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Analytical Investigation of Hydrodynamic Cavitation Control by Ultrasonics

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Abstract

In recent experimental work, Chatterjee and Arakeri have demonstrated that an imposed acoustic field of sufficiently high strength and frequency can suppress or control cavitation. In this paper, we analytically study the equation governing the dynamics of a single bubble in a time-varying pressure field, for parameter ranges representative of those experimental conditions. The governing equation is strongly nonlinear and intractable in general; however, for the parameter ranges of interest, we are able to nondimensionalize and scale the governing equation into a form that, though still strongly nonlinear, is amenable to analysis using the method of multiple scales (MMS) based on an arbitrarily chosen “small” parameter ∊. Removal of secular terms, a key step in the MMS, raises an interesting issue which we discuss. Second order MMS gives the slow average evolution of the bubble radius. Numerical solutions of the original equation match the MMS approximation well on time scales of \(\cal O\)(1/∊). The MMS approximation also provides insight into the roles played by relevant physical parameters in the system. Our results provide theoretical support for the abovementioned experimental results.

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Authors and Affiliations

  1. Mechanical Engineering, Indian Institute of Science, Bangalore, India

    Anindya Chatterjee

  2. Mechanical Engineering, Indian Institute of Technology, (Madras), Chennai, India

    Dhiman Chatterjee

Authors
  1. Anindya Chatterjee
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  2. Dhiman Chatterjee
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Correspondence to Anindya Chatterjee.

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Chatterjee, A., Chatterjee, D. Analytical Investigation of Hydrodynamic Cavitation Control by Ultrasonics. Nonlinear Dyn 46, 179–194 (2006). https://doi.org/10.1007/s11071-006-9022-3

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  • DOI: https://doi.org/10.1007/s11071-006-9022-3

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