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Oscillatory flow in a stepped channel

Published online by Cambridge University Press:  26 April 2006

O. R. Tutty  and
T. J. Pedley
O. R. Tutty
Affiliation:
Department of Aeronautics and Astronautics, University of Southampton, Southampton SO9 5NH, UK
T. J. Pedley
Affiliation:
Department of Applied Mathematical Studies, University of Leeds, Leeds LS2 9JT, UK
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Abstract

Two-dimensional, unsteady flow of a viscous, incompressible fluid in a stepped channel has been studied by the numerical solution of the Navier–Stokes equation using an accurate finite-difference method.

With a sinusoidal mass flow rate, the problem has three governing parameters: the Reynolds number, the Strouhal number, and the step height. The effects on the flow of varying all three parameters has been investigated systematically. In appropriate parameter regimes, a strong ‘vortex wave’ is generated during the forward phase when the flow is over the step into the expansion. Secondary effects on the wave can result in a complex flow pattern with each major structure of the flow consisting of an eddy with more than one core. No such wave is found during the reverse phase of the flow. The generation and development of the wave is examined in some detail, and our results are compared and contrasted with those of previous studies, both experimental and theoretical, of flow in non-uniform vessels.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 247 , February 1993 , pp. 179 - 204
Copyright
© 1993 Cambridge University Press

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References

Armaly, B. F., Durst, F., Pereira, J. C. F. & Schonung, B. 1983 Experimental and theoretical investigation of backward-facing step flow. J. Fluid Mech. 127, 473– 496.Google Scholar
Cherdron, W., Durst, F. & Whitelaw, J. H. 1978 Asymmetric flows and instabilities in symmetric ducts with sudden expansions. J. Fluid Mech. 84, 13– 31.Google Scholar
Dennis, S. C. R. & Hudson, J. D. 1989 Compact explicit h4 finite-difference approximations to operators of Navier–Stokes type. J. Comput. Phys. 85, 390– 416.Google Scholar
Durst, F. & Pereira, J. C. F. 1988 Time-dependent laminar backward-facing step flow in a two-dimensional duct. Trans. ASME I: J. Fluids Engng 110, 289– 296.Google Scholar
Ghaddar, N. K., Korczak, K. Z., Mikic, B. B. & Patera, A. T. 1986a Numerical investigation of incompressible flow in grooved channels. Part 1. Stability and self-sustained oscillations. J. Fluid Mech. 163, 99– 127.Google Scholar
Ghaddar, N. K., Magen, M., Mikic, B. B. & Patera, A. T. 1986b Numerical investigation of incompressible flow in grooved channels. Part 2. Resonance and oscillatory heat-transfer enhancement. J. Fluid Mech. 168, 541– 567.Google Scholar
Ku, D. N., Giddens, D. P., Zarins, C. K. & Glagov, S. 1985a Pulsatile flow and atherosclerosis in the human carotid bifurcation: positive correlation between plaque location and low and oscillating shear stress. Arteriosclerosis 5, 293– 302.Google Scholar
Ku, D. N., Phillips, D. J., Giddens, D. P. & Strandness, D. E. 1985b Hemodynamics of the normal human carotid bifurcation: in vitro and in vivo studies. Ultrasound Med. Biol. 11, 13– 26.Google Scholar
Pedley, T. J. & Stephanoff, K. D. 1985 Flow along a channel with a time-dependent indentation in one wall: the generation of vorticity waves. J. Fluid Mech. 160, 337– 367.Google Scholar
Ralph, M. E. & Pedley, J. T. 1988 Flow in a channel with a moving indentation. J. Fluid Mech. 190, 87– 112.Google Scholar
Ralph, M. E. & Pedley, T. J. 1989 Viscous and inviscid flows in a channel with a moving indentation. J. Fluid Mech. 209, 543– 566.Google Scholar
Ralph, M. E. & Pedley, T. J. 1990 Flow in a channel with a time dependent indentation in one wall. Trans. ASME I: J. Fluids Engng 112, 468– 475.Google Scholar
Sobey, I. J. 1985 Observation of waves during oscillatory channel flow. J. Fluid Mech. 151, 395– 426.Google Scholar
Sridhar, K. P. & Davis, R. T. 1985 A Schwarz–Christoffel method for generating two-dimensional flow grids. Trans. ASME I: J. Fluids Engng 107, 330– 337.Google Scholar
Tutty, O. R. 1992 Pulsatile flow in a constricted channel. J. Biomech. Engng 114, 50– 54.Google Scholar
Tutty, O. R. & Pedley, T. J. 1992 Unsteady flow in a non-uniform channel: a model for wave generation. (In preparation.)
Woods, L. C. 1954 Aeronaut. Q. 5. 176.