Abstract
The free-interaction influence of a thermal expansion process in boundary-layer gas flow is analyzed using the formalism of triple-deck theory. The physical model considered is the forced convection of a gas flowing over a flat plate subject to a heated slab. Both linearized and full nonlinear solutions are obtained using Fourier transform methods and spectral numerical techniques. The influence of monochromatic thermal perturbation on boundary-layer stability (lower branch) is studied and first-order correction of the lower branch neutral stability curve for the boundary-layer flow has been obtained. The shift of neutral stability is then computed for different values of the thermal perturbation wave number, making unstable some otherwise stable modes.
This is a preview of subscription content, log in via an institution to check access.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
K. Stewartson and P.G. Williams, Self-induced separation, Proc. Roy. Soc. London Ser. A, vol. 312, pp. 181–206 (1969).
A.F. Messiter, Boundary layer flow near the trailing edge of a flat plate, SIAM J. Appl. Math., vol. 18, pp. 241–257 (1970).
K. Stewartson, D'Almbert's paradox, SIAM Rev., vol. 23, pp. 308–343 (1981).
F.T. Smith, On the high Reynolds number theory of laminar flows, J. Appl. Math., vol. 28, pp. 207–281 (1982).
A.F. Messiter and A. Liñán, The vertical flat plate in laminar free convection: effects of leading and trailing edges and discontinuous temperature, Z. Angew. Math. Phys., vol. 27, pp. 633–651 (1976).
F. Méndez, C. Treviño, and A. Liñán, Boundary layer separation by a step in surface temperature, Inernat. J. Heat Mass Transf., vol. 35, pp. 2725–2738 (1992).
F.T. Smith, On the non-parallel boundary layer stability of the Blasius boundary layer, Proc. Roy. Soc. London Ser. A., vol. 366, pp. 91–109 (1979).
F.T. Smith, Non-linear stability of boundary layers for disturbances of various sizes, Proc. Roy. Soc. London Ser. A, vol. 368, pp. 573–589 (1979).
F.T. Smith, Proc. Roy. Soc. London Ser. A, vol. 371, p. 439 (1980).
M.E. Goldstein, Scattering of acoustic waves into Tolmien-Schlichting waves by small streamwise variations in surface geomety, J. Fluid Mech., vol. 154, p. 509 (1985).
M.E. Goldstein and L.S. Hultgren, A note on the generation of Tollmein-Schlichting waves by sudden surface-curvature change, J. Fluid Mech., vol. 181, p. 519 (1987).
P. Leehey and P. Shapiro, Leading edge effect in laminar boundary layer excitation by sound, in Laminar-Turbulent Transition (ed. R. Eppler and H. Fasel), Springer-Verlag, New York, pp. 321–331 (1979).
R.J. Bodonyi, W.J.C. Welch, P.W. Duck, and M. Tadjfar, A numerical study of the interaction between unsteady free-stream disturbances and localized variations in surface geometry, J. Fluid Mech., vol. 209, p. 285 (1989).
S.O. Seedougui, R.I. Bowles, and F.T. Smith, Surface-cooling effects on compressible boundary-layer instability, and on upstream influence, European J. Mech. B/Fluids, vol. 10, p. 117 (1991).
V.I. Lysenko and A.A. Maslov, The effect of cooling on supersonic boundary-layer stability, J. Fluid Mech., vol. 147, p. 39 (1984).
S.N. Brown, H.K. Cheng, and C.J. Lee, Inviscid—viscous interaction on triple-deck scales in a hypersonic flow with strong wall cooling. J. Fluid Mech., vol. 220, p. 309 (1990).
D.L. Turcotte, Stable combustion of a high velocity gas in a heated boundary layer, J. Aeronaut. Sci., vol. 27, pp. 509–516 (1960).
T. Hirano and Y. Kanno, Aerodynamical and thermal structures of a laminar boundary layer over a flat plate with a diffusion flame, Proc. XIV Internat. Symp. on Combustion, p. 391 (1973).
C. Treviño, W. Stüttgen, and N. Peters, Pressure gradients due to gas expansion and gasification effects in a boundary layer combustion of a condensed fuel, Wärme Stoffübertrag., vol. 25, pp. 309–319, (1990).
C. Treviño, W. Stüttgen, and N. Peters, Higher order effects in the premixed boundary layer combustion, J. Propul. Power, vol. 6, no. 3, pp. 237–242 (1990).
L. Howarth, Concerning the effect of compressibility on laminar boundary layers and their separation, Proc. Roy. Soc. London Ser. A, vol. 194, p. 16 (1948).
P.W. Duck and O.R. Burggraf, Spectral solutions for three-dimensional triple-deck flow over surface topography, J. Fluid Mech., vol. 162, pp. 1–22 (1986).
O.R. Burggraf and P.W. Duck, Spectral computation of triple-deck flows, in Numerical and Physical Aspects of Aerodynamic Flows (ed. T. Cebeci), Springer-Verlag, New York (1981).
C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang, Spectral Methods in Fluid Dynamics, Springer-Verlag, New York (1988).
F.T. Smith and O.R. Burggraf, On the development of large-sized short scaled disturbances in boundary layers, J. Proc. Roy. Soc. London Ser. A, vol. 399, p. 25 (1985).
F.T. Smith, On the first mode instability in subsonic, supersonic or hypersonic boundary layers, J. Fluid Mech., vol. 198, pp. 127–153 (1989).
Author information
Authors and Affiliations
Additional information
Communicated by M.Y. Hussaini
This work has been supported by the Cray Research Inc. through a grant on supercomputing.
Rights and permissions
About this article
Cite this article
Treviño, C., Liñán, A. The effects of displacement induced by thermal perturbations on the structure and stability of boundary-layer flows. Theoret. Comput. Fluid Dynamics 8, 57–72 (1996). https://doi.org/10.1007/BF00312402
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00312402