Boundary conditions for High Pressure venting
 

Hi Foamers,

My problem is simple yet could not find an acceptable solution.

I have a relatively large cylinder pressurised with gas up to 200MPa and it has one relatively very small outlet exposed to atmospheric pressure.

Using the wedge domain I am trying to find out the rate of the pressure loss inside the cylinder. I am using rhoPimpleFoam V10

I have used following combinations of P and U so far

1. P - fixedPressure and
U - zeroGradient/inletoutlet/pressureInletOutletVelocity

(for this, solver is stable but time stepping is too small despite the meshing. practically insolvable with very small time steps.)



2. P - totalPressure and
U - zeroGradient/inletoutlet/pressureInletOutletVelocity

(for this, solver is stable but time stepping is too small despite the meshing. practically insolvable with very small time steps.)



3. P - waveTransmissive and
U - zeroGradient/inletoutlet/pressureInletOutletVelocity

(Currently working on this, time stepping is reasonable but I am not sure if waveTransmissive condition can mimic the venting scenario. depending on the Inf value pressure loss varies)

Any suggestion of P and U boundary conditions for this particular condition, is greatly appreciated. Thank you

Dasith

Any suggestions ?

It seems to me that you have already found the best boundary conditions (#1), and that your problem is that you have a venting process that lasts a long time (high pressure, large inventory), but which generates a small scale, high velocity (sonic) vent flow. With this set up it is inevitable that you will have a small time step and a looong simulation time, if you want to model it as a full transient simulation.

Given the above, and assuming that the pressure field is approximately uniform in the vessel, would it not make more sense to assume that the flow at any point (apart from the very initial starting flow) is pseudo-steady? If that is the case, you can do a set of steady-state simulations with an assumed inventory pressure representing conditions at various points during the depressurisation. You can then just focus on the vent and surroundings, rather than modelling the whole vessel.

Forgive me if I have misunderstood your setup/goals, but I hope this is useful.

Hi Tobermory,

Thank you very much for your response on this.

However I have to admit I do not fully grasp your idea of using Steady State solver. The main goal of the study is to estimate the pressure drop rate and therefor the total time for the vessel to get to atmospheric pressure from the initial pressure (200MPa).

yes, I think, with a compromise, I can assume pressure is uniform in the vessel during the venting.

There is no any additional accessories attached to wedge domain ( No matter how much I liked, intended to using the most simple model possible). I have defined a small section of the wedge domain itself to be the outlet.

Perhaps I understood you incorrectly but are you suggesting that I focus on the venting line ? In my case, I have zero interest in this. Even so, without the knowledge of time dependant pressure, how can I maintain the inlet BC of the vent ? I think I am missing something from your explanation. Please advice me otherwise.

perhaps this is more of me being lazy to use my pencil :confused:.

Thank you.
Dasith

Aaah - okay, I understand now ... but why try do this with CFD? You can do this instead with a simple hand calculation.

For a given vessel pressure, you can easily calculate the mass flow rate through the vent (for an assumed orifice discharge coefficient) - this will be a sonic, choked release until the pressure drops below around 2bar (a simple search on the web will find you the relevant expressions). This mass flow rate equals the negative of the rate of change of the mass of the gas inside the vessel, which is simply related to the rate of change of the density of the gas, via the vessel volume. Now, choose either isentropic or isenthalpic expansion of the gas (depending on the thermal boundary condition for the vessel) and you can relate this density derivative to the rate of change of the gas pressure ... indeed you can do this analytically and then integrate to get pressure as a function of time.

Just a warning though - the time taken to get to ambient is infinity. Better to choose something higher than ambient, e.g. 1.01 atm.

I thought I could capture the adiabatic expansion easily with the simulations but there are now more pressing issues than that.

yep, turning into my paper and pencil, thank you very much for the clarifications, helps a lot.