Spray freezing technology has been shown its exceptional efficiency, safety, and sustainability for underground mine heating. Designing spray freezing systems requires a mathematical model with the rigorous formulation and fast computation methods, capable of predicting performance indicators. Existing models for spray freezing often take the droplet motion and velocity distribution as a priori, thus making it less feasible in practice. In the present work, a novel reduced-order model is developed to calculate the distributions of droplet velocity and residence time for various spray configurations (namely, flat fan, hollow cone, and full cone) and droplet diameters. The velocity distributions are then incorporated into a robust heat transfer model for mine heating to improve the prediction of the droplets freezing time and overall heat transfer rate (HTR). Consequently, the residence time distribution is used along with droplets diameter distribution to calculate the ice packing factor (IPF) and cooling capacity of the system.
