Coupled heat and moisture transfer in elliptical semi-permeable membrane fiber bundles for membrane distillation desalination

Hollow fiber membrane contactors (HFMCs) are effective heat and moisture exchangers for membrane distillation desalination. To address the elliptical deformation with equal perimeter during the processing of fiber tubes, the low-Reynolds-number turbulent phenomena in cross-flow configurations, and the coupled heat and moisture transfer across semi-permeable membranes between the solution and air, this study establishes a low-Re k-ε turbulence model under natural boundary conditions for a cross-flow elliptical fiber membrane contactor (EHFMC). The flow fields, turbulent kinetic energy fields, temperature fields, and concentration/humidity fields of the solution and air inside the membrane contactor were analyzed in detail. The effects of air Reynolds number, semi-axial ratio and pitch-diameter ratio of elliptical fiber are studied. A membrane-based air humidification-dehumidification desalination experimental platform was constructed to validate the mathematical model. The average Nusselt and Sherwood number (Nu_a, Sh_a) under naturally formed boundary conditions are compared with those under constant wall temperature boundary conditions. The results show that the air flow field significantly affects the temperature and concentration fields of the air. The cross-membrane heat transfer between air and solution is significantly more pronounced than the cross-membrane moisture transfer. Maximizing the semi-axis ratio and adopting a tighter fiber packing arrangement are recommended to achieve optimal comprehensive performance factor j/(f_a)^1/3. The constant wall temperature boundary is barely used to predict the heat transfer performance of fiber bundles at low turbulence intensity (with a deviation of 18.3 % for Nu_a at b/a < 1.0). The Chilton-Colburn heat-mass analogy is not suitable for calculating the turbulent mass transfer performance of EHFMC (even if the b/a < 1.0, the Sh_a deviation is about 29.5 %). These research findings are of significant guidance for the design and optimization of EHFMC.