Direct numerical simulation of secondary currents in annular sector ducts

This study investigates Prandtl's secondary flow of the second kind in annular sector ducts (angle π/3) through direct numerical simulations based on high-order spectral element methods. Simulations cover fully developed turbulent conditions at Reτ=150−519, aiming to fill a key literature gap on secondary flow in complex ducts and support the refined design and performance optimization of propulsion pumps. Results indicate that the secondary flow intensity reaches ∼2%–3% of the bulk velocity; although this level exceeds that in square ducts, its impact on the mean flow is weaker. As Reτ increases, the secondary flow strength diminishes, where the dimensionless secondary flow intensity for Reτ=519 is reduced by 32.35% compared to Reτ=150, and the flow pattern evolves from the wall center toward the corners, forming a distinct eight-vortex triangular pattern. The geometric aspect ratio also influences the dynamics: the secondary flow intensity of the flattened configuration (η=1/2) is reduced by 3% compared with η=1/3 and 1/4 and yields a more uniform wall shear stress. Statistical distributions in the concave sector exhibit self-similarity, while those in the convex region display strong Reynolds number dependence, converging at high Reτ. At Reτ=150 and 227, the anisotropy of Reynolds stresses serves as the primary driver for generating and sustaining the secondary flow. In contrast, at Reτ=519, turbulence is governed by intricate three-dimensional vortical structures and broad-scale energy cascades, diminishing the secondary flow's relative influence. Finally, the non-monotonic variation in flow distortion and wall friction reflects a weakening geometric influence, signaling a qualitative transition: from scale-free separation at low Reynolds numbers to a regime dominated by corner vortex separation and core circulation at high Reynolds numbers.