A strict formulation of a nonlinear Helmholtz equation for the propagation of sound in bubbly liquids. Part II: Application to ultrasonic cavitation

Coffee brewing sonoreactor for reducing the time of cold brew from several hours to minutes while maintaining sensory attributes

This research designed and developed an ultrasonic reactor for a fast and on demand production of cold brew coffee, remarkably reducing the brewing time from 24 h to less than 3 min. The technology was engineered by utilizing resonance to induce ultrasonic waves around the walls of the brewing basket of an espresso machine. The sound transmission system comprised a transducer, a horn and a brewing basket. This arrangement transformed the coffee basket into an effective sonoreactor that injected sound waves at multiple points through its walls, thereby generating multiple regions for acoustic cavitation within the reactor. Furthermore, acoustic streaming induced greater mixing and enhanced mass transfer during brewing. The design was accomplished by modeling the transmission of sound, and acoustic cavitation. Brew characterization and chemical composition analysis was performed, considering factors such as pH, acidity, color, and the composition of caffeine, fatty acids, and volatiles. The efficiency of the extraction increased by decreasing the basket loading percentage (BLP). For instance, sonicating at 100 W doubled the extraction yield and caffeine concentration, from 15.05 % to 33.44 % at BLP = 33 %, and from 0.91 mg/mL to 1.84 mg/mL at BLP = 67 %, respectively. The total fatty acids increased from 1.16 mg/mL to 9.20 mg/mL, representing an eightfold increase, at BLP = 33 %. Finally, a sensory analysis was conducted to evaluate appearance, aroma, texture, flavor, and aftertaste, which demonstrated that coffee brewed for 1 and 3 min in the sonoreactor exhibited almost undistinguishable properties compared to a standard 24 h brewing without ultrasound.

Extensive investigation of geometric effects in sonoreactors: Analysis by luminol mapping and comparison with numerical predictions

This investigation focuses on the influence of geometric factors on cavitational activity within a 20kHz sonoreactor containing water. Three vessels with different shapes were used, and the transducer immersion depth and liquid height were varied, resulting in a total of 126 experiments conducted under constant driving current. For each one, the dissipated power was quantified using calorimetry, while luminol mapping was employed to identify the shape and location of cavitation zones. The raw images of blueish light emission were transformed into false colors and corrected to compensate for refraction by the water-glass and glass-air interfaces. Additionally, all configurations were simulated using a sonoreactor model that incorporates a nonlinear propagation of acoustic waves in cavitating liquids. A systematic visual comparison between luminol maps and color-plots displaying the computed bubble collapse temperature in bubbly regions was conducted. The calorimetric power exhibited a nearly constant yield of approximately 70% across all experiments, thus validating the transducer command strategy. However, the numerical predictions consistently overestimated the electrical and calorimetric powers by a factor of roughly 2, indicating an overestimation of dissipation in the cavitating liquid model. Geometric variations revealed non-monotonic relationships between transducer immersion depth and dissipated power, emphasizing the importance of geometric effects in sonoreactor. Complex features were revealed by luminol maps, exhibiting appearance, disappearance, and merging of different luminol zones. In certain parametric regions, the luminol bright regions are reminiscent of linear eigenmodes of the water/vessel system. In the complementary parametric space, these structures either combine with, or are obliterated by typical elongated axial structures. The latter were found to coincide with an increased calorimetric power, and are conjectured to result from a strong cavitation field beneath the transducer producing acoustic streaming. Similar methods were applied to an additional set of 57 experiments conducted under constant geometry but with varying current, and suggested that the transition to elongated structures occurs above some amplitude threshold. While the model partially reproduced some experimental observations, further refinement is required to accurately account for the intricate acoustic phenomena involved.

Probing the pressure dependence of sound speed and attenuation in bubbly media: Experimental observations, a theoretical model and numerical calculations

The problem of attenuation and sound speed of bubbly media has remained partially unsolved. Comprehensive data regarding pressure-dependent changes of the attenuation and sound speed of a bubbly medium are not available. Our theoretical understanding of the problem is limited to linear or semi-linear theoretical models, which are not accurate in the regime of large amplitude bubble oscillations. Here, by controlling the size of the lipid coated bubbles (mean diameter of ≈5.4μm), we report the first time observation and characterization of the simultaneous pressure dependence of sound speed and attenuation in bubbly water below, at and above microbubbles resonance (frequency range between 1-3 MHz). With increasing acoustic pressure (between 12.5-100 kPa), the frequency of the peak attenuation and sound speed decreases while maximum and minimum amplitudes of the sound speed increase. We propose a nonlinear model for the estimation of the pressure dependent sound speed and attenuation with good agreement with the experiments. The model calculations are validated by comparing with the linear and semi-linear models predictions. One of the major challenges of the previously developed models is the significant overestimation of the attenuation at the bubble resonance at higher void fractions (e.g. 0.005). We addressed this problem by incorporating bubble-bubble interactions and comparing the results to experiments. Influence of the bubble-bubble interactions increases with increasing pressure. Within the examined exposure parameters, we numerically show that, even for low void fractions (e.g. 5.1×10-6) with increasing pressure the sound speed may become 4 times higher than the sound speed in the non-bubbly medium.

Simulations of a full sonoreactor accounting for cavitation

In spite of the increasing interest in ultrasound processing applications, industrial scale-up remains limited, in particular by the unavailability of predictive computer tools. In this study, using a previously published model of cavitating liquids implementable as a non-linear Helmholtz equation, it is shown that a full sonoreactor can be modelled and simulated. The model includes the full transducer and the vibrations of the vessel walls, using the physics of elastic solids and piezo-electricity. The control-loop used by the generator to set the optimal frequency is also accounted for. Apart from the geometry, the unique input of the model is the current feeding the transducer whereas the dissipated electrical power, transducer complex impedance and working frequency are available as outputs. The model is put to the test against experiments realized in different geometries, varying either the input current or the transducer immersion depth. Despite the overestimation of the power dissipated in the liquid, the evolution of the acoustic load in both cases is reasonably well reproduced by simulation, which partially validates the method used.

Identification approach of acoustic cavitation via frequency spectrum of sound pressure wave signals in numerical simulation

In a sono-reactor, complex ultrasound pressure wave signal can be detected, containing multiple information related to acoustic cavitation. In this present study, acoustic cavitation in a cylinder is investigated numerically. Via Fast Fourier Transfer (FFT), the sound pressure signals from sonotrode emitting surface are separated into harmonics, sub/ultra-harmonics and cavitation white noise: (1) the appearance of harmonics proved the non-linear propagation of ultrasound, (2) at the vibratory amplitude from 5∼20μm, only harmonics exists in the frequency spectra, corresponding to expansion and compression of non-condensable gas (NCG), (3) at the vibratory amplitude range of 30∼50μm, the occurrence of sub/ultra-harmonics demonstrated gaseous cavitation occurred, and (4) at the vibratory amplitude higher than 55μm, cavitation white noise arose, pointing out the initiation of vaporous cavitation. Based on the combination of frequency spectra and cavitation zones distribution, the acoustic cavitation state in water liquid is determined.

Comparison of frequency domain and time domain methods for the numerical simulation of contactless ultrasonic cavitation

The use of a top-mounted electromagnetic induction coil has been demonstrated as a contactless alternative to traditional ultrasonic treatment (UST) techniques that use an immersed mechanical sonotrode for the treatment of metals in the liquid state. This method offers similar benefits to existing UST approaches, including degassing, grain refinement, and dispersion of nanoparticles, while also preventing contact contamination due to erosion of the sonotrode. Contactless treatment potentially extends UST to high temperature or reactive melts. Generally, the method relies on acoustic resonance to reach pressure levels suitable for inertial cavitation and as a result the active cavitation volume tends to lie deep in the melt rather than in the small volume surrounding the immersed sonotrode probe. Consequently, (i) with suitable tuning of the coil supply frequency for resonance, the treatment volume can be made arbitrarily large, (ii) the problem of shielding and pressure wave attenuation suffered by the immersed sonotrode is avoided. However, relying on acoustic resonance presents problems: (i) the emergence of bubbles alters the speed of sound, resonance is momentarily lost, and cavitation becomes intermittent, (ii) as sound waves travel through and reflect on all the materials surrounding the melt, the sound characteristics of the crucible and supporting structures need to be carefully considered. The physics of cavitation coupled with this intermittent behaviour poses a challenge to sonotrode modelling orthodoxy, a problem we are trying to address in this publication. Two alternative approaches will be discussed, one of which is in the time domain and one in the frequency domain, which couple the solution of a bubble dynamics solver with that of an acoustics solver, to give an accurate prediction of the acoustic pressure generated by the induction coil. The time domain solver uses a novel algorithm to improve simulation time, by detecting an imminent bubble collapse and prescribing its subsequent behaviour, rather than directly solving a region that would normally require extremely small time steps. This way, it is shown to predict intermittent cavitation. The frequency domain solver for the first time couples the nonlinear Helmholtz model used for studying cavitation, with a background source term for the contribution of Lorentz forces. It predicts comparable RMS pressures to the time domain solver, but not the intermittent behaviour due to the underlying harmonic assumption. As further validation, the frequency domain method is also used to compare the generated acoustic pressure with that of traditional UST using a mechanical sonotrode.

Multiphysics Modelling of Ultrasonic Melt Treatment in the Hot-Top and Launder during Direct-Chill Casting: Path to Indirect Microstructure Simulation

This study concerns the numerical simulation of two competing ultrasonic treatment (UST) strategies for microstructure refinement in the direct-chill (DC) casting of aluminium alloys. In the first, more conventional, case, the sonotrode vibrating at 17.3 kHz is immersed in the hop-top to treat the sump melt pool, in the second case, the sonotrode is inserted between baffles in the launder. It is known that microstructure refinement depends on the intensity of acoustic cavitation and the residence time of the treated fluid in the cavitation zone. The geometry, acoustic field intensity, induced flow velocities, and local temperature are factors which affect this treatment. The mathematical model developed in this work couples flow velocity, acoustics modified by cavitation, heat transfer, and solidification at the macroscale, with Lagrangian refiner particles, used to determine: (a) their residence time in the active zones, and (b) their eventual distribution in the sump as a function of the velocity field. This is the first attempt at using particle models as an efficient, though indirect, alternative to microstructure simulation, and the results indicate that UST in the launder, assisted with baffle separators, yields a more uniform distribution of refining particles, avoiding the strong acoustic streaming jet that, otherwise, accompanies hot-top treatment, and may lead to the strong segregation of refining particles. Experiments conducted in parallel to the numerical studies in this work appeared to support the results obtained in the simulation.