Interpolation of probability-driven model to predict hydrodynamic forces and torques in particle-laden flows

The development of hydrodynamic force/torque closure models with physical fidelity is crucial for ensuring reliable Euler-Lagrange simulations in particle-laden flows. Our previous work (Seyed-Ahmadi and Wachs. J Fluid Mech. 2020;900:A21) proposed a microstructure-informed probability-driven point-particle (MPP) method to construct a data-driven particle-position-dependent closure model, incorporating the effect of surrounding particle positions on forces/torques. However, the MPP model is not pluggable in Euler-Lagrange simulations due to the computation of constant coefficients through linear regression and reliance on statistical arguments to obtain the probability map for a pair of values of solid volume fraction (f) and Reynolds number (Re). To overcome this limitation, we propose an interpolated MPP (iMPP) method, involving interpolation in the f and Re spaces. Our results demonstrate that the iMPP method can capture over 70% of the total fluctuations in hydrodynamic forces/torques in approximately 97.8% of the tested cases. This advancement contributes to a more versatile closure model suitable for integration into E-L simulations.