  A large number of models which address the dynamics of particle-laden
turbulent flows have been developed based on the assumption of local isotropy
and use the Kolmogorov constant that correlates the spectral distribution of
turbulent kinetic energy with the turbulent dissipation rate. Many turbulence
models (Stochastic and LES models) use the Kolmogorov constant in the
formulation. Compilation of a large number of experimental data for different
flow configurations has revealed that the Kolmogorov constant is independent of
Reynolds number in the limit of high Reynolds number (Sreenivasan, 1995).
However, several numerical studies at low and intermediate Reynolds numbers
which address the flow situations of practical importance consider that the
Kolmogorov constant remains unchanged irrespective of whether the flow is
single phase or multiphase. In the present work, we assess the variation of
local isotropy of fluid fluctuations with the increase in particle loading in
particle-laden turbulent channel flows. We also estimate the Kolmogorov
constant using second-order velocity structure functions and compensated
spectra in case of low Reynolds number turbulent flows. Our study reveals that
the Kolmogorov constant decreases in the channel center with an increase in the
particle volume fraction for the range of Reynolds number investigated here.
The estimated variation of the Kolmogorov constant is used to express the
Smagorinsky coefficient as a function of solid loading in particle-laden flows.
Then, a new modeling technique is adopted using the large eddy simulation (LES)
to predict the fluid phase statistics without solving simultaneous particle
phase equations. This new methodology also helps understand the drastic
decrease in turbulence intensity at critical particle volume loading.
