Modelling a restriction orifice
 

OK, here goes. I've been kicking this around the park, now, for over a year and I don't seem to have got anywhere near a solution. I am trying to model a restriction orifice in a pipe using OPENFOAM. I have been conversing on the OpenFoam Forum and I've been advised to ask for advise from this forum.

The flowing fluid is gas, there is only a small liquid drop out across the orifice so I consider it to be a totally gas phase problem. The upstream pressure is 167 BarA and the downstream pressure, initially, is 1 BarA. (This is a blowdown orifice discharging into a flare network) On the face of it I thought that this would be a relatively straightforward model to run as the geometry is pretty simple and the conditions, so I thought, are simple to simulate. The dimensions are roughly: piping ID=50mm, orifice ID=10mm, the orifice is nominally 10mm thick.

Since I have such a large pressure difference I decided that the OpenFoam solver should be compressible. Doing the initial calculation to determine the mass throughput of the orifice, using the R.W.Miller method, I determined that the velocities downstream of the orifice would be extremely high, certainly greater than Mach=0.3 which I think should also drive me to using a compressible solver.

The problem I am facing is the fact the the solver crashes very quickly with the full pressure drop (which is what I want to model!) I have tried increasing the upstream pressure slowly but the model still crashes out. I don't seem to be able to achieve a steady state run using one of the compressible steady state solvers which does make me wonder.

I THINK I have determined why the model crashes. When I look at the moment of crash (I'm using rhoPimpleFoam) the density crashes out (<0.1). If I look at how the temperature changes across a shock I think I see why the density does this since the pressure drop is so great! The temperature drop I see is significantly greater than what I would expect using simple thermodynamics.

I would really appreciate someone's advise as to HOW I might actually model this problem. Am I using the wrong solver, am I making wrong or too simple/complex assumptions? Should it be this difficult to model this domain?

I look forward to hearing from anyone!

Thanks and regards

Andrew Glassby

Hi Andrew,

I can help with this problem, if you are still in need of assistance.

The problem looks simple, with a simple geometry and seemingly simple boundary conditions. However, the difficulty arises from the high pressure difference across the orifice. The emerging jet will be highly under-expanded and will contain strong waves. A shock-capturing solver is needed (rhoPimpleFoam will struggle). This is the kind of model I have developed for a number of applications. Please contact me via my company website for more details:

www.tourbillion-technology.com

Best regards,

Paul Garlick.