*2.2. Volume Fraction*

The Ansys-Fluent 14.5 commercial software was used in the study. The volume fraction represents the volume percentage of each phase, and each phase satisfies the law of conservation of mass and momentum. The volume fraction of the q phase (*V*q) is defined as

$$V\_{\mathbb{Q}} = \int\_{V} a\_{\mathbb{Q}}dV\tag{1}$$

where <sup>n</sup> q=1 α<sup>q</sup> = 1.

The effective density of the q phase is

$$
\widehat{\rho}\_{\mathbf{q}} = a\_{\mathbf{q}} \rho\_{\mathbf{q}} \tag{2}
$$

where ρ<sup>q</sup> is the physical density of the q phase.
