A probability model for fully developed annular flow in vertical pipes: Prediction of the droplet entrainment

The phase distributions and mechanical properties of annular flow can be regarded as random states. Hence the probability analysis is an appropriate method to investigate the possibilities of the relevant events and the statistic results of some characteristic parameters. In the present work, a probability model for fully developed annular flow in vertical pipes is proposed to predict the phase distributions and mechanical characteristics. The probability model works in three mechanisms. First, a vortex generation theory on energy transfer from vortexes to droplets is supposed to describe the atomization process. Second, a random walk theory is applied to track the droplet deposition on the liquid film. Third, the atomization and deposition rates are respectively related to the probabilities of droplet generation and elimination by analyzing the interaction between vortexes and droplets. Based on the knowledge of dynamic equilibrium between atomization and deposition processes, a balance equation is established to close the equation set and the representative parameters of annular flow can be solved. The new model is a statistical method and almost links all the parameters involved in annular flow. By comparing the predicted droplet entrainment with experimental data available in the literature, the present model is well verified and demonstrates advantages both in accuracy and in convenience. Furthermore, the effects on the entrainment of many parameters, including the gas flow rate, liquid flow rate, gas density, liquid density, gas viscosity, surface tension and pipe diameter, are discussed in detail. (C) 2015 Elsevier Ltd. All rights reserved.