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Numerical and asymptotic solutions for merging flow through a channel with an upstream splitter plate

Published online by Cambridge University Press:  20 April 2006

H. Badr ,
S. C. R. Dennis ,
S. Bates  and
F. T. Smith
H. Badr
Affiliation:
Department of Mechanical Engineering, University of Petroleum and Minerals, Dhahran, Saudi Arabia
S. C. R. Dennis
Affiliation:
Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B9, Canada
S. Bates
Affiliation:
Department of Mathematics, University College, London WC1E 6BT, U.K.
F. T. Smith
Affiliation:
Department of Mathematics, University College, London WC1E 6BT, U.K.
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Abstract

A numerical and analytical study is described for the divided flow field produced when the flows in two equal parallel channels, separated upstream by an aligned splitter plate, join together to form a single channel beyond the enclosed trailing edge of the plate. On the numerical side the second-order-accurate finite-difference scheme is based on a modified procedure to preserve accuracy and iterative convergence at higher Reynolds numbers R. Account is taken also of the influence of the boundedness of the computational domain and of the irregular behaviour of the flow solution at the trailing edge. The numerical solutions are presented for values of R up to 1000. On the analytical side the asymptotic structure of the solution for large R is governed mainly by a long $O(R^{\frac{1}{7}})$ relative lengthscale upstream and beyond the trailing edge. This is followed by a longer O(R) scale far downstream, but effects of practical significance also arise on the nominally tiny scale of O(R−½). Comparisons between the numerical and the asymptotic results for the wall shear stresses and the wake centreline velocity are made, and overall the agreement seems reasonable. The use of comparisons is believed to strengthen the value of both the numerical and the analytical approaches for these flows.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 156 , July 1985 , pp. 63 - 81
Copyright
© 1985 Cambridge University Press

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