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TECHNICAL PAPERS

Numerical Simulation of Vortex Cavitation in a Three-Dimensional Submerged Transitional Jet

[+] Author and Article Information
Tao Xing1

School of Mechanical Engineering,  Purdue University, West Lafayette, IN 47907

Zhenyin Li2

School of Mechanical Engineering,  Purdue University, West Lafayette, IN 47907

Steven H. Frankel3

School of Mechanical Engineering,  Purdue University, West Lafayette, IN 47907

1

Ph.D., currently Postdoctoral Researcher at The University of Iowa

2

Doctoral student

3

Professor, Member ASME, corresponding author, E-mail: frankel@ecn.purdue.edu

J. Fluids Eng 127(4), 714-725 (Apr 07, 2005) (12 pages) doi:10.1115/1.1976742 History: Received May 02, 2003; Revised April 07, 2005

Vortex cavitation in a submerged transitional jet is studied with unsteady three-dimensional direct numerical simulations. A locally homogeneous cavitation model that accounts for non-linear bubble dynamics and bubble/bubble interactions within spherical bubble clusters is employed. The velocity, vorticity, and pressure fields are compared for both cavitating and noncavitating jets. It is found that cavitation occurs in the cores of the primary vortical structures, distorting and breaking up the vortex ring into several sections. The velocity and transverse vorticity in the cavitating regions are intensified due to vapor formation, while the streamwise vorticity is weakened. An analysis of the vorticity transport equation reveals the influence of cavitation on the relative importance of the vortex stretching, baroclinic torque, and dilatation terms. Statistical analysis shows that cavitation suppresses jet growth and decreases velocity fluctuations within the vaporous regions of the jet.

Copyright © 2005 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Computational domain showing boundary surfaces and inflow plane

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Figure 2

Instantaneous isosurface of Q-criterion magnitude at t*=22. The isolevel shown is 3.2. (a) σ=1.8, (b) σ=0.6, (c) σ=0.5.

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Figure 3

Instantaneous isosurface of Q-criterion magnitude at t*=26. The isolevel shown is 3.2. (a) σ=1.8, (b) σ=0.6, (c) σ=0.5.

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Figure 4

Void fraction and vorticity plots at t*=22. The isolevel shown is 3.2. (a) Contour plot showing void fraction (flood) and out-of-plane vorticity (σ=0.6). (b) Q-criterion isosurface colored by the contour of void fraction (σ=0.6). (c) Contour plot showing void fraction (flood) and out-of-plane vorticity (σ=0.5). (d) Q-criterion isosurface colored by the contour of void fraction (σ=0.5).

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Figure 5

Instantaneous minimum pressure within domain versus time. (a) σ=1.8, pυ=0.10, (b) σ=0.6, pυ=0.70, (c) σ=0.5, pυ=0.75

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Figure 6

Axial slices showing instantaneous contour plot of pressure at x*=2.0 and t*=22. (a) σ=1.8, (b) σ=0.6, (c) σ=0.5.

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Figure 7

Axial slices showing instantaneous contour plot of pressure at x*=4.0 and t*=22. (a) σ=1.8, (b) σ=0.6, (c) σ=0.5.

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Figure 8

Instantaneous velocity vector at stream cross-section x*=2.0 at t*=22. The vector was subtracted by the vector of σ=1.8. (a) σ=0.6, (b) σ=0.5.

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Figure 9

Instantaneous velocity vector at stream cross-section x*=4.0 at t*=22. The vector was subtracted by the vector of σ=1.8. (a) σ=0.6, (b) σ=0.5.

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Figure 10

Axial slices showing instantaneous contour plot of streamwise vorticity at x*=2.0 and t*=22. (a) σ=1.8, (b) σ=0.6, (c) σ=0.5.

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Figure 11

Axial slices showing instantaneous contour plot of streamwise vorticity at x*=4.0 and t*=22. (a) σ=1.8, (b) σ=0.6, (c) σ=0.5.

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Figure 12

Isosurface showing magnitude of vortex stretching term at t*=22. The isolevel shown is 3.7. (a) σ=1.8, (b) σ=0.6, (c) σ=0.5.

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Figure 13

Isosurface showing magnitude of the dilatation term in (a) and (b) and the baroclinic torque term in (c) and (d) at t*=22. The isolevel shown is 1.5 for the dilatation term and 0.005 for the baroclinic torque term. (a) σ=0.6, (b) σ=0.5, (c) σ=0.6, (d) σ=0.5.

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Figure 14

Momentum thickness versus axial distance

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Figure 15

Profiles of Reynolds stress component <u′u′>∕Uc2 at axial stations for all cases. Solid line is σ=1.8, long dashed line is σ=0.6 and short dashed line is σ=0.5. (a) x*=2.0, (b) x*=4.0, (c) x*=6.0.

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Figure 16

Profiles of Reynolds stress component <υ′υ′>∕Uc2 at axial stations for all cases. Solid line is σ=1.8, long dashed line is σ=0.6 and short dashed line is σ=0.5. (a) x*=2.0, (b) x*=4.0, (c) x*=6.0.

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Figure 17

Profiles of Reynolds stress component <u′υ′>∕Uc2 at axial stations for all cases. Solid line is σ=1.8, long dashed line is σ=0.6 and short dashed line is σ=0.5. (a) x*=2.0, (b) x*=4.0, (c) x*=6.0.

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