Study of the Dynamics of a Single Bubble
Abstract
:1. Introduction
- -
- approximate analytical solutions. This approach involves simplifying assumptions, often with questionable physical justifications, to derive approximate analytical estimates.
- -
- numerical solutions. This approach involves the numerical solution of the original equations. The advancement of computer technology in recent years has undoubtedly contributed to a more detailed study of steam bubble dynamics, as it enables the numerical solution of even highly complex systems of equations with high accuracy in a relatively short time [68,69,70].
2. Factors Affecting the Behaviour of Cavitation Bubbles
2.1. Bubble Surface Motion and Rayleigh Equation
2.2. Pressure and Density in the Bubble
2.3. Heat and Mass Transfer across a Phase Interface
2.4. Heat Transfer in the Liquid Phase
2.5. Impact of External Pressure Changes on Bubble Dynamics
3. Discussion
- Thermophysical property-based approach. This method emphasises the temperature-dependent thermophysical properties of the bubble and surrounding liquid. The energy equation is employed to capture the temperature distribution and its influence on bubble behaviour. This approach provides a detailed representation of heat transfer and temperature effects within the bubble.
- Vapour pressure and temperature approach. In this approach, the focus is on determining the vapour pressure and corresponding temperature within the bubble. The energy equation is not explicitly used, simplifying the model’s equations but potentially affecting the accuracy of numerical predictions. This approach offers computational efficiency, but may compromise the accuracy of heat transfer simulations.
- Rayleigh equation approach. This method utilises the Rayleigh equation to calculate the current bubble radius based on the velocity of the phase boundary interface. It is primarily applied to the inertial stage of bubble dynamics, where inertia and pressure forces dominate the bubble’s motion. This approach is well-suited to capturing the initial growth and collapse of bubbles.
- Modified Rayleigh–Plesset equation approach. This approach employs a modified form of the Rayleigh–Plesset equation to determine the bubble radius during the dynamic stage of bubble dynamics. It accounts for the influence of heat and mass transfer on bubble behaviour. This approach provides a more comprehensive representation of bubble dynamics, including heat and mass transfer effects during the collapse and rebound stages.
- Bubble cluster dynamics approach. This method focusses on modelling the dynamics of bubble clusters, considering the interactions and collective behaviour of multiple bubbles within a cluster. The aim of this is to capture the influence of neighbouring bubbles on the overall dynamics of the cluster. This approach is particularly relevant for applications involving cavitation, where bubble clusters play a significant role.
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
Nomenclature
R | radius |
τ | time |
c | specific heat |
λ | surface tension |
j | mass flow |
L | latent heat of vaporisation (condensation) |
m | mass |
p | pressure |
q | specific heat flux |
r | radial coordinate |
T | temperature |
wr | radial velocity |
ρ | density |
σ | interfacial tension coefficient |
Indexes | |
l | liquid |
0 | initial value |
b | boiling |
c | continuous phase |
R | value of the parameter at the boundary with the bubble |
sat | parameter value in saturation condition |
s | vapour |
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Types of Models | The Modelling Approach Used | Publications |
---|---|---|
Modelling bubbles with separate schemes | These models employ distinct equations for the inertial and thermal stages of bubble growth | [39,40,41,42,43] |
Models using equations of state | These models incorporate equations of state to describe the relationship between fluid properties and thermodynamic parameters | [44,45,46,47,48] |
Modelling the thermodynamic state of liquid–vapour phase interfaces | These models focus on the thermodynamic behaviour of the phase boundaries between the liquid and vapour phases | [49,50] |
Models with transport equations | These models utilise transport equations to account for heat and mass transfer processes during bubble dynamics | [30,31,51] |
Bubble dynamics models based on the Rayleigh–Plesset equation | These models employ the Rayleigh-Plesset equation to describe the radial motion of bubbles | [52,53,54,55] |
Machine learning models | These models leverage machine learning techniques to predict bubble dynamics based on experimental data or simulations | [35,36] |
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Pavlenko, A.; Koshlak, H. Study of the Dynamics of a Single Bubble. Energies 2024, 17, 4236. https://doi.org/10.3390/en17174236
Pavlenko A, Koshlak H. Study of the Dynamics of a Single Bubble. Energies. 2024; 17(17):4236. https://doi.org/10.3390/en17174236
Chicago/Turabian StylePavlenko, Anatoliy, and Hanna Koshlak. 2024. "Study of the Dynamics of a Single Bubble" Energies 17, no. 17: 4236. https://doi.org/10.3390/en17174236
APA StylePavlenko, A., & Koshlak, H. (2024). Study of the Dynamics of a Single Bubble. Energies, 17(17), 4236. https://doi.org/10.3390/en17174236