Assessment of local isotropy, energetics, and modified eddy-viscosity based modelling for particle-laden turbulent channel flows

A large number of turbulence models (stochastic and large-eddy simulation (LES) models) developed to describe the dynamics of particle-laden turbulent flows are 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. 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, Phys. Fluids , vol. 7, no. 11, 1995, pp. 2778–2784). However, several numerical studies, majorly in the area of multiphase flows at low and intermediate Reynolds numbers, consider that the Kolmogorov constant remains unchanged irrespective of whether the flow is single phase or multiphase. In this article, we assess the variation of local isotropy of the 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 the case of low-Reynolds-number turbulent flows. Our study reveals that the Kolmogorov constant decreases in the channel centre with an increase in the particle volume fraction for the range of Reynolds numbers 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 modelling technique is adopted using the large-eddy simulation (LES) to predict the fluid phase statistics without solving simultaneous particle phase equations. The new methodology also helps to qualitatively understand the phenomena of drastic collapse in turbulence intensity.