Consistent closures for Euler-Lagrange models of bi-disperse gas-particle suspensions derived from particle-resolved direct numerical simulations

Particle-Resolved Direct Numerical Simulation (PR-DNS) is employed to simulate momentum and energy transport in bi-disperse gas-solid suspensions by means of a novel hybrid immersed-boundary/fictitious domain (HFD-IB) method. First, we demonstrate the accuracy of the new HFD-IB method against several verification tests. Subsequently, we simulate momentum and energy transfer in bi-disperse suspensions in the limit of high Stokes number, and the predicted flow and temperature fields are used, in conjunction with the open-source parallel data processing library CPPPO (Municchi et al., 2016), to assess the validity of existing closures for momentum and heat transfer in the frame of Particle-Unresolved Euler-Lagrange (PU-EL) models. We propose a correction to the drag force model proposed by Beetstra et al. (2009) which consistently takes into account the pressure contribution to the total fluid-particle interaction force in PU-EL models. Also, we propose a stochastic closure model for the per-particle drag coefficient based on a modified log-normal distribution. Finally, we assess the existence of an analogy between the particle-based drag coefficient and the conditionally-averaged Nusselt number. Indeed, our PR-DNS data indicates that a stochastic closure similar to that for the drag can be used to close the particle-based Nusselt number in dense bidisperse suspensions.