Quantitative characterization of triangular leakage flow in a shell-and-tube heat exchanger with Y-shaped helical baffles

Triangular leakage flow near adjacent baffle junctions is a typical bypass-flow problem in discontinuous helical baffle shell-and-tube heat exchangers, which weakens transverse disturbance and local heat transfer. However, existing evaluations still rely largely on qualitative flow visualization, and a quantitative criterion for characterizing leakage intensity remains lacking. To address this limitation, a physically interpretable flow–thermal leakage index, Lx , was developed for a shell-and-tube heat exchanger equipped with Y-shaped helical baffles, extending triangular leakage assessment beyond conventional qualitative visualization. Based on a numerical model validated against experimental data, four dimensionless descriptors representing direct-flow tendency, transverse disturbance, velocity deviation, and temperature-gradient variation were integrated using a multivariable power-law function and calibrated against section-wise leakage-rate data. Among these descriptors, velocity deviation shows the strongest positive contribution to Lx , whereas transverse disturbance and temperature-gradient variation are negatively correlated with leakage intensity. The fitted expression shows good agreement with the calibration data, with R 2 = 0.9968 and a mean absolute percentage error of 6.15%. In the core heat-transfer region, the Y-shaped structure reduces the axial mean Lx from 0.0830 to 0.0591, corresponding to a decrease of approximately 28.8%. The proportion of high-leakage cross-sections with Lx > 0.08 decreases from 65.52% to 10.34%, while the mean area-averaged wall heat flux increases by approximately 19.8%. These results demonstrate that Lx provides a quantitative flow–thermal criterion for identifying and comparing triangular leakage and offers a useful basis for leakage-suppression-oriented design of discontinuous helical baffle heat exchangers.