Heat Transfer Model of Superheated Vapor Bubbling in Liquid in Multi-Stage Refrigeration Systems

In low-temperature refrigeration systems, the multi stage approach with inter-cooled compression allows energy demand reduction, increased reliability, financial balance and maintenance costs decrease. An intercooling process between low and high pressure levels, consists of desuperheating the vapor coming from the low-pressure compressor by bubbling it in the saturated liquid intermediate pressure tank towards the saturation conditions. In this work, a semi-analytical heat transfer model of a single superheated vapor bubble injected in the liquid is proposed by adapting the Fourier equation to defined conditions and by including the effects of sensible and latent heat. The results show trends and highlight the influence of the liquid surface tension, of the injection depth and of the thermal diffusivity of the vapor. The existence of an optimal injection depth can be found, that accounts for the energy transfer at given thermodynamic conditions of the vapor and the injected bubble dimensions.