Modeling drop breakage using the full energy spectrum and a specific realization of turbulence anisotropy

Abstract

The assumption of homogeneous isotropic turbulence when modeling drop breakage in industrially relevant geometries is questionable. We describe the development of an anisotropic breakage model, where the anisotropy is introduced via the inclusion of a perturbed turbulence spectrum. The selection of the perturbed spectrum is itself motivated by our previous large-eddy simulations of high-pressure homogenizers. The model redistributes energy from small to large scales, and assumes that the anisotropic part of the Reynolds stresses is confined to the energy-containing range. The second-order structure function arising from the perturbed spectrum is used in the standard framework of Coulaloglou and Tavlarides to calculate breakage frequency. While the base model exhibits non-monotonic behavior (by predicting a maximum value for a certain drop size), the effect of anisotropy is shown to increase breakage frequency in length scales larger than this peak, thereby reducing non-monotonicity. This effect is more pronounced for small turbulence Reynolds numbers.