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

Abstract

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 (CD, CL, and CT respectively) are proposed. The mean deviations between the correlations and the simulation data for CD, CL, and CT 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 (CD and CL) solutions available for prolate spheroids in the limit Re≈0. At high Re, the correlations mimic the asymptotic flattening of CD 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.