  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.
