Nonstationary heat and mass transfer in evaporative cooling of flowing liquid films

Abstract

A mathematical model of nonstationary evaporative cooling of a laminar liquid film flowing down a vertical surface in its blowing with a countercurrent steam-air flow has been developed. The problem of heat and mass transfer has been formulated in a conjugate statement. The calculated data on the time change in the temperature and concentration fields in the steam-air flow and the liquid film as well as in the density of the heat flux on the flowing-film surface have been given.The operating efficiency of thermal and nuclear power stations is largely determined by the efficiency of cooling of a circulating water in chimney-type evaporative cooling towers, where the evaporation of the liquid from the surface of gravitational films flowing down the shields of a wetting device is of primary importance for reduction in the temperature of water arriving from the turbine condenser. Furthermore, if we take into account the capital outlays for development and building of such megastructures, intensification of the processes of cooling in chimney-type evaporative cooling towers finally ensures a considerable economy of financial funds and material resources.The nonstationary regime of wetting [1-3] is the most promising for increasing the cooling power of chimney-type evaporative cooling towers. However, to implement such an intensification method in practice one must know the regularities of nonstationary processes of evaporation and heat transfer in gravitational flow of a film.Theoretical and experimental investigation of hydrodynamics and heat exchange in gravitational film flow of a liquid is the focus of numerous domestic and foreign works (see, e.g., [4][5][6][7][8][9][10][11][12][13][14]). In such works, consideration has been mainly given to the stationary regimes of heat and mass transfer, where the regularities of heat and mass exchange are determined experimentally or from calculations based on empirical dependences for the coefficients of heat and mass exchange. A one-dimensional mathematical model of combined cooling of water in a cooling tower due to both evaporative film cooling and the cooling of water droplets in the wetting zone has been proposed in [15]. An expression for determination of the thermal efficiency of the cooling tower, which is in proportion to the ratio of the specific flow rate of air and water and depends on the dimensionless parameter P _ _ = h 2 V ∞ /(D 12 L), has been obtained. Analogous results have been obtained in [16], where one-dimensional and two-dimensional models of stationary heat and mass transfer in the case of flow of a steam-air mixture past a film have been considered and the range of applicability of a one-dimensional model in a film-type heat exchanger has been determined. The boundary conditions (temperature and density of a steam near the wall) for solution of a two-dimensional problem are taken from the solution of the corresponding one-dimensional problem.The present work seeks to numerically model nonstationary processes of evaporation and heat transfer from the...