Calculation of Droplet Size Distribution in Condensing Flow

Abstract

Condensing flows can be found in a large variety of industrial machinery such as steam turbines and supersonic gas conditioners. In many of these applications, it is very important to predict the droplet size distributions accurately. In the present research, the droplet size distribution in condensing flows is investigated numerically. We consider condensing flows with droplets that nucleate and grow, but do not slip with respect to the surrounding gas phase. To compute the coupling between the condensed phase and the carrier flow, one could solve the general dynamic equation and the fluid dynamics equations simultaneously. In order to reduce the overall computational effort of this procedure by roughly an order of magnitude, we use an alternative procedure, in which the general dynamic equation is initially replaced by moment equations complemented with a closure assumption. This closure assumption is based on Hill’s approximation of the droplet growth law. The method thus obtained, the so-called Method of Moments, is assumed to approximately accommodate the thermodynamic effects of condensation, such as the temperature, pressure and velocity field of the carrier flow. We use the Method of Moments as a basis for the calculation of the droplet size distribution function. We propose to solve the general dynamic equation a posteriori along a number of selected fluid trajectories, keeping the flow field fixed. This procedure, called Phase Path Analysis [1], leads to accurate size distribution estimates, at a far lower computational cost than solving the general dynamic equation and the fluid dynamics equations simultaneously. In the present paper, we investigate the effect of a variation in the liquid mass density on the droplet size distribution, using the proposed method. In case of a varying liquid mass density, both the equation for the dropltet growth rate and the moment equations are modified. This modified form coincides with the usual form of the moment equations in the event that the variation in liquid density is negligible. This research is relevant for condensation in flows where large temperature differences may occur which lead to significant variations in the liquid mass density. We show that the implementation of a variable liquid mass density in the Method of Moments and the Phase Path Analysis results in a higher extremum in the droplet size distribution, whereas the skewed shape of the distribution function is nearly similar to that obtained in the constant liquid density case.