Influence of dimple configuration on torque reduction in Taylor–Couette flow

Dimple roughness substantially modifies the torque response of Taylor–Couette (TC) flow, yet the respective roles of dimple depth, curvature radius, and dimple orientation remain unclear. Here, direct numerical simulations are performed for a TC system with radius ratio η=0.714 and aspect ratio Γ=4 at Re=400 (laminar) and Re=3960 (turbulent) to quantify how dimple geometry affects the total torque. The inner-cylinder torque is decomposed into friction- and pressure-induced components, T=Tτ+Tp, to assess dimples with varying configurations. Two geometric parameters are investigated systematically: dimple depth and curvature radius. First, increasing the dimple depth consistently decreases Tτ but increases Tp in both regimes. Consequently, shallow dimples yield the largest net torque reduction in the laminar regime, whereas deeper dimples amplify the pressure contribution and lead to net torque enhancement in the turbulent regime. Furthermore, variations in curvature radius produce only weak changes in the laminar regime but pronounced differences in turbulence; increasing the curvature radius increases roughness coverage and tends to reduce Tτ, while simultaneously enlarging the effective pressure-acting area and enhancing Tp. Finally, guided by these trends, an optimized high-coverage configuration with shallow depth and small curvature radius is designed and achieves net torque reduction in both regimes, yielding reductions of 8.5% (laminar) and 3.1% (turbulent). These results provide physics-based guidance for designing dimpled surfaces to reduce torque losses in rotating machinery, such as electric motors and turbine shafts.