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Three-dimensional viscous flows with large secondary velocity

Published online by Cambridge University Press:  20 April 2006

W. R. Briley  and
H. Mcdonald
W. R. Briley
Affiliation:
Scientific Research Associates, Inc., Glastonbury, CT 06033, U.S.A.
H. Mcdonald
Affiliation:
Scientific Research Associates, Inc., Glastonbury, CT 06033, U.S.A.
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Abstract

A new system of approximating equations is derived for three-dimensional steady viscous compressible flows in which a primary flow direction is present, but in which both transverse velocity components can be large. If the transverse velocity vector which corrects a given potential flow is first decomposed into ‘potential’ and ‘rotational’ vector components, then a re-examination of three-dimensional boundary-layer theory shows that both components (vϕ, wϕ) of the potential-velocity vector may be assumed small, whereas both components (vψ, wψ) of the rotational-velocity vector and hence of the composite secondary flow (v, w) can remain of order unity. An assumption of small scalar potential then leads to a system of governing equations whose characteristic polynomial has a non-elliptic form for arbitrary Mach number, without introducing any direct approximation of either streamwise or transverse pressure gradient terms. These non-elliptic equations can be solved very economically as a well-posed initial/boundary-value problem. Computed results for laminar subsonic flow in a curved square duct confirm the small scalar-potential approximation for both large (R/d = 100) and small (R/d = 2) radius of curvature. Other computations for R/d = 2.3 are in good agreement with the measurements of Taylor, Whitelaw & Yianneskis (1980).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 144 , July 1984 , pp. 47 - 77
Copyright
© 1984 Cambridge University Press

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