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A numerical and experimental study of transition processes in an obstructed channel flow

Published online by Cambridge University Press:  26 April 2006

E. P. L. Roberts
E. P. L. Roberts
Affiliation:
Department of Chemical Engineering, University of Cambridge, Pembroke Street, Cambridge, CB2 3RA, UK Present address: EA Technology, Environmental Technology Division, Capenhurst, Chester, CH1 6ES, UK.
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Abstract

Incompressible Newtonian flow in a two-dimensional channel with periodically placed sharp edged baffles has been studied both by numerical simulation and by experimental flow visualization. The flow was observed to be steady and symmetric at low Reynolds numbers, with recirculating eddies downstream of each baffle. At a critical Reynolds number (based on channel width and cross-sectional mean velocity) of approximately 100 the flow became asymmetric and unsteady. This transition to unsteadiness led to an eddy shedding regime, with eddies formed and shed successively from each baffle. A stability study suggested that the mechanism for transition to unsteady flow is a Kelvin–Helmholtz instability associated with the shear layer formed downstream of the sharp edged baffles. The frequency of the unsteadiness is, however, dependent on the full flow field, and not only the shear layer characteristics. Experimental observations show that the instability is followed by a secondary transition to three-dimensional disordered flow. Experimentally observed flows in the two-dimensional regime were found to be in close agreement with the numerical simulation for both the steady and unsteady flows.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 260 , 10 February 1994 , pp. 185 - 209
Copyright
© 1994 Cambridge University Press

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References

Aref, H. 1984 Stirring by chaotic advection. J. Fluid Mech. 143, 1.Google Scholar
Betchov, R. & Criminale, W. O. 1967 Stability of Parallel Flows. Academic Press.
Brunold, C. R., Hunns, J. C. B., Mackley, M. R. & Thompson, J. W. 1989 Experimental observations on flow patterns and energy losses for oscillatory flow in ducts containing sharp edges. Chem. Engng Sci. 44, 1227.Google Scholar
Drazin, P. G. & Reid, W. H. 1981 Hydronamic Stability. Cambridge University Press.
Durst, F., Melling, A. & Whitelaw, T. H. 1974 Low Reynolds number flow over a plane symmetrical sudden expansion. J. Fluid Mech. 64, 111.Google Scholar
Fearn, R. M., Mulun, T. & Cliffe, K. A. 1989 Nonlinear flow phenomena in a symmetric sudden expansion. J. Fluid Mech. 211, 595.Google Scholar
Fortin, A., Fortin, M. & Gervais, J. J. 1987 A numerical simulation of the transition to turbulence in a two dimensional flow. J. Comput. Phys. 70, 295.Google Scholar
Ghaddar, N. K., Korzak, K. Z., Mikic, B. B. & Patera, A. T. 1986 Numerical investigation of incompressible flow in grooved channels. Part 1. Stability and self-sustained oscillations. J. Fluid Mech. 163, 99.Google Scholar
Ho, E. M. & Huerre, H. 1984 Perturbed free shear layers. Ann. Rev. of Fluid Mech. 16, 365.Google Scholar
Howes, T. 1988 Dispersion and unsteady flow in baffled tubes PhD Thesis, Department of Chemical Engineering, University of Cambridge.
Howes, T., Mackley, M. R. & Roberts, E. P. L. 1991 The numerical simulation of chaotic mixing and dispersion for periodic flows in baffles channels. Chem. Engng Sci. 46, 1669.Google Scholar
Kays, W. M. & London, A. L. 1964 Compact Heat Exchangers, 2nd edn. McGraw Hill.
Kao, T. W. & Park, C. 1970 Experimental investigation of the stability of channel flows. Part 1. Flow of a single liquid in a rectangular channel. J. Fluid Mech. 43, 145.Google Scholar
Karniadakis, G. E., Mikic, B. B. & Patera, A. T. 1988 Minimum dissipation transport enhancement by flow destabilization: Reynolds analogy revisited. J. Fluid Mech. 192, 365.Google Scholar
Lin, C. C. 1955 The Theory of Hydrodynamic Stability. Cambridge University Press.
Mackley, M. R. & Sherman, N. E. 1992 Cake filtration mechanisms in steady and unsteady flows. Engineering of Membrane Processes, Bavaria, May 1992.
Mackley, M. R., Tweddle, G. M. & Wyatt, I. D. 1990 Experimental heat transfer measurements for pulsatile flow in a baffled tube. Chem. Engng Sci. 45, 1237.Google Scholar
Mills, R. D. 1968 Numerical solutions of viscous flow through a pipe orifice at low Reynolds numbers. J. Mech. Engng Sci. 10, 133.Google Scholar
Moffatt, H. K. 1964 Viscous and restricted eddies near a sharp corner. J. Fluid Mech. 18, 1.Google Scholar
Orszag, S. A. 1971 Accurate solutions of the Orr Sommerfeld stability equation. J. Fluid Mech. 50, 689.Google Scholar
Orszag, S. A. & Kells, L. C. 1980 The transition to turbulence in plane Poiseuille flow and plane Couette flow. J. Fluid Mech. 96, 159.Google Scholar
Orszag, S. A. & Patera, A. T. 1983 Secondary stability of wall bounded shear flows. J. Fluid Mech. 128, 347.Google Scholar
Ralph, M. E. 1986 Oscillatory flow in wavy walled tubes. J. Fluid Mech. 168, 515.Google Scholar
Ralph, M. E. 1987 Steady flow structures and pressure drops in wavy walled tubes. J. Fluids Engng 109, 255.Google Scholar
Ralph, M. E. & Pedley, T. J. 1988 Flow in a channel with amoving indentation. J. Fluid Mech. 190, 87.Google Scholar
Rayleigh, J. W. S. 1945 The Theory of Sound reprint of 2nd edn (first published 1896) Dover, New York.
Roache, P. J. 1976 Computational Fluid Dynamics. Hermosa, Albuquerque.
Roberts, E. P. L. 1992 Unsteady Flow and Mixing in Baffled Channels PhD Thesis, Department of Chemical Engineering, University of Cambridge.
Rowley, G. J. & Patankar, S. V. 1984 Analysis of laminar flow and heat transfer in tubes with internal circumferential fins. Intl J, Heat Mass Transfer 27, 553.Google Scholar
Sato, H. 1961 Transition of a two dimensional jet. J. Fluid Mech. 7, 53.Google Scholar
Sobey, I. J. 1980 On flow through furrowed channels. Part 1. Calculated flow patterns. J. Fluid Mech. 96, 1.Google Scholar
Sobey, I. J. 1985 Observation of waves during oscillatory channel flow. J. Fluid Mech. 151, 395.Google Scholar
Sobey, I. J. & Drazin, P. G. 1986 Bifurcations of two-dimensional channel flows. J. Fluid Mech. 171, 263.Google Scholar
Sreenivasan, F. R. & Strykowski, P. T. 1987 An instability associated with a sudden pipe expansion. Phys. Fluids 26, 2766.Google Scholar
Thompson, J. M. T. & Stewart, H. B. 1986 Nonlinear Dynamics and Chaos. Wiley.
White, F.M. 1974 Viscous Fluid Flow. McGraw Hill.