Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-19T03:43:49.507Z Has data issue: false hasContentIssue false
  • English
  • Français

Simulations of the viscous flow normal to an impulsively started and uniformly accelerated flat plate

Published online by Cambridge University Press:  26 April 2006

P. Koumoutsakos  and
D. Shiels
P. Koumoutsakos
Affiliation:
Center for Turbulence Research, NASA Ames 202A-1, Moffett Field, 94035 CA, USA
D. Shiels
Affiliation:
Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, 91125 CA, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The development of a two-dimensional viscous incompressible flow generated from an infinitesimally thin flat plate, impulsively started or uniformly accelerated normal to the free stream is studied computationally. An adaptive numerical scheme, based on vortex methods, is used to integrate the vorticity–velocity formulation of the Navier–Stokes equations. The results of the computations complement relevant experimental works while providing us with quantities such as the vorticity field and the unsteady forces experienced by the body. For the uniformly accelerated plate the present simulations capture the development of a number of centers of vorticity along the primary separating shear layer. This phenomenon has been observed in experimental works but has not been predicted by inviscid models. The present simulations suggest that this Kelvin–Helmholtz-type instability is driven by the interaction of primary and secondary vorticity near the tips of the plate and depends on the acceleration of the plate.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 328 , 10 December 1996 , pp. 177 - 227
Copyright
© 1996 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.)

References

Anton, L. 1939 Formation of a vortex at the edge of a plate. Ing. Arch. 10, 411.Google Scholar
Barnes, J. E. & Hut, P. 1986 A hierarchical (N logN) force-calculation algorithm. Nature 324, 446–449.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics.. Cambridge University Press.
Beale, J. T. 1986 On the accuracy of vortex methods at large times. Proc. Workshop on Comp. Fluid Dyn. and React. Gas Flows IMA, Univ. of Minnesota.Google Scholar
Chorin, A. J. 1973 Numerical study of slightly viscous flow. J. Fluid Mech. 57, 380–392.Google Scholar
Chua, K. 1990 Vortex simulation of separated flows in two and three dimensions. PhD Thesis California Institute of Technology.
Coutanceau, M. & Bouard, R. 1977 Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. Part 2: Unsteady flow. J. Fluid Mech. 79, 257–272.CrossRefGoogle Scholar
Degond, P. & Mas-Gallic, S. 1989 The weighted particle method for convection — diffusion equations, Part I : The case of an isotropic viscosity, Part II : The anisotropic case. Math. Comput. 53, 485–526.Google Scholar
Dennis, S. C. R., Qiang, W., Coutanceau, M. & Launay, J-L. 1993 Viscous flow normal to a flat plate at moderate Reynolds numbers. J. Fluid Mech. 248, 605–635.Google Scholar
Fornberg, B. 1980 A numerical study of steady viscous flow past a circular cylinder. J. Fluid Mech. 98, 819–855.Google Scholar
Greengard, L. & Rohklin, V. 1987 A fast algorithm for particle simulations. J. Comput. Phys. 73, 325–348.Google Scholar
Hudson, J. D. & Dennis, S. C. R. 1985 The flow of a viscous incompressible fluid past a normal flat plate at low and intermidiate Reynolds numbers: the wake. J. Fluid Mech. 160, 369–383.Google Scholar
In, K. M., Choi, D. H. & Kim, M. U. 1995 2-dimensional viscous flow past a flat plate. Fluid Dyn. Res. 15, 13–24.Google Scholar
Ingham, T. B., Tang, T. & Morton, B. R. 1991 Steady two-dimensional flow past a normal flat plate. Z. Agnew. Math. Phys. 42, 584–604 (referred to herein as ITM).Google Scholar
Koumoutsakos, P. 1993 Direct numerical simulations of unsteady separated flows using vortex methods. PhD thesis, California Institute of Technology.
Koumoutsakos, P. 1996 Inviscid axisymmetrization of an elliptical vortex. submitted.
Koumoutsakos, P. & Leonard, A. 1995 High Resolution simulations of the flow around an impulsively started cylinder using vortex methods. J. Fluid Mech. 296, 1–38.Google Scholar
Koumoutsakos, P., Leonard, A. & Pepin, F. 1994 Boundary conditions for viscous vortex methods. J. Comput. Phys. 113, 52–61 (referred to herein as KLP).Google Scholar
Krasny, R. 1991 Vortex sheet computations : roll-up, wakes, separation. Lect. Appl. Maths 28, 385.Google Scholar
Laval, H. & Quartapelle, L. 1990 A fractional step Taylor-Galerkin method for unsteady incompressible flows. Intl J. Numer. Meth. Fluids, 11, 501.Google Scholar
Leonard, A. 1980 Vortex methods for flow simulation. J. Comput. Phys. 37, 289–335.Google Scholar
Lian, Q. X. & Huang, Z. 1989 Starting flow and structures of the starting vortex behind bluff bodies with sharp edges. Exps. Fluids 8, 95.Google Scholar
Lighthill, M. J. 1963 Introduction. In Boundary Layer Theory (ed. J Rosenhead), pp. 54–61. Oxford University Press.
Messiter, A. F. 1970 Boundary layer flow near the trailing edge of a flat plate. SIAM J. Appl. Maths 18, 241–257.Google Scholar
Moore, D. W. 1976 The stability of an evolving two-dimensional vortex sheet. Mathematika 23, 35.Google Scholar
Najjar, R. M. & Vanka, A. P. 1995 Simulations of the unsteady separated flow past a normal flat plate. Intl J. Numer. Meth. Fluids 21, 525–547.Google Scholar
Natarajan, R., Fornberg, B. & Acrivos, A. 1993 Flow past a row of flat plates at large Reynolds numbers. Proc. R. Soc. Lond. A441, 211–235.Google Scholar
Noca, F. 1990 Flow similarity for uniformly accelerated motions. Ae200-Research Report, California Institute of Technology.
Pepin, F. 1990 Simulation of the flow past an impulsively started cylinder using a discrete vortex method. PhD thesis, California Institute of Technology.
Pierce, D. 1961 Photographic evidence of the formation and growth of vorticity behind plates accelerated from rest in still air. J. Fluid Mech. 11, 460–464.Google Scholar
Prandtl, L. 1904 Über Flüssigkeitsbewegung bei sehr kleiner Reibung. Verhandlungen des III. Internationalen Mathematiker-Kongresses, Heidelberg, 1904, pp. 484–491. Leipzig: B. G. Teubner, 1905.
Pullin, D. & Perry, A. E. 1980 Some flow visualization experiments on the starting vortex. J. Fluid Mech. 88, 239–255.Google Scholar
Sarpkaya, T. 1975 An inviscid model of two-dimensional vortex shedding for transient and asymptotically steady separated flow over an inclined plate. J. Fluid Mech. 68, 109–128.Google Scholar
Schmall, R. A. & Kinney, R. B. 1974 Numerical study of unsteady viscous flow past a lifting plate. AIAA J. 12, 1566.Google Scholar
Schoenberg, I. J. 1973 Cardinal Spline Interpolation. SIAM, Philadelphia.
Stewartson, K. 1974 Multistructured boundary layers on flat plates and related bodies. Adv. Appl. Mech. 14, 146–239.Google Scholar
Tamaddon-Jahromi, H. R., Townsend, P. & Webster, M. F. 1994 Unsteady viscous flow past a flat plate orthogonal to the flow. Comput. Fluids 23, 433.Google Scholar
Taneda, S. & Honji, H. 1971 Unsteady flow past a flat plate normal to the direction of motion. J. Phys. Soc. Japan 30, 262.Google Scholar
Tsai, W-T. & Yue, D. K. P. 1993 Interactions between a free surface and a vortex sheet shed in the wake of a surface piercing plate. J. Fluid Mech. 257, 691–721.Google Scholar
Villat, H. 1930 Lecons sur la Theorie des Tourbillons. Gauthiers-Villars.
Wedemeyer, X. 1961 Ausbildung eines wirbelpaares an den kanten einer platte. Max-Planck Institut für Ströungsforschung, Bericht. 56-B-06.
Yoshida, Y. & Nomura, T. 1985 A transient solution method for the finite element incompressible Navier—Stokes equations. Intl J. Numer. Meth. Fluids 5, 873.Google Scholar