Development and validation of a quasi-steady-state linear Element-by-Element cooling coil model in wet and dry part-load conditions

Cooling coils are multipass crossflow heat exchangers, yet they are often approximated as pure counterflow in modelling. This approximation can introduce significant deviations, particularly at reduced water flow rates. This study develops and validates a linear quasi-steady-state element-by-element cooling coil model to investigate detailed waterside part-load behaviour under combined dry and wet airside conditions. The cooling coil is divided into multiple elements aligned with the fluid flow of water through the coil. The enthalpy approach is decomposed into sensible and latent components, allowing for simultaneous solution of wet and dry cases within a single matrix. Actual fluid properties are used for each element to compute heat transfer from the water to the cooling coil's tube, including a correction factor for the serpentine number. The results of the developed element-by-element model were successfully compared with a lumped, single serpentine, pure counterflow model from existing literature under full-load conditions. At full load, the lumped model achieved a normalized mean absolute error of 2.3 %, while the element-by-element model exhibited a comparable normalized mean absolute error of 2.5 % for total capacity. In part-load scenarios, based on data from an operational chilled water system employing three cooling coils with a serpentine number below unity, the element-by-element model yielded normalized mean absolute errors of 5.3 %, 4.7 %, and 14.5 %. In contrast, the lumped model produced less accurate normalized mean absolute errors of 18.4 %, 13.8 %, and 23.6 %, respectively. For all four models investigated in this study, errors increased with fluid velocity up to a maximum around Re = 2,300, after which they decreased with further increases in velocity. During optimization, it was determined that the number of fins could be reduced to between 0.8 % and 3.0 % of the original count in the element-by-element model, achieving computation time savings of 98.2 %, 95.5 %, and 98.2 %, depending on the model size. This optimization resulted in only slightly increased normalized mean absolute errors with 0.2 %pt, 0.4 %pt, and 2.3 %pt, respectively. The findings indicate that both the heat exchanger arrangement and the serpentine number must be considered in part-load analysis when the cooling coil's capacity is controlled by varying the water mass flow rate.