GPU accelerated study of a dual-frequency driven single bubble in a 6-dimensional parameter space: the active cavitation threshold

Abstract The active cavitation threshold of a dual-frequency driven single spherical gas bubble is studied numerically. This threshold is defined as the minimum energy required to generate a given relative expansion ( R max - R E ) / R E , where R E is the equilibrium size of the bubble and R max is the maximum bubble radius during its oscillation. The model employed is the Keller–Miksis equation that is a second order ordinary differential equation. The parameter space investigated is composed by the pressure amplitudes, excitation frequencies, phase shift between the two harmonic components and by the equilibrium bubble radius (bubble size). Due to the large 6-dimensional parameter space, the number of the parameter combinations investigated is approximately two billion. Therefore, the high performance of graphics processing units is exploited; our in-house code is written in C++ and CUDA C software environments. The results show that for ( R max - R E ) / R E = 2 , the best choice of the frequency pairs depends on the bubble size. For small bubbles, below 3 μ m , the best option is to use equal frequencies and low ones in the giant response region. For medium sized bubbles, between 3 μ m and 6 μ m , the optimal choice is the mixture of low frequency (giant response) and main resonance frequency. For large bubbles, above 6 μ m , the main resonance dominates the active cavitation threshold. Increasing the prescribed relative expansion value to ( R max - R E ) / R E = 3 , the optimal choice is always equal frequencies with the lowest values ( 20 kHz here). Thus, in this case, the giant response always dominates the active cavitation threshold. The phase shift between the harmonic components of the driving has no effect on the threshold.