Modeling a gas jet using particles

[mst-parkhachev]

Dear colleagues,

I am investigating the modeling of gas plumes (methane or hydrogen). I have reviewed publications on this topic, including those by prominent FDS developers. As I understand it, the most appropriate approach is to use a particle-based method.
If I am correct, the particle parameters should be selected based on the jet characteristics at the cross-section where the pressure equals atmospheric pressure. I have consulted several recommendations [1–3] regarding the calculation of gas parameters at this level (level "3").

As I understand the information in the papers, the temperature at section "3" can be assumed equal to the gas temperature in the reservoir, which often corresponds to the ambient temperature. The velocity at section "3" is calculated based on the velocity at section "2" and the pressure at the orifice. The formulas are provided below.

Next, I examined the "Loughborough Jet Fire Experiments" example from the validation database.
https://github.com/firemodels/fds/tree/master/Validation/Loughborough_Jet_Fires/FDS_Input_Files
jet1.fds corresponds to the case where the pressure in the methane tank is 60 bar and the orifice diameter is 20 mm.

Particle parameters:
&PART ID='methane droplets', SPEC_ID='METHANE', DIAMETER=1000., INITIAL_TEMPERATURE=-160. /
&PROP ID='nozzle', PART_ID='methane droplets', MASS_FLOW_RATE=2.9, PARTICLE_VELOCITY=1000., SPRAY_ANGLE=0.,5., PARTICLES_PER_SECOND=20000, OFFSET=1. /

The gas flow rate (value Q2), calculated using the formulas shown below, was 3 kg/s, which corresponds reasonably well to the value MASS_FLOW_RATE=2.9. (A discharge coefficient 0.9 was used.)

However, the temperature and velocity raised some questions. First, the INITIAL_TEMPERATURE is -160 degrees, which is significantly lower than the ambient temperature. This value is suspiciously close to the boiling point of methane (-161.5 degrees). Presumably, this is because liquid methane droplets are being injected. However, it is not entirely clear to me why this specific temperature was chosen. Perhaps it was done to prevent the droplets from evaporating instantly or to avoid numerical instability. Is it always necessary to use a temperature close to the boiling point? Does this apply to hydrogen as well?
I realize that the heat of droplet evaporation is much lower than the combustion energy of the jet and can be neglected, but I would like to understand the general principle behind the temperature selection.

Second, the gas velocity at section "3," calculated using the formulas presented here, differs from the 1000 m/s value found in jet1.fds. For methane at a pressure of 60 bar, the value of γ is 1.43. The velocity calculated via the formulas below was 770 m/s, rather than 1000 m/s. While the discrepancy is not too large, I would like to understand how to apply a correction. In report [4], Mr. McGrattan notes: "Of course, there is some trial and error involved in prescribing a jet." Could you advise on how to proceed when there is no experimental data available for comparison? What velocity value should be used?

Q2 is the mass flow rate of gas through a circular orifice, where d is the orifice diameter and Cd is the discharge coefficient.
For circular orifices in a thin-walled section, Cd is approximately 0.60–0.62.
In the event of a complete pipeline rupture, Cd = 0.9–0.95.

jet_matlab.txt

1. A. D. BIRCH , D. R. BROWN , M. G. DODSON & F. SWAFFIELD, The Structure and Concentration Decay of High Pressure Jets of Natural Gas (1984)
2. A. D. BIRCH , D. J. HUGHES & F. SWAFFIELD, Velocity Decay of High Pressure Jets (1987)
3. R.W. Schefer, W.G. Houf, T.C.Williams, B. Bourne, J. Colton, Characterization of high-pressure, underexpanded hydrogen-jet flames (2007)
4. Kevin McGrattan, MODELING LARGE LIQUEFIED NATURAL GAS FIRES / PROCEEDINGS, Fire and Evacuation Modeling Technical Conference (FEMTC) 2022

[drjfloyd]

Droplets are one approach. I don't know that I would call it the best or most appropriate approach in all circumstances. FDS is a low mach number code. If you have a gas leak from high pressure you often have two issues to wrestle with: a compressible flow at the leak and a small leak diameter compared to the domain the resulting fire will occupy. Droplets are one approach to deal with this. Another is compute the leak exit flow and temperature. Using correlations and data in the literature you can determine the amount of entraiment expected into the jet as a function of distance from the leak. The entrained air will allow some amount of combustion generating some amount of combustion products and raise the enthalpy of the jet flow (minus heat radiated away). You can estimate as a function of distance the jet radius, velocity, temperature, and species as a result of the entrainment and combustion. At some distance from the leak, enough air will be entrained to drop the velocity to be low Mach. Compared to the overall jet length this distance will not be large and only a small fraction of the fuel flow will burn. At that distance you can define a new boundary condition for the jet flow. To account for the air that was entrained and is now part of the new boundary condition, behind the new leaking surface you can define a suction boundary condition to remove the entrained air.

[mcgratta]

I set up the Loughborough cases. As you noticed, some of the parameters are just order of magnitude estimates. The reason is that there is certain parameters like droplet size, drag, etc, that are not easily chosen. The temperature was given in the test report. Initial conditions are tricky because sometimes the fluid exiting the hole is partially gaseous, partially liquid.

In any case, Jason is right---there really is no "appropriate" or "accepted" approach for these jet fires. They have been added to the validation guide to give us a sense of how good or bad the estimate of the flame length is.

[mst-parkhachev]

Thanks, colleagues!

While reviewing articles, I came across a brief description of the approach outlined by Dr. Floyd. However, a quick look didn't reveal a detailed explanation of how to calculate the mass of entrained air. Furthermore, as I understand it, the diameter of the equivalent source at the point where the flow reaches a low Mach number is still quite small. To resolve the source surface, you need at least a few grid cells; typically, this implies a cell size of around 0.5 cm in the source region. It seems to me that this approach would also require the entire jet volume to be covered by a grid with relatively fine cells, on the order of a few centimeters. This would result in a very high total cell count. Moreover, simulating jet in a large enclosure would require complex matching between grids of varying resolution.

That is why the droplet-based option seemed more attractive to me. It seemed sufficient to simply calculate the flow parameters for an equivalent source, where the gas pressure equals atmospheric pressure, and assign those properties to the particles. Particles do not require a fine grid.
I realize, of course, that this does not guarantee an accurate result.

I will try to compare the two approaches, provided I can find a description of how to calculate the mass of entrained air.

Dr. Floyd’s remark - suggesting that it is more correct to remove "excess" air from the scene using a suction boundary condition - came as a surprise to me. I hadn't considered that at all when thinking about the first modeling approach.