Thermo-hydraulic performance of TPMS transpiration cooling with directional porosity gradients

Spatial porosity gradients have been explored as an effective design strategy for triply periodic minimal surface (TPMS) heat exchangers. However, their influence on TPMS-based transpiration cooling remains insufficiently understood, especially regarding the coupled responses of film coverage, conjugate heat transfer and injection pressure penalty. Pore scale conjugate numerical simulations are performed to investigate TPMS transpiration cooling structures with linear porosity gradients along the mainstream direction and the secondary flow direction. Two typical topologies, P and G, are introduced to represent pore throat dominated and continuous curved channel structures, with linear porosity gradients along the mainstream and secondary flow directions at blowing ratios of 0.45% and 3.3%. The results show that the negative porosity gradient under mainstream direction exhibits a favorable thermo-hydraulic performance, especially at the low blowing ratio. The maximum enhancement reaches 6.46% for the P structure and 8.18% for the G structure. In contrast, a positive mainstream direction gradient delays upstream film formation and deteriorates cooling performance. The secondary flow direction gradient shows stronger dependence on topology and blowing ratio. Local low porosity bottlenecks in the P structure can induce throttling, film detachment, and an injection pressure increase of up to 997.3%, whereas the corresponding G cases show a maximum increase of only 12.4%. Conjugate heat transfer analysis further shows that porosity grading simultaneously redistributes external film protection and internal convective heat removal, while solid conduction spreads residual heat through the TPMS skeleton. Earlier film protection is spatially synchronized with an upstream shift in internal heat removal. By linking cooling enhancement with the associated injection pressure penalty, this study provides a mechanistic basis for selecting gradient direction and topology in TPMS based transpiration cooling.