Mechanisms of lift generation and drag invariance by asymmetric surface roughness on a sphere

Abstract

The mechanisms governing transverse force generation on a sphere with asymmetric dimpled roughness are investigated using wall-resolved large eddy simulation at $Re=U_\infty d/\nu=100{,}000$ for $k/d=0.004$, $0.006$, and $0.008$. Previous experiments by Sudarsana et al. (2024) showed that asymmetric roughness can generate lift comparable to the peak Magnus force on a rotating sphere while leaving the mean drag nearly unchanged. The present simulations reproduce this behavior and reveal the coupled mechanisms responsible for lift generation and drag invariance. Pressure-force decomposition shows that asymmetric dimples redistribute the streamwise pressure contribution between the upstream and downstream hemispheres with little change in net drag, while producing a finite transverse pressure imbalance that generates lift. A Fourier decomposition further shows that pressure drag is governed primarily by the axisymmetric pressure component, whereas lift is governed by the non-axisymmetric component. The dimples also produce distinct transition pathways on the two hemispheres: the dimpled side undergoes near-wall transition before separation, delaying separation non-uniformly to $\phi_s\sim105^\circ - 125^\circ$, while the smooth side separates in a laminar state at $\phi_s\sim80^\circ$. The resulting pressure asymmetry drives sidewash from the smooth to the dimpled side, which rolls up into a counter-rotating streamwise vortex pair that amplifies wake deflection beyond that expected from separation-angle differences alone. These results show that lift generation arises from the coupled interaction of asymmetric transition, non-uniform separation, pressure-driven sidewash, and coherent wake reorganization.