A geometry-sensitive strouhal number approach for characterizing spacer-induced convective transport in membrane distillation channels

Direct Contact Membrane Distillation (DCMD) performance is strongly influenced by spacer-induced hydrodynamics within the feed channel. Although spacers are widely used to enhance convective transport, a geometry-normalized dimensionless metric for consistent spacer comparison remains lacking. In this study, a Strouhal number defined in the channel-height direction (St_y) is introduced as a dimensionless indicator of spacer-induced transverse flow restructuring and boundary-layer disruption. Unlike classical frequency-based Strouhal formulations, St_yis derived from convective scaling and reflects effective streamline displacement normalized by channel height. Five DCMD configurations (no spacer, 1-, 3-, and 5-cylinder spacers, and a commercial net spacer) were investigated experimentally and through validated three-dimensional CFD simulations. The results demonstrate a monotonic relationship between St_y, Temperature Polarization Coefficient (TPC), convective heat transfer coefficient, and permeate flux. The net spacer increased the convective heat transfer coefficient by approximately 3.5 times and permeate flux by 33% relative to the baseline configuration. However, spacer-induced enhancement was accompanied by substantial hydraulic penalties. Pressure drop increased up to 60-fold compared to the no-spacer case. When evaluated using a Performance Evaluation Criterion (PEC) under constant pumping power conditions, moderate spacer insertion provided the most balanced performance, while highly obstructive geometries exhibited diminishing energetic returns. The proposed St_ycomplements Reynolds and Nusselt numbers by providing a geometry-sensitive hydrodynamic descriptor, while PEC enables integrated transport–hydraulic assessment. Together, they establish a consistent framework for spacer performance evaluation in DCMD channels.