Droplet distributions from the breakup of a cylindrical liquid jet

Abstract

A phase/Doppler particle analyzer is used to measure the size and velocity distributions of the droplets generated by the disintegration of a cylindrical liquid jet. This type of liquid jet breakup is commonly called Rayleigh breakup. Metered liquid flow rates agree with the rates computed from the droplet measurements made with the phase/Doppler particle analyzer. The maximum entropy principle is used to predict the droplet size and velocity distributions. The constraints imposed in this model involve conservation of mass, momentum, surface energy, and kinetic energy. Agreement between measurements and predictions is very good.

The Maximum Entropy Formalism and the Prediction of Liquid Spray Drop-Size Distribution

“…Following Li and Tankin [16], the control volume extended from the nozzle exit down to a plane where all droplets were formed. However, Chin et al [24] reconsidered the used of a single energy constraint in Li and Tankin's approach by noting that when a single constraint is used no information is provided to how the total energy source is distributed between the kinetic energy and the surface energy. Thus, any combination of constant total energy source will result in the same probability density function.…”

“…Thus, any combination of constant total energy source will result in the same probability density function. In consequence, as recommended by Sellens [21], Chin et al [24] used separate constraints for kinetic energy and surface energy. Using the jet velocity U jet at the nozzle exit and the mass mean drop-diameter D 30 to calculate the dimensionless parameters, the normalization, mass conservation, momentum conservation and kinetic energy conservation constraints were similar to Equations 18-21, respectively (without the explicit appearance of the source term S m as in Equation 33) and the surface energy conservation was written as:…”

“…The investigations due to Sellens' group [12,14,21,25] and to Li and Tankin's group [15,16,24] have motivated developments and applications of models based on the MEF to predict liquid spray drop-diameter distributions. Van der Geld and Vermeer [26] proposed a model to predict the diameter distribution of satellite droplets produced during the breakup of a cylindrical liquid column, the main droplets being distributed according to a Gaussian distribution.…”

“…Chin et al [24] reconsidered Li and Tankin's approach [16] to predict the volume and velocity distribution (d = dVdU) of the drops produced by a cylindrical liquid jet subject to a Rayleigh breakup process. This well-known process has been described in many references (see [1,2] for instance).…”

Trends in Comprehensive Modeling of Spray Formation

“…Chin et al [227] adopted the approach of Li and Tankin [217] to predict the droplet distribution in the volume and velocity space using the MEP approach. However, they considered separate conservation of kinetic energy and surface energy as constraints, as they observed that the conservation of the total energy could not capture the information regarding the distribution of the energy source as kinetic energy and surface energy components.…”