Hostname: page-component-6bb9c88b65-znhjv Total loading time: 0 Render date: 2025-07-25T10:11:10.478Z Has data issue: false hasContentIssue false
  • English
  • Français

Internal separated flows at large Reynolds number

Published online by Cambridge University Press:  19 April 2006

Anand Kumar  and
Kirit S. Yajnik
Anand Kumar
Affiliation:
Aerodynamics Division, National Aeronautical Laboratory, Bangalore 560017, India
Kirit S. Yajnik
Affiliation:
Aerodynamics Division, National Aeronautical Laboratory, Bangalore 560017, India
Get access Rights & Permissions [Opens in a new window]

Abstract

Large-Reynolds-number analysis is given for separated flows that have the characteristic feature of being confined in the transverse direction. Two principal limits of the governing equation are obtained depending on whether the streamwise length scale is of order one or of the order of the Reynolds number. The corresponding two types of separated flows are discussed. A method of calculation is given for the second type of flow. It employs an expansion in the eigenfunctions of the Poiseuille flow development and the problem is reduced to solving nonlinear first-order ordinary differential equations that have a tendency to decouple rapidly. The method is tested by a detailed comparison of the results of the present calculation with finite-difference solutions of the Navier–Stokes equations for a channel with sudden expansion. Applicability to other configurations is illustrated by solving the problem of the flow in a channel with a base.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 97 , Issue 1 , 11 March 1980 , pp. 27 - 51
Copyright
© 1980 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Batchelor, G. K. 1956 On steady laminar flow with closed streamlines at large Reynolds number. J. Fluid Mech. 1, 177–190.Google Scholar
Carter, J. E. 1975 Inverse solution for laminar boundary layer flows with separation and reattachment. N.A.S.A. Tech. Rep. R-447.
Catherall, D. & Mangler, K. W. 1966 The integration of the two-dimensional laminar boundary-layer equations past the point of vanishing skin friction. J. Fluid Mech. 26, 163–182.Google Scholar
Cheng, R. T. 1972 Numerical solution of the Navier—Stokes equations by the finite element method. Phys. Fluids 15, 2098–2105.Google Scholar
Deshpande, M. D. 1977 Steady laminar and turbulent flow through vascular stenoses model. Ph.D. thesis, Georgia Inst. of Tech., Atlanta.
Deshpande, M. D., Giddens, D. P. & Mabon, R. F. 1976 Steady laminar flow through modelled vascular stenoses. J. Biomech. 9, 165–174.Google Scholar
Dorodnitsyn, A. A. & Meller, N. A. 1970 Application of the small parameter method to the solution of Navier—Stokes equations. Fluid Dyn. Trans. 5 (II), 67–82.Google Scholar
Durst, F., Melling, A. & Whitelaw, J. H. 1974 Low Reynolds number flow over a plane symmetric sudden expansion. J. Fluid Mech. 64, 111–128.Google Scholar
Friedman, M. 1972 Laminar flow in a channel with a step. J. Engng Math. 6, 285–290.Google Scholar
Gillis, J. & Brandt, A. 1964 The numerical integration of the equations of motion of a viscous fluid. Weizmann Institute Rep. AF EOAR 63-73 SR-1.
Greenspan, D. 1969 Numerical studies of steady viscous, incompressible flow in a channel with a step. J. Engng Math. 3, 21–28.Google Scholar
Hung, T. K. & Macagno, E. O. 1966 Laminar eddies in a two-dimensional conduit expansion. La Houille Blanche 21, 391–401.Google Scholar
Kitchens, C. W. 1974 Calculation of low Reynolds number flow past a square protuberance. A.I.A.A. J. 12, 1005–1007.Google Scholar
Klemp, J. B. & Acrivos, A. 1972 A method for integrating the boundary-layer equations through a region of reverse flow. J. Fluid Mech. 53, 177–191.Google Scholar
Klineberg, J. M. & Steger, J. L. 1974 The numerical calculation of laminar boundary-layer separation. N.A.S.A. Tech. Note D-7732.
Kovasznay, L. I. G. 1948 Laminar flow behind a two-dimensional grid. Proc. Camb. Phil. Soc. 44, 58–62.Google Scholar
Kumar, A. 1976 Analysis and calculation of internal separated flow at large Reynolds number. Ph.D. thesis, IIT Kanpur.
Kumar, A. 1977 Eigenfunctions of the Poiseuille flow development. NAL Bangalore Rep. AE-TM-15-77.
Kumar, A. 1978 On the solution of the boundary layer equation in the presence of reverse flow. NAL Bangalore Rep. AE-TM-9-78.
Kumar, A. & Yajnik, K. S. 1976 Poiseuille flow development by eigenfunction expansion method. NAL Bangalore Rep. AE-TM-19-76.
Kumar, A. & Yajnik, K. S. 1977 Flow in a channel with a symmetric sudden expansion. 6th Australasian Hydraulics and Fluid Mech. Conf., Adelaide.
Macagno, E. O. & Hung, T. K. 1967 Computational and experimental study of a captive annular eddy. J. Fluid Mech. 28, 43–64.Google Scholar
Morihara, H. 1972 Numerical integration of the Navier—Stokes equations. Ph.D. thesis, State U. of New York at Buffalo.
Mueller, T. J. & O'Leary, R. A. 1970 Physical and numerical experiments in laminar incompressible separating and reattaching flows. A.I.A.A. Paper no. 70–763.
Nallasamy, M. 1975 Numerical studies on laminar internal separated flow. Ph.D. thesis, IISc Bangalore.
Phandtl, L. 1904 Motion of fluid with very little viscosity. English Translation: N.A.S.A. TM 452. 1928.
Roache, P. J. & Mueller, T. J. 1970 Numerical solutions of laminar separated flows. A.I.A.A. J. 8, 530–538.Google Scholar
Schlichting, H. 1934 Laminare Kanaleinlaufströmung. Z. angew. Math. Mech. 14, 368–373.Google Scholar
Smith, F. T. 1977 Upstream interactions in channel flows. J. Fluid Mech. 79, 631–656.Google Scholar
Taylor, T. D. & Ndefo, E. 1970 Computation of viscous flow in a channel by the method of splitting. II Intl. Conf. on Numerical Methods in Fluid Dyn., pp. 356–364.
Wang, Y. L. & Longwell, P. A. 1964 Laminar flow in the inlet section of parallel plates. A.I.Ch.E. J. 10, 323–329.Google Scholar
Wilson, S. 1969 The development of Poiseuille flow. J. Fluid Mech. 38, 793–806.Google Scholar