Inertial loads on a finite-length cylinder embedded in a steady uniform flow

Direct numerical simulations are performed to evaluate the hydrodynamic forces and torque on finite-length cylinders embedded in a uniform flow for a wide range of aspect ratios (2 chi 30). Both viscous-dominated and moderately inertial regimes are investi-gated. We start the investigation by comparing the numerical results to the predictions of the Khayat and Cox [J. Fluid Mech. 209, 435 (1989)] slender-body theory. We show that this theory can predict with reasonable accuracy the drag force on the cylinder for a large range of aspect ratios. However, the theory is unable to predict accurately the lift force and torque for moderately long cylinders of chi < 30. By performing a careful analysis of the local contributions to the loads, we show that the disagreement with the theory is mainly explained by the contribution of the cylinder ends which are not properly taken into account by the theory. Semiempirical models based on theoretical results for small but finite inertia are then built to provide a better match with the numerical predictions. We show as in the slender-body theory that the relevant Reynolds number is based on the particle length. We also derive a ready-to-use tensorial formulation for the forces and inertial torque. Additionally, we compare the whole model to experimental results of settling cylinder showing better agreement than the slender-body theory.