Methodology for modeling spray cooling of a cylindrical tube heated in the film boiling regime

This study examines spray cooling of horizontal, circular tubes when the surface temperature exceeds the Leidenfrost point, and the individual drop impacts are in the film boiling regime. Although film boiling is not an optimal condition for heat transfer, it is encountered in transient cooling processes or when high temperatures persist along the tube. The goal of the study is to apply existing models for drop impact and heat transfer to surfaces more complex than flat plates and to determine the overall steady state heat removal rate as an essential parameter for heat exchanger design. The spray characteristics are prescribed by a local number flux and drop size, assuming a random distribution in space and a uniform velocity of all drops. The angle of individual drop impingement on the cylindrical tube is accounted for through the maximum spreading diameter of the drop on the surface and the normal component of impact velocity. Furthermore, drop-drop interaction on the heated surface is accounted for at high local number flux values through an effective coverage area coefficient. The results are expressed in the form of a local heat transfer coefficient.These results confirm that the most influential parameters regarding heat transfer are the liquid mass flow rate in the nozzle and the drop diameter; however, they also indicate that the non-normal impact of drops over portions of the cylindrical tube leads to a highly reduced number flux; hence heat transfer. This oblique impact angle arises for one from the local spray angle, but more drastically from the curved, cylindrical surface; the latter leading to a dramatic sharp decrease in heat transfer. This is important information when considering the use of multiple spray nozzles, either circumferentially or longitudinally along the tube, since it dictates the optimal spacing between neighbouring nozzles.