A geometry-aware Bi-level reduced-order model for state-field reconstruction and exergy-flux evaluation in closed wet cooling towers

Tube-bundle geometry governs the coupled airflow, evaporation, heat transfer, and pressure loss in closed wet cooling towers, making repeated computational fluid dynamics (CFD) simulations costly for design under uncertain ambient conditions. This study develops a geometry-aware bi-level reduced-order framework for steady-state field reconstruction, exergy-flux analysis, and stochastic tube-bundle design in a bench-scale cooling tower. Geometry-dependent CFD fields are interpolated and smoothly extended onto a fixed background, while sample-specific masks recover the physical fluid regions for each geometry. This representation accommodates moving tube boundaries while retaining geometry-dependent near-wall information. Level 1 provides scalar surrogates for the system-level exergy efficiency ratio (EER) and outlet circulating-water temperature. Level 2 combines principal component analysis with artificial neural networks to reconstruct temperature, gauge pressure, velocity magnitude, and humidity ratio on a central two-dimensional observation section, from which thermal, mechanical, and chemical advective exergy-flux fields are derived. A 1000-case CFD database is used for model development and evaluation, with 150 cases reserved for testing. Mean relative errors in outlet temperatures and air relative humidity are below 1%. The mean relative L₂ errors of the reconstructed temperature, gauge-pressure, velocity-magnitude, and humidity-ratio fields are 0.018, 0.056, 0.064, and 0.023, respectively. Scenario-based stochastic optimization using the Level-1 surrogates increases the expected system EER from 0.222 to 0.238 relative to the baseline design, an improvement of 7.2%. Within the sampled parameter domain, the Level-2 model provides a spatial interpretation of the optimized design through the distributions of the three advective exergy-flux components.