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TECHNICAL PAPERS

All-Speed Time-Accurate Underwater Projectile Calculations Using a Preconditioning Algorithm

[+] Author and Article Information
Michael Dean Neaves

 Naval Surface Warfare Center–Panama City, Integration and Experimentation Branch (HS15), 110 Vernon Avenue, Panama City, FL 32407michael.neaves@navy.mil

Jack R. Edwards

 North Carolina State University, Mechanical and Aerospace Engineering, 4223 Broughton Hall, Box 7910, Raleigh, NC 27695jredward@eos.ncsu.edu

J. Fluids Eng 128(2), 284-296 (Aug 30, 2005) (13 pages) doi:10.1115/1.2169816 History: Received September 20, 2004; Revised August 30, 2005

An algorithm based on the combination of time-derivative preconditioning strategies with low-diffusion upwinding methods is developed and applied to multiphase, compressible flows characteristic of underwater projectile motion. Multiphase compressible flows are assumed to be in kinematic and thermodynamic equilibrium and are modeled using a homogeneous mixture formulation. Compressibility effects in liquid-phase water are modeled using a temperature-adjusted Tait equation, and gaseous phases (water vapor and air) are treated as an ideal gas. The algorithm is applied to subsonic and supersonic projectiles in water, general multiphase shock tubes, and a high-speed water entry problem. Low-speed solutions are presented and compared to experimental results for validation. Solutions for high-subsonic and transonic projectile flows are compared to experimental imaging results and theoretical results. Results are also presented for several multiphase shock tube calculations. Finally, calculations are presented for a high-speed axisymmetric supercavitating projectile during the important water entry phase of flight.

Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Effective speed of sound versus void fraction

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Figure 2

Surface pressure distributions: K=0.2, 0.3, and 0.4

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Figure 3

High-subsonic projectile cavity shadowgraph and computed void fraction contours

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Figure 4

Cavity thickness of high-subsonic projectile

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Figure 5

Pressure contours (log scale), density contours, and movie camera image of transonic projectile

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Figure 6

Temperature contours near cavitator for transonic projectile

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Figure 7

Convecting liquid sheet solution (0.25ms)

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Figure 8

Convecting liquid sheet percent error (0.25ms)

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Figure 9

Order of scheme for convecting liquid sheet calculation

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Figure 10

Pressure and velocity for high-pressure water shock tube (0.15ms)

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Figure 11

Density and temperature for high-pressure water shock tube (0.15ms)

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Figure 12

Pressure and velocity for low-pressure water shock tube (0.15ms)

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Figure 13

Pressure, velocity, and void fraction for air-water shock tube (0.15ms)

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Figure 14

Density, temperature, and void fraction for air-water shock tube (0.15ms)

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Figure 15

Pressure, velocity, and void fraction for water-vapor shock tube (0.15ms)

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Figure 16

Density, temperature, and void fraction for water-vapor shock tube (0.15ms)

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Figure 17

Grid for generic supercavitating projectile

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Figure 18

Supercavitating projectile water entry calculation (water volume fraction contours)

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Figure 19

Vapor and air void fractions after water entry (1.23ms)

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Figure 20

Projectile drag during water entry

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