the cavitation threshold, the cavitation effects are not observed, and effects such as acoustic streaming are observed [108]. Thus, to scale up a cavitational reactor, benefits of both low-frequency and high-frequency ultrasound to retain the advantages of micro- and mili-fluidic-reactor, and to control the acoustic pressure distribution across the scales is necessary.
Over the last two decades, two strategies have been developed to scale-up cavitational reactors. The first approach is to increase the characteristic size of the channel and the second one by operating several identical units in parallel or series. The characterization of primary and secondary effects of the ultrasound across the scale is important, and the main parameter to be controlled across reactor scales is the acoustic pressure field distribution in the liquid media. Verhaagane et al. [109] scaled up micro-reactor with increasing efficiency and reproducibility using the numbering up strategy and overserved the cavitation phenomena. Jamshid et al. [110] have used channel characteristics approach to scale-up cavitational reactors and used numerical simulation to obtain acoustic pressure distribution through the reactor. A combination of both the scale-up approach has also been studied by many researchers [107, 108, 111].
However, the scale-up of the cavitational reactor also depends on the understanding of the mechanism of ultrasound and efficient coupling between the ultrasonic device and the reactor. Currently, numerical method to quantify thermal or viscus loss due to cavitation is done by COMSOL simulations to connect and optimize the vibration response of solid materials, dynamic behavior of piezoelectric materials, structure vibrations and its connection to the surrounding fluid, both outside and inside of the closed volumes in the reactor. Further, modification of the numerical model for nonlinear response caused by cavitation can also be done in the software and thus COMSOL offers a powerful tool for scaling-up cavitational reactor efficiently. Figure 2.3 the graphical illustration of acoustic pressure field variation across the reactor configuration by the COMOSOL.
Johansson et al. [111] reported the design of a scalable cavitational reactor using COMSOL. Delacour et al. [108] also successfully demonstrated the scale-up of cavitational reactor using COMSOL multiphasic. They highlighted the importance of developing experimental and numerical characterization methods of the ultrasound and cavitation effect for the design of scaled-up ultrasonic milli reactors. Bashir et al. [112] have reported computational fluid dynamics (CFD) tool to optimize the geometry of ultrasound reactors as given in Figure 2.4. The authors have used three parameters viz., the location of cavity inception, the pressure recovery rate, and the cavity growth time for optimization of venturi for cavitation application.
Figure 2.3 Contours of the absolute acoustic pressure field based on COMSOL simulations for a total power of 120W (20W per transducer) [adapted form Delacour, C. et al., [109] with permission of copyright@ 2020, American Chemical Society].
Figure 2.4 Grid sensitivity analysis of the CFD simulations [112].
Prabhu et al. [113] have reported the details of the numerical method to optimize multi-frequency sonochemical reactors. They have studied operating parameters such as frequency of irradiation, intensity of irradiation, initial radius of the cavity, the gas content of the cavity, and the operating temperature on the cavitational activity using numerical solutions of the cavity dynamics equations. The numerical method supported by strong experimental proof revealed that the authors have helped establish optimum design specification and scale-up cavitational reactors. Similarly, Gogate et al. [114] also reported the numerical method to scale-up cavitational reactors and recommended a series of steps while scaling-up of a cavitational reactor.
Moholkar [115] reported dual-frequency design of the ultrasonic reactor to address the non-uniform volumetric energy dissipation issue associated with single frequency ultrasound reactors. He has developed numerical models to optimize the multi-frequency ultrasound reactor and concluded that out of two design parameters, frequency ratio and phase difference, the latter is more effective in designing and scaling of ultrasound reactors. Several authors previously reported multi-frequency ultrasound reactor for potential scale-up of ultrasound reactors [116–118]. In another study, Gogate and Pandit [118] reported design of large-scale sonochemical reactors using numerical model devolvement and experimental validation with different reactor types and reactions, including esterification and transesterification. They also recommended the use of multi-frequency reactors for large-scale commercial application.
Nevertheless, an ongoing effort on the scale-up of the ultrasonic reactor in the future will be done by a numeric method and computer-based simulations method such as CFD [112] using tools such as COMSOL or ANSYS.
2.6 Application of Cavitational Reactors for Large-Scale Biodiesel Production
Sonochemistry induced by cavitational phenomena and its beneficial application for biodiesel production has attracted the interest of the research community and the industrial domain. Nevertheless, the complex design of the system and its effective implementation in a large-scale process still needs significant R&D efforts. The principal merit of cavitational reactors for biodiesel synthesis at a commercial scale is its reduced operational cost (in terms of energy requirement) and higher energy efficiencies and yields. In lab-scale studies, exergy analysis looks promising, but translating these ideas into commercial processing is still a challenge [119]. As discussed in the previous section, the two types of pilot-scale reactors have been designed, viz., multi-frequency sonochemical reactors and hydrodynamic cavitation reactors. The research group of Pandit and Gogate has demonstrated the successful application of pilot-scale hydrodynamic cavitational reactors for biodiesel synthesis in numerous studies [23, 97, 120]. These reactors achieve higher conversation rates in a shorter time and reduce solvent requirements compared to conventional mechanical mixing. However, these reactors are not compatible with the heterogeneous catalysts. This doesn’t improve the downstream processing of biodiesel, and thus becomes the main limitation in scale-up. The multi-frequency sonochemical reactors will be an ideal solution in such cases, but limited case studies have been carried out using such reactors. The main advantages of such reactors are their flexibility of operation in both batch and continuous model and the compatibility with heterogeneous catalysts. On the other hand, the high energy input of these reactors is the major limiting factor [79, 114, 121]. Murillo et al. [122] and others [86] have successfully demonstrated 3 L capacity ultrasonic reactor for biodiesel synthesis. Comprehensive work is still required to achieve the commercialization of biodiesel production.
2.7 Future Prospects and Challenges
Biodiesel via transesterification is one of the emerging processes for meeting the increased demand for renewable fuels. Transesterification, being a heterogeneous reaction system, is a mass-transfer controlled process. Moreover, the selection of feedstock controls the economics of the overall process. In order to improve the overall economy of the process, the feedstock of non-edible oils and heterogeneous catalysts are the best feasible solutions. The use of heterogeneous catalysts further increases the mass transfer barriers and lowers the conversion rate. To improve the reaction kinetics and yield of the process, sonication is found to be a useful tool in lab-scale studies. Research on ultrasound-assisted or cavitation-assisted biodiesel processes is promising and demands further R&D efforts to develop large-scale operations. Significant research is also required on ultrasound-assisted heterogeneously catalyzed transesterification
