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On pressure and temperature waves within a cavitation bubble

Pelz, Peter F. ; Ferbert, Andreas (2022):
On pressure and temperature waves within a cavitation bubble. (Publisher's Version)
1, In: Proceedings of the 7th International Symposium on Cavitation 2009 ; Vol. 1, pp. 112-120,
Darmstadt, University of Michigan, International Symposium on Cavitation 2009, Ann Arbor, 16.-20.08.2009, ISBN 978-1-61782-642-9,
DOI: 10.26083/tuprints-00020825,
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Item Type: Conference or Workshop Item
Origin: Secondary publication service
Status: Publisher's Version
Title: On pressure and temperature waves within a cavitation bubble
Language: English

The presented work is about the detailed pressure, temperature and velocity distribution within a plane, cylindrical and spherical cavitation bubble. The review of Plesset & Prosperetti (1977) and more recently the review of Feng & Leal (1997) describe the time behavior of the gas within a spherical bubble due to forced harmonic oscillations of the bubble wall. We reconsider and extend those previous works by developing from the conversation laws and the ideal gas law a boundary value problem for the distribution of temperature and velocity amplitude within the bubble. This is done for a plane, cylindrical, or spherical bubble. The consequences due to shape differences are discussed. The results show that an oscillating temperature boundary layer is formed in which the heat conduction takes places. With increasing dimensionless frequency, i.e. Péclet number, the boundary-layer thickness decreases and compression modulus approaches its adiabatic value. This adiabatic behaviour is reached at lower frequencies for the plane geometry in comparison with cylindrical and spherical geometry. This is due to the difference in the volume specific surface, which is 1, 2, 3 times the inverse bubble height/radius r₀ for the plane, cylindrical and spherical bubble respectively. For the plane bubble the analysis ends up in an eigenvalue problem with four eigenvalues and modes. The analytical result is not distinguishable from the numerical result for the plane case gained by a finite element solution. Interestingly if the diffusion time for the temperature distribution is of the order of the traveling time of a pressure wave no adiabatic behavior is observed. A parameter map for the different regimes is given. The influence on the bubble natural frequency for the cylindrical and spherical case is discussed in the usual way of a perturbation analysis of the equation of motion for the bubble radius

Book Title: Proceedings of the 7th International Symposium on Cavitation 2009 ; Vol. 1
Series Volume: 1
Place of Publication: Darmstadt
Publisher: University of Michigan
Classification DDC: 600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften
Divisions: 16 Department of Mechanical Engineering > Institute for Fluid Systems (FST)
Event Title: International Symposium on Cavitation 2009
Event Location: Ann Arbor
Event Dates: 16.-20.08.2009
Date Deposited: 29 Apr 2022 12:27
Last Modified: 29 Apr 2022 12:27
DOI: 10.26083/tuprints-00020825
URN: urn:nbn:de:tuda-tuprints-208257
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/20825
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