The MUSIG (Multiple Size Group) model has been developed for polydispersed multiphase flows. Here, Polydispersed means that the dispersed phase has a large variation in bubble size.
In the MUSIG model, bubbles of the dispersed phase are grouped by bubble diameter into different size groups.
With the homogeneous MUSIG model, all size groups move according to the same shared velocity field. By contrast, the Inhomogeneous MUSIG or IMUSIG model is a variant of MUSIG that has velocity groups, each with its own velocity field, fluid properties, and corresponding momentum, energy, and scalar field equations. Each velocity group contains one or more of the defined size groups.
For example:
One velocity group could contain all size groups that correspond to small-diameter bubbles,
A second velocity group could contain all size groups that correspond to medium-diameter bubbles, and
A third velocity group could contain all size groups that correspond to large-diameter bubbles.
Note: In the IMUSIG implementation in CFX, each velocity group of a given polydispersed fluid has its own associated fluid. It is important that the fluid properties for all velocity groups are consistent because they are for the same polydispersed phase.
In a real application with vertical walls, small bubbles tend to flow towards the walls of the domain while big bubbles tend to flow towards the core of the geometry. Velocity groups add the flexibility needed to allow smaller bubbles to move independently of larger bubbles. The so-called Tomiyama critical diameter may be used as a guide for identifying a divide between velocity groups; Bubbles below this critical diameter tend to experience a different lift force and so tend to move independently from bubbles above this critical diameter.
For a given small volume of the domain, the volume of all bubbles contained in a given size group
divided by the volume of all bubbles contained in all size groups of the containing velocity group
is computed and held in a variable called Conservative Size Fraction.
A related variable called Size Fraction, which is derived from the computed value of Conservative Size Fraction,
represents, for a given small volume of the domain, the volume of all bubbles contained in a given size group divided by the volume of all bubbles
contained in all size groups (of all velocity groups) for a polydispersed fluid.
The different size groups of the dispersed phase interact with each other through the mechanisms of breakup and coalescence. Population balance equations are used to update the size fractions of each size group while upholding conservation of mass. In addition to the mechanisms of breakup and coalescence, size groups can grow or shrink due to other mechanisms, such as phase change.