Turbulence modulation by suspended finite-sized particles: Toward physics-based multiphase subgrid modeling

The presence of a dispersed phase substantially modifies small-scale turbulence. However, there has not been a comprehensive mechanistically based understanding to predict turbulence modulation. Based on the energy flux balance, we propose a theoretical model to predict the turbulent kinetic energy modulation in isotropic turbulence due to the dispersed phase. The comparison between model predictions and results from prior particle-resolved simulations and existing high-fidelity experiments supports the performance of the model over a range of turbulence and particle parameters. The model is then used to explore turbulence modulation characteristics over a wider parameter space formed by five independent system-controlling parameters, showing rather complicated dependence on the particle size and particle-to-fluid density ratio.

Figure 1

Comparison of turbulence modulation obtained in simulations/experiments ($y$ axis) against theoretical prediction using Eq. (4) ($x$ axis).

Figure 2

The ratio of multi to single-phase kinetic energy as a function of $D/\eta$ for the nonsettling case $u_r=0$: $R{e}_{\mathrm{\Delta }}=5$ (cross), 40 (circle), 400 (diamond). The blue, red, black, and purple color of the symbols indicate the condition falls into regime (i), (ii), (iii), and (iv) of $\mathrm{\Delta }u/u_{k,sp}$, respectively.

Figure 3

Same as Fig. 2 but for the settling case $u_r=2$.

Figure 4

Particle Reynolds number based on $\mathrm{\Delta }u$ plotted as a function of $D/\eta$. The different symbols correspond to $(R{e}_{\mathrm{\Delta }},u_r)=(5,0)$ (blue $+$), (40,0) (red circle), (400,0) (black diamond), (5,2) (blue asterisk), (40,2) (red right arrowhead), and (400,2) (black downward arrowhead). This figure is for nondimensional mean relative velocity for both $u_r=0.0$ and $u_r=2.0$