[random_soldier1337 (OP)]

Hi,

In my situation, I am dealing with two ideal gases traveling down a pipe at the same bulk velocities. I am only considering a 1-D treatment at the moment and I would like to find out at which point the two gases should be considered a well mixed, homogeneous mixture. Would anyone know either the particular formulation or even the subject matter to consult to determine the well-mixing of gases?

Thanks and regards.

[Kryptid]

Would these be of any help?

https://en.wikipedia.org/wiki/Graham%27s_law
https://en.wikipedia.org/wiki/Fick%27s_laws_of_diffusion
https://www.engineeringtoolbox.com/air-diffusion-coefficient-gas-mixture-temperature-d_2010.html
https://www.calculatoratoz.com/en/diffusion-flux-calculator/Calc-591

[random_soldier1337 (OP)]

I don't think Graham's law applies. I don't actually have a starting chamber, so to speak. The gases are introduced directly to the pipe.

I thought about using Fick's law and diffusion earlier as well until I realized I don't have an actual concentration function,
with respect to the direction, to work with to apply Fick's law.

[Kryptid]

Are the gases entering from opposite ends of the pipe and then meeting in the middle? I think knowing how long it takes until they are mixed would require knowing the total volume of the gases.

[Bored chemist]

They mix quickly, if you have the right design.
e.g.

[random_soldier1337 (OP)]

@Kryptid , The gases are constantly being introduced from the same end, so there is really no given volume.

FYI, thought I should clarify (probably should have mentioned in OP), I am making a CFD simulation in ANSYS Fluent and the containment which forms the domain of interest should be receiving the well mixed gas mixture. I have to figure out the pipe length leading to it so that I do not add unnecessary spatial meshing.

The real world setup the simulation is based on, the pipes leading to the containment are definitely over a meter or 2 long but only 0.25" in diameter so there is no provision for the method described in that video.

[Bored chemist]

1/4 inch isn't a problem.
https://www.coleparmer.co.uk/i/koflo-1-4-21-316-ss-tube-mixer-21-elements-1-4-od/0466956

What problem are you actually trying to solve?

[random_soldier1337 (OP)]

Hi,

Apologies for the late reply. In case anyone is still wishing to discuss, I am looking to simulate the steady state distribution, in ANSYS Fluent, of a two gas mixture inside of a 30 L stainless steel cylinder. The mixture will be flowing in at constant flow rate through an inlet pipe and flowing out through an outlet pipe also at a constant rate.

Are there any more details I can offer to clarify?

Thanks and regards.

[evan_au]

Numerical simulations are probably ok for laminar flow, but become extremely difficult with turbulent flow.
- The Navier-Stokes equations describe the behaviour quite well
- In turbulent flow, the behaviour at large scales depends strongly on the behaviour at small scales, which makes it difficult to select a suitable granularity for the simulation in both time and space.
- In practise, aerodynamic simulation for aircraft design, weather and climate use experimentally-derived approximations for the behaviour at small scales. But it still needs to run on a supercomputer.
- There is a $1 million prize for finding a solution to some fundamental questions about the Navier-Stokes equations.
https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existence_and_smoothness

Turbulence brings the two gases into intimate contact in a way that laminar flow does not.
- Since the two gases are closer together, Graham's Law operates over much shorter distances to achieve good mixing.

For practical use, I recommend a vortex mixer, and using empirical measurements of the mixing efficiency.
- For an exercise in learning how to do numerical simulation, stick with laminar flow and apply Graham's Law. You will need to take into account the near-parabolic distribution of flow speed across the pipe - fastest in the center, almost stationary on the walls.

https://en.wikipedia.org/wiki/Turbulence

[random_soldier1337 (OP)]

I apologize. I should have mentioned earlier, I have calculated the Reynolds number and the highest I get for the maximum flow rate I am dealing with is ~2215. It's an internal flow where I understand 2300 to be the transition regime. So I am assuming there would be significant transition flow but very little turbulence i.e. turbulence can be neglected.

I though it would also help to mention that I am using the SST k-omega model as the manual for ANSYS Fluent mentions that it is the most general purpose model.

Finally, I do have access to a supercomputer. However, I have avoided it thus far due to latency issues and poor quality of streaming from remote log ins. If you deem it necessary, I will use it but the one I run simulations on currently is a high end personal computer with a GTX 1070 and between that and the issues above, I have not considered it until now.

Also, thank you for your suggestion of Graham's Law.