Modelling drag coefficients of ellipsoidal particles in rarefied flow conditions

The importance of accurately capturing two-way coupled interactions between particles with complex shapes and rarefied gas flows is rapidly rising in different practical applications such as aerospace industry and semiconductor manufacturing. The transport of particles in these conditions is often modelled via an Euler-Lagrangian Point-Particles approach, where rarefaction effects are included through the phenomenological Cunningham corrections on the drag force experienced by the particles. In Point-Particles approaches, any explicit relation to the finite size of the particles, shape, orientation and momentum accommodation coefficient is typically neglected. In this work we aim to cover this gap by deriving, from fully-resolved DSMC simulations, heuristic models for the drag force acting on ellipsoidal particles with different aspect ratios. We include in the models the capability to predict effects related to gas-surface interactions via the tangential momentum accommodation coefficient (TMAC). The derived models can be used as corrections (to include shape, orientation and TMAC effects) in standard Euler-Lagrangian Point Particles simulations in rarefied gas flows. Additionally, we show that the obtained drag corrections, formally valid for unbounded gas flows, can potentially be applied also in cases where the particle moves in proximity to a solid wall. We do so by investigating near-wall effects on the drag of a prolate ellipsoidal particle. Due to confinement effects, the drag increases when compared to the unbounded case, but such effects are typically negligible for large $Kn$ also in cases in which the particle is in contact with the solid wall.