 LGC :
Immersed membrane bioreactor ## Two-phase model

### Euler-Euler model

#### VOF

The Volume of Fluid model is an area track technique applied to an fixed eulerian meshgrid. He is mainly used to deal with problems of stratified flows, free surface flows or dam break. In fact, he handles fine the interfacial problems. Nevertheless, he operates with the hypothesis of the immiscibility of the fluids, so he doesn't handle the mass transfert on the interface. For my project, this model isn't interessing.

#### Mixture

The mixture model doesn't handle the phases singly, he regroups them to solve a unique additional equation. To use this model, we must have a volume fraction of the discrete phase upper than 10-12% (it depends on the sources). You can use this model for problems of bubbly flows, sedimentation or cyclones. My project deals with a bubbly flow, I can also use this model if my volume fraction of the discrete phase is upper than 10-12%.

#### Eulerian

This model is a complication of the preceding. Therefore, we need have a volume fraction of the discrete phase upper than 10-12% to use this model. He handles the phases singly, adding an additional equation for each phase. The calculation time is also longer than with the mixture model. He is notably interesting when there are some coupling between the phases (for example : mass tranferts). We will also prefer to use this model for problems of fluidized beds, particles in suspension ou bubbles collumn or simply for more precision. Therefore, this model can be used in my project if the volume fraction is enough high.

### Euler-Lagrange model

#### Discrete phase model

This discrete phase model neglects the interactions between the particles (drops, bubbles or grains) and the effects of the dispersed phase volume fraction on the continous phase. This model considers also a smal volume fraction of the dispersed phase (lower than 10%). About the computing, he handles the phases singly. Moreover, this model allows to track the particles thanks to the lagrangian approach (he solves an trajectory equation). However, the use is more complicated, the user must make a computation in several steps :

• Solve for the continous phase
• Creation of the discrete phase
• Solve with the two phases