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Research Papers: Multiphase Flows

The Optimum Design of a Cavitator for High-Speed Axisymmetric Bodies in Partially Cavitating Flows

[+] Author and Article Information
I. Rashidi

e-mail: im.rashidi@gmail.com

Ma. Pasandideh-Fard

Department of Mechanical Engineering,
Ferdowsi University of Mashhad,
Mashhad, 91775-1111, Iran

1Corresponding author.

Manuscript received March 17, 2012; final manuscript received November 8, 2012; published online December 21, 2012. Assoc. Editor: Edward M. Bennett.

J. Fluids Eng 135(1), 011301 (Dec 21, 2012) (12 pages) Paper No: FE-12-1132; doi: 10.1115/1.4023078 History: Received March 17, 2012; Revised November 08, 2012

In this paper, the partially cavitating flow over an axisymmetric projectile is studied in order to obtain the optimum cavitator such that, at a given cavitation number, the total drag coefficient of the projectile is minimum. For this purpose, the boundary element method and numerical simulations are used. A large number of cavitator profiles are produced using a parabolic expression with three geometric parameters. The potential flow around these cavitators is then solved using the boundary element method. In order to examine the optimization results, several cavitators with a total drag coefficient close to that of the optimum cavitators are also numerically simulated. Eventually, the optimum cavitator is selected using both the boundary element method and numerical simulations. The effects of the body radius and the length of the conical section of the projectile on the shape of the optimized cavitator are also investigated. The results show that for all cavitation numbers, the cavitator that creates a cavity covering the entire conical section of the projectile with a minimum total drag coefficient is optimal. It can be seen that increasing the cavitation number causes the optimum cavitator to approach the disk cavitator. The results also show that at a fixed cavitation number, the increase in both the radius and length of the conical section causes the cavitator shape to approach that of the disk cavitator.

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References

Savchenko, Y. N., Vlasenko, Y. D., and Semenenko, V. N., 1999, “Experimental Study of High-Speed Cavitated Flows,” Int. J. Fluid Mech. Res., 26(3), pp. 365–374.
Vlasenko, Y. D., 2003, “Experimental Investigation of Supercavitation Flow Regimes at Subsonic and Transonic Speeds,” Proceedings of the 5th International Symposium on Cavitation, Osaka, Japan, Paper No. Cav03-GS-6-006, pp. 1–8.
Hrubes, J. D., 2001, “High-Speed Imaging of Supercavitation Underwater Projectiles,” Exp. Fluids, 30(1), pp. 57–64. [CrossRef]
Martin, W., Travis, J. S., and Roger, E. A., 2003, “Experimental Study of a Ventilated Supercavitating Vehicle,” Proceedings of the 5th International Symposium on Cavitation, Osaka, Japan, Paper No. Cav03-OS-7-008, pp. 1–7.
Kuklinski, R., Henoch, C., and Castano, J., 2001, “Experimental Study of Ventilated Cavities on Dynamic Test Model,” Proceedings of the 4th International Symposium on Cavitation, Pasadena, CA, Paper No. Cav01-B3-004, pp. 1–8.
Savchenko, Y. N., and Semenenko, V. N., 1998, “The Gas Absorption Into Supercavity From Liquid-Gas Bubble Mixture,” Proceedings of the 3rd International Symposium on Cavitation, Grenoble, France, pp. 49–53.
Michel, J. M., 2001, “Oscillations of Ventilated Cavities: Experimental Aspects,” VKI Special Course on Supercavitating Flows, Brussels, Belgium, pp. 29–41.
Feng, X.-M., Lu, C.-J., and Hu, T.-Q., 2002, “Experimental Research on a Supercavitating Slender Body of Revolution With Ventilation,” J. Hydrodyn., 14(2), pp. 17–23.
Feng, X.-M., Lu, C.-J., and Hu, T.-Q., 2005, “The Fluctuation Characteristics of Natural and Ventilated Cavities on an Axisymmetric Body,” J. Hydrodyn., 17(1), pp. 87–91.
Zhang, X.-W., Wei, Y.-J., and Zhang, J.-Z., 2007, “Experimental Research on the Shape Characters of Natural and Ventilated Supercavitation,” J. Hydrodyn., 19(5), pp. 564–571. [CrossRef]
Lee, Q.-T., Xue, L.-P., and He, Y.-S., 2008, “Experimental Study of Ventilated Supercavities With a Dynamic Pitching Model,” J. Hydrodyn., 20(4), pp. 456–460. [CrossRef]
Wang, G., Senocak, I., Shyy, W., Ikohagi, T., and Cao, S., 2001, “Dynamics of Attached Turbulent Cavitating Flows,” Prog. Aerosp. Sci., 37, pp. 551–581. [CrossRef]
Passandideh-Fard, M., and Roohi, E., 2008, “Transient Simulations of Cavitating Flows Using a Modified Volume-of-Fluid (VOF) Technique,” Int. J. Comput. Fluid Dyn., 22(1-2), pp. 97–114. [CrossRef]
Yuan, W., Sauer, J., and Schnerr, G. H., 2001, “Modeling and Computation of Unsteady Cavitation Flows in Injection Nozzles,” J. Mech. Ind., 2, pp. 383–394. [CrossRef]
Singhal, A. K., Athavale, M. M., Li, H., and Jiang, Y., 2002, “Mathematical Basis and Validation of the Full Cavitation Model,” ASME J. Fluids Eng., 124(3), pp. 617–624. [CrossRef]
Merkle, C. L., Feng, J., and Buelow, P. E. O., 1998, “Computational Modeling of the Dynamics of Sheet Cavitation,” Proceedings of the 3rd International Symposium on Cavitation (CAV1998), Grenoble, France, pp. 307–311.
Kunz, R. F., Boger, D. A., Stinebring, D. R., Chyczewski, T. S., Lindau, J. W., Gibeling, H. J., Venkateswaran, S., and Govindan, T. R., 2000, “A Preconditioned Navier–Stokes Method for Two-Phase Flows With Application to Cavitation Prediction,” Comput. Fluids, 29, pp. 849–875. [CrossRef]
Frobenius, M., Schilling, R., Bachert, R., and Stoffel, B., 2003, “Three-Dimensional Unsteady Cavitating Effects on a Single Hydrofoil and in a Radial Pump–Measurement and Numerical Simulation,” Proceedings of the 5th International Symposium on Cavitation (CAV2003), Osaka, Japan, Paper No. GS-9-004.
aus der Wiesche, S., 2005, “Numerical Simulation of Cavitation Effects Behind Obstacles and in an Automotive Fuel Jet Pump,” Heat Mass Transfer, 41(7), pp. 615–624. [CrossRef]
Efros, D. A., 1946, “Hydrodynamic Theory of Two-Dimensional Flow With Cavitation,” Dokl. Akad. Nauk SSSR, 51, pp. 267–270.
Tulin, M. P., 1964, “Supercavitating Flows—Small Perturbation Theory,” J. Ship Res., 7(3), pp. 16–37.
Cuthbert, J., and Street, R., 1964, “An Approximate Theory for Supercavitating Flow About Slender Bodies of Revolution,” Lockheed Missiles and Space Co., Sunnyvale, CA, LMSC Report No. TM81-73/39.
Chou, Y. S., 1974, “Axisymmetric Cavity Flows Past Slender Bodies of Revolution,” J. Hydronaut., 8(1), pp. 13–18. [CrossRef]
Vorus, W. S., 1991, “A Theoretical Study of the Use of Supercavitation/Ventilation for Underwater Body Drag Reduction,” VAI Technical Report, Vorus & Associates, Inc., Gregory, MI.
Kuria, I. M., Kirschner, I. N., Varghese, A. N., and Uhlman, J. S., 1997, “Compressible Cavity Flows Past Slender Non-Lifting Bodies of Revolution,” Proceedings of the ASME and JSME Fluids Engineering Annual Conference and Exhibition, Cavitation and Multiphase Flow Forum, Vancouver, BC, Paper No. FEDSM97-3262.
Uhlman, J. S., 1987, “The Surface Singularity Method Applied to Partially Cavitating Hydrofoils,” J. Ship Res., 31(2), pp. 107–124.
Uhlman, J. S., 1989, “The Surface Singularity or Boundary Integral Method Applied to Supercavitating Hydrofoils,” J. Ship Res., 33(1), pp. 16–20.
Hase, P. M., 2003, “Interior Source Methods for Planar and Axisymmetric Supercavitating Flows,” Ph.D. thesis, University of Adelaide, Adelaide, Australia.
Varghese, A. N., Uhlman, J. S., and Kirschner, I. N., 2005, “Numerical Analysis of High-Speed Bodies in Partially Cavitating Axisymmetric Flow,” ASME J. Fluids Eng., 127(1), pp. 41–54. [CrossRef]
Rashidi, I., Moin, H., Fard, Mo. P., and Fard, Ma. P., 2008, “Numerical Simulation of Partial Cavitation Over Axisymmetric Bodies VOF Method vs. Potential Flow Theory,” J. Aerosp.Sci. Technol., 5(1), pp. 23–33.
Kinnas, S. A., Mishima, S. H., and Savineau, C., 1995, “Application of Optimization Techniques to the Design of Cavitating Hydrofoils and Wings,” Proceedings of the International Symposium on Cavitation, Deauville, France.
Mishima, S. H. and Kinnas, S. A., 1995, “A Numerical Optimization Technique Applied to the Design of Two-Dimensional Cavitating Hydrofoil Sections,” J. Ship Res., 40, pp. 28–38.
Alyanak, E., Venkayya, V., Grandhi, R. V., and Penmetsa, R. C., “Variable Shape Cavitator Design for a Supercavitating Torpedo,” 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Dayton, OH.
Choi, J. H., Penmetsa, R. C., and Grandhi, R. V., 2005, “Shape Optimization of the Cavitator for a Supercavitating Torpedo,” Struct. Multidiscip. Optim., 29, pp. 159–167. [CrossRef]
Shafaghat, R., Hosseinalipour, S. M., Nouri, N. M., and Lashgari, I., 2008, “Shape Optimization of Two-Dimensional Cavitators in Supercavitating Flows, Using the NSGA II Algorithm,” Appl. Ocean Res., 30, pp. 305–310. [CrossRef]
Shafaghat, R., Hosseinalipour, S. M., and Lashgari, I., and Vahedgermi, A., 2011, “Shape Optimization of Axisymmetric Cavitators in Supercavitating Flows, Using the NSGA II Algorithm,” Appl. Ocean Res., 33, pp. 193–198. [CrossRef]
Kinnas, S. A., and Fine, N. E., 1993, “A Numerical Nonlinear Analysis of the Flow Around Two- and Three-Dimensional Partially Cavitating Hydrofoils,” J. Fluid Mech., 254, pp. 151–158. [CrossRef]
Shames, I. H., 2003, Mechanics of Fluids, 4th ed., McGraw-Hill, New York.
Patankar, S. V., 1980, Numerical Heat Transfer and Fluid, Hemisphere, Washington, DC.
Leonard, B. P., and Mokhtari, S., 1990, “ULTRA-SHARP Nonoscillatory Convection Schemes for High-Speed Steady Multidimensional Flow,” NASA Lewis Research Center, Report No. NASA-TM-102568 (ICOMP-90-12).
Franc, J., and Michel, J., 2005, Fundamentals of Cavitation, Springer, Dordrecht, The Netherlands.

Figures

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Fig. 1

A partially cavitating projectile

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Fig. 2

The schematic of the projectile considered in this study

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Fig. 3

The boundary conditions used in the numerical simulations

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Fig. 4

Design parameters of the cavitator geometry

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Fig. 5

The supercavity length (Lc) and the drag coefficient (CD) versus the number of cells per disk radius for the BEM method

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Fig. 6

The supercavity length (Lc) and the drag coefficient (CD) versus the number of cells per disk radius for the CFD method

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Fig. 7

The variation of the cavity length versus the cavitation number from the BEM method, CFD simulations, and experiments [41]

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Fig. 8

The variation of the total drag coefficient versus the cavitation number from the BEM method, CFD simulations, and experiments [41]

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Fig. 9

The comparison of the cavity length from the BEM and CFD for the cavitators presented in Table 1 at σ = 0.12

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Fig. 10

The comparison of the pressure drag coefficient from the BEM and CFD for the cavitators presented in Table 1 at σ = 0.12

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Fig. 11

The comparison of the shape of the cavity interface calculated using the BEM and CFD (αv = 0.5) methods for the optimum cavitator (cavitator number 7 in Table 1) at a cavitation number of σ = 0.12 for a dimensionless body radius of 0.9 and a dimensionless conical length of 5

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Fig. 12

The comparison of the cavity shape and length of (a) the disk cavitator with that of (b) the optimum cavitator at a cavitation number of σ = 0.12 for a dimensionless body radius of 0.9 and a dimensionless conical length of 5

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Fig. 13

Drag coefficients versus the cavitation number for the optimum cavitator as compared with those of a disk cavitator

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Fig. 14

The pressure coefficient distributions using the CFD method for (a) the disk cavitator, and (b) the optimum cavitator at a cavitation number of 0.12 for a dimensionless body radius of 0.9 and a dimensionless conical length of 5. The cavity interface from the BEM method is also displayed in the figure.

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Fig. 15

Variation of the pressure cofficient distributions on the optimum and disk cavitators from the BEM and CFD methods at a cavitation number of 0.12 for a dimensionless body radius of 0.9 and a dimensionless conical length of 5

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Fig. 16

The optimum shapes of the cavitators at different cavitation numbers for a dimensionless projectile radius of 0.7 and a dimensionless conical section length of 5

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Fig. 17

The optimum shapes of the cavitators at different cavitation numbers for a dimensionless projectile radius of 0.9 and a dimensionless conical section length of 5

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Fig. 18

The optimum shapes of the cavitators at different cavitation numbers for a dimensionless projectile radius of 1.1 and a dimensionless conical section length of 5

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Fig. 19

The variations of the geometric parameters of the optimized cavitator against the body radius at σ = 0.15 for a dimensionless conical section length of 5

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Fig. 20

The variations of the geometric parameters of the optimized cavitator against the body radius at σ = 0.12 for a dimensionless conical section length of 5

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Fig. 21

The variations of the geometric parameters of the optimized cavitator against the body radius at σ = 0.1 for a dimensionless conical section length of 5

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Fig. 22

The variation of the total drag coefficient versus the projectile radius at different cavitation numbers for a dimensionless conical length of 5

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Fig. 23

The optimum shapes of the cavitators at different cavitation numbers for a dimensionless projectile radius of 0.9 and a dimensionless conical section length of 4

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Fig. 24

The optimum shapes of the cavitators at different cavitation numbers for a dimensionless projectile radius of 0.9 and a dimensionless conical section length of 5

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Fig. 25

The optimum shapes of the cavitators at different cavitation numbers for a dimensionless projectile radius of 0.9 and a dimensionless conical section length of 6

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Fig. 26

The variations of the geometric parameters of the optimized cavitator against the length of the conical section at σ = 0.15 for a dimensionless body radius of 0.9

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Fig. 27

The variations of the geometric parameters of the optimized cavitator against the length of the conical section at σ = 0.12 for a dimensionless body radius of 0.9

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Fig. 28

The variations of the geometric parameters of the optimized cavitator against the length of the conical section at σ = 0.1 for a dimensionless body radius of 0.9

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Fig. 29

The variation of the total drag coefficient versus the conical length of the projectile at different cavitation numbers for a dimensionless body radius of 0.9

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