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TECHNICAL PAPERS

Steady-State Cavitating Nozzle Flows With Nucleation

[+] Author and Article Information
Can F. Delale

Faculty of Aeronautics and Astronautics,  Istanbul Technical University, 34469 Maslak, Istanbul, and Tübitak Feza Gürsey Institute, P.O. Box 6, 81220 Çengelköy, Istanbul, Turkeydelale@gursey.gov.tr

Kohei Okita

Department of Mechanical Engineering,  The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, Japanokita@fel.t.u-tokyo.ac.jp

Yoichiro Matsumoto

Department of Mechanical Engineering,  The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, Japanmats@mech.t.u-tokyo.ac.jp

J. Fluids Eng 127(4), 770-777 (Apr 02, 2005) (8 pages) doi:10.1115/1.1949643 History: Received May 11, 2004; Revised April 02, 2005

Quasi-one-dimensional steady-state cavitating nozzle flows with homogeneous bubble nucleation and nonlinear bubble dynamics are considered using a continuum bubbly liquid flow model. The onset of cavitation is modeled using an improved version of the classical theory of homogeneous nucleation, and the nonlinear dynamics of cavitating bubbles is described by the classical Rayleigh-Plesset equation. Using a polytropic law for the partial gas pressure within the bubble and accounting for the classical damping mechanisms, in a crude manner, by an effective viscosity, stable steady-state solutions with stationary shock waves as well as unstable flashing flow solutions were obtained, similar to the homogeneous bubbly flow solutions given by Wang and Brennen [J. Fluids Eng., 120, 166–170, 1998] and by Delale, Schnerr, and Sauer [J. Fluid Mech., 427, 167–204, 2001]. In particular, reductions in the maximum bubble radius and bubble collapse periods are observed for stable nucleating nozzle flows as compared to the nonnucleating stable solution of Wang and Brennen under similar conditions.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Geometric configuration of the nozzle employed by Wang and Brennen (1) (in our normalization L=5)

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Figure 2

Distributions of the flow speed u along the axis of the nozzle in Fig. 1 under the flow conditions with flow speed Ui′=10m∕s, inlet cavitation number σi=0.8, and nucleation rate parameters α=0.4999999927 and δ=0.5 for the values of the critical bubble radius Ri′=14.0, 14.2, and 20.0μm at the onset of cavitation in nucleating bubbly flows of the present investigation and for the values of the void fractions βi=2.5×10−6 and βi=3.1×10−6 in the nonnucleating bubbly flow of Wang and Brennen (1) (stable nucleating and nonnucleating cavitating flow solutions with a downstream ringing structure are shown, respectively, for Ri′=14.0μm and for βi=2.5×10−6)

Grahic Jump Location
Figure 3

Distributions of the pressure coefficient Cp along the axis of the nozzle in Fig. 1 under the flow conditions and nucleation rate parameters stated in Fig. 2 for the values of the critical bubble radius Ri′=14.0, 14.2, and 20.0μm at the onset of cavitation in nucleating bubbly flows of the present investigation and for the values of the void fractions βi=2.5×10−6 and βi=3.1×10−6 in the nonnucleating bubbly flow of Wang and Brennen (1) (stable nucleating and nonnucleating cavitating flow solutions with a downstream ringing structure are shown, respectively, for Ri′=14.0μm and for βi=2.5×10−6)

Grahic Jump Location
Figure 4

Distributions of the normalized radius R along the axis of the nozzle in Fig. 1 under the flow conditions and nucleation rate parameters stated in Fig. 2 for the values of the critical bubble radius Ri′=14.0, 14.2, and 20.0μm at the onset of cavitation in nucleating bubbly flows of the present investigation and for the values of the void fractions βi=2.5×10−6 and βi=3.1×10−6 in the nonnucleating bubbly flow of Wang and Brennen (1) (stable nucleating and nonnucleating cavitating flow solutions with a downstream ringing structure are shown, respectively, for Ri′=14.0μm and for βi=2.5×10−6)

Grahic Jump Location
Figure 5

Distributions of the void fraction β along the axis of the nozzle in Fig. 1 under the flow conditions and nucleation rate parameters stated in Fig. 2 for the values of the critical bubble radius Ri′=14.0, 14.2, and 20.0μm at the onset of cavitation in nucleating bubbly flows of the present investigation and for the values of the void fractions βi=2.5×10−6 and βi=3.1×10−6 in the nonnucleating bubbly flow of Wang and Brennen (1) (stable nucleating and nonnucleating cavitating flow solutions with a downstream ringing structure are shown, respectively, for Ri′=14.0μm and for βi=2.5×10−6)

Grahic Jump Location
Figure 6

Distributions of the nucleation rate J′ along the axis of the nozzle in Fig. 1 under the flow conditions and nucleation rate parameters stated in Fig. 2 for the values of the critical bubble radius Ri′=14.0, 14.2, and 20.0μm at the onset of cavitation in nucleating bubbly flows of the present investigation (a stable cavitating flow solution is shown for Ri′=14.0μm)

Grahic Jump Location
Figure 7

Distributions of the flow speed u along the axis of the nozzle in Fig. 1 under the flow conditions with flow speed Ui′=10m∕s, inlet cavitation number σi=0.8, and nucleation rate parameters α=0.4999999930 and δ=1.0 for the values of the critical bubble radius Ri′=9.0, 9.1, and 14.0μm at the onset of cavitation in nucleating bubbly flows of the present investigation (a stable cavitating flow solution with a stationary bubbly shock wave is shown for Ri′=9.0μm)

Grahic Jump Location
Figure 8

Distributions of the pressure coefficient Cp along the axis of the nozzle in Fig. 1 under the flow conditions and nucleation rate parameters stated in Fig. 7 for the values of the critical bubble radius Ri′=9.0, 9.1, and 14.0μm at the onset of cavitation in nucleating bubbly flows of the present investigation (a stable cavitating flow solution with a stationary bubbly shock wave is shown for Ri′=9.0μm)

Grahic Jump Location
Figure 9

Distributions of the normalized radius R along the axis of the nozzle in Fig. 1 under the flow conditions and nucleation rate parameters stated in Fig. 7 for the values of the critical bubble radius Ri′=9.0, 9.1, and 14.0μm at the onset of cavitation in nucleating bubbly flows of the present investigation (a stable cavitating flow solution with a stationary bubbly shock wave is shown for Ri′=9.0μm)

Grahic Jump Location
Figure 10

Distributions of the void fraction β along the axis of the nozzle in Fig. 1 under the flow conditions and nucleation rate parameters stated in Fig. 7 for the values of the critical bubble radius Ri′=9.0, 9.1, and 14.0μm at the onset of cavitation in nucleating bubbly flows of the present investigation (a stable cavitating flow solution with a stationary bubbly shock wave is shown for Ri′=9.0μm)

Grahic Jump Location
Figure 11

Distributions of the nucleation rate J′ along the axis of the nozzle in Fig. 1 under the flow conditions and nucleation rate parameters stated in Fig. 7 for the values of the critical bubble radius Ri′=9.0, 9.1, and 14.0μm at the onset of cavitation in nucleating bubbly flows of the present investigation (a stable cavitating flow solution with a stationary bubbly shock wave is shown for Ri′=9.0μm)

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