Ignition of Non Dilute Clusters of Drops in Convective Flows

Abstract

A global model has been developed for the qualitative prediction of ignition of clusters of drops evaporating in a convective flow. This model incorporates the description of convective droplet-cluster evaporation through a model which is valid for both dense and dilute clusters. The model takes into account drop interactions and the resulting possible limitations on evaporation in the limit of dense clusters. An Eulerian description is used to predict both drop and gas velocities. To complement the fluid mechanics model which is self-contained, the bulk interaction between the convective flow around the cluster and the cluster is evaluated using a penetration ratio criterion. The penetration distance itself is calculated in a Lagrangian frame. The model of droplet-cluster ignition can predict both the ignition time of the cluster and the location of the flame rs) at that time (under the, assumption of a spherical cluster). The ignition-timing part of the ignition criterion is valid only for diffusion-controlled ignition. The various possible combustion regimes for droplet-clusters are identified using a two dimensional map which compares convective and diffusive effects. Further numerical calculations show that in practical systems dense droplet-cluster ignition is always diffusion-dominated. The dependence of the ignition time upon both the initial drop temperature and gas temperature is studied as well. It is shown that the initial conditions determine whether a cluster ignites in anyone of the regimes previously identified.