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Laminar separation in buoyant channel flows

Published online by Cambridge University Press:  21 April 2006

Vijay Modi  and
F. K. Moore
Vijay Modi
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA Present address: Department of Aeronautics and Astronautics, Gas Turbine Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
F. K. Moore
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
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Abstract

A slow moving flow in a duct emerging into a quiescent negatively buoyant environment may separate from its inner wall prior to the lip. Buoyancy accelerates the flow, curving the streamlines within the duct away from the walls. The resulting deceleration at the wall may be sufficient to provoke separation. The problem of the location of this separation point in a two-dimensional channel is studied. A potential-flow model is examined first to explore the large-Reynolds-number behaviour. The form of the potential-flow description in the vicinity of the assumed location of separation is characterized by the presence of a square-root singularity in the pressure gradient at the wall. This permits use of the ideas of viscous-inviscid interaction, proposed by Sychev (1972), to determine the separation location as a function of Froude and Reynolds numbers. Results obtained in the high-Reynoldsnumber limit show that the channel flow separates at shorter distances from the entrance as Froude number is reduced.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 177 , April 1987 , pp. 37 - 47
Copyright
© 1987 Cambridge University Press

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References

Birkhoff, G. & Zarantonello, E. H. 1957 Jets, Wakes and Cavities. Academic.
Cheng, H. K. & Smith, F. T. 1982 The influence of airfoil thickness and Reynolds number on separation. Z. Angew. Math. Phys. 33, 151–180.Google Scholar
Jöng, O. & Scorer, R. S. 1967 An experimental study of cold inflow into chimneys. Atmos. Environ. 1, 645–654.Google Scholar
Korolev, G. L. 1980 Numerical solution of asymptotic problem on separating laminar boundary layer at a smooth surface. Tsentral'Nyi Aero-Gidro-Dinamicheskii Institute. Uchenye Zaposki Tsagi. Moscow. Volume XI, pp. 27–36.
Liggett, J. A. & Liu, P. L.-F. 1983 The Boundary Integral Equation Method for Porous Media Flows. George Allen and Unwin.
Messiter, A. F. 1970 Boundary-layer flow near the trailing edge of a flat plate. SIAM J. Appl. Maths 18, 241–257.Google Scholar
Modi, V. 1984 A study of laminar separation in buoyant channel flows. Ph.D. thesis, Cornell University.
Smith, F. T. 1977 The laminar separation of an incompressible fluid streaming past a smooth surface. Proc. R. Soc. Land. A 356, 433–463.Google Scholar
Smith, F. T. 1979 Laminar flow of an incompressible fluid past a bluff body: the separation. reattachment, eddy properties and drag. J. Fluid Mech. 92, 171–205.Google Scholar
Smith, F. T. 1982 On the high Reynolds number theory of laminar flows. IMA J. App. Maths 28, 207–281.Google Scholar
Stewartson, K. 1970 Is the singularity at separation removable?. J. Fluid Mech. 44, 347–364.Google Scholar
Stewartson, K. & Williams, P. G. 1969 Self-induced separation. Proc. R. Soc. Lond. A319. 181–206.Google Scholar
Sychev, V. V. 1972 Laminar separation. Fluid Dyn. 7, 407–418. (Translated from Izv. Akad. Nauk SSSR, Mekh. Zidk. Gaza 3, 47–59.)Google Scholar
Thwaites, B. 1960 Incompressible Aerodynamics. Oxford University Press.
Van Dommelen, L. L. & She., S. F. 1984 Interactivce separation from a fixed wall. In Numerical and Physical Aspects of Aerodynamic Flows, Part 2 (ed. T. Cebeci), pp. 392–402. Springer.
Vanden-Broeck, J.-M. 1984 Bubbles risig in a tube and jets falling from a nozzle. Phys. Fluids 27, 1090–1093.Google Scholar