability of inviscid stationary modes. We calculate the effective wavenumber and orientation of the stationary disturbance when the fluids have identical physical properties. Using perturbation methods we obtain corrections due to a small stratification in viscosity, thus quantifying the interfacial effects. Our analytical results are in agreement with the numerical solution which we obtain for arbitrary fluid properties.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 329 , 25 December 1996 , pp. 247 - 273
Copyright
© 1996 Cambridge University Press

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References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Blennerhassett, P. J. 1980 The generation of waves by wind. Phil. Trans. R. Soc. Lond. A 298, 451–493.Google Scholar
Charles, M. E. & Lilleleht, L. U. 1965 An experimental investigation of stability and interfacial waves in co-current flow of two liquids. J. Fluid Mech. 22, 217–224.Google Scholar
Coddington, E. A. & Levinson, N. 1955 Theory of Ordinary Differential Equations. McGraw-Hill.
Coward, A. V. 1994 The stability of two-phase flows. PhD Thesis, University of Manchester, UK.
Dunham, D. J., Dunham, R. E. Jr. & Bezos, G. M. 1991 A summary of NASA research on effects of heavy rain on airfoils. AGARD Rep 496.Google Scholar
Federov, B. I., Plavnik, G. Z., Prokhorov, I. V. & Zhukhovitskii, L. G. 1976 Transitional flow conditions on a rotating disc. J. Engng Phys. 31, 1448–1453.Google Scholar
Gaster, M. 1967 On the flow along swept leading edges. Aero. Q. 18, 165–184.Google Scholar
Gregory, N., Stuart, J. T. & Walker, W. S. 1953 On the stability of three-dimensional boundary layers with application to the flow due to a rotating disk. Phil. Trans. R. Soc. Lond. A 248, 155–199.Google Scholar
Hall, P. 1986 An asymptotic investigation of the stationary modes of instability of the boundary layer on a rotating disc. Proc. R. Soc. Lond. A 406, 93–106.Google Scholar
Hall, P. & Malik, M. R. 1986 On the instability of a three dimensional attachment-line boundary layer; weakly nonlinear theory and a numerical approach. J. Fluid Mech. 163, 257–282.Google Scholar
Hall, P., Malik, M. R. & Poll, D. I. A. 1984 On the stability of an infinite swept attachment line boundary layer. Proc. R. Soc. Lond. A 395, 229–245.Google Scholar
Heurre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Ann. Rev. Fluid Mech. 22, 473–537.Google Scholar
Hooper, A. P. 1985 Long-wave instability at the interface between two viscous fluids: thin layer effects. Phys. Fluids 28, 1613–1618.Google Scholar
Hooper, A. P. & Boyd, W. G. C. 1983 Shear-flow instability at the interface between two viscous fluids. J. Fluid Mech. 128, 507–528.Google Scholar
Hooper, A. P. & Boyd, W. G. C. 1987 Shear-flow instability due to a wall and a viscosity discontinuity at the interface. J. Fluid Mech. 179, 201–225.Google Scholar
Joseph, D. D. & Renardy, Y. Y. 1993 Fundamentals of Two-Fluid Dynamics, Vols. 1 & 2. Springer.
Kao, T. W. & Park, C. 1972 Experimental investigations of the stability of channel flows. Part 2. Two-layered co-current flow in a rectangular region. J. Fluid Mech. 52, 401–423.Google Scholar
Malik, M. 1986 The neutral curve for stationary disturbances in rotating-disk flow. J. Fluid Mech. 164, 275–287.Google Scholar
Malik, M. R., Chuang, S. & Hussaini, M. Y. 1982 Accurate numerical solution of compressible, linear stability equations. Z. Angew. Math. Phys. 33, 189–201.Google Scholar
Pfenninger, W. & Bacon, J. W. 1969 Viscous Drag Reduction (ed. C. S. Wells), pp. 85–105. Plenum.
Poll, D. I. A. 1979 Transition in the infinite swept attachment line boundary layer. Aero. Q. 30, 607–528.Google Scholar
Poll, D. I. A. 1980 In IUTAM Symp. on Laminar-Turbulent Transition, Stuttgart. Springer.
Prandtl, L. 1946 On boundary layers in three-dimensional flow. Rep. Aero Res. Coun., Lond. No. 9828.
Renardy, Y. Y. 1985 Instability at the interface between two shearing fluids in a channel. Phys. Fluids 28, 3441–3443.Google Scholar
Rosenhead, L. (ed.) 1963 Laminar Boundary Layers. Oxford University Press.
Sears, W. R. 1948 The boundary layer of yawed cylinders. J. Aero. Sci. 15, 49–52.Google Scholar
Yih, C. S. 1967 Instability due to viscosity stratification. J. Fluid Mech. 27, 337–352.Google Scholar