Computational investigation of flow dynamics in acoustically driven cavitating flow in horn-type reactors

Acoustic cavitation remains, to this day, a peculiar acoustofluidic phenomenon that has recently attained highly concentrated research traction, as many seek new passive solutions to intensify a variety of chemical processes. However, the ever-increasing severity of water crisis serves as the primary driver to expand on this research. It has been previously established that ultrasonically induced cavitation retains the ability to induce high yields of volatile hydroxyl radicals within the working fluid domain through generating severe flow conditions upon their collapse. However, the underlying coupled behaviour of the acoustically induced flow behaviours and the acoustic cavitation remains prominently inconclusive. Therefore, the presented investigation revolves around numerically exploring multiphase flow behaviours observed in a horn-type reactor environment. This is performed by configuring a computational fluid dynamics (CFD) setup with a new cavitation model and a dynamic mesh model, generalizing the coupled flow behaviours observed under multiple horn tips of varying diameters, and establishing the relationship between the cavitating flow with the reactor performances observed. In that manner, the CFD setup was coupled with a newly derived cavitation model based on a series of derivations of the Rayleigh-Plesset equation that define the bubble radial development in terms of water tension and inertial growth. Empirical values that surfaced from the model were statistically optimized through a Design of Experiments approach, coupled with Monte Carlo simulations, to assess the influence of empirical model constants on the model’s performance by examining variations in amplitude and frequency responses. This was then coupled with a dynamic meshing model that defines the oscillating ultrasonic horn walls as uniformly and sinusoidally deforming. Upon comparatively assessing each model’s performance, it was ultimately revealed that Kirchhoff-based model generally underpredicts the acoustic cavitation structure experimentally observed under the horn tip. Based on the Finite Time Lyapunov Exponent (FTLE) results, key differences lied within the vortex shape and position proximally generated; the Kirchhoff-based model predicted an eccentric vortex that induced an impinging jet that facilitates a two-step collapse of the cavitation, as opposed to the single-step collapse typically observed. As the vortex was revealed to have a key role in the flow-cavitation coupling, a parametric analysis was conducted on a horn-type reactor domain considering multiple diameters, namely 3, 6, 13, 16, and 19 mm, to further explore the extent of this coupling. It was uncovered that the acoustic cavity structure falls between two geometrical structures, namely, mushroom-like structure (MBS) and cone-like bubble structure (CBS), based on the actuated ultrasonic horn tip diameter. The cavity structure is molded into MBS by the presence of a symmetric locomotive vortex structure that extends up to 1.5 times the horn tip diameter. Meanwhile, CBS takes shape in the presence of an eccentric locomotive vortex that attains a size within 0.2–0.6 times the horn tip diameter. Upon time-averaging the flow, the stream-linked vortex produced in all cases was found to consistently create a stagnation plane at a distance two times the horn tip diameter (2D) from the horn tip. A one-dimensional mathematical formulation was derived and solved based on the Stuart streaming conservation of momentum and its respective definition of the acoustic force. This revealed that compound attenuation of the acoustic force decreases exponentially at a maximum rate of ≈1.70 with the doubling of Reynolds number. However, an inverse trend was demonstrated, upon considering the influence of the diameter, by the dimensionless attenuation, as it gradually increased by a factor of ≈1.28. Ultimately, the practical significance of this trend of acoustic attenuation induced by the presence of the cavitation structure was most pronounced after conducting yet another parametric investigation scrutinizing the reactor performance of horn-type reactors of the following sizes: 3 mm, 7 mm, 14 mm, 24 mm, 32 mm, and 40 mm. A numerical investigation of these cases highlighted that the vortex gradually becomes more viscous-dominant under larger horns, which, in turn, prevents it from creating the low-pressure nodes previously observed within the vicinity of smaller horns. As a result, this led to the shrinkage of the cavitation structure, and ultimately, creating a slowly oscillating thin flat attached cavitation structure. Due to the recurrence of this observation in cases of 24 mm, 32 mm, and 40 mm horns, it was concluded that such low frequency oscillations of such structures release more hydroxyl radicals and create more activity zones.