Abstract:The standard approach to the analysis of the pulsations of a driven gas bubble is to assume that the pressure within the bubble follows a polytropic relation of the form p=p0(R0/R)3κ, where p is the pressure within the bubble, R is the radius, κ is the polytropic exponent, and the subscript zero indicates equilibrium values. For nonlinear oscillations of the gas bubble, however, this approximation has several limitations and needs to be reconsidered. A new formulation of the dynamics of bubble oscillations is … Show more
“…Therefore, we incorporate the nonlinear model based on solving the continuity and the energy conservation equations for a gas (as in Ref. [30]) into the formulation.…”
Section: Theorymentioning
confidence: 99%
“…The explicit expressions for the damping coefficient ܾ ୲୭୲ and the bubble resonance frequency ߱ can be found in [28,30].…”
Please cite this article as: H. Dogan, V. Popov, Numerical simulation of the nonlinear ultrasonic pressure wave propagation in a cavitating bubbly liquid inside a sonochemical reactor, Ultrasonics Sonochemistry (2015), doi: http://dx
“…Therefore, we incorporate the nonlinear model based on solving the continuity and the energy conservation equations for a gas (as in Ref. [30]) into the formulation.…”
Section: Theorymentioning
confidence: 99%
“…The explicit expressions for the damping coefficient ܾ ୲୭୲ and the bubble resonance frequency ߱ can be found in [28,30].…”
Please cite this article as: H. Dogan, V. Popov, Numerical simulation of the nonlinear ultrasonic pressure wave propagation in a cavitating bubbly liquid inside a sonochemical reactor, Ultrasonics Sonochemistry (2015), doi: http://dx
“…The following assumptions are made in the remainder of this paper: ͑i͒ The internal bubble pressure is spatially uniform, 1,11 ͑ii͒ the liquid temperature is uniform, 12 ͑iii͒ there is no diffusion of noncondensable gas in the liquid, 12 and ͑iv͒ the vapor pressure is in equilibrium at the gas-liquid interface. 12 Each of these additional assumptions has been validated for all the cases considered by comparisons with the full computations of the preceding section.…”
Section: B Additional Assumptionsmentioning
confidence: 99%
“…[1][2][3][4] The alternative is to solve the full set of coupled radial transport equations for each bubble, but this is too computationally intensive to implement in continuum models of complex bubbly flows. Consequently, reduced-order models that accurately capture diffusive effects are needed.…”
We propose a new reduced-order model for spherical bubble dynamics that accurately captures the effects of heat and mass diffusion. The objective is to reduce the full system of partial differential equations to a set of coupled ordinary differential equations that are efficient enough to implement into complex bubbly flow computations. Comparisons to computations of the full partial differential equations and of other reduced-order models are used to validate the model and establish its range of validity.
“…So even a small amount of noncondensable gas is of great importance! Sorne non-essential simplifications are made: spherical symmetric bubbles ; condensation only occurs at the surface of a bubble ; pressure is uniform within each bubble (PROSPERETTI [2]); damping is assumed to be caused mainly by thermal conduction and radiation of sound. If the radius of the bubbles is not too smaIl and aIl velocities are small compared to the velocity of sound in the vapour, surface tension, viscosity and compressibility can be neglected.…”
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