Concentration Evolution of Gas

Species Within a Collapsing Bubble

Wonyong Jang and Mustafa M. Aral

Multimedia Environmental Simulations Laboratory

School of Civil and Environmental Engineering

Georgia Institute of Technology

Atlanta, GA 30332

 

 

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Abstract

In this study numerical methods are used to investigate the relationship between chemical concentration of gas species within a cavitating bubble, equilibrium radius of the gas bubble and pressure variations in the ambient liquid. For this purpose, governing equations are developed to describe the dynamic equilibrium of a bubble in a flowing fluid and mass transfer between gas and liquid phases, where it was assumed that gases undergo isothermal compression, obey the ideal gas law, Henry law. It is further assumed that the concentration of each phase within the bubble is uniform. The resulting nonlinear equations are solved using implicit Trapezoidal method with Newton iteration. Four gas species are modeled under various initial and ambient pressure variation conditions. These conditions maybe considered to represent typical cavitation events. The numerical results obtained are presented in terms of dimensionless numbers. These results indicate that chemical damage maybe an important component of cavitation surface damage, since high concentration profiles may develop within a collapsing bubble.  Proposed formulation and numerical solutions are simple and cost effective to implement. The results presented in this study maybe used to benchmark experimental investigations or other more complex solutions, which are outside the scope of this study.

Published in Environmental Fluid Mechanics Journal (2003)

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Table of Contents

Concentration Evolution of Gas Species Within a Collapsing Bubble

Abstract

Assumptions

Assumptions (continued)

Assumptions (continued)

Governing Equations

Governing Equations (continued)

Governing Equations (continued)

Governing Equations (continued)

Governing Equations (continued)

Governing Equations (continued)

Table 1. Physical Properties of Four Gasses

Figure 1a.

Figure 1b.

Figure 2a.

Figure 2b.

Figure 3a.

Figure 3b.

Figure 4a.

Figure 4b.

Figure 5a.

Figure 5b.

Figure 6a.

Figure 6b.

Figure 7a.

Figure 7b.

Conclusions

Conclusions (continued)

Conclusions (continued)

 

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