In the scope of the background gas collision module being used to model self-collisions between particles of a given gas, or even in multiple gas situations, the mean-free path is very much dependent on the background gas density. Since said density is expected to vary in time-dependent simulations, would it be possible to make it so that the mean free path can be set to be one of the time-dependent parameters in a future version? What about facet temperature?
All the best,
Jeremy
How would you know where the next scattering is, if the scattering probabilty can change in-flight?
A simple way would be to just use the current MFP to determine the next scattering while disregarding any change to MFP (which isn’t that bad considering that if the MFP changes that much between two scatterings, then the scatterings probably weren’t that frequent in the first place and inaccurately estimating them wouldn’t have that much impact). Slightly more accurate would be to take a first estimate for the time until the next scattering (T=A/v with A the current MFP (t=0) and v the particle speed), then take the average of the MFP on the following time T. For a linearly varying MFP (M(t)=A+dt, with d in units of m/s) you’d have B (the effective MFP) be B=A+dT/2=A(1+0.5d/v).
It may be more accurate to, instead of averaging MFP, instead averaging the inverse of the MFP (the collision frequency).
Then we have : B=(1/T \int_0^T dt 1/(A+dt))^-1=xT/ln(1+dT/A)
Building on that, we could find what B gives us a T=B/v such that dT/ln(1+dT/A)=B (the convergence point of the series)
We have d/v=ln(1+dB/vA)
As such, B/A=(exp(x)-1)/x, with x=d/v.
To be noted is that the parameter x describes the variation of A. For a non-extreme variation of MFP, x<<1 (for example, for air at 300K, v=500m/s, so a variation of the MFP by 1m in 1s, which is already quite high, would only make x=2e-3), and the variation of MFP between just choosing the current one and choosing the converged value is negligible.
At first glance, any of these methods would give satisfactory results, barring quick pressure variations, so you choose whichever you’d rather implement.
Hello Jeremy, and thanks for your insight and suggestions about this topic, we’ll think about it, would be nice to develop it, quite interesting.
Just a small comment while I’ll discuss your proposal with Roberto: in your original question, you asked about facet temperature. Since MolFlow 2.9.15, facets temperatures can be time-dependent (just write a parameter name in the temperature field). One limitation is that these facets that change temperature cannot be outgassing (the outgassing-rate / molecule-rate conversion would be too difficult).
We’ll get back to you about the MFP.
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