A Lagrangian particle cloud model is proposed that accounts for the effectsof Reynolds-averaged particle and turbulent stresses and the averagedcarrier-phase velocity of the sub-particle-cloud scale on the averaged motionand velocity of the cloud. The SPARSE (Subgrid Particle Average Reynolds StressEquivalent) model is based on a combination of a truncated Taylor expansion ofa drag correction function and Reynolds averaging. It reduces the requirednumber of computational parcels to trace a cloud of particles inEulerian-Lagrangian methods for the simulation of particle-laden flow. Closureis performed in an a priori manner using a reference simulation where allparticles in the cloud are traced individually with a point particle model.Comparison of a first-order model and SPARSE with the reference simulation inone-dimension shows that both the stress and the averaging of the carrier-phasevelocity on the cloud subscale affect the averaged motion of the particle. Athree-dimensional isotropic turbulence computation shows that only onecomputational parcel is sufficient to accurately trace a cloud of tens ofthousand of particles.
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