Mass conservation problem in mixing tank multiphase simulation
 

I am simulating a mixing tank with Eulerian multiphase model. Water is the primary phase, air is the second phase. The tank has a volume of 22 liters. However, there is only 12 liters water inside, so 10 liters of air is in the headspace. There are air inlets (mass flow inlet) at the bottom of the tank and an outlet (pressure outlet) at the top. Realizable k-e model is used. The convergence criteria is 1e-4 for vof equation and 1e-3 for all others.

Everything seems fine except that the mass of water inside seems to change gradually (actually, the change of water mass is almost linear after a short period of time after certain condition is changed). So if the simulation is allowed to run a long time, the mass of water will change quite a lot. For example, it would decrease from 12 kg to 11.3 kg within 10 real seconds. This is undesirable. I do need a long period of simulation time to reach steady state and I'd like the water volume (or mass) to stay as close to 12L (12 kg) as possible since there is no feed or exit for water. However, I do notice that the water flux at the top pressure outlet is not 0 as it does at the bottom inlets. It is usually a very small number such as 6e-5 kg/s. However, I don't know if there is any way to prohibit water from leaving the tank. Since water is the primary phase, it is everywhere in the tank as long as the air volume fraction is not exactly 1. So if the cells adjacent to the outlet have air fraction of 0.9999, they would still have the possibility of blowing out small quantity of water from the outlet, right? Of course, it is unlikely to happen physically since water surface is about 25cm below the pressure outlet.

In addition, I do have the infamous "reversed flow in xx faces on pressure-outlet xx" problem under many conditions that I tested, but I think that's not the main reason for the mass change since the reversed flow has an air vof of 1.

Now I think it has more to do with the vof convergence criteria. The vof residual may not even reach the 1e-4 criteria for every time steps. The further away from this criteria, the faster the change in water mass is observed. I could tighten the vof convergence criteria and allow more iterations per time step in order to get better convergence, however, that is going to take a lot more time to do the calculation and I don't know if it will ever go down to 1e-5 or 1e-6. Currently, the time step size is 0.02s and 60 iterations per time step. And I tried both MRF and SMM methods, similar results were obtained. I could also play with the relaxation factors, but I am not sure if I am in the right direction.

Thanks in advance for any suggestion.