Local head loss range analysis in sudden-expansion pipelines based on the S-A turbulence model

ABSTRACT In pressurized pipe systems, sudden expansions induce significant local head loss and cavitation-prone low-pressure zones, threatening pipe structural safety. By coupling theoretical scaling arguments with the Spalart–Allmaras (S-A) turbulence model, we quantify the recirculation zone and energy dissipation across Reynolds numbers Re = 1–105 and sudden-expansion ratios E = D/d = 1.5–5. Critical thresholds are identified for the post-expansion recirculation zone. When Re ≤ 20, a larger E increases the dimensionless post-expansion recirculation length L2/D; when Re ≥ 20, a higher E shortens L2/D. One additional critical thresholds are identified for the pre-expansion recirculation zone. Below Reb-cri2 = 5,000, viscous forces dictate the dimensionless pre-expansion recirculation length L1/D; above Reb-cri2 = 5,000, turbulence suppresses the bubble, and L1/D becomes virtually Re-independent. A physics-based correction model is introduced, explicitly linking the local head loss coefficient to L1/D and L2/D. From the resulting model, we derive three design principles: (i) maintain L1/D > 0.005 in laminar flow; (ii) minimize L2/D and select E = 3–4 in turbulent flow; and (iii) avoid the transitional range near the critical Reynolds number Reb-cri2 = 5,000, due to flow instability and high head loss dispersion. The findings clarify the coupling between geometric and flow that governs energy dissipation and cavitation inception, offering a theoretical basis for designing safer and more efficient hydraulic networks.