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.
Highlights
A direct contact heat exchanger is a highly effective device for transferring heat between two immiscible fluids while they are flowing co-currently or countercurrently inside a column
Assume the droplets swarm to be spherical in shape and that they move in potential flow fields with a constant drop radius, and by solving the steady-state energy equation for the spherical coordinate using a potential flow configuration for the velocity components, and a cell model assumption, Mahood (2012) [12] has found the heat transfer coefficient in terms of Nu number, for the multidrops evaporation in an immiscible liquid as
According to (42) and (43), only the initial phases temperatures and mass flow rates are needed to obtain the temperature distribution along the spray column, assuming a value for holdup ratio within the range calculated by Golafshani [28]
Summary
A direct contact heat exchanger is a highly effective device for transferring heat between two immiscible fluids while they are flowing co-currently or countercurrently inside a column. The temperature profiles of the dispersed (kerosene) and continuous phases (water) in a spray-column direct contact heat exchanger, were investigated both experimentally and theoretically by Letan and Kehat [6]. They proposed that the mechanism of heat transfer inside the spray column could be characterized by five regions: wake growth, intermediate, continuous wake shedding, mixing, and coalesce regimes, respectively. The effect of the superficial velocity and the initial temperature of the continuous phase and the dispersed phase on the volumetric heat transfer coefficient of an n-pentane-water, three-phase, direct-contact heat exchanger were investigated by Peng et al [3] experimentally and theoretically. It is important here to note that no analytical model is currently available to describe the temperature distribution of the temperature inside the direct contact column
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