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A cascade model is described based on multiplier distributions determinedfrom 3D direct numerical simulations (DNS) of turbulent particle laden flows,which include two-way coupling between the phases at global mass loadings equalto unity. The governing Eulerian equations are solved using pseudo-spectralmethods on up to 512**3 computional grid points. DNS results for particleconcentration and enstrophy at Taylor microscale Reynolds numbers in the range34 - 170 were used to directly determine multiplier distributions (PDFs) onspatial scales 3 times the Kolmogorov length scale. The width of the PDFs,which is a measure of intermittency, decreases with increasing mass loadingwithin the local region where the multipliers are measured. The functional formof this dependence is not sensitive to Reynolds numbers in the rangeconsidered. A partition correlation probability is included in the cascademodel to account for the observed spatial anticorrelation between particleconcentration and enstrophy. Joint probability distribution functions ofconcentration and enstrophy generated using the cascade model are shown to bein excellent agreement with those derived directly from our 3D simulations.Probabilities predicted by the cascade model are presented at Reynolds numberswell beyond what is achievable by direct simulation. These results clearlyindicate that particle mass loading significantly reduces the probabilities ofhigh particle concentration and enstrophy relative to those resulting fromunloaded runs. Particle mass density appears to reach a limit at around 100times the gas density. This approach has promise for significant computationalsavings in certain applications.

A Cascade Model for Particle Concentration and Enstrophy in Fully Developed Turbulence with Mass Loading Feedback