Conditional damped random surface velocity model of turbulent jet breakup

Abstract

A turbulent jet breakup model is derived using concepts from probability theory. Velocity fluctuations at the free surface are hypothesized to be the cause of turbulent jet breakup. We formalize this idea by treating the fluctuations as random variables, subject to damping from the free surface. In contrast to previous theories, we use a conditional ensemble average to determine quantities of interest because not all fluctuations produce droplets. An energy balance and a closure model are used to determine the Sauter mean diameter. Similar approaches are used to determine the breakup onset location, breakup length, and spray angle. A criteria for the transition to the turbulent atomization regime is derived under the hypothesis that the cause is a change in the minimum velocity from the Hinze scale to the Kolmogorov scale. To validate the model, we compiled data from previous experimental studies using long pipe nozzles. The little data for rough pipes was used to include turbulence intensity in our study.