Physics-Based Modeling of Spray Cooling on a Moving Substrates

Spray cooling is an efficient technique for removing high heat fluxes through droplet impingement on heated surfaces. However, when applied to moving substrates, the complex interplay between droplet dynamics and transient heat transfer remains insufficiently understood. Relative motion between substrate and spray alters impact angle, spreading behavior, and local droplet arrival rates, leading to spatially non-uniform cooling observed in systems such as turbine blades, continuous casting, brake discs. The local droplet arrival rate and mass flux distribution become functions of surface velocity, creating spatially varying cooling patterns.

This study introduces a novel physics-based simulation framework that captures spray cooling on moving surfaces while incorporating conjugate heat transfer within the substrate. Spray characteristics - mass flow rate, cone angle, and droplet size/velocity distributions are defined at the nozzle and the local droplet flux is dynamically computed considering oblique impacts. Heat transfer is evaluated across film, transition, and nucleate boiling regimes, with total heat flux obtained through the superposition of droplet interactions and film formation effects. The conjugate substrate response is resolved using a finite difference scheme. This framework provides a predictive and mechanistic tool to elucidate how surface motion, spray properties and material characteristics collectively govern cooling efficiency and temperature uniformity.