A quasi-bivariate approach to tracking secondary particle properties within the class method framework

In many polydisperse multiphase flows, the fluid or solid particles are not only distributed over size, but also with respect to other variables such as their velocity, shape, temperature or chemical composition, in which case the corresponding population balance is referred to as bi- or multivariate, respectively as two- or multidimensional. While industrial Computational Fluid Dynamics (CFD) simulations of disperse multiphase flows increasingly include approximate solutions of univariate population balance equations, e.g. for tracking the particle size distribution by means of class or quadrature-based moment methods, bivariate solution approaches are still a subject of research. This contribution highlights an aspect of recently published work (Lehnigk et al. 2022) [1], wherein a quasi-bivariate approach to tracking secondary particle properties in the class method framework is presented and demonstrated for the simulation of a bubbly flow in a vertical pipe as well as the synthesis of titania powder in a furnace reactor. In the former case, the velocity is selected as secondary property, since shear in the liquid phase can result in a pronounced radial separation of bubbles depending on their size. For the latter case, the surface area to volume ratio of the particle aggregates is used to describe the fractal-like shape of the aggregates, which influences the collision frequency and by extension also the aggregate size distribution.

[1] R. Lehnigk, W. Bainbridge, Y. Liao, D. Lucas, T. Niemi, J. Peltola, F. Schlegel, An open-source population balance modeling framework for the simulation of polydisperse multiphase flows, AIChe J. 68[3] (2022) e17539. https://doi.org/10.1002/aic.17539.