Theory of dynamical cavitation threshold for diesel fuel atomization

Abstract

Theory of dynamical cavitation threshold for vapor and non-condensable gas bubble nuclei is proposed based on a model equation constructed from Rayleigh-Plesset equation for glycerol, the liquid with viscosity higher than that of water by 1500 times, under a finite duration of strong tension. The model equation is ascertained to be valid in cases of strong tension under which cavitation occurs. Our model enables the study of dynamics of nuclei on the phase plane of the nucleus radius and the growth velocity, by which the full details of the threshold are revealed. We propose a dimensionless parameter to be used to classify the threshold of cavitation. Our model offers a simple mathematical expression to calculate the maximum radii attained, while under tension, for each of these three recognized patterns. For each observed pattern, we present unique predictive correlations for the radius of the nucleus growing for the tension duration. Moreover, we elucidate that the dynamics of the nuclei, grown up to certain sizes, is fully controlled by tension independent of the viscosity. The discrepancy between the dynamical threshold and the conventional Blake’s threshold is discussed. Finally, the utility of the theory presented here is demonstrated through numerical examples.