Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-26T14:39:14.804Z Has data issue: false hasContentIssue false
  • English
  • Français

Error Estimation for Neglecting Unsteady Hydrodynamic Forces in the Equation of Motion for an Immersed Pendulum

Published online by Cambridge University Press:  20 December 2012

F.-L. Yang
F.-L. Yang*
Affiliation:
Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
*
Corresponding author ([email protected])
Get access

Abstract

The unsteady motion of a fully immersed solid sphere at low to moderate particle Reynolds number, from 1 to about 1600, has been modeled by considering the quasi-steady viscous drag, the added mass force, and the history force. The last force results from unsteady boundary layer growth and is often neglected in multiphase flow applications due to its complex formula. However, it has been shown that this unsteady viscous force is more crucial than the widely employed added mass force to describe an unsteady sphere motion. Thus, targeting the flow regime when the quasi-steady viscous drag is dominating, this work proposes two simple formulae to approximate the errors of neglecting either the history force or the added mass force in describing a fully immersed spherical pendulum motion. The proposed formulae are shown to capture the actual error when the numerical solution of a partial model that omits one force component is compared to the full model prediction when the sphere density is not too close to the ambient liquid.

Keywords

Immersed pendulum motionHistory forceAdded mass forceError estimation
Type
Articles
Information
Journal of Mechanics , Volume 29 , Issue 1 , March 2013 , pp. 1 - 6
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

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

REFERENCES

1. Landau, L. D. and Lifshitz, E. M., Fluid Mechanics, Elsevier, London (1987).Google Scholar
2. Clift, R., Grace, J. R. and Weber, M. E., Bubbles, Drops, and Particles, Academic Press, New York (1978).Google Scholar
3. Batchelor, G. K., An Introduction to Fluid Dynamics, Cambridge University Press (1937).Google Scholar
4. Chang, E. J. and Maxey, M. R., “Unsteady Flow About a Sphere at Low to Moderate Reynolds Number, Part 2,” Journal of Fluid Mechanics, 303, pp. 133–153 (1995).Google Scholar
5. Mei, R. and Adrian, R. J., “Flow Past a Sphere with an Oscillation in the Free-Stream Velocity and Unsteady Drag at Finite Reynolds Number,” Journal of Fluid Mechanics, 237, pp. 323–341 (1992).Google Scholar
6. Harada, S., Tanaka, T. and Tsuji., Y., “Fluid Force Acting on a Falling Particle Toward a Plane Wall,” Proceedings of the 2000 ASME Fluid Engineering Division Summer Meeting, Paper No. FEDSM2000-11267 (2000).Google Scholar
7. Chang, T. J. and Yen, B. C., “Gravitational Fall Velocity of Sphere in Viscous Fluid,” Journal of Engineering Mechanics, pp. 1193–1199 (1998).Google Scholar
8. Yang, F.-L., “A Formula for the Wall-Amplified Added Mass Coefficient for a Solid Sphere in Normal Approach to a Wall and Its Application for Such Motion at Low Reynolds Number,” Physics of Fluids, 22, p. 123303 (2010).CrossRefGoogle Scholar
9. Milne-Thomson, L. M., Theoretical Hydrodynamics, 5th Ed., Dover, New York (1968).CrossRefGoogle Scholar
10. Press, W. H., Teukolsky, S. A., Vetterling, W. T. and Flannery, B. P., Numerical Recipes, Cambridge University Press, New York (1996).Google Scholar