Drag reduction in numerical two-phase Taylor–Couette turbulence using an Euler–Lagrange approach

Abstract

Two-phase turbulent Taylor–Couette (TC) flow is simulated using an Euler–Lagrange approach to study the effects of a secondary phase dispersed into a turbulent carrier phase (here bubbles dispersed into water). The dynamics of the carrier phase is computed using direct numerical simulations (DNS) in an Eulerian framework, while the bubbles are tracked in a Lagrangian manner by modelling the effective drag, lift, added mass and buoyancy force acting on them. Two-way coupling is implemented between the dispersed phase and the carrier phase which allows for momentum exchange among both phases and to study the effect of the dispersed phase on the carrier phase dynamics. The radius ratio of the TC setup is fixed to ${\it\eta}=0.833$, and a maximum inner cylinder Reynolds number of $Re_{i}=8000$ is reached. We vary the Froude number ($Fr$), which is the ratio of the centripetal to the gravitational acceleration of the dispersed phase and study its effect on the net torque required to drive the TC system. For the two-phase TC system, we observe drag reduction, i.e. the torque required to drive the inner cylinder is lower compared with that of the single-phase system. The net drag reduction decreases with increasing Reynolds number $Re_{i}$, which is consistent with previous experimental findings (Murai et al., J. Phys.: Conf. Ser., vol. 14, 2005, pp. 143–156; Phys. Fluids, vol. 20(3), 2008, 034101). The drag reduction is strongly related to the Froude number: for fixed Reynolds number we observe higher drag reduction when $Fr<1$ than for with $Fr>1$. This buoyancy effect is more prominent in low $Re_{i}$ systems and decreases with increasing Reynolds number $Re_{i}$. We trace the drag reduction back to the weakening of the angular momentum carrying Taylor rolls by the rising bubbles. We also investigate how the motion of the dispersed phase depends on $Re_{i}$ and $Fr$, by studying the individual trajectories and mean dispersion of bubbles in the radial and axial directions. Indeed, the less buoyant bubbles (large $Fr$) tend to get trapped by the Taylor rolls, while the more buoyant bubbles (small $Fr$) rise through and weaken them.