[1] I think you will need the compressible pressure correction equation.

[2] You can also try under relaxation for density (in addition to the pressure).

[3] Do your initial conditions satisfy mass conservation?

Enforcing SUM( void_fractions ) = 1 is good. You may want to try under-relaxing
the density and see if that helps to stabilize your iterations.

Best regards,
Madhukar Rao

Yes, I agree. I investigated it further, and forcing sum of the voids to 1 is definitely accelerating the divergence, so I'm searching for the root of the problem. I did try underrelaxing the density so that new iteration density is 0.1*rho_new+0.9*rho_old, but while that allowed the iterations to go a little further, the solution still diverged. What I did the last few days was I stripped the code down to bare-basics. Got rid of my droplet field, got rid of the temporal terms (made it steady state), got rid of the density correction and void fraction models.

I found what I think was a problem with one of my boundary conditions. For the very last momentum cell in the pipe, I was setting the momentum flux out of the cell equal to zero. I thought this was the right thing to do at first because I planned on modeling a pipe discharging into a vessel. I figured that the lateral momentum would have to go to zero in the vessel, so that there would be no flux out of the cell. But what this was doing for my case where I model just a pipe, was to cause the velocity to build up in the last momentum cell and cause a very strange velocity profile through the pipe. I'm guessing that when I do attach the pipe to a vessel, I'll have axial momentum cells in the vessel that will allow the building pressure at the end of the pipe to drive axial velocity and mass flow out of the vessel top.

Doing this got the code working correctly when only momentum and pressure correction are on. Now I turned back on density correction and void and I'm trying to get that to work now... Do you think I'll need to have the energy equation on as well for this to work? I have no heat input in the pipe, so I thought I'd be okay without it until I get momentum and continuity working correctly.

If your Mach number is very low and pressure changes are small you could
probably just neglect the density corrections and set the temperature to
a constant and suppress solving the energy equation.

Regards,
Madhukar Rao