A comprehensive numerical analysis of heat and mass transfer phenomenons during cavitation sono-process

Abstract

The present study treats the effects of mass transport, heat transfer and chemical reactions heat on the bubble dynamics by spanning a range of ambient bubble radii. The thermodynamic behavior of the acoustic bubble was shown for three wave frequencies, 355, 515 and 1000 kHz. The used acoustic amplitude ranges from 1 to 3 atm. It has been demonstrated that the ambient bubble radius, R 0 , of the maximal response ( i.e., maximal bubble temperature and pressure, T max and P max ) is shifted toward lower values if the acoustic amplitude (at fixed frequency) or the ultrasonic frequency (at fixed amplitude) are increased. The range of the ambient bubble radius narrows as the ultrasonic frequency increases. Heat exchange at the bubble interface was found to be the most important mechanism within the bubble internal energy balance for acoustic amplitudes lower than 2.5 and 3 atm for ultrasonic frequencies of 355 and 515 kHz, respectively. For acoustic amplitudes greater or equal to 2.5 and 3 atm, corresponding to 355 and 515 kHz, respectively, mass transport mechanism ( i.e., evaporation and condensation of water vapor) becomes dominant compared to the other mechanisms. At 1000 kHz, the mechanism of heat transfer persists to be dominant for all the used acoustic amplitudes (from 1 to 3 atm). Practically, all the above observations were maintained for bubbles at and around the optimum bubble radius, whereas no significant impact of the three energetic mechanisms was observed for bubbles of too lower and too higher values of R 0 (limits of the investigated ranges of R 0 ).

Numerical modelling of acoustic cavitation threshold in water with non-condensable bubble nuclei

“…The phase-change mass flux G at the bubble surface is determined from , where and are the liquid and bubble side heat fluxes directly evaluated by temperature gradients. The heat fluxes and are determined by solving the full energy equations in the bubble and liquid domains, unlike most previous works [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [31] using the boundary layer approximations with adjusting factors.…”

“…Using the kinetic theory and assuming that the phase-change mass flux is low, G can be expressed as [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] where the accommodation coefficient varies in the range of 0–0.35 depending on [25] , [28] , [31] , the saturated vapor pressure at is determined by the Antoine Eq. (17 ), and the vapor pressure at the bubble surface, is calculated from the VDW Eq.…”

“…Recently, Peng et al [25] conducted a similar analysis for acoustic cavitation of vapor and argon mixture bubbles with initial radii of 1.5 and 4.5 and obtained the optimum liquid temperature that maximizes the bubble collapse intensity, depending on the acoustic frequency and amplitude. Dehane et al [26] , [27] , [28] , [29] also performed a numerical analysis for acoustic cavitation of ambient (or initial) bubbles with radii of 0.5–14 , including the effects of heat and mass transfer and chemical reaction. They investigated the bubble collapse temperature and pressure in various acoustic amplitude and frequency conditions.…”

“…Although the previous works [23] , [24] , [25] , [26] , [27] , [28] , [29] have advanced the analysis of acoustic cavitation including the phase-change effect, their analysis was limited in that the heat and mass transfer rates were calculated from the boundary layer approximations with adjusting factors instead of solving the conservation equations. Their applications were mainly acoustic cavitation of microbubbles, which are relatively larger than the nanobubble nuclei [13] expected in real tap or degassed water.…”

An alternative technique for determining the number density of acoustic cavitation bubbles in sonochemical reactors

“…This approach has been adopted from the work of Toegel et al [75] ( i.e. which is one of the pioneers in sonoluminescence and sonochemistry fields) and it is largely used in several theoretical studies giving interesting results in sonochemistry [60] , [65] , [67] , [75] , [79] , [82] , [83] . This assumption is supported by the short lifetime of the bubble and the very short collapsing time especially at higher ultrasound frequencies, which is the case of our study (200–1078 kHz).…”