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The stability of unsteady axisymmetric incompressible pipe flow close to a piston. Part 1. Numerical analysis

Published online by Cambridge University Press:  29 March 2006

J. H. Gerrard
J. H. Gerrard
Affiliation:
Department of the Mechanics of Fluids, University of Manchester
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Abstract

A numerical solution of the Navier-Stokes equations of motion by means of finite-difference forms of the vorticity and continuity equations is presented. This is applied to the study of the flow of an incompressible fluid produced by the motion from rest of a piston in a cylindrical tube of circular cross-section.

Experiments at high Reynolds number indicated the presence in the starting flow of a ring vortex which was not reproduced by computation. Iteration to determine the stream function was not found to be necessary to achieve 1% accuracy. Omitting iteration is equivalent to only slightly disturbing the flow. An additional random disturbance applied to the flow at each time step was found to result in the production of the ring vortex.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 50 , Issue 4 , 29 December 1971 , pp. 625 - 644
Copyright
© 1971 Cambridge University Press

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