Regime transitions in flow past porous spheres: the competition between internal inertial dissipation and wake suppression

The aerodynamic drag of porous spheres is governed by a regime-dependent competition between permeability-induced drag reduction and internal inertial dissipation. Using a hierarchical constructive solid geometry framework and pore-resolved lattice Boltzmann simulations (

), we identify two non-monotonic transitions. First, a porosity-driven drag reversal occurs near

upper R e Subscript p Baseline almost equals 20 R e p ≈ 20 $Re_{{p}} \approx 20$

: in the viscous regime, increased porosity mitigates resistance by relieving windward stagnation pressure; conversely, in the inertial regime, the dominance of distributed internal Forchheimer resistance creates a drag penalty that offsets the benefits of macroscopic wake suppression. Second, a surface-area-driven drag crossover emerges in the transitional regime (

upper R e Subscript p Baseline almost equals 20 minus 50 R e p ≈ 20 − 50 $Re_{{p}} \approx 20 {-} 50$

), where a finer internal skeleton structurally reorganises the penetrating flow to attenuate the near-wake recirculation intensity. We propose a physically based semi-empirical drag correlation that explicitly superposes viscous friction, boundary-layer development and inertial drag terms. The model captures the simulated aerodynamic responses and is validated against independent experiments, providing a quantitative framework for characterising the aerodynamic behaviour of permeable particles.