Numerical investigation on friction factor of rectangular mini-channel with staggered Pin-Fin: Effects of pitch geometry

Abstract

This study presents a comprehensive numerical investigation of friction-factor behavior in staggered square pin-fin minichannels across a wide Reynolds-number range (30 ≤ Re ≤7000). Three geometric configurations defined by the spacing ratio SH/S= 0.5, 1, 2 were evaluated to quantify the influence of pin spacing on pressure drop, flow development, and turbulence onset. The simulations employed the k-ε model with enhanced wall treatment, with near-wall resolution verified through y + analysis and a mesh-independence assessment supported by the Grid Convergence Index. Results show that all geometries exhibit a smooth, monotonic transition from laminar to turbulent flow without a distinct transition point, owing to the strong disturbance induced by the staggered pin arrangement. Flow visualization confirms attached flow at low Reynolds numbers and progressively stronger recirculation and vortex structures as inertia increases, with the densest spacing (SH/S=0.5)producing the highest turbulence intensity and hydraulic resistance. Based on the numerical database, a new friction-factor correlation was developed. Regime-specific expressions were first obtained for laminar, transitional, and turbulent regions, after which the geometric effects were generalized through a power-law dependence on SH/S. These expressions were consolidated into a single unified correlation using a maximum-based blending approach. Validation against CFD data demonstrates deviations below 10 % across all spacing ratios and flow regimes. The proposed correlation provides an accurate and practical predictive tool for pressure-loss estimation in compact heat exchangers and thermal management systems employing staggered square pin-fin structures.