Ideal stochastic forcing for the motion of particles in large-eddy simulation extracted from direct numerical simulation of turbulent channel flow

The motion of small particles in turbulent conditions is influenced by the entire range of length- and time-scales of the flow. At high Reynolds numbers this range of scales is too broad for direct numerical simulation (DNS). Such flows can only be approached using large-eddy simulation (LES), which requires the introduction of a sub-filter model for the momentum dynamics. Likewise, for the particle motion the effect of sub-filter scales needs to be reconstructed approximately, as there is no explicit access to turbulent sub-filter scales. To recover the dynamic consequences of the unresolved scales, partial reconstruction through approximate deconvolution of the LES-filter is combined with explicit stochastic forcing in the equations of motion of the particles. We analyze DNS of high-Reynolds turbulent channel flow to a priori extract the ideal forcing that should be added to retain correct statistical properties of the dispersed particle phase in LES. The probability density function of the velocity differences that need to be included in the particle equations and their temporal correlation display a striking and simple structure with little dependence on Reynolds number and particle inertia, provided the differences are normalized by their RMS, and the correlations expressed in wall units. This is key to the development of a general "stand-alone" stochastic forcing for inertial particles in LES