Flow and thermal behavior of hexagonal versus square jets in multi-jet impingement systems: A numerical perspective

This study presents a novel numerical investigation of the influence of jet geometry on flow dynamics and thermodynamic performance in multi-jet impingement systems, comparing hexagonal and square jet arrays using air as the working fluid across a Reynolds number range of 8000–24000. The ANSYS Fluent was used to perform three-dimensional simulations with the shear stress transport (SST) k-ω turbulent flow model and second-order upwind discretization. Flow behaviour was measured through vorticity magnitude, Q-criterion, and swirl strength index, and thermal performance was measured using the thermal uniformity index (U _thermal ) as well as the local entropy generation (S _gen ) and thermal mixing index (TMI). Compared to square jets, hexagonal jets showed a maximum of 0.41% improvement in U _thermal -field uniformity. An improvement of about 0.41% is modest, as the area covered by the jets is comparatively confined. Though there was an increase in total entropy generation by 42.6 percent at Re = 12000, it was attributed to enhanced vortex breakdown and shear-layer interactions that increased mixing. On the same Reynolds number, hexagonal jets exhibited up to 61.3% higher TMI, which indicated excellent near-wall mixing and thermal dispersion. Flow diagnostics confirmed that hexagonal jets generated stronger swirl intensity and more spatially distributed, isotropic vortical structures--characterized by strong vorticity, coherent vortex core (Q-criterion), and fine-scale λ₂ features-enhancing convective mixing and disruption of the boundary layer. Although these were improved, the pressure drop was within the range of ±5% of square jets in all cases, indicating no significant hydraulic penalty. The hexagonal jet is a good potential solution in high-performance cooling applications, including turbine blade cooling and small electronic thermal management, due to its balanced performance profile with better thermal uniformity, improved mixing, and reasonable entropy cost.