Estimation of turbulent dissipation rates and its implications for the particle-bubble interactions in flotation

Increasing turbulence intensity has been traditionally applied to the beneficiation of fine particles for process intensification with higher flotation recovery. Nevertheless, quantifying turbulent dissipation rate directly from local velocity gradients is challenging as it requires measurements of flow fields down to the Kolmogorov length scales. Spatial resolution in velocity measurements using existing experimental techniques is insufficient. In this paper, we study the effects of spatial resolution on the estimated turbulent dissipation rate and its effects on predicted particle-bubble interactions are further discussed. Direct numerical simulation of a homogeneous isotropic turbulence has been performed using the pseudo-spectral method. An instantaneous 3D velocity field is used to calculate true values of turbulent dissipation rate, which is used as benchmark to compare turbulent dissipation rates estimated from the same velocity fields of different resolutions. This velocity field is then coarsened to different levels relative to the Kolmogorov length scale, which are used to calculate turbulent dissipation rate from local velocity gradients of different spatial resolution. The underestimation of turbulent dissipation rate is quantified as a function of spatial resolution relative to the Kolmogorov length scales. This clarifies that special care should be paid to the understanding of turbulence effects on particle-bubble interactions.