Effects of curvature on turbulent flow in concentric annuli and curved channels

We investigate turbulent flow between two concentric cylinders, oriented either axially or azimuthally. The axial configuration corresponds to a concentric annulus, where curvature is transverse to the flow, while the azimuthal configuration represents a curved channel with longitudinal curvature. Using direct numerical simulations, we examine the effects of both types of curvature on turbulence, varying the inner radius from $r_i=0.025\delta$ to $r_i=95.5\delta$ , where $\delta$ is the gap width. The bulk Reynolds number, based on bulk velocity and $\delta$ , is set at $R_b\approx 5000$ , ensuring fully turbulent conditions. Our results show that transverse curvature, although breaking the symmetry of axial flows, induces limited changes in the flow structure, leading to an increase in friction at the inner wall. In contrast, longitudinal curvature has a significant impact on the structure and statistics of azimuthal flows. For mild to moderate longitudinal curvatures ( $r_i\gt 1.5\delta$ ), the convex wall stabilises the flow, reducing turbulence intensity, wall friction and turbulent kinetic energy (TKE) production. For extreme longitudinal curvatures ( $r_i\leqslant 0.25\delta$ ), spanwise-coherent flow structures develop near the inner wall, leading to a complete redistribution of the TKE budget: production becomes negligible near the inner wall, while pressure–velocity correlations increase substantially. As a result, the mean TKE peaks near the inner wall, thereby weakening the stabilising effect of convex curvature.