Drag, lift and torque correlations for axi-symmetric non-spherical particles in locally non-uniform flows

This paper derives new correlations to predict the drag, lift and torque coefficients of axi-symmetric non-spherical rod-like particles for several fluid flow regimes and velocity profiles. The fluid velocity profiles considered are locally uniform flow and locally linear shear flow. The novel correlations for the drag, lift and torque coefficients depend on the particle Reynolds number \Rep, the orientation of the particle with respect to the main fluid direction $\theta$, the aspect ratio of the rod-like particle $\alpha$, and the dimensionless local shear rate $\tilde{G}$. The effect of the linear shear flow on the hydrodynamic forces is modeled as an additional component for the resultant of forces acting on a particle in a locally uniform flow, hence the independent expressions for the drag, lift and torque coefficients of axi-symmetric particles in a locally uniform flow are also provided in this work. The data provided to fit the coefficient in the new correlation are generated using available analytical expressions in the viscous regime, and performing direct numerical simulations (DNS) of the flow past the axi-symmetric particles at finite particle Reynolds number. The DNS are performed using the direct-forcing immersed boundary method. The coefficients in the proposed drag, lift and torque correlations are determined with a high degree of accuracy, where the mean error in the prediction lies below $2\%$ for the locally uniform flow correlations, and below $1.67\%$, $5.35\%$, $6.78\%$ for the correlations accounting for the change in the drag, lift, and torque coefficients in case of a linear shear flow, respectively. The proposed correlations for the drag, lift and torque coefficients can be used in large-scale simulations performed in the Eulerian-Lagrangian framework with locally uniform and non-uniform flows.