We report the first direct numerical simulations using a recently introduced exact director-based formulation of the equations of motion for inertial spheroids in turbulence. The simulations consider homogeneous isotropic flow across a broad range of particle aspect ratios (from disklike to rodlike) and Stokes numbers (masses), both with and without gravity. The results reveal that particle shape and finite inertia induce complex, nonmonotonic trends in preferential clustering. Gravity markedly alters these dynamics, enhancing small-scale clustering for rod- and disklike particles while suppressing clustering for nearly spherical particles; we propose an explanation for this behavior. We confirm that at weak inertia, rodlike spheroids tend to align with the flow's major stretching direction, whereas disklike spheroids align with its major shrinking direction. We derive a generalization to the case of finite inertia, establishing preferred alignment directions that do not coincide with the flow's principal Lagrangian stretching or shrinking axes, and provide preferential alignment directions across all examined Stokes numbers and gravity conditions. We also confirm that gravity makes the symmetry axis of disklike particles orient preferentially horizontally. Finally, we introduce an efficient framework for computing Lyapunov exponents and their generalizations for inertial particles. Given its superior efficiency and ability to unify previously disparate data, we believe our approach should serve as a foundation for future simulations and a powerful tool for both theoretical and numerical studies of spheroids in turbulence.

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• Fluid-particle interactions
• Particle-laden flows