Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-05T04:28:04.910Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Calculation of Two-Dimensional Added Mass Coefficients by the Taylor Theorem and the Method of Fundamental Solutions

Published online by Cambridge University Press:  22 March 2012

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

Abstract

This work integrates the Taylor theorem and the method of fundamental solutions to develop a numerical tool for estimating the added mass coefficient tensor for a solid object of any convex shape moving in potential flow. In potential flow theory, the Taylor theorem calculates the added mass coefficient tensor for a Rankine body with algebraic manipulations of the properties of the internal singularities employed to generate the corresponding flow. To apply this theorem for objects in other shapes, the singularity strength and locations are required information which is facilitated numerically in this work by the method of fundamental solutions (MFS). The developed scheme is tested on a circle, an ellipse, a square, and a rhombus and the numerical results are in good agreement with the corresponding analytical values. A final example of a Cassini oval is also considered to show the potential applications on bio-engineering problems.

Keywords

Added mass coefficient tensorPotential flowTaylor theoremMethod of fundamental solutions
Type
Articles
Information
Journal of Mechanics , Volume 28 , Issue 1 , March 2012 , pp. 107 - 112
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. Lamb, H., Hydrodynamics, Dover (1932).Google Scholar
2. Milne-Thompson, L. M., Theoretical Hydrodynamics, Dover (1968).CrossRefGoogle Scholar
3. Yih, C. S., Fluid mechanics: A Concise Introduction to the Theory, West River (1977).Google Scholar
4. Taylor, G. I., “The Energy of a Body Moving in an Infinite Fluid, with an Application to Airships,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 120, pp. 13–21 (1928).Google Scholar
5. Birkhoff, G., Hydrodynamics, Princeton (1953).Google Scholar
6. Landweber, L., “On a Generalization of Taylor's Virtual Mass Relation for Rankine Bodies,” Quarterly of Applied Mathematics, 14, pp. 51–56 (1956).CrossRefGoogle Scholar
7. Landweber, L. and Yih, C. S., “Forces, Moments, and Added Masses for Rankine Bodies,” Journal of Fluid Mechanics, 1, pp. 319–336 (1956).CrossRefGoogle Scholar
8. Landweber, L. and Chwang, A. T., “Generalization of Taylor's Added-Mass Formula for Two Bodies,” Journal of Ship Research, 33, pp. 1–9 (1989).CrossRefGoogle Scholar
9. Fairweather, G. and Karageorghis, A., “The Method of Fundamental Solutions for Elliptic Boundary Value Problems,” Advances in Computational Mathematics, 9, pp. 69–95 (1998).CrossRefGoogle Scholar
10. Golberg, M. A. and Chen, C. S., “The Method of Fundamental Solutions for Potential, Helmholtz and Diffusion Problems,” Boundary Integral Methods: Numerical and Mathematical Aspects, Ed. Golberg, M. A., WIT Press/Computational Mechanics Publications, Boston, pp. 103–176 (1998).Google Scholar
11. Young, D. L., Jane, S. J., Fan, C. M., Murugesan, K. and Tsai, C. C., “The Method of Fundamental Solutions for 2D and 3D Stokes Problems,” Journal of Computational Physics, 211, pp. 1–8 (2006).CrossRefGoogle Scholar
12. Johnston, R. L. and Fairweather, G., “The Method of Fundamental Solutions for Problems in Potential Flow,” Applied Mathematical Modelling, 8, pp. 265–270 (1984).CrossRefGoogle Scholar
13. Wang, J. G., Ahmed, M. T. and Leavers, J. D., “Nonlinear Least Squares Optimization Applied to the Method of Fundamental Solutions for Eddy Current Problems,” IEEE Transactions on Magnetics, 26, pp. 2385–2387 (1990).CrossRefGoogle Scholar
14. Moré, J. J., Garbow, B. S. and Hillstrom, K. E., “User Guide for MINPACK-1,” Argonne National Laboratory Report ANL-80-74, Argonne, III. (1980).CrossRefGoogle Scholar
15. Katsurada, M., “A Mathematical Study of the Charge Simulation Method II,” Journal of The Faculty of Science, The University of Tokyo, Section Ia, Mathematics, 36, pp. 135–162 (1989).Google Scholar
16. Angelov, B, and Mladenov, I. M., “On the Geometry of Red Blood Cell,” Geometry, Integrability and Quantization, Varna, Bulgaria (1999).Google Scholar
17. Kennard, E. H., “Irrotational Flow of Frictionless Fluids, Mostly of Invariable Density,” David Taylor Model Basin, USA Rep. 2299, pp. 108–112 (1967).Google Scholar
18. Lewis, F. M., “The Inertia of the Water Surrounding a Vibrating Ship,” Transactions of the SNAME, 37, pp. 1–20 (1929).Google Scholar