I am doing a physics experiment that involves releasing gas from a reservoir into a vacuum chamber via a pulsed nozzle and I am interested in knowing what would be a simple (and reasonably accurate) way to simulate the gas density distribution over a certain volume in space in front of the nozzle and over time after the nozzle is opened.

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  • The pressures involved in the reservoir, $P_R$, range from few mbars to 500 mbar (nitrogen).

  • The background vacuum pressure, $P_0$, is on the order of 1e-6 mbar.

  • The nozzle length, $L$, is about 20 cm, with opening diameter, $a$, of about 2 mm.

  • The distance from the opening of the nozzle, $D$, is about 20 cm.

  • The problem is to solve for the pressure, $P(\mathbf{x},t)$, which is the pressure as a function of space and time after the nozzle opens (over a time period of say 5 ms) within a small volume (say 1 cm diameter sphere) centered at the point an axial distance $D$ away from the nozzle.

I believe within the ranges of these parameters, there is an intermediate transition from molecular to continuous (or supersonic) flow, which is why a fluid dynamical approach seems appropriate.

I am not that well read on fluid dynamics, so I could use help in terms of what to read up on that can get me up to speed on how I might do this particular simulation, i.e., how I can model this using fluid mechanical equations, or the Lattice Boltzmann method if applicable, and whether there are software packages available.

If the simulations can be extended to include various nozzle shapes (conical) and use of skimmers (which can probably be defined as boundary conditions) and various gas species like argon (which can probably be accounted for by various parameters in the fluid equations) that would also be useful.

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    $\begingroup$ What is the goal of the simulation? We can suggest that you do a full dilute-gas Boltzmann simulation, but if all you want to know is how long it takes to equilibrate pressures, one can model this with equations that will be 1e9 times faster to solve. $\endgroup$ Commented Dec 23, 2021 at 5:18
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    $\begingroup$ It kinda sounds like you are looking for a simple solution to a complicated issue. For starters, as the distance from the nozzle throat grows, you go from a gas continuum to rarefied gases which require different approaches. Also, pulsed thruster in a chamber doesn't sound like you have a steady state, unless your vacuum chamber is very sophisticated. Just to get you started, here is something on simulations elib.dlr.de/55152 and here the kind of effort you have to put into a proper test chamber for ideal conditions elib.dlr.de/114177 $\endgroup$
    – Homer512
    Commented Dec 23, 2021 at 14:57
  • $\begingroup$ @Wolfgang Bangerth The goal of the simulation is to model real experimental conditions of the gas, which we can then use in a different simulation involving laser induced ionization whose results we want to compare with experimental detection of photons and charged particles. I am not sure if these conditions mean the gas can be considered to equilibrate, but if using equilibrium methods get us within a order of magnitude of the gas density distribution, that would be better than a guess using intuition. $\endgroup$
    – user279043
    Commented Dec 30, 2021 at 2:50

1 Answer 1


Probably a reasonably easy way to do it is to use this FCT code developed at US NRL, https://github.com/scivision/LCPFCT. It is designed for CFD problems of the kind that you are interested in, and it has some examples included. This example https://github.com/scivision/LCPFCT/blob/main/runfast2d.py looks rather similar to your problem, I would suggest working from it.


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