Accurate hydrodynamic force and torque correlations for prolate spheroids from Stokes regime to high Reynolds numbers

Detailed simulations of flow around various prolate spheroids are performed using multi-relaxation time lattice Boltzmann method (LBM). The simulations are performed in the Reynolds numbers range 0.1≤Re≤2000 at different incident angles 0^∘≤ϕ≤90^∘ for various prolate spheroids of aspect ratios 1≤λ≤8. The Re is based on the volume equivalent sphere diameter. From the simulations, accurate correlations for average drag, lift and torque coefficients (C_D, C_L, and C_T respectively) are proposed. The mean deviations between the correlations and the simulation data for C_D, C_L, and C_T are 2%, 6.5%, and 4.7% respectively. Furthermore, the correlations are fitted with the physics in mind such that they can be extrapolated beyond the regimes simulated. The fits are designed such that correlations reduce to analytical (C_D and C_L) solutions available for prolate spheroids in the limit Re≈0. At high Re, the correlations mimic the asymptotic flattening of C_D as for spheres and therefore, we expect the correlations to be valid until the critical Re (≈10⁵). Furthermore, extensive comparison of our correlations with other high-fidelity simulations from literature demonstrate the accuracy of our work compared to other correlations from literature. This work enables researchers to perform accurate unresolved Euler-Lagrangian simulations for a wide range of elongated particles.