McLachlan, Robert (1991) A steady separated viscous corner flow. Journal of Fluid Mechanics, 231 . pp. 1-34. ISSN 0022-1120 http://resolver.caltech.edu/CaltechAUTHORS:20120417-150318710
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An example is presented of a separated flow in an unbounded domain in which, as the Reynolds number becomes large, the separated region remains of size 0(1) and tends to a non-trivial Prandtl-Batchelor flow. The multigrid method is used to obtain rapid convergence to the solution of the discretized Navier-Stokes equations at Reynolds numbers of up to 5000. Extremely fine grids and tests of an integral property of the flow ensure accuracy. The flow exhibits the separation of a boundary layer with ensuing formation of a downstream eddy and reattachment of a free shear layer. The asymptotic (’triple deck’) theory of laminar separation from a leading edge, due to Sychev (1979), is clarified and compared to the numerical solutions. Much better qualitative agreement is obtained than has been reported previously. Together with a plausible choice of two free parameters, the data can be extrapolated to infinite Reynolds number, giving quantitative agreement with triple-deck theory with errors of 20% or less. The development of a region of constant vorticity is observed in the downstream eddy, and the global infinite-Reynolds-number limit is a Prandtl-Batchelor flow; however, when the plate is stationary, the occurrence of secondary separation suggests that the limiting flow contains an infinite sequence of eddies behind the separation point. Secondary separation can be averted by driving the plate, and in this case the limit is a single-vortex Prandtl-Batchelor flow of the type found by Moore, Saffman & Tanveer (1988); detailed, encouraging comparisons are made to the vortex-sheet strength and position. Altering the boundary condition on the plate gives viscous eddies that approximate different members of the family of inviscid solutions.
|Additional Information:||© 1991 Cambridge University Press. Received 15 June 1990 and in revised form 2 January 1991. Published Online April 26 2006. This work could not have been completed without the help of my thesis advisor, H. B. Keller. I would also like to thank P. G. Saffman, for discussions on the physical basis of triple-deck theory; D. W. Moore, for suggesting the corner flow as worthy of study, to which I owe any positive results; S. J. Cowley, for suggesting the integral test of §2.4; E. F. van de Velde, for providing me with his clearly coded multigrid Poisson solver (Velde & Keller 1987); and the referees for aiding the presentation. This work was supported in part by contracts DOE DE-FG03-89ER25073 and ARO DAAL03-89-K-0014, and by a New Zealand University Grants Committee Scholarship.|
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|Deposited By:||Tony Diaz|
|Deposited On:||17 Apr 2012 22:12|
|Last Modified:||26 Dec 2012 15:04|
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