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 ( 0.02 less than or equals upper R e Subscript p Baseline less than or equals 200 0.02 ≤ R e p ≤ 200 0.02 ≤ Re_p ≤ 200 ), 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 ≈ 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 ≈ 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.