A Theoretical Mass Transfer Approach for Prediction of Droplets Growth Inside Supersonic Laval Nozzle

Abstract

Proper estimation of droplet growth rate plays a crucial role on appropriate prediction of supersonic separators performance for separation of fine droplets from a gas stream. Up to now, all available researches employ empirical or semi-empirical correlations to define the relationship between droplet growth rate (dr/dt) and other operating variables such as temperatures (T and T_L), Pressure (P) and condensation rate (m_L). These empirical or semi-empirical equations are developed for pure component systems and should not be extended to binary or multi-components systems. A novel theoretical approach is presented in this article which provides a fundamental equation to find the droplet growth rate by resorting to mass transfer equations. The new model uses a combination of mass transfer equations and mass and energy balances to estimate the droplet growth rate, droplet temperature and condensation rate simultaneously. Although the simulation results indicate that the proposed method provides impressive results when validated with several real experimental data, however, the main advantage of the present approach is that it can be easily extended to binary or multi-components systems. To the best of our knowledge, the proposed approach has not been addressed previously.