Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-22T01:39:55.505Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamic equations of motion for a rigid or deformable body in an arbitrary non-uniform potential flow field

Published online by Cambridge University Press:  26 April 2006

A. Galper  and
T. Miloh
A. Galper
Affiliation:
School of Engineering, Tel-Aviv University, Israel 69978
T. Miloh
Affiliation:
School of Engineering, Tel-Aviv University, Israel 69978
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we present a general method for calculating the hydrodynamic loads (forces and moments) acting on a deformable body moving with six degrees of freedom in a non-uniform ambient potential flow field. The corresponding expressions for the force and moment are given in a moving (body-fixed) coordinate system. The newly derived system of nonlinear differential equations of motion is shown to possess an important antisymmetry property. As a consequence of this special property, it is demonstrated that the motion of a rigid body embedded into a stationary flow field always renders a first integral. In a similar manner, we show that the motion of a deformable body in the presence of an arbitrary ambient flow field is Hamiltonian. A few practical applications of the proposed formulation for quadratic shapes and for weakly non-uniform external fields are presented. Also discussed is the self-propulsion mechanism of a deformable body moving in a non-uniform stationary flow field. It leads to a new parametric resonance phenomenon.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 295 , 25 July 1995 , pp. 91 - 120
Copyright
© 1995 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

Aref, H. & Jones S. W. 1993 Chaotic motion of a solid through ideal fluid. Phys. Fluids A 5, 3026–3028.Google Scholar
Auton, T. R., Hunt, J. C. R. & Prud'Homme, M. 1988 The force exerted on a body in inviscid unsteady non-uniform rotational flow. J. Fluid Mech. 197, 241–257.Google Scholar
Batchelor, G. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Benjamin, T. B. 1987 Hamiltonian theory for motions of bubbles in an infinite liquid. J. Fluid Mech. 181, 349–379.Google Scholar
Benjamin, T. B. & Ellis, A. T. 1990 Self-propulsion of asymmetrically vibrating bubbles. J. Fluid Mech. 212, 65–80.Google Scholar
Best, J. P. 1993 Formation of toroidal bubbles upon cavity collapse J. Fluid Mech. 251, 79–107.Google Scholar
Biesheuvel, A. 1985 A note on the generalized Lagally theorem. J. Engng Maths 19, 69–77.Google Scholar
Childress, S. 1981 Mechanics of Swimming and Flying. Cambridge University Press.
Dahlen, M. D. 1992 The behavior of active and passive particles in a chaotic flow. In Topological Aspects of the Dynamics of Fluids and Plasma. pp. 505–517. Kluwer
Dirac, P. A. M. 1964 Lecture on Quantum Mechanics. Belfer Graduate School of Science, NY Yieshiva University.
Galper, A. & Miloh, T. 1994 Generalized Kirchhoff equations for a rigid body moving in a weakly non-uniform flow field. Proc. R. Soc. Lond. A 446, 169–193.Google Scholar
Galper, A. & Miloh, T. 1995 On the motion of a non-rigid sphere in a perfect fluid. Z. Angew. Math. Mech. (in press).Google Scholar
Kochin, N. E., Kibel, I. A. & Rose, N. V. 1965 Theoretical Hydrodynamics. John Wiley & Sons.
Kozlov, V. V. & Onichenko, D. A. 1982 Nonintegrability of Kirchhoff equations. Sov. Math. Dokl. 26, 495.Google Scholar
Lamb, H. 1945 Hydrodynamics. Dover.
Landau, L. & Lifschitz, E. 1989 Field Theory. Pergamon.
Marsden, J. E. 1992 Lectures on Mechanics. Cambridge University Press.
Milne-Thomson, L. 1968 Theoretical Hydrodynamics. Macmillan.
Miloh, T. 1994 Pressure forces on deformable bodies in non-uniform inviscid flows. Q. J. Mech. Appl. Maths 47, 635–661.Google Scholar
Miloh, T. & Galper, A. 1993 Self-propulsion of a manoeuvring deformable body in a perfect fluid. Proc. R. Soc. Lond. A 442, 273–299.Google Scholar
Novikov, S. 1981 Variational methods and periodic solutions of equations of Kirchhoff type. 2. Functional Anal. Appl. 15, 263–274.Google Scholar
Olver, J. P. 1986 Applications of Lie Groups to Differential Equations. Springer.
Saffman, P. G. 1956 On the rise of small bubbles in water. J. Fluid Mech. 1, 249–275.Google Scholar
Shiffer, M. 1975 Sur la polarisation et la masse virtuelle C.R. Acad. Sci. Paris 244, 3118–3120.Google Scholar
Taylor, G. I. 1928 The forces on a body placed in a curved or converging stream of fluid. Proc. R. Soc. Lond. A 120, 260–283.Google Scholar
Wijngaarden, L. van 1976 Hydrodynamic interaction between gas bubbles in liquid J. Fluid Mech. 77, 27–44.Google Scholar
Zhang, D. Z. & Prosperetti, A. 1994 Averaged equations for inviscid disperse two-phase flow. J. Fluid Mech. 267, 185–221.Google Scholar