Effects of Submerged Swirl-Generating Pier Geometry on Discharge Capacity and Swirling Flow in an Annular-Weir Shaft Spillway

Submerged swirl-generating piers guide inflow toward an annular weir and promote rotating flow in the upper shaft, but also restrict the inlet passages. This study examines the resulting tradeoff using a 1:50 Froude-scaled physical model and three-dimensional Reynolds-averaged Navier–Stokes simulations with an RNG k–ε closure and a volume-of-fluid (VOF) formulation. Pier number N, connection angle θ, and length L are varied over 4~12, 5–25°, and 12~20 m, respectively, in prototype dimensions. Three inlet regimes are observed within the tested range: free-pier flow at H/P < 0.9, transitional flow at 0.9 ≤ H/P ≤ 1.1, and submerged-pier flow at H/P > 1.1. A local discharge-coefficient minimum is observed near H/P ≈ 1.05, coinciding with the onset of overtopping; interaction between the upper and lower flow paths is a proposed explanation. Increasing pier number or length, or decreasing connection angle, generally increases predicted tangential velocity while reducing discharge capacity at a given head. At Q = 400 m3/s, increasing L from 12 to 20 m reduces the maximum inlet velocity magnitude from approximately 4.17 to 2.77 m/s while increasing predicted tangential velocity. These fixed-discharge comparisons include the accompanying change in head. The results describe the tested configurations; shaft velocities and air-core dynamics have not been independently validated.