Analytical Modelling of a Spray Column Three-Phase Direct Contact Heat Exchanger

Abstract

An analytical model for the temperature distribution of a spray column, three-phase direct contact heat exchanger is developed. So far there were only numerical models available for this process; however to understand the dynamic behaviour of these systems, characteristic models are required. In this work, using cell model configuration and irrotational potential flow approximation characteristic models has been developed for the relative velocity and the drag coefficient of the evaporation swarm of drops in an immiscible liquid, using a convective heat transfer coefficient of those drops included the drop interaction effect, which derived by authors already. Moreover, one-dimensional energy equation was formulated involving the direct contact heat transfer coefficient, the holdup ratio, the drop radius, the relative velocity, and the physical phases properties. In addition, time-dependent drops sizes were taken into account as a function of vaporization ratio inside the drops, while a constant holdup ratio along the column was assumed. Furthermore, the model correlated well against experimental data.

Experimental measurements and theoretical prediction for the transient characteristic of a two-phase two-component direct contact condenser

“…Due to immiscibility between the two phases, neither the dispersed phase nor the continuous phase goes into solution in the other phase, therefore, the change of mass of each phase with time can be assumed constant [19,23,24]. Therefore, Eqs.…”

“…Here, k v denotes a velocity factor by which the solution based on a potential flow assumption is converted to an actual or viscous solution [4,5,16,19,23,30]. where:…”

Experimental measurements and theoretical prediction for the volumetric heat transfer coefficient of a three-phase direct contact condenser

“…This can be made reasonably acceptable by means of a constant holdup ratio along the column height, which has been demonstrated for the direct contact evaporator [27][28][29]. -The heat losses from the direct contact column to the environment are ignored.…”

Transient volumetric heat transfer coefficient prediction of a three-phase direct contact condenser

“…• Both continuous phase and dispersed phase mass flow rates are assumed constant along the column. This can be made reasonably acceptable by means of a constant holdup ratio along the column height which has been demonstrated for both direct contact evaporator [22][23][24] and direct contact condenser [17,18]. • The heat losses from the direct contact column to the environment are ignored.…”