Acoustic cavitation model based on a novel reduced order gas pressure law

The thermal behavior of a spherical gas bubble in a liquid excited by an acoustic pressure signal is investigated by constructing an iterative solution of the energy balance equations between the gas bubble and the surrounding liquid in the uniform pressure approximation. This iterative solution lea...

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Autores principales:	Can F. Delale, Şenay Pasinlioğlu
Formato:	article
Lenguaje:	EN
Publicado:	AIP Publishing LLC 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/a58a0aaa704245a58fa3294234ce8a40
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spelling	oai:doaj.org-article:a58a0aaa704245a58fa3294234ce8a402021-12-01T18:52:06ZAcoustic cavitation model based on a novel reduced order gas pressure law2158-322610.1063/5.0068152https://doaj.org/article/a58a0aaa704245a58fa3294234ce8a402021-11-01T00:00:00Zhttp://dx.doi.org/10.1063/5.0068152https://doaj.org/toc/2158-3226The thermal behavior of a spherical gas bubble in a liquid excited by an acoustic pressure signal is investigated by constructing an iterative solution of the energy balance equations between the gas bubble and the surrounding liquid in the uniform pressure approximation. This iterative solution leads to hierarchy equations for the radial partial derivatives of the temperature at the bubble wall, which control the temporal rate of change of the gas pressure and gas temperature within the bubble. In particular, a closure relation for the hierarchy equations is introduced based on the ansatz that approximates the rapid change of state during the collapse of the bubble from almost isothermal to almost adiabatic behavior by time averaging the complex dynamics of change of state over a relatively short characteristic time. This, in turn, leads to the desired reduced order gas pressure law exhibiting power law dependence on the bubble wall temperature and on the bubble radius, with the polytropic index depending on the isentropic exponent of the gas and on a parameter that is a function of the Péclet number and a characteristic time scale. Results of the linear theory for gas bubbles are recovered by identifying this parameter as a function of the Péclet number based on the Minnaert frequency. The novel gas pressure law is then validated against the near-isothermal solution and against the results of the numerical simulations of the original energy balance equations for large amplitude oscillations using spectral methods. Consequently, an acoustic cavitation model that accounts for phase change but that neglects mass diffusion is constructed by employing the reduced order gas pressure law together with the Plesset–Zwick solution for the bubble wall temperature and the Keller–Miksis equation for spherical bubble dynamics. Results obtained using variable interface properties for acoustically driven cavitation bubbles in water show that the time variations of the bubble radius and the bubble wall temperature lie between those obtained by the isothermal and adiabatic laws depending on the value of the Péclet number and the characteristic time scale.Can F. DelaleŞenay PasinlioğluAIP Publishing LLCarticlePhysicsQC1-999ENAIP Advances, Vol 11, Iss 11, Pp 115309-115309-23 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Can F. Delale Şenay Pasinlioğlu Acoustic cavitation model based on a novel reduced order gas pressure law
description	The thermal behavior of a spherical gas bubble in a liquid excited by an acoustic pressure signal is investigated by constructing an iterative solution of the energy balance equations between the gas bubble and the surrounding liquid in the uniform pressure approximation. This iterative solution leads to hierarchy equations for the radial partial derivatives of the temperature at the bubble wall, which control the temporal rate of change of the gas pressure and gas temperature within the bubble. In particular, a closure relation for the hierarchy equations is introduced based on the ansatz that approximates the rapid change of state during the collapse of the bubble from almost isothermal to almost adiabatic behavior by time averaging the complex dynamics of change of state over a relatively short characteristic time. This, in turn, leads to the desired reduced order gas pressure law exhibiting power law dependence on the bubble wall temperature and on the bubble radius, with the polytropic index depending on the isentropic exponent of the gas and on a parameter that is a function of the Péclet number and a characteristic time scale. Results of the linear theory for gas bubbles are recovered by identifying this parameter as a function of the Péclet number based on the Minnaert frequency. The novel gas pressure law is then validated against the near-isothermal solution and against the results of the numerical simulations of the original energy balance equations for large amplitude oscillations using spectral methods. Consequently, an acoustic cavitation model that accounts for phase change but that neglects mass diffusion is constructed by employing the reduced order gas pressure law together with the Plesset–Zwick solution for the bubble wall temperature and the Keller–Miksis equation for spherical bubble dynamics. Results obtained using variable interface properties for acoustically driven cavitation bubbles in water show that the time variations of the bubble radius and the bubble wall temperature lie between those obtained by the isothermal and adiabatic laws depending on the value of the Péclet number and the characteristic time scale.
format	article
author	Can F. Delale Şenay Pasinlioğlu
author_facet	Can F. Delale Şenay Pasinlioğlu
author_sort	Can F. Delale
title	Acoustic cavitation model based on a novel reduced order gas pressure law
title_short	Acoustic cavitation model based on a novel reduced order gas pressure law
title_full	Acoustic cavitation model based on a novel reduced order gas pressure law
title_fullStr	Acoustic cavitation model based on a novel reduced order gas pressure law
title_full_unstemmed	Acoustic cavitation model based on a novel reduced order gas pressure law
title_sort	acoustic cavitation model based on a novel reduced order gas pressure law
publisher	AIP Publishing LLC
publishDate	2021
url	https://doaj.org/article/a58a0aaa704245a58fa3294234ce8a40
work_keys_str_mv	AT canfdelale acousticcavitationmodelbasedonanovelreducedordergaspressurelaw AT senaypasinlioglu acousticcavitationmodelbasedonanovelreducedordergaspressurelaw
_version_	1718404710058164224

Acoustic cavitation model based on a novel reduced order gas pressure law

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