Dear Marton,
first I would like to thank you for your great work and the great effort you put into Molflow+.
As the discussion is quite long, I would like to ask, if I understood it correctly, as I couldn´t get the information about the distribution from your reference.
For the following different accommodation factors A_TAC, you assume to get these distributions:
A_TAC=0: Maxwellian
0<A_TAC<1: non Maxwellian
A_TAC: Maxwellian
Is this correct?
Thank you in advance
Andreas
Dear Andreas,
Yes, that is correct, and it is visualized in the first post (by Thomas).
(Please note that this is true when simulating constant A_TAC values, it is up to an other discussion whether it is physical to assume A_TAC<1 in a real-life system.)
Regards, Marton
Dear Marton,
Thanks a lot for the fast reply, but to be honest it´s not reasonable to me that you somehow “switch” from Non-Maxwellian to Maxwellian back and forth. Especially if you keep your argument in mind, that in the region of A_TAC being 0 to 1 it´s not Maxwellian due to the particles, that hit the surface (but are only partially thermalized).
I also have problems following your argument, in the discussion Thomas cited at the initial post, that the velocity increases. If you look at the upper Fig. 3 of your reference Tantos et.al., there is no change in the velocity upstream of a system at different A_TAC with T_wall/T_gas_inlet=1.
.
As the upstream velocity depends on the energy change inside the system, it´s obvious to me, that there is no change of the energy of the gas particles. If you look very closely it even looks like the values for the lower A_TAC are a bit lower. This fits very well with the second law of thermodynamics, as the energy losses increase in realation to the transferred energy as the transferred energy decreases.
In addition Jitschin and Reich checked if in real life systems the MB distribution is able to describe the system at high Knudsen numbers after passing the molecules through a pipe. The outcome was that this is the case.
Hello Andreas, nice to meet you here.
Thanks for the message, and the link to the paper of Jintschin&Reich (reminds me the beginning of my career, these two guys were vacuum gurus at conferences).
Just to tell you that Marton is preparing a long-ish reply to your message.
On my side I’d like just to say that the paper by J&R do not make any assumptions on the accomodation factor, in fact the system they describe is at a uniform temperature.
During the years I’ve tested/validated Molflow+ against results published by other people on different journals, and I always got very good/perfect results. Often Molflow+ gives very reasonable and qualitatively correct number even in non-molecular flow, i.e. transitional.
Unfortunately I have not published much of this, mostly here and there some comments at conferences or workshop, but I would be very surprised if I would find Molflow+ calculating something wrong in molecular flow.
Cheers.
Dear Andreas,
Monte Carlo simulations are advantageous because they solve physical problems by billions of random events. However, when the results aren’t as expected, they are inherently difficult to debug because one cannot follow all random events - plus they are not perfectly deterministic either.
Concretely, the system of Thomas, while simple in physical sense, is still somewhat complex, for example there is a net gas flow towards the exit, making the ideal gas equation not (fully) valid - pressure is not isotropic, it will be higher in the flow direction.
So instead of comparing MolFlow with the papers that you refer to (thank you very much), first what I recommend instead is to debug the “building blocks” of the simulation. If we agree, then we can discuss why the results are not as expected. Credit must be given to Thomas for his Excel sheet, that takes a Maxwellian distribution as initial state and applies the thermal accomodation coefficient thorugh a hit with the wall, that we hope agree that has the form:
where Ei is the energy of the incident molecules, Er is the energy of reflected molecules, Ew is the energy which would be carried away by all reflected molecules if the gas has had time to come to thermal equilibrium with the wall (I.e. “wall energy”).
I slightly modify the sheet as follows:
The results speak for themselves (Excel attached molflow_5_collisions.xlsx (5.3 MB) ):
You can see that simply by executing 5 wall collisions, in a way that Thomas himself set up, the speed distribution changes. This is not MolFlow running, this is simple repeated execution of the acc. coefficient to get a new random speed - using Excel’s random() function.
At this point, your kind feedback is welcome why - executing a well known mathematical formula - the speed distribution changes, and the average speed increases (while v_rms is constant except some statistical fluctuation - showing that the energy of the gas is constant).
If the calculation, based on Thomas’ Excel sheet is correct (as I believe it is), we have just proven that it is reasonable to switch from Non-Maxwellian to Maxwellian back and forth. If I have made a mistake, either in the Excel sheet, or somewhere else, your input is welcome to find it.
Regards, Marton
