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High-Reynolds-number asymptotics of the steady flow through a row of bluff bodies

Published online by Cambridge University Press:  26 April 2006

S. I. Chernyshenko  and
Ian P. Castro
S. I. Chernyshenko
Affiliation:
Institute of Mechanics, Moscow University, 117192 Moscow, Russia
Ian P. Castro
Affiliation:
Department of Mechanical Engineering, University of Surrey., Guildford GU2 5XH, UK
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Abstract

An extension of an earlier theory of the two-dimensional incompressible flow past an isolated body is described. For a crossflow cascade of bodies, each of unit size in the crossflow direction and distance 2H apart, the region of validity of the extended theory covers H [Gt ] 1. A comparison with recent numerical calculations is favourable and a tentative asymptotic structure for the case of H = O(1) is described.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 257 , December 1993 , pp. 421 - 449
Copyright
© 1993 Cambridge University Press

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References

Acrivos, A., Leal, L. G., Snowden, D. D. & Pan, F. 1968 Further experiments on steady separated flow past bluff objects. J. Fluid Mech. 34, 25.Google Scholar
Acrivos, A., Snowden, D. D., Grove, A. S. & Petersen, E. E. 1965 The steady separated flow past a circular cylinder at large Reynolds numbers. J. Fluid Mech. 21, 737–760.Google Scholar
Batchelor, G. K. 1956 A proposal concerning laminar wakes behind bluff bodies at large Reynolds number. J. Fluid Mech. 1, 338–398.Google Scholar
Bukovshin, V. G. & Taganov, G. I. 1976 Numerical results of the asymptotic theory of the flow past a body with stationary separation eddy at large Reynolds number. Chislennye metody mechaniki sploshnoi sredy. Novosibirsk: VC SO AN SSSR 7, 13–26 (in Russian.)Google Scholar
Chernyshenko, S. I. 1982 An approximate method of determining the vorticity in the separation region as the viscosity tends to zero. Fluid Dyn. 17 (1), 7–11. (Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza 1, 10–15.)Google Scholar
Chernyshenko, S. I. 1984 Calculation of low-viscosity flows with separation by means of Batchelor's model. Fluid Dyn. 19 (2), 206–210. (Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza 2, 40–45.)Google Scholar
Chernyshenko, S. I. 1988 The asymptotic form of the stationary separated circumfluence of a body at high Reynolds number. Appl. Math. Mech. 52, 746. (Prikl. Matem. Mekh. 52 (6), 958–966.)Google Scholar
Chernyshenko, S. I. 1991 Separated flow over a backward-facing step whose height is much greater than the thickness of the lower sublayer of the interaction zone. Fluid Dyn. 26 (4), 496–501. (Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza 4, 25–30.)Google Scholar
Chernyshenko, S. I. 1993 Stratified Sadovskii flow in a channel. J. Fluid Mech. 250. 423–431.Google Scholar
Fornberg, B. 1985 Steady viscous flow past a circular cylinder up to Reynolds number 600. J. Comput. Phys. 61, 297–320.Google Scholar
Fornberg, B. 1991 Steady incompressible flow past a row of circular cylinders. J. Fluid Mech. 225, 655–671.Google Scholar
Fornberg, B. 1993 Computing steady incompressible flows past blunt bodies — a historical overview. In Numerical Methods for Fluid Dynamics IV (ed. M. J. Baines & K. W. Morton), pp. 115–134, Oxford University Press.
Herwig, H. 1982 Die Anwendung der asymptotischen Theorie auf laminare Stromungen mit endlichen Ablosegebieter. Z.Flugwiss. Weltraumforsh. B 46, (4), 266–279 (in German.)Google Scholar
Ingham, D. B., Tang, T. & Morton, B. R. 1990 Steady two-dimensional flow through a row of normal flat plates. J. Fluid Mech. 210, 281–302.Google Scholar
Kolosov, B. V. & Shifrin, E. G. 1975 On a particular boundary value problem arising in the investigation of closed stationary separation zones in an incompressible fluid. Appl. Math. Mech. 39, (5), 802–811. (Prikl. Mat. Mech. 39 (5), 773–779.)Google Scholar
Lukerchenko, N. N. 1990 A comparison of two structures for impinging jets with different Bernoulli's constants. Zh. Prikl. Mech. i Techn. Phys. No. 6, 97–101 (In Russian).Google Scholar
Milos, F. S. & Acrivos, A. 1986 Steady flow past sudden expansions at large Reynolds numbers. Part I. Boundary layer solutions. Phys. Fluids 29, 1353–1359.Google Scholar
Milos, F. S., Acrivos, A. & Kim, J. 1987 Steady flow past sudden expansions at large Reynolds numbers. Part II. Navier–Stokes solutions for the cascade expansion. Phys. Fluids 30, 7–18.Google Scholar
Moore, D. W., Saffman, P. G. & Tanveer, S. 1988 The calculation of some Batchelor flows: The Sadovskii vortex and rotational corner flow. Phys. Fluids 31, 978.CrossRefGoogle Scholar
Natarajan, R., Fornberg, B. & Acrivos, A. 1992 Flow past a row of flat plates at large Reynolds number. Proc. R. Soc. Lond. A 441, 211–235.Google Scholar
Peregrine, D. H. 1985 A note on the steady high-Reynolds-number flow about a circular cylinder. J. Fluid Mech. 157, 493–500.Google Scholar
Sadovskii, V. S. 1970 The region of constant vorticity in plain potential flow. Uch. Zap. TsAGI 1 (4), 1–9 (in Russian).Google Scholar
Sadovskii, V. S. 1971a Vortex regions in a potential stream with a jump in Bernoulli's constant across the boundary. Appl Math. Mech. 35, 729. (Prikl. Matem. Mekh. 35 (5), 773–779.)Google Scholar
Sadovskii, V. S. 1971b Some properties of vortex and potential flows touching along a closed fluid streamline. Uch. Zap. TsAGI 2 (1), 113–116 (in Russian.)Google Scholar
Sadovskii, V. S. 1973 A study of the solutions to Euler's equations containing regions of constant vorticity. Trudy TsAGI. 1474, 1–14 (in Russian.)Google Scholar
Sadovskii, V. S. & Kozhuro, L. A. 1977 On two one-parameter families of vortex flows of inviscid fluid. Chislennye metody mechaniki sploshnoi sredy, Novosibirsk. 8 (7). 126–140 (in Russian.)Google Scholar
Saffman, P. G. & Tanveer, S. 1982 The touching pair of equal and opposite uniform vortices. Phys. Fluids 25, 1929.Google Scholar
Serrin, J. 1959 Mathematical Principles of Classical Fluid Mechanics.
Smith, F. T. 1979 Laminar flow of an incompressible fluid past a bluff body: the separation, reattachment, eddy properties and drag. J. Fluid Mech. 92, 171–205.Google Scholar
Smith, F. T. 1985a On large-scale eddy closure. J. Math. Phys. Sci. 19, 1–80.Google Scholar
Smith, F. T. 1985b A structure for laminar flow past a bluff body at high Reynolds number. J. Fluid Mech. 155, 175–191.Google Scholar
Smith, F. T. 1988 A reversed flow singularity in interacting boundary layers. Proc. R. Soc. Lond. A 420, 21–52.Google Scholar
Sychev, V. V. 1967 Rep. to 8th Symp. Recent Problems in Mech. Liquids & Gases, Tarda, Poland.
Taganov, G. I. 1968 Contribution to the theory of stationary separation zones. Fluid Dyn. 3, (5), 1–11 (Izv. AN SSSR. Mekhanika Zhidkosti i Gaza 3 (5), 3–19.)Google Scholar
Taganov, G. I. 1970 On limiting flows of viscous fluid with stationary separation for Re → ∞. Uch. Zap. TsAGI. 1 (3), 1–14 (in Russian.)Google Scholar
Tihonov, A. N. & Samarskii, A. A. 1972 Equations of Mathematical Physics. Moscow; Nauka (in Russian.)
Turfus, C. 1993 Prandtl-Batchelor flow past a flat plat at normal incidence in a channel – inviscid analysis. J. Fluid Mech. 249, 59–72.Google Scholar