A Prandtl-Batchelor model of flow in the wake of a cascade of normal flat plates
A Prandtl-Batchelor model of flow in the wake of a cascade of normal flat plates
The steady large-Re flow through a cascade of normal flat plates is considered in the limit of small blockage ratio. Evidence is presented suggesting the existence of a branch of Prandtl-Batchelor solutions comprising two symmetric inviscid regions, each with constant vorticity, surrounded by thin shear layers which enable smooth matching with the external flow. The wake length is proportional to the cascade half-width.
The solutions are of particular note in that they constitute non-unique solutions of the system, i.e. a bifurcated branch. The calculation requires however the postulation of an infinite sequence of small secondary vortices near the plate's rear stagnation point; elucidation of the implied structure is seen not to be possible without full Navier-Stokes computation.
[mathematical subject codes] 76c05, [mathematical subject codes] 76D10, [mathematical subject codes] 76d15, prandtl-batchelor, cascade, flat plate, large re, steady flow, boundary layer, shear layer, recirculating wake
181-202
Turfus, C.
895b69d1-0a9d-4926-b209-9c74c59f2a4d
Castro, I.P.
66e6330d-d93a-439a-a69b-e061e660de61
2000
Turfus, C.
895b69d1-0a9d-4926-b209-9c74c59f2a4d
Castro, I.P.
66e6330d-d93a-439a-a69b-e061e660de61
Turfus, C. and Castro, I.P.
(2000)
A Prandtl-Batchelor model of flow in the wake of a cascade of normal flat plates.
Fluid Dynamics Research, 26 (3), .
(doi:10.1016/S0169-5983(99)00023-4).
Abstract
The steady large-Re flow through a cascade of normal flat plates is considered in the limit of small blockage ratio. Evidence is presented suggesting the existence of a branch of Prandtl-Batchelor solutions comprising two symmetric inviscid regions, each with constant vorticity, surrounded by thin shear layers which enable smooth matching with the external flow. The wake length is proportional to the cascade half-width.
The solutions are of particular note in that they constitute non-unique solutions of the system, i.e. a bifurcated branch. The calculation requires however the postulation of an infinite sequence of small secondary vortices near the plate's rear stagnation point; elucidation of the implied structure is seen not to be possible without full Navier-Stokes computation.
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Published date: 2000
Keywords:
[mathematical subject codes] 76c05, [mathematical subject codes] 76D10, [mathematical subject codes] 76d15, prandtl-batchelor, cascade, flat plate, large re, steady flow, boundary layer, shear layer, recirculating wake
Identifiers
Local EPrints ID: 21323
URI: http://eprints.soton.ac.uk/id/eprint/21323
ISSN: 0169-5983
PURE UUID: d6fa4738-1be2-4073-b748-b4a880ededac
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Date deposited: 19 Jul 2006
Last modified: 15 Mar 2024 06:29
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Author:
C. Turfus
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