Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-28T11:49:26.790Z Has data issue: false hasContentIssue false
  • English
  • Français

Decomposition of the forces on a body moving in an incompressible fluid

Published online by Cambridge University Press:  28 October 2019

W. R. Graham Open the ORCID record for W. R. Graham [Opens in a new window]
Get access Rights & Permissions [Opens in a new window]

Abstract

In analysing fluid forces on a moving body, a natural approach is to seek a component due to viscosity and an ‘inviscid’ remainder. It is also attractive to decompose the velocity field into irrotational and rotational parts, and apportion the force resultants accordingly. The ‘irrotational’ resultants can then be identified as classical ‘added mass’, but the remaining, ‘rotational’, resultants appear not to be consistent with the physical interpretation of the rotational velocity field (as that arising from the fluid vorticity with the body stationary). The alternative presented here splits the inviscid resultants into components that are unquestionably due to independent aspects of the problem: ‘convective’ and ‘accelerative’. The former are associated with the pressure field that would arise in an inviscid flow with (instantaneously) the same velocities as the real one, and with the body’s velocity parameters – angular and translational – unchanging. The latter correspond to the pressure generated when the body accelerates from rest in quiescent fluid with its given rates of change of angular and translational velocity. They are reminiscent of the added-mass force resultants, but are simpler, and closer to the standard rigid-body inertia formulae, than the developed expressions for added-mass force and moment. Finally, the force resultants due to viscosity also include a contribution from pressure. Its presence is necessary in order to satisfy the equations governing the pressure field, and it has previously been recognised in the context of ‘excess’ stagnation-point pressure. However, its existence does not yet seem to be widely appreciated.

JFM classification

Mathematical Foundations: General fluid mechanics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 881 , 25 December 2019 , pp. 1097 - 1122
Check for updates
Copyright
© 2019 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

Batchelor, G. K. 2000 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Chang, C. C. 1992 Potential flow and forces for incompressible viscous flow. Proc. R. Soc. Lond. A 437, 517–525.Google Scholar
Corkery, S. J., Babinsky, H. & Graham, W. R. 2019 Quantification of added mass effects using particle image velocimetry data for a translating and rotating flat plate. J. Fluid Mech. 870, 492–518.Google Scholar
Eldredge, J. D. 2010 A reconciliation of viscous and inviscid approaches to computing locomotion of deforming bodies. Exp. Mech. 50 (9), 1349–1353.Google Scholar
Howe, M. S. 1995 On the force and moment on a body in an incompressible fluid, with application to rigid bodies and bubbles at high and low Reynolds numbers. Q. J. Mech. Appl. Maths 48 (3), 401–426.Google Scholar
Issa, R. I. 1995 Rise of total pressure in frictional flow. AIAA J. 33 (4), 772–774.Google Scholar
Lamb, H. 1993 Hydrodynamics. Cambridge University Press.Google Scholar
Leonard, A. & Roshko, A. 2001 Aspects of flow-induced vibration. J. Fluids Struct. 15 (3), 415–425.Google Scholar
Lighthill, M. J. 1963 Introduction. Boundary layer theory. In Laminar Boundary Layers (ed. Rosenhead, L.), pp. 46–113. Oxford University Press.Google Scholar
Limacher, E., Morton, C. & Wood, D. 2018 Generalized derivation of the added-mass and circulatory forces for viscous flows. Phys. Rev. Fluids 3 (1), 014701.Google Scholar
Limacher, E., Morton, C. & Wood, D. 2019 On the calculation of force from PIV data using the generalized added-mass and circulatory force decomposition. Exp. Fluids 60 (1), 4.Google Scholar
Saffman, P. G. 1993 Vortex Dynamics. Cambridge University Press.Google Scholar
Wang, C. Y. 1991 Exact solutions of the steady-state Navier–Stokes equations. Annu. Rev. Fluid Mech. 23 (1), 159–177.Google Scholar
White, F. M. 2006 Viscous Fluid Flow. McGraw-Hill (International Edition).Google Scholar
Williams, J. C. 2002 Rise of total pressure near the stagnation point on a sphere. AIAA J. 40 (3), 576–579.Google Scholar
Wu, J. C. 1981 Theory for aerodynamic force and moment in viscous flows. AIAA J. 19 (4), 432–441.Google Scholar
Zangwill, A. 2013 Modern Electrodynamics. Cambridge University Press.Google Scholar