Computational Fluid Dynamics Study on Head Loss Through 90° Elbows with Curvature Radius Variation

Pipe elbows are vital components in industrial fluid transport systems, where changes in flow direction often lead to energy losses and complex secondary flow phenomena. This study presents a Computational Fluid Dynamics (CFD)-based investigation on how the curvature ratio (R/D) of 90° elbows influences head loss, pressure distribution, velocity recovery, and downstream flow development. Simulations were performed for five R/D values (1.0, 1.47, 3.33, 3.67, and 7.66) under turbulent, single-phase flow at Reynolds numbers of 17,631.71 and 23,888.13. The results show that the head loss coefficient (K) decreases with increasing R/D up to approximately 3.67, beyond which it rises again due to extended wall friction. Elbows with larger R/D enable smoother flow redirection, faster velocity stabilization, and more uniform pressure fields, while small-radius elbows induce stronger separation, asymmetric profiles, and higher energy dissipation. These findings confirm a nonlinear relationship between geometry and hydraulic performance, highlighting an optimal curvature range for efficient design. The study adds scientific value by extending R/D coverage beyond common industrial standards and systematically analyzing flow recovery behavior. It concludes that elbows with R/D near 3.67 provide a favorable balance between minimizing separation and limiting frictional loss at moderate Re. These insights support more energy-efficient design strategies in piping networks. Future work is recommended to explore unsteady, multiphase, or thermally coupled flows for broader applicability.