On the robustness of adjoint shape optimization method when applied to the optimal design of vortex generators: The impact of the Reynolds number

This study systematically investigates the Reynolds number impact on the robustness of an adjoint shape-optimized winglet pair (OWP) vortex generator (VG). Computational Fluid Dynamics (CFD) investigations are performed at different Reynolds numbers 500 ≤ Re ≤ 15 , 000 . Results are compared to the delta winglet pair (DWP) VG design and to empty channel case. For all Reynolds numbers, both VGs (DWP and OWP) showed a net improvement over the smooth empty channel ( TPF > 1 ), with highest gains occurring at intermediate Reynolds numbers values. The optimal OWP design, initially optimized at Re = 4600 , consistently outperformed the DWP for all 500 ≤ Re ≤ 15 , 000 . This was combined with comparable heat-transfer enhancement with a systematically lower friction penalty as an advantage widening under turbulent flow regime. At Re = 4600 , the OWP achieves Nu / Nu 0 ≃ 1 . 52 with f / f 0 ≃ 1 . 77 , yielding TPF ≃ 1 . 26 , whereas the DWP yields Nu / Nu 0 ≃ 1 . 47 , f / f 0 ≃ 2 . 01 and TPF ≃ 1 . 16 . The out-performance is induced by more coherent and persistent vortex system generated by the OWP, evidenced by slower downstream circulation decay and broader near-wall mixing footprints. The present research findings demonstrate, that an optimal GV design obtained under a single Reynolds number condition can still be robust in terms of its thermo-hydraulic performance even when operating under a wide range of Reynolds numbers. This motivates investigating multi-condition and multi-space design optimization exploration as a future perspective when it comes to broadband VGs multidisciplinary design and optimization.