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Dynamics of axisymmetric bodies rising along a zigzag path

Published online by Cambridge University Press:  10 July 2008

PEDRO C. FERNANDES ,
PATRICIA ERN ,
FRÉDÉRIC RISSO  and
JACQUES MAGNAUDET
PEDRO C. FERNANDES
Affiliation:
Institut de Mécanique des Fluides, UMR 5502 CNRS-INP-UPS Allée du Prof. Camille Soula, 31400 Toulouse, France
PATRICIA ERN
Affiliation:
Institut de Mécanique des Fluides, UMR 5502 CNRS-INP-UPS Allée du Prof. Camille Soula, 31400 Toulouse, France
FRÉDÉRIC RISSO
Affiliation:
Institut de Mécanique des Fluides, UMR 5502 CNRS-INP-UPS Allée du Prof. Camille Soula, 31400 Toulouse, France
JACQUES MAGNAUDET
Affiliation:
Institut de Mécanique des Fluides, UMR 5502 CNRS-INP-UPS Allée du Prof. Camille Soula, 31400 Toulouse, France
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Abstract

The forces and torques governing the planar zigzag motion of thick, slightly buoyant disks rising freely in a liquid at rest are determined by applying the generalized Kirchhoff equations to experimental measurements of the body motion performed for a single body-to-fluid density ratio ρs/ρf ≈ 1. The evolution of the amplitude and phase of the various contributions is discussed as a function of the two control parameters, i.e. the body aspect ratio (the diameter-to-thickness ratio χ = d/h ranges from 2 to 10) and the Reynolds number (100 < Re < 330), Re being based on the rise velocity and diameter of the body. The body oscillatory behaviour is found to be governed by the force balance along the transverse direction and the torque balance. In the transverse direction, the wake-induced force is mainly balanced by two forces that depend on the body inclination, i.e. the inertia force generated by the body rotation and the transverse component of the buoyancy force. The torque balance is dominated by the wake-induced torque and the restoring added-mass torque generated by the transverse velocity component. The results show a major influence of the aspect ratio on the relative magnitude and phase of the various contributions to the hydrodynamic loads. The vortical transverse force scales as fo = (ρf − ρs)ghπd2 whereas the vortical torque involves two contributions, one scaling as fod and the other as f1d with f1 = χfo. Using this normalization, the amplitudes and phases of the vortical loads are made independent of the aspect ratio, the amplitudes evolving as (Re/Rec1 − 1)1/2, where Rec1 is the threshold of the first instability of the wake behind the corresponding body held fixed in a uniform stream.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 606 , 10 July 2008 , pp. 209 - 223
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Andersen, A., Pesavento, U. & Wang, Z. J. 2005 Unsteady aerodynamics of fluttering and tumbling plates. J. Fluid. Mech. 541, 65–90.CrossRefGoogle Scholar
Ern, P., Fernandes, P. C., Risso, F. & Magnaudet, J. 2007 Evolution of the wake structure and wake-induced loads along the path of freely rising axisymmetric bodies. Phys. Fluids 19, 113302.CrossRefGoogle Scholar
Fernandes, P. C., Ern, P., Risso, F. & Magnaudet, J. 2005 On the zigzag dynamics of freely moving axisymmetric bodies. Phys. Fluids 17, 098107.CrossRefGoogle Scholar
Fernandes, P. C., Risso, F., Ern, P. & Magnaudet, J. 2007 Oscillatory motion and wake instability of freely-rising axisymmetric bodies. J. Fluid Mech. 573, 479–502.CrossRefGoogle Scholar
Howe, M. 1995 On the force and moment on a body in an incompressible fluid, with application to rigid bodies and bubbles at low and high Reynolds numbers. Q. J. Mech. Appl. Maths 48, 401–426.CrossRefGoogle Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn.Cambridge University Press.Google Scholar
Loewenberg, M. 1993 a Stokes resistance, added mass, and Basset force for arbitrarily oriented finite-length cylinders. Phys. Fluids A 5, 765–767.CrossRefGoogle Scholar
Loewenberg, M. 1993 b The unsteady Stokes resistance of arbitrarily oriented, finite-length cylinders. Phys. Fluids A 5, 3004–3006.CrossRefGoogle Scholar
Loewenberg, M. 1994 Asymmetric, oscillatory motion of a finite-length cylinder: the macroscopic effect of particle edges. Phys. Fluids 6, 1095–1107.CrossRefGoogle Scholar
Lugt, H. J. 1983 Autorotation. Annu. Rev. Fluid. Mech. 15, 123–147.CrossRefGoogle Scholar
Magnaudet, J. & Eames, I. 2000 The motion of high-Reynolds-number bubbles in inhomogeneous flows. Annu. Rev. Fluid Mech. 32, 659–708.CrossRefGoogle Scholar
Mougin, G. & Magnaudet, J. 2002 a The generalized Kirchhoff equations and their application to the interaction between a rigid body and an arbitrary time-dependent viscous flow. Intl J. Multiphase Flow 28, 1837–1851.CrossRefGoogle Scholar
Mougin, G. & Magnaudet, J. 2002 b Path instability of a rising bubble. Phys. Rev. Lett. 88, 014502.CrossRefGoogle ScholarPubMed
Mougin, G. & Magnaudet, J. 2006 Wake-induced forces and torques on a zigzagging/spiralling bubble. J. Fluid Mech. 567, 185–194.CrossRefGoogle Scholar
Shew, W., Poncet, S. & Pinton, J.-F. 2006 Force measurements on rising bubbles. J. Fluid Mech. 569, 51–60.CrossRefGoogle Scholar
Wang, Z. J. 2005 Dissecting insect flight. Annu. Rev. Fluid Mech. 37 183–210.CrossRefGoogle Scholar