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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

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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