UNSTEADY AND QUASI-STEADY VAPORIZATION OF SPHERICAL DROPLET CLOUDS

Group phenomena for droplets in a spray have often been analyzed on th e basis of the quasi-steady assumption even though this assumption has not been completely justified in this article the applicability of th e quasi-steady assumption to the vaporization of spherical droplet clo uds is first analyzed qualitatively by considering the magnitudes of a ppropriate characteristic scales. Then the governing equations for the unsteady vaporization of a droplet cloud are formulated and solved by numerical methods. The numerical results indicate that cloud vaporiza tion is inherently unsteady and consistent with the analysis of charac teristic scales. The unsteady vaporization of saturated clouds nearly follows a ''D law,'' where D refers to the cloud diameter, rather than the well-known ''D-2 law'' for single droplet vaporization and combus tion Further, it is found that saturation conditions within the cloud cannot be uniquely determined as shown by the quasi-steady theory. How ever, the quasi-steady theory still provides a good prediction of clou d lifetime if both of the following two conditions are satisfied: (1) droplet mass loading ratio O(1); (2) the existence of a thin vaporizat ion layer or wave at the cloud edge.