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Added mass of a pair of disks at small separation

Published online by Cambridge University Press:  01 December 2016

C. ATKINSON  and
J. D. SHERWOOD
C. ATKINSON
Affiliation:
Department of Mathematics, Imperial College, Queen's Gate, South Kensington, London SW7 2NB, UK email: c.atkinson@imperial.ac.uk
J. D. SHERWOOD
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK email: jds60@cam.ac.uk
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Abstract

Inviscid irrotational flow around a pair of coaxial disks is considered in the limit in which the distance 2h between the disks is small compared to their radius a. The disks have zero thickness and accelerate away from one another along their common axis. The added mass M of each accelerating disk is increased by the presence of the other disk. Analytic predictions are obtained when h/a ≪ 1, with M ~ πa/(8h)-ln(h/a)/2+0.77875+. . . The term O(a/h) can be obtained by means of an inviscid analysis of approximately unidirectional flow within the gap between the disks, but the correction terms have not been reported previously. The irrotational flow problem satisfies Neumann boundary conditions on the surface of the disks, but is otherwise analogous to the Dirichlet problem of the capacitance of a pair of charged disks, which has been the subject of much study and controversy.

Keywords

Laplace EquationAdded MassDisks
Type
Papers
Information
European Journal of Applied Mathematics , Volume 28 , Issue 4 , August 2017 , pp. 687 - 706
Copyright
Copyright © Cambridge University Press 2016 

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