Abstract
In order to calculate resonating gas bubbles, the mathematical model was supplemented by taking into account phase-transition processes on the surface of a bubble in gas-vapor media, as well as the thermal effects at gas dissolution in fluid. A series of calculations of the resonance mode for bubbles of dimensions of 0.5‒3 mm in water at temperatures from +1 to +99 °C and atmospheric pressure was performed. As a result of mathematical modeling, the possibility of resonance in gas-vapor bubbles in water in the frequency range of 0.5–5 kHz was established. It was shown that in the resonance mode the amplitude of oscillations of the wall of a bubble first increases rapidly and then is stabilized at the level of 30‒50 % of the radius. It was established that motion velocity of the walls of a bubble under resonance conditions can exceed 6 m/s. It was shown that in the compression mode internal pressure of a bubble can increase by three times or decrease by two times compared with ambient pressure. Dependence of approximation resonance frequency of air bubbles in water on their diameter was established. It was found that in the resonance mode, temperature of gas-vapor medium of a bubble periodically decreases by 6 °C and increases by 12 °C in comparison with the original one. In this case, the temperature of the surface of a bubble decreases by 1 °C and increases by 7 °C. It was shown that favorable conditions for water vapor condensation (fog formation) are created at the stage of the growth of a bubble. The schematic of the research setup and the results of field observations of gas-vapor bubbles under condition of the influence of sound waves was presented. The existence of resonance of bubbles at calculation frequencies was proved and formation of bubbles was established experimentally. The phenomena of a bubble division and its explosion were illustrated. It was found that addition of surface active substances extends the frequency range of formation of multi-bubbles by five times and contributes to an increase in the number of small bubbles inside a large one. The research results can be applied to intensification of various technological processes related to heat and mass exchange in gas-vapor systems.
Highlights
– a gas bubble is of spherical shape; – a fluid is viscous and non-compressed; – inside a gas bubble, there is a mixture of gases, the weight of which may vary as a result of mass exchange processes both on the boundary of a bubble, and in its volume; – gases inside a bubble are considered as actual gas
The aim of present research is to study the influence of sound oscillations of resonance frequency of thermodynamic processes that occur in a gas-vapor medium of an oscillating bubble
The obtained results are caused by taking into account heat and mass exchange that occur on the surface and inside an oscillating gas-vapor bubble
Summary
Thermodynamic processes that occur on the surface of gas-vapor bubbles, such as absorption [1], aeration [2], bubbling [3], and vacuum distillation [4], are at the heart of many advanced industrial technologies. In the work by V.R. Kulinchen [15], mathematical problem statement takes into account phase transition and heat exchange near the surface of an oscillating bubble. Kulinchen [15], mathematical problem statement takes into account phase transition and heat exchange near the surface of an oscillating bubble This model is designed for the bubbles that are formed as a result of cavitation and inside of which there is greatly rarified gas. – a gas bubble is of spherical shape; – a fluid is viscous and non-compressed; – inside a gas bubble, there is a mixture of gases (air and water vapor), the weight of which may vary as a result of mass exchange processes both on the boundary of a bubble, and in its volume; – gases inside a bubble are considered as actual gas (taking into account the van der Waals forces). Let us consider the equations describing thermodynamic characteristics of a gas-vapor bubble during transition to a new state of thermodynamic equilibrium [17]: dR dτ
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