A Similarity Solution with Two-Equation Turbulence Model for Computation of Turbulent Film Condensation on a Vertical Surface

Abstract

In this paper, we presented a similarity solution for turbulent film condensation of stationary vapor on an isothermal vertical flat plate. In this method, some similarity transformations are employed and the set of governing partial differential equations (PDE) of conservation together with transport equations of turbulent kinetic energy and dissipation rate are transformed into a set of ordinary differential equations (ODE). Calculated data for the flow field, velocity profile, wall shear stress, condensate film thickness, turbulent kinetic energy, rate of dissipation, and heat transfer properties are discussed. The effect of Prandtl (Pr) number was also investigated in a wide range of variations. The obtained results showed that at high Prandtl numbers, the velocity profile becomes more uniform across the condensation film and therefore, the kinetic energy of turbulence is reduced. Furthermore, the effect of change in Pr is negligible at high Pr numbers and consequently, the flow parameters have no significant change in this range. The friction coefficient changes linearly through the condensation film and the slope of friction lines diminishes slightly by the Pr number. The rate of turbulent kinetic energy increases linearly from the wall up to about 20% of condensate film, then rises asymptotically and converges to a constant value near the liquid-vapor interface. Also, the rate of turbulent dissipation grows linearly up to 40% of condensate film thickness and then increases slightly while it oscillates.