Learning Forum

[atul.srivastava216]

Hello,

I am currently doing a transient multiphase simulation for a pressure swirl atomizer. I used VOF model which works well. I then tried to use the mixture model to see how it works. I am using the implicit time stepping and the slip velocity formualtion is turned on. The pressure-velocity coupling scheme is coupled and the solver is pressure based. Spatial discretization is all second order upwind and all the solution controls are default.

I did a few simulations and what I got is this:

1. secondary phase diameter = 1e-5, time step size=1e-6, solution diverges.
2. secondary phase diameter = 1e-8, time step size=1e-6, solution converges. 
3. secondary phase diameter = 1e-8, time step size=1e-15, solution diverges. 　

I want to ask if there is something going on between the secondary phase diameter and the time step size. From my amateur analysis, I realized that when I set the time step size greater than the relaxation time of the droplet, the solution converges. Obviously, I cannot make the time step arbitrarily higher than the relaxaton time as the upper limit of the time step size is limited by the Courant's number. I read in the theory guide that the setting of the secondary phase diameter affects the relaxation time of the droplets, the drag and the interfacial area. But, why it should affect the time step size for convergence alludes me. Is it something to do with the local equlibrium assumption of mixture model? Any inputs are welcome.

[Rob]

The phase diameter effects the drag, combine that with the momentum and it'll govern the droplet trajectories. Not sure why the solver would diverge with a really small step, typically if the time step is too small nothing happens. Note, as you decrease the diameter below about 10microns the relaxation time means you're near enough modelling a mist, and we often use the species model for that. 

Were you resolving VOF down to 10microns? 

[atul.srivastava216]

Thanks Robert. I was resolving VOF down to ten microns. With this simulation my aim is to understand the limits of the mixture model. 

[Rob]

OK, if you want 10micron droplets you'll want 1-2micron cells. Very impressed if you have resolved to that level. 

[atul.srivastava216]

However, the problem of divergence at extremely small time step for mixture model still remains.