An efficient model for the breakage of agglomerates by wall impact applied to Euler-Lagrange LES predictions

Abstract

The present study completes the development of a model for predicting the effect of wall impacts on agglomerates in turbulent flows. Relying on an Euler-Lagrange hard-sphere approach this physical phenomenon is described in an efficient manner allowing practically relevant multiphase flow simulations at high mass loadings. In a recent study \citep{khalifa2020data} conditions for the onset of breakage and the resulting \added[id=2]{fragment} size distribution were derived. In the present investigation a data-driven description of the post-breakage kinetics of the fragments is developed based on extensive DEM simulations taking a variety of impact conditions (impact velocity, impact angle, agglomerate size) into account. The description relates the velocity vectors of the fragments after breakage to three parameters: The reflection angle, the spreading angle and a velocity ratio of the magnitude of the fragment velocity to the impact velocity of the agglomerate. Relying on the DEM results Weibull distribution functions are used to describe the parameters of the wall-impact model. The shape and scale parameters of the Weibull distributions are found to mainly depend on the impact angle of the agglomerate. Consequently, relationships between the shape and the scale parameters and the impact angle are established for each of the three parameters based on a fourth-order regression. This allows to determine the velocity vectors of the fragments randomly based on the corresponding Weibull distributions of the reflection angle, the spreading angle and the fragment velocity ratio.

The devised model is evaluated in a turbulent duct flow at five Reynolds numbers and three agglomerate strengths given by powders consisting of primary particles of different size. The analysis first concentrates on the pure wall-impact breakage but then also includes agglomerate breakup due to turbulence, drag forces and rotation allowing to determine the shares of the different physical phenomena. It is found that with increasing Stokes number the wall-impact breakage occurs less effectively due to the reduced responsiveness of the agglomerates to the secondary flow motions in the duct. However, in the very high range of St$^+$ other mechanisms such as the turbophoresis and the lift force augment the breakage at walls. Comparing the contributions of the different breakage mechanism reveals that the wall impact is dominant at the lowest Reynolds numbers, whereas the drag stress prevails at high Re.