title: Transitional Boiling Phenomena in Single Drop Impact and Spray Cooling
Creators: name: Schmidt, Johannes Benedikt
Publisher: name: UNSPECIFIED
Year: 2024

description: Spray cooling is a technology that can be easily applied to the surfaces of various geometries and achieve high cooling rates under some conditions. It has numerous applications, such as medical laser treatments, metal quenching, cooling hot forging dies, and powerful electrical systems.

Predicting optimal spray cooling parameters is a challenging task. The cooling performance depends on interactions of various hydrodynamic and thermodynamic phenomena. Multiple factors influence this complex interplay, such as the size and velocity of the single drops, mass flux density, material properties, and substrate temperature. The best approach to model spray cooling is based on the results of single drop impacts on a hot substrate since this phenomenon is a fundamental part of spray wall interactions. This approach already resulted in reliable spray cooling models for nucleate and film boiling regimes. However, the transitional boiling regime is still not fully understood and lacks reliable models that account for the relevant physical phenomena.

The aim of this study is to expand the current knowledge of the transitional boiling phenomena that appears during spray cooling in the range of wall temperatures separating the nucleate boiling and film boiling regime in spray cooling. The main focus is the experimental and theoretical study of a single drop impact, drop interactions at the substrate, and, finally, the modeling of spray cooling. The experimental setup allows to observe the drop impacts and to measure the heat flux, characteristic times, and impact parameters of the impacting drops at various initial substrate temperatures. 

The single drop impact is studied for the main outcome regimes associated with transitional boiling: drop dancing, wet drop rebound, and thermal atomization. The drop dancing regime is characterized by droplets hovering and "dancing" above the substrate after some characteristic time. The phenomenon is modeled on the assumption of percolating vapor bubbles in the liquid lamella, which, at some conditions, can form an infinite vapor cluster. The modeled percolation time is compared to the experimentally determined characteristic time with an excellent agreement. Further, the threshold temperature between the drop dancing regime and wet rebound regime is determined experimentally by the drop residence time. It is assumed that the percolation of vapor bubbles causes an impacting drop to rebound while wetting the surface. The threshold temperature is described by the instance when the percolation time is in the order of the natural drop oscillation time. This theoretically predicted threshold temperature, also called thermosuperrepellency temperature, agrees well with the experimentally determined threshold temperature between the drop dancing and wet rebound regime. Finally, the heat flux at the hot substrate is measured with a high spatial and temporal resolution in the thermal atomization regime. The heat flux is modeled on the assumption of direct wetting and heat conduction at the liquid/solid interface. The experimental data and theoretical prediction are in the same order of magnitude.

When transferring single drop results to spray cooling, it is essential to understand also the interactions of impacting drops at the hot substrate. The interactions are investigated by the transient cooling of a hot substrate with an impacting drop train in the drop rebound regime. The impacting drops cause a temperature gradient in the substrate, which is measured during the experiments. The temperature decrease is modeled by the superposition of drop impacts and the heat removed by each impacting drop. The experimental and theoretical results agree well. Further, the theory is used to describe the formation of liquid patches during spray cooling. These patches appear by interacting drops at wall temperatures close to the thermosuperrepellency temperature.

The results from both the single drop impact and drop interactions are then combined to develop a model of spray cooling in the transitional boiling regime. The findings of vapor percolation in the drop dancing regime and drop interactions are used to model the heat flux. The theoretical predictions agree well with the experimental heat flux for sprays with low number flux, although no adjustable parameters are used in the modeling. Further, the so-called Leidenfrost temperature, associated with the minimum heat flux during transient spray cooling, is determined. It is shown that the Leidenfrost temperature for sprays correlates very well with the theoretically predicted thermosuperrepellency temperature. This result indicates that the minimum heat flux temperature is determined not by the onset of film boiling but by the appearance of thermosuperrepellency caused by the percolation of vapor channels at the liquid/substrate interface.