Assessment of local isotropy, Kolmogorov constant, and modified eddy viscosity-based modeling for particle-laden turbulent channel flows

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.