  A cascade model is described based on multiplier distributions determined
from 3D direct numerical simulations (DNS) of turbulent particle laden flows,
which include two-way coupling between the phases at global mass loadings equal
to unity. The governing Eulerian equations are solved using pseudo-spectral
methods on up to 512**3 computional grid points. DNS results for particle
concentration and enstrophy at Taylor microscale Reynolds numbers in the range
34 - 170 were used to directly determine multiplier distributions (PDFs) on
spatial scales 3 times the Kolmogorov length scale. The width of the PDFs,
which is a measure of intermittency, decreases with increasing mass loading
within the local region where the multipliers are measured. The functional form
of this dependence is not sensitive to Reynolds numbers in the range
considered. A partition correlation probability is included in the cascade
model to account for the observed spatial anticorrelation between particle
concentration and enstrophy. Joint probability distribution functions of
concentration and enstrophy generated using the cascade model are shown to be
in excellent agreement with those derived directly from our 3D simulations.
Probabilities predicted by the cascade model are presented at Reynolds numbers
well beyond what is achievable by direct simulation. These results clearly
indicate that particle mass loading significantly reduces the probabilities of
high particle concentration and enstrophy relative to those resulting from
unloaded runs. Particle mass density appears to reach a limit at around 100
times the gas density. This approach has promise for significant computational
savings in certain applications.
