Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-23T15:13:07.976Z Has data issue: false hasContentIssue false
  • English
  • Français

Mathematical Approach to Investigate the Behaviour of the Principal Parameters in Axisymmetric Supercavitating Flows, Using Boundary Element Method

Published online by Cambridge University Press:  05 May 2011

R. Shafaghat ,
S. M. Hosseinalipour ,
N. M. Nouri  and
A. Vahedgermi
R. Shafaghat*
Affiliation:
Department of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
S. M. Hosseinalipour*
Affiliation:
Department of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
N. M. Nouri*
Affiliation:
Department of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
A. Vahedgermi*
Affiliation:
Department of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
*
*Ph.D. student
**Associate Professor, corresponding author
***Assistant Professor
****M.Sc. student
Get access

Abstract

In this paper, a direct boundary element method (DBEM) is formulated numerically for the problems of the unbounded potential flows past supercavitating bodies of revolution (cones and also disks which are special case of cones with tip vertex angle of 180 degree) at zero degree angle of attack. In the analysis of potential flows past supercavitating cones and disks, a cavity closure model must be employed in order to make the mathematical formulation close and the solution unique. In the present study, we employ Riabouchinsky closure model. Since the location of the cavity surface is unknown at prior, an iterative scheme is used. Where, for the first stage, an arbitrary cavity surface is assumed. The flow field is then solved and by an iterative process, the location of the cavity surface is corrected. Upon convergence, the exact boundary conditions are satisfied on the body-cavity boundary. For this work, powerful software, based on CFD code, is developed in CAE center of IUST. The predictions of the software are compared with those generated by analytical solution and with the experimental data. The predictions of software for supercavitating cones and disks are seen to be excellent. Using the obtained data from software, we investigate the mathematical behavior of axisymmetric supercavitating flow parameters including drag coefficients of supercavitating cones and disks, cavitation number and maximum cavity width for a wide range of cone and disk diameters, cone tip angles and cavity lengths. The main objective of this study is to propose appropriate mathematical functions describing the behavior of these parameters. As a result, among all available functions such as linear, polynomial, logarithmic, power and exponential, only power functions can describe the behavior of mentioned parameters, very well.

Keywords

SupercavitationAxisymmetricBoundary element method.
Type
Articles
Information
Journal of Mechanics , Volume 25 , Issue 4 , December 2009 , pp. 465 - 473
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2009

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.Kuklinski, R., Henoch, C. and Castano, J., “Experimental Study of Ventilated Cavities on Dynamic Test Model,” Naval Undersea Warfare Center, Cav2001: Session B3.004 (2001).Google Scholar
2.Reichardt, H., “The Physical Laws Governing the Cavitation Bubbles Produced Behind Solids of Revolution in a Fluid Flow,” The Kaiser Wilhelm Institute for Hydrodynamic Research, Gottingen, Rep. UM 6628 (1945).Google Scholar
3.Garabedian, P. R., “The Calculation of Axially Symmetric Cavities and Jets,” Pacific Journal of Mathematics, 6, pp. 611–689 (1956).CrossRefGoogle Scholar
4.Cuthbert, J. and Street, R., “An Approximate Theory for Supercavitating Flow About Slender Bodies of Revolution,” LMSC Report TM81–73/39, Lockheed Missiles and Space Co., Sunnyvale, California (1964).Google Scholar
5.Brennen, C. A., “Numerical Solution of Axisymmetric Cavity Flows,” Journal of Fluid Mechanics, 37, pp. 4, 671–688 (1969).CrossRefGoogle Scholar
6.Chou, Y. S., “Axisymmetric Cavity Flows Past Slender Bodies of Revolution,” Journal of Hydronautics, 8, pp. 13–18 (1974).CrossRefGoogle Scholar
7.Aitchison, J. M., “The Numerical Solution of Planar and Axisymmetric Cavitational Flow Problems,” Computers and Fluids, 12, pp. 55–65 (1984).CrossRefGoogle Scholar
8.Hase, P. M., Interior Source Methods for Planar and Axisymmetric Supercavitating Flows, Thesis submitted for the Degree of Doctor of Philosophy (2003).Google Scholar
9.Verghese, A. N., Uhlman, J. S. and Kirschner, I. N., “Numerical Analysis of High - Speed Bodies in Partially Cavitation Axisymmetric Flow,” Transactions of ASME, Journal of Engineering, 127, pp. 41–54 (2005).Google Scholar
10.Wrobel, L. C., “A Simple and Efficient BEM Algorithm for Planar Cavity Flows,” International Journal for Numerical Methods in Fluids, 14, pp. 524–537 (1992).CrossRefGoogle Scholar
11.Becker, A. A., “The Boundary Element Method in Engineering,” McGraw- Hill Book Company (1992).Google Scholar
12.Kennon, S. R., “Boundary Element Method,” Graduate Research Assistant, Dept. of Aerospace Engineering and Engineering Mechanics, University of Texas at Austin, Austin, TX. (1986).Google Scholar
13.Mukherjee, S. and Morjaria, M., “On the Efficiency and Accuracy of the Boundary Element Method,” International Journal For Numerical Methods In Engineering, 20, pp. 515–522 (1984).CrossRefGoogle Scholar
14.Kirschner, I. N., Fine, N. E., Uhlman, J. S., and Kring, D. C., Numerical Modeling of Supercavitating Flows, Paper presented at the RTO AVT lecture series on “Supercavitating Flows”, held on the Von Karman Institute (VKI) in Belgium, and published in RTO EN-010, pp. 12–16 (2001).Google Scholar
15.Shafaghat, R., Hosseinalipour, S. M. and Shariatifard, A., “Numerical Analysis of a Two Dimensional Bounded Supercavitation Flow,” 15th Annual Conferences of the CFD Society of CanadaToronto, Canada pp. 27–31 (2007).Google Scholar
16.Shafaghat, R., Hosseinalipour, S. M. and Shariatifard, A., “Numerical Analysis of Two-Dimensional Supercavitation Flow Using a Boundary Element Method,” Journal of Numerical Simulations in Engineering, University of Mazandaran, pp. 216–223 (2008).Google Scholar
17.Chen, J. T., Hsiao, C. C. and Chen, K. H., “Study of Free Surface Seepage Problems Using Hypersingular Equations,” Communications in Numerical Methods in Engineering, 23, pp. 755–769 (2007).CrossRefGoogle Scholar
18.Brebbia, C. A., Telles, J. C. F and Wrobel, L. C., Boundary Element Techniques. Springer, Berlin (1984).CrossRefGoogle Scholar
19.Self, M. and Ripken, J. F., Steady-State Cavity Studies in a Free-jet Water Tunnel, St. Anthony Falls Hydr. Lab. Rep. 47 (1955).Google Scholar