Entrained liquid fraction calculation in adiabatic disperse-annular flows at low rate in film

Abstract

In this work, we continue our study [1] and extend further an approach to low reduced pressures. An approximate model of droplets entrainment from the laminar film surface and an equation for calculating entrainment intensity are proposed. To carry out direct verification of this equation using experimental data is extremely difficult because the integral effect—liquid flow rate in a film at a dynamic equilibrium between entrainment and deposition—is usually measured in the experiments. The balance between flows of droplets entrainment and deposition corresponds to the dynamic equilibrium because of turbulent diffusion. The transcendental equation, which was obtained on the basis of this balance, contains one unknown numerical factor and allows one to calculate the liquid rate. Comparing calculation results with the experimental data for the water–air and water–helium flows at low reduced pressures (less than 0.03) has shown their good agreement at the universal value of a numerical constant, if an additional dimensionless parameter, a fourth root of vaporliquid densities ratio, is introduced. The criterion that determines the boundary of using methods of this work and that of [1] in calculations and that reflects effect of pressure and state of film surface on distribution of the liquid in the annular flow is proposed; the numerical value of this criterion has been determined.