Optimization and Predictive Correlation of Thermal-Hydraulic Performance for Transcritical Methane in an Airfoil-Fin Printed Circuit Heat Exchanger

This study investigates the flow and heat transfer characteristics within a printed circuit heat exchanger (PCHE) equipped with airfoil fins. A numerical model of a counter-flow airfoil-fin PCHE was developed, using transcritical methane as the cold medium and a 50 wt% ethylene glycol aqueous solution (50% EGWS) as the hot medium. The effects of the airfoil fin array longitudinal staggering ratio (Ks), transverse pitch ratio (Kb), and longitudinal pitch ratio (Ka) on the thermal-hydraulic performance of the PCHE were systematically analyzed using the thermal performance factor (TPF) for comprehensive evaluation. The optimal configuration was determined to be Ks = 0.2, Kb = 0.5, and Ka = 1.0, achieving a TPF up to 1.18 times higher than that of the baseline structure (Ks = 1.0). The analysis highlights that aggressive heat transfer enhancement incurs a substantial pressure drop penalty; for instance, reducing Ka from 2.0 to 1.0 increases the Nusselt number (Nu) by approximately 13%, while simultaneously increasing the Fanning friction factor (fFanning) by 22%, indicating a significant pressure drop cost. The developed correlations exhibit deviations within ±10% of the simulated values over the Reynolds number (Re) range of 8000–25,000, providing a reliable tool for the optimized design of PCHEs.