Thermohydraulic performance of spray cooling systems: a general model by machine learning

With the rapid development of high-power density instruments, spray cooling has drawn increasing interest in industry as a high-efficiency thermal management technology. Despite extensive research, typical spray cooling systems only function effectively within constrained conditions. Therefore, creating a general model for spray cooling is essential for accurately predicting its functionalities. In this work, we employed six machine learning (ML) algorithms to analyze the thermal performance and hydraulic properties of spray cooling. Leveraging data from 25 previous studies encompassing different working fluids, spray atomization types, Reynolds numbers ( $$\:Re$$ ), Nusselt numbers $$\:\left(Nu\right)$$ , and Weber numbers ( $$\:We$$ ), our ML models significantly enhance the prediction of spray cooling functionalities compared to traditional correlations. The effectiveness of these ML algorithms was experimentally validated, yielding mean absolute percentage errors (MAPEs) of 6 $$\% -$$ 20 $$\% -$$ for $$\:Nu$$ and 4 $$\% -$$ 16 $$\% -$$ for mean droplet diameter $$\:{d}_{d}$$ , respectively. Then, we proposed a general correlation for the thermal performances of various working fluids, atomization methods, and operational conditions, achieving a 38% reduction in MAPE compared to the most accurate existing correlation. Subsequently, this general correlation was integrated into the ML models, resulting in MAPEs ranging from 0.48% to 2.3%. Furthermore, we optimized the key factors of spray cooling with the $$\:Nu$$ number reaching 220. Finally, we employed SHapley Additive exPlanations (SHAP) approach to interpret the ML models and to identify an optimal strategy towards greatly enhanced thermal performance. This study demonstrates that ML significantly outperforms the empirical correlations for evaluating spray cooling performance and functionalities, paving a new avenue for thermoregulation of modern power systems.