Looking for basic theory on mixing of gases

[random_soldier1337]

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.

[John Cuthber]

If you are seeking to mix gases, I have good news for you; the laws of thermodynamics are on your side.
If you arrange the gas feeds to the tube to be fast and tangential so that they "swirl" down the pipe, they will mix very rapidly.

[exchemist]

11 hours ago, random_soldier1337 said:

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.

You can also get "static mixers" to put in the pipe, to speed up the mixing and ensure it is complete: https://komax.com/the-gas-static-mixer-produce-high-quality-process-gases-for-many-application/

 

[sethoflagos]

11 hours ago, random_soldier1337 said:

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.

Radial mixing of two fluids moving coaxially in a pipe is a function of the flow regime. In laminar flow, the dominant mechanism is molecular diffusion which ends up with a form of the heat equation to solve. in the turbulent regime, it's eddy diffusion, and that results in a Lagrangian function. 

The classic text covering this is 'Transport Phenomena' by Bird, Stewart and Lightfoot. Though https://en.wikipedia.org/wiki/Eddy_diffusion gives a reasonable introduction.

In practical terms, chemical engineers generally default to allowing a conservative mixing length of 100 pipe diameters before presuming the two gases are well mixed. (Because the maths is a lot easier).

If there isn't room for so much straight pipe, installing two 90 degree pipe elbows in different planes immediately downstream of the injection point has been used to justify dropping the mixing length to perhaps 30 or 40D. Alternatively, as @exchemist notes, there are a number of designs of inline mixing device that can be used. 

[random_soldier1337]

Hi,

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.

[exchemist]

51 minutes ago, random_soldier1337 said:

Hi,

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.

I suppose you might get some help from Fick's Second Law of Diffusion for gases: https://en.wikipedia.org/wiki/Fick's_laws_of_diffusion

But I can't help thinking it is a bit artificial to assume two parallel, laminar flows down the pipe, which mix solely by diffusion from each into the other. I's have thought that introducing some turbulence would shorten the length of pipe needed considerably.