Research Papers: Multiphase Flows

Scaling of Gas Diffusion Into Limited Partial Cavities

[+] Author and Article Information
In-ho Lee

Department of Naval Architecture and
Marine Engineering,
University of Michigan,
1231 Beal Avenue,
2010 Walter E. Lay Automotive Laboratory,
Ann Arbor, MI 48109
e-mail: leeinho@umich.edu

Simo A. Mäkiharju

Department of Naval Architecture and
Marine Engineering,
University of Michigan,
1085 S. University Avenue,
126B West Hall,
Ann Arbor, MI 48109
e-mail: smakihar@umich.edu

Harish Ganesh

Department of Mechanical Engineering,
University of Michigan,
1231 Beal Avenue,
2010 Walter E. Lay Automotive Laboratory,
Ann Arbor, MI 48109
e-mail: gharish@umich.edu

Steven L. Ceccio

Department of Naval Architecture and
Marine Engineering,
University of Michigan,
2600 Draper Drive,
Naval Architecture and Marine
Engineering Building,
Ann Arbor, MI 48109
e-mail: ceccio@umich.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received November 17, 2014; final manuscript received October 15, 2015; published online January 4, 2016. Assoc. Editor: Olivier Coutier-Delgosha.

J. Fluids Eng 138(5), 051301 (Jan 04, 2016) (9 pages) Paper No: FE-14-1672; doi: 10.1115/1.4031850 History: Received November 17, 2014; Revised October 15, 2015

Bubbles populations in the wake of a partial cavity resulting from gas diffusion were measured to determine the noncondensable gas flux into the cavity. The diffusion rate is related to the dissolved gas content, the local cavity pressure, and the flow within and around the cavity. The measurements are used to revisit various scaling relationships for the gas diffusion, and it is found that traditional scaling that assumes the presence of a gas pocket overpredicts the gas diffusion. A new scaling based on diffusion into the low void fraction bubbly mixture within the partial cavity is proposed, and it is shown to adequately scale the observed production of gas bubbles for dissolved air saturation from 30% to 70% at 1 atm, limited cavities on the order of 0.3–3 cm in length at a freestream speed of 8 m/s (σ = 2.3–3.3 and Reynolds number based on the cavity length of order 105).

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Billet, M. L. , and Weir, D. S. , 1975, “ The Effect of Gas Diffusion on the Flow Coefficient for a Ventilated Cavity,” ASME J. Fluids Eng., 97(4), pp. 501–506. [CrossRef]
Brennen, C. E. , 1969, “ The Dynamic Balances of Dissolved Air and Heat in Natural Cavity Flow,” J. Fluid Mech., 37(1), pp. 115–127. [CrossRef]
Gadd, G. E. , and Grant, S. , 1965, “ Some Experiments on Cavities Behind Disks,” J. Fluid Mech., 23(4), pp. 645–656. [CrossRef]
Maeda, M. , Yamaguchi, H. , and Kato, H. , 1991, “ Laser Holography Measurement of Bubble Population in Cavitation Cloud on a Foil Section,” Cavitation ‘91 Symposium, FED-Vol. 116, pp. 67–75.
Parkin, B. R. , and Kermeen, R. W. , 1962, “ The Roles of Convective Air Diffusion and Liquid Tensile Stresses During Cavitation Inception,” I.A.H.R. Symposium on Cavitation and Hydraulic Machinery, Sendai, Japan, Sept. 3–8, pp. 21–24.
Yu, P.-W. , and Ceccio, S. L. , 1997, “ Diffusion Induced Bubble Populations Downstream of a Partial Cavity,” ASME J. Fluids Eng., 119(4), pp. 782–787. [CrossRef]
Parkin, B. R. , and Ravindra, K. , 1991, “ Convective Gaseous Diffusion in Steady Axisymmetric Cavity Flows,” ASME J. Fluids Eng., 113(2), pp. 285–289. [CrossRef]
Coutier-Delgosha, O. , Stutz, B. , Vabre, A. , and Legoupil, S. , 2007, “ Analysis of Cavitating Flow Structure by Experimental and Numerical Investigations,” J. Fluid Mech., 578, pp. 171–222. [CrossRef]
Stutz, B. , and Legoupil, S. , 2003, “ X-Ray Measurements Within Unsteady Cavitation,” Exp. Fluids, 35(2), pp. 130–138. [CrossRef]
Mäkiharju, S. A. , Chang, N. , Gabillet, C. , Paik, B.-G. , Perlin, M. , and Ceccio, S. L. , 2013, “ Time-Resolved Two-Dimensional X-Ray Densitometry of a Two-Phase Flow Downstream of a Ventilated Cavity,” Exp. Fluids, 54(7), pp. 1561–1582. [CrossRef]
Laberteaux, K. R. , and Ceccio, S. L. , 2001, “ Partial Cavity Flows. Part 1. Cavities Forming on Models Without Spanwise Variation,” J. Fluid Mech., 431, pp. 1–41. [CrossRef]
Epstein, P. S. , and Plesset, M. S. , 1950, “ On the Stability of Gas Bubbles in Liquid–Gas Solutions,” J. Chem. Phys., 18(11), pp. 1505–1508. [CrossRef]
Coutier-Delgosha, O. , Devillers, J.-F. , Pichon, T. , Vabre, A. , Woo, R. , and Legoupil, S. , 2013, “ Internal Structure and Dynamics of Sheet Cavitation,” Phys. Fluids, 18, pp. 1–12.


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Fig. 1

Schematic drawings of the partial cavity flows: (a) the classical depiction of the cavity as a vapor pocket with a free surface and (b) representation of the cavity as a bubbly mixture

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Fig. 2

Top and side schematic views of the wedge in the test section of the water channel. All dimensions are in millimeters. An “X” indicates locations of the pressure taps used to measure the freestream pressure, P, and average flow velocity, U. The fields of view for visualizing the bubbly wake behind the cavity are also shown.

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Fig. 3

A detailed view of the fields of view used to determine the void fraction profiles in the wake of the wedge. All dimensions are in millimeters.

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Fig. 4

Profiles of void fraction (a) and gas-phase velocity (b) are plotted with error bars and fitted curve. (a) Three cases are plotted: DO 30%/σ = 2.4, DO 50%/σ = 2.3, and DO 70%/σ = 2.7. Lognormal fitting is used. (b) The average velocity on each location from all cases is used.

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Fig. 5

The measured bubble size distributions for the case of injected air at the wedge apex for injected gas flux of (a) 2.5 × 10−3 g/s and (b) 6.4 × 10−3 g/s. Data were collected from 6500 independent frames for each case, at σ = 3.4.

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Fig. 6

Both images are cavitating wedge with LC=2 cm and σ = 2.5: (a) the top and side photographic images and (b) the void fraction field for the cavitating flow with an inset showing a close-up of void fraction near the apex. Inner contour is void fraction 15% and outer contour is void fraction 5%.

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Fig. 7

The average cavity length, LC (a), volume, VC (b), and void fraction αC (c) as a function of cavitation number, σ. The curve fits are also shown that were used to compute values for scaling. (a) Uncertainty of average cavity length is ±0.03 cm.

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Fig. 8

The measured bubble populations in the cavity wake for DO contents of 30% σ = 2.3 (a), 50% σ = 2.3 (b), and 70% σ = 2.3 (c). Data were collected from 6500 images.

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Fig. 9

The measured net gas flux, m˙B, produced as a result of diffusion into the partial cavity as a function of cavitation number, σ. The uncertainty shown in m˙B spans between two times and 0.5 times the values measured. Results for three DO contents are shown.




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