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On cavity flow at high Reynolds numbers

  • M. Nallasamy (a1) and K. Krishna Prasad (a1)

The flow in a square cavity is studied by solving the full Navier–Stokes and energy equations numerically, employing finite-difference techniques. Solutions are obtained over a wide range of Reynolds numbers from 0 to 50000. The solutions show that only at very high Reynolds numbers (Re [ges ] 30000) does the flow in the cavity completely correspond to that assumed by Batchelor's model for separated flows. The flow and thermal fields at such high Reynolds numbers clearly exhibit a boundary-layer character. For the first time, it is demonstrated that the downstream secondary eddy grows and decays in a manner similar to the upstream one. The upstream and downstream secondary eddies remain completely viscous throughout the range of Reynolds numbers of their existence. It is suggested that the behaviour of the secondary eddies may be characteristic of internal separated flows.

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Abarbanel, S., Bennet, S., Brandt, A. & Gillis, J. 1970 Velocity profiles of flow at low Reynolds numbers. J. Appl. Mech., Trans. A.S.M.E. 37, 2.
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.
Acrivos, A., Snowden, D. D., Grove, A. S. & Peterson, E. E. 1965 The steady separated flow past a circular cylinder at large Reynolds numbers. J. Fluid Mech. 21, 373.
Batchelor, G. K. 1956 A proposal concerning laminar wakes behind bluff bodies at large Reynolds number. J. Fluid Mech. 1, 388.
Berger, S. A. 1971 Laminar Wakes. Elsevier.
Bodia, J. R. & Osterle, J. F. 1961 Finite difference analysis of plane Poiseuille and Couette flow development. Appl. Sci. Res. A 13, 265.
Bozeman, J. D. & Dalton, C. 1973 Numerical study of viscous flow in a cavity. J. Comp. Phys. 12, 348.
Brandt, A. & Gillis, J. 1966 Magnetohydrodynamic flow in the entrance region of a straight channel. Phys. Fluids, 9, 690.
Burggraf, O. R. 1966 Analytical and numerical studies of the structure of steady separated flows. J. Fluid Mech. 24, 113.
Evans, H. L. 1968 Laminar Boundary-Layer Theory. Addison-Wesley.
Gosman, A. A., Pun, W. M., Runchal, A. K., Spalding, D. B. & Wolfshtein, M. 1969 Heat and Mass Transfer in Recirculating Flows. Academic.
Greenspan, D. 1969 Numerical studies on prototype cavity flow problems. Comp. J. 12, 89.
Grove, A. S., Shair, F. H., Peterson, E. E. & Acrivos, A. 1964 An experimental investigation of the steady separated flow past a circular cylinder. J. Fluid Mech. 19, 60.
Leal, L. G. 1973 Steady separated flow in a linearly decelerated free stream. J. Fluid Mech. 59, 513.
Leal, L. G. & Acrivos, A. 1969 Structure of steady streamline flows within a boundary-layer. High-speed computing in fluid dynamics. Phys. Fluids Suppl. 12, II 105.
Mehta, U. B. & Lavan, Z. 1975 Starting vortex, separation bubbles and stall: a numerical study of laminar unsteady flow around an airfoil. J. Fluid Mech. 67, 227.
Mills, R. D. 1965 Numerical solution of viscous flow equations for a class of closed flows. J. Roy. Aero. Soc. 69, 714.
Nallasamy, M. 1975 Numerical studies on laminar internal separated flows. Ph.D. thesis, Indian Institute of Science, Bangalore
Nallasamy, M. & Krishna Prasad, K. 1974 Numerical studies on quasilinear and linear elliptic equations. J. Comp. Phys. 15, 429.
Nallasamy, M. & Krishna Prasad, K. 1976 Transient entry flow. To be published.
O'Brien, V. 1972 Closed streamlines associated with channel flow over a cavity. Phys. Fluids, 15, 2089.
Orszag, S. A. & Israel, M. 1974 Numerical simulation of viscous incompressible flows. Ann. Rev. Fluid Mech. 6, 281.
Pan, F. & Acrivos, A. 1967 Steady flow in rectangular cavities. J. Fluid Mech. 28, 643.
Runchal, A. K., Spalding, D. B. & Wolfshtein, M. 1969 Numerical solution of the elliptic equations for transport of vorticity, heat and matter in two dimensional flow. Phys. Fluids Suppl. 12, II 21.
Runchal, A. K. & Wolfshtein, M. 1969 Numerical integration procedure for steady state Navier–Stokes equations. J. Mech. Engng Sci. 11, 445.
Schlichting, H. 1968 Boundary Layer Theory, 6th edn. McGraw-Hill.
Van Dyke, M. 1970 Entry flow in a channel. J. Fluid Mech. 44, 813.
Wang, Y. L. & Longwell, P. A. 1964 Laminar flow in the inlet section of parallel plates. A.I.Ch.E. J. 10, 323.
Wu, T. Y. 1972 Cavity and wake flows. Ann. Rev. Fluid Mech. 4, 243.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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