How to calculate the mass flux at a disturbed surface?
 

Hello everyone,

I am modeling a stirred bioreactor that has air sparged into it. There is also a headspace region at the top to accommodate liquid expansion due to the air injection (using the adapt/patch method) and I use a pressure outlet BC at the top.

I want to see if the air mass conservation is fulfilled in the simulation. I know m-dot at the inlet, but my question is, how can I calculate the mass flow rate of air in the outlet which is a changing surface?

Your help is very much appreciated.
Thank you