Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-08T05:37:51.507Z Has data issue: false hasContentIssue false
  • English
  • Français

Lateral motion of a slender body between two parallel walls

Published online by Cambridge University Press:  29 March 2006

J. N. Newman
J. N. Newman
Affiliation:
Department of Naval Architecture and Marine Engineering Massachusetts Institute of Technology
Get access Rights & Permissions [Opens in a new window]

Abstract

The method of matched asymptotic expansions is used to determine the lateral flow of an ideal fluid past a slender body, when the flow is constrained by a pair of closely spaced walls parallel to the long axis of the body. In the absence of walls, the flow field would be nearly two-dimensional in the cross-flow plane normal to the body axis, but the walls introduce an effective blockage in the cross-flow plane, which causes the flow field to become three-dimensional. Part of the flow is diverted around the body ends, and part flows past the body in the inner cross-flow plane with a reduced ‘inner stream velocity’. An integro-differential equation of identical form to Prandtl's lifting-line equation is derived for the determination of this unknown inner stream velocity in the cross-flow plane. Approximate solutions are applied to determine the added mass and moment of inertia for accelerated body motions and the lift force and moment acting on a wing of low aspect ratio. It is found that the walls generally increase these forces and moments, but that the effect is significant only when the clearance between the body and the walls is very small.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 39 , Issue 1 , 23 October 1969 , pp. 97 - 115
Copyright
© 1969 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

Glauert, H. 1948 The Elements of Aerofoil and Airscrew Theory (second edition). Cambridge University Press.
Lamb, H. 1932 Hydrodynamics. New York: Dover.
Lighthill, M. J. 1960 Note on the swimming of slender fish J. Fluid Mech. 9, 305–317.Google Scholar
Miles, J. W. 1959 The Potential Theory of Unsteady Supersonic Flow. Cambridge University Press.
Miles, J. W. 1967 Surface-wave scattering matrix for a shelf J. Fluid Mech. 28, 755–767.Google Scholar
Muskhelishvili, N. I. 1946, Singular Integral Equations (second edition). Moscow. (English translation, 1953. Groningen: P. Noordhoff N.V.)
Newman, J. N. 1965 The force and moment on a slender body of revolution moving near a wall. David Taylor Model Basin Report no. 2127.Google Scholar
Norrbin, N. H. 1969 Analytical modelling and experimental results for confined water tanker manoeuvring. Statens Skeppsprovningsanstalt Publication no. 67.
Sedov, L. I. 1950 Two-Dimensional Problems in Hydrodynamics and Aerodynamics. Moscow-Leningrad. (English translation, 1965. New York: Interscience.)
Thwaites, B. (ed.) 1960 Incompressible Aerodynamics. Oxford: Clarendon Press.
Tuck, E. O. 1966 Shallow-water flows past slender bodies J. Fluid Mech. 26, 81–96.Google Scholar
Van Dyke, M. D. 1964 Perturbation Methods in Fluid Mechanics. New York: Academic.