Theory of the Effects of Small Gravitational Levels on Droplet Gasification

摘要

A mathematical model taking into account small (and constant) gravitational levels is developed for vaporization of an isolated liquid droplet suspended in a stagnant atmosphere. A goal of the present analysis is to see how small gravitational levels affect droplet gasification characteristics. Attention is focused upon determining the effects on gas-phase phenomena. The conservation equations arc normalized and nondimensionalized, and a small parameter that accounts for the effects of gravity is identified. This parameter is the square of the inverse of a Froude number based on the gravitational acceleration, the droplet radius, and a characteristic gas-phase velocity at the droplet surface. Asymptotic analyses are developed in terms of this parameter. In the analyses, different spatial regions are identified. Near a droplet, gravitational effects are negligible in the first approximation, and the flowfield is spherically symmetric to the leading order. Analysis shows, however, that outer zones exist where gravitational effects cannot be neglected; it is expected that a stagnation point will be present in an outer zone that is not present when gravity is totally absent. The leading order and higher-order differential equations for each zone are derived and solved. The solutions allow the effects of gravity on vaporization rates and temperature, velocity and species fields to be determined.