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Research Papers: Multiphase Flows

An Assessment of Computational Fluid Dynamics Cavitation Models Using Bubble Growth Theory and Bubble Transport Modeling

[+] Author and Article Information
Michael P. Kinzel

Applied Research Laboratory,
The Pennsylvania State University,
University Park, PA 16802
e-mail: mpk176@psu.edu

Jules W. Lindau

Applied Research Laboratory,
The Pennsylvania State University,
University Park, PA 16802
e-mail: jwl10@psu.edu

Robert F. Kunz

Professor
Department of Mechanical Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: rfk102@psu.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 1, 2018; final manuscript received December 21, 2018; published online February 8, 2019. Assoc. Editor: Olivier Coutier-Delgosha.

J. Fluids Eng 141(4), 041301 (Feb 08, 2019) (9 pages) Paper No: FE-18-1140; doi: 10.1115/1.4042421 History: Received March 01, 2018; Revised December 21, 2018

This effort investigates advancing cavitation modeling relevant to computational fluid dynamics (CFD) through two strategies. The first aims to reformulate the cavitation models and the second explores adding liquid–vapor slippage effects. The first aspect of the paper revisits cavitation model formulations with respect to the Rayleigh–Plesset equation (RPE). The present approach reformulates the cavitation model using analytic solutions to the RPE. The benefit of this reformulation is displayed by maintaining model sensitivities similar to RPE, whereas the standard models fail these tests. In addition, the model approach is extended beyond standard homogeneous models, to a two-fluid modeling framework that explicitly models the slippage between cavitation bubbles and the liquid. The results indicate a significant impact of slip on the predicted cavitation solution, suggesting that the inclusion of such modeling can potentially improve CFD cavitation models. Overall, the results of this effort point to various aspects that may be considered in future CFD-modeling efforts with the goal of improving the model accuracy and reducing computational time.

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References

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Figures

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Fig. 1

Computational mesh used in the CFD studies throughout this effort. The left figure plots the full CFD domain and the right figure plots a blowup near the hydrofoil.

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Fig. 2

Comparison of the predictions from the RPE, Singhal, Kunz, and reformulated models for the growth and collapse of an isolated bubble exposed to pressure in part (b). This plot indicates that the cavitation models can replicate the RPE. (a) Case 1: R0 = 20 μm, plow = 0.1pv and (b) general pressure profile.

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Fig. 3

Comparison of the predictions from the RPE (black-dashed line), Singhal (upper plot), Kunz (center), and reformulated (lower) models for the growth and collapse of an isolated bubble exposed to a pressure similar to the profile in Fig. 2(b). This plot highlights the sensitivity of model results to the cavitation constants for case 1. The dotted lines indicate the results when changing the cavitation constants by ±20%.

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Fig. 4

Comparison of the predictions from the RPE, Singhal, Kunz, and Reformulated models for the growth and collapse of an isolated bubble exposed to a pressure similar to the profile in Fig. 2(b). This plot indicates the impact of nuclei size (case 2, R0=40 μm, plow=0.1pv).

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Fig. 5

Comparison of the predictions from the RPE, Singhal, and Kunz models for the growth and collapse of an isolated bubble exposed to a pressure similar to the profile in Fig. 2(b). This plot indicates the impact of the minimum pressure (case 3, R0=20 μm, plow=0.9pv).

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Fig. 6

Comparison of the predictions from the RPE, Singhal, and Kunz models for the growth and collapse of an isolated bubble exposed to a pressure similar to the profile in Fig. 2(b). This plot indicates the impact of nuclei exposed to a minimum pressure above vapor pressure (case 4, R0=20 μm, plow=2.0pv).

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Fig. 7

Quantified comparisons of the predictions from the RPE, Singhal, and Kunz models for maximum bubble radius based on the results from Figs. 46. Note that the characteristics of the bubble are altered for each plot and the Singhal- and Kunz-model constants are tuned for case 1.

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Fig. 8

Comparison of (a) homogeneous and (b) two-fluid cavitation predictions for a NACA 0012, α=10 deg, Rec=5×106, σv=2.4. For (a) and (b), the contour lines plotted are pressure coefficient (Cp) and filled contours are the gas volume fraction (αv) at three corresponding timesteps. In part (c) are normalized slip velocity for the two-fluid model, at a given time-step.

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Fig. 9

Evaluation of the bubble-liquid slippage. Results indicate an increase in bubble size and Re, hence, drag coefficient drops. The trajectories of the bubbles (black streamlines) as compared to the liquid (white streamlines) indicates slippage is strongest in high curvature regions near the aft end of the cavity.

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Fig. 10

Comparison of the homogeneous model formulations (left column) to the two-fluid models that account for bubble slippage (right column). This process is evaluated for both the Singhal model (top row) and the reformulated cavitation model (bottom row).

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