Role of settling inertial particles in modulating flow structures and drag in Taylor-Couette turbulence

The modulation of drag through dispersed phases in wall turbulence has been a longstanding focus. This study examines the effects of particle Stokes number ($St$) and Froude number ($Fr$) on drag modulation in turbulent Taylor-Couette (TC) flow, using a two-way coupled Eulerian-Lagrangian approach with Reynolds number $Re_i = r_i \omega_i d/\nu$ fixed at 3500. For light particles (small $St$), drag reduction is observed in the TC system, exhibiting a non-monotonic dependence on $Fr$. In specific, drag reduction initially increases and then decreases with stronger influence of gravitational settling (characterized by inverse of $Fr$), indicating the presence of an optimal $Fr$ for maximum drag reduction. For heavy particles, similar non-monotonic trend can also be observed, but significant drag enhancement is resulted at large $Fr^{-1}$. We further elucidate the role of settling particles in modulating the flow structure in TC by decomposing the advective flux into contributions from coherent Taylor vortices and background turbulent fluctuations. At moderate effects of particle inertia and gravitational settling, particles suppress the coherence of Taylor vortices which remarkably reduces angular velocity transport and thus leads to drag reduction. However, with increasing influence of particle inertia and gravitational settling, the flow undergoes abrupt change. Rapidly settling particles disrupt the Taylor vortices, shifting the bulk flow from a vortex-dominated regime to one characterized by particle-induced turbulence. With the dominance by particle-induced turbulence, velocity plumes -- initially transported by small-scale G{\"{o}}rtler vortices near the cylinder wall and large-scale Taylor vortices in bulk region -- are instead carried into the bulk by turbulent fluctuations driven by the settling particles.