Nusselt Number Correlation for Elliptical Helical Coils Based on Computational Fluid Dynamics and Experiments

A helical coil is an important component of wrapped helical-coil heat exchangers around an external tank, which helps reduce direct contact between the working fluid in the coil and the fluid inside the tank. Therefore, it is suitable for applications requiring contamination control. However, the design of this type of coil still has limitations, because the correlations used to predict the Nusselt number (𝑁𝑢), which is an indicator of heat transfer performance, have mostly been developed for circular-cross-section helical coils. Meanwhile, elliptical cross-section tubes have the potential to increase the contact area with the tank wall and modify the flow structure inside the tube. This study investigates the effects of cross-sectional ovality (δ) and coil curvature. Dh / Dcoil , and flow conditions on the Nusselt number (𝑁𝑢) and internal flow behavior of elliptical helical coils. Three elliptical cross-section coil configurations were used as experimental reference data, and nine computational fluid dynamics simulation cases were conducted under different values of δ and Dh / Dcoil ​. The results showed that increased with Reynolds number (𝑅𝑒) and Dean number (𝐷𝑛), while variations in and modified the secondary-flow distribution and the effectiveness of thermal boundary-layer disturbance. Higher ovality produced a more concentrated asymmetric velocity field, whereas lower ovality resulted in a broader velocity distribution across the tube cross-section. The newly developed correlation predicted with high accuracy, yielding R2. = 0.972, MAPE = 5.36%, RMSE = 1.84, and a cross-validation of MAPE 5.94%, supporting its use within the studied range.