Pressure statistics of gas nuclei in homogeneous isotropic turbulence with an application to cavitation inception

Abstract

The behavior of the pressure along the trajectories of finite-sized nuclei in isotropic homogeneous turbulence is investigated using direct numerical simulations at Reλ = 150. The trajectories of nuclei of different sizes are computed by solving a modified Maxey–Riley equation under different buoyancy conditions. Results show that larger nuclei are more attracted to the vortex cores and spend more time at low-pressure regions than smaller nuclei. The average frequency of pressure fluctuations toward negative values also increases with size. These effects level off as the Stokes number becomes greater than 1. Buoyancy, characterized by the terminal velocity w, counteracts the attraction force toward vortex cores while simultaneously imposing an average vertical drift between the nuclei and the fluid. Computational results indicate that weak vortices, associated with moderately low pressures, lose their ability to capture finite-sized nuclei if w ≥ u′. The attraction exerted by the strongest vortices on the largest of the considered nuclei, on the other hand, can only be overcome by buoyancy if w ≥ 8u′. The quantitative results of this study are shown to have a significant impact on modeling cavitation inception in water. For this purpose, the Rayleigh–Plesset equation is solved along the nuclei trajectories with realistic sizes and turbulence intensities. The simulations predict cavitation inception at mean pressures several kPa above vapor pressure.