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Flow of stratified fluid through curved screens

Published online by Cambridge University Press:  28 March 2006

Y. L. Lau  and
W. D. Baines
Y. L. Lau
Affiliation:
Department of Mechanical Engineering, University of Toronto Present address; Hydraulics Laboratory, National Research Council, Ottawa, Canada.
W. D. Baines
Affiliation:
Department of Mechanical Engineering, University of Toronto
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Abstract

A curved screen placed across a two-dimensional channel causes the streamlines to be deflected on passing through because of the variation in pressure drop across the section and the refraction effect at the screen. Uniform flows far upstream and far downstream are required by the boundary conditions. An analytical description is based on the separation of the field into two regions distant from the screen in which viscosity and molecular diffusion are negligible, plus a thin layer along the screen in which energy loss and streamline deflexion are concentrated. These are described by empirical relationships. For linear velocity and density distribution upstream of the screen, equations can be simplified so that algebraic relationships between the variables at the screen surface are obtained. These have been solved numerically for the shape of screen required to produce a specified velocity distribution. An approximate solution is also obtained for general velocity profiles and the screen shape which produces uniform shear is derived. Experimental verification of the analysis is obtained from measurements of the velocity and temperature distributions downstream of the derived screen shapes mounted in a wind tunnel 45.6 cm square.

It is also shown that the boundary layers along a tunnel wall are accelerated or retarded by the screen depending on the loss coefficient. This effect is evident in all observations.

The case of homogeneous fluid is described by a simplified version of the analysis and several examples of velocity distributions are produced. These are verified by experiment and compared with those predicted by Elder (1959).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 33 , Issue 4 , 23 September 1968 , pp. 721 - 738
Copyright
© 1968 Cambridge University Press

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References

Baines, W. D. & Peterson, E. G. 1951 Trans. ASME 73, 467–77.
Elder, J. W. 1959 J. Fluid Mech. 5, 355–68.
Lau, Y. L. 1966 Ph. D. thesis, University of Toronto.
Owen, P. R. & Zienkiewicz, H. K. 1957 J. Fluid Mech. 2, 521–31.
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Yih, C. S. 1962 Dynamics of Non-Homogeneous Fluids. New York: MacMillan.
Yih, C. S., O'DELL, W. & Debler, W. R. 1958 Proc. 4th U.S. Nat. Congr. Appl. Mech. pp. 1441–53.