Evaluation of the polyatomic Boltzmann collision operator and comparison with experimental data for N2, O2, NO, CO, H2
Author
Milana Colic, Vladimir Djordjic, Manuel Torrilhon
Title
Evaluation of the polyatomic Boltzmann collision operator and comparison with experimental data for N2, O2, NO, CO, H2
Description
We present a user-friendly notebook that, for a specific collision kernel of the Boltzmann operator, offers a possibility to check if derived transport coefficients recover experimental data.
Category
Working Material
Keywords
collision kernel, Boltzmann operator, transport coefficients
URL
http://www.notebookarchive.org/2025-02-54nhkri/
DOI
https://notebookarchive.org/2025-02-54nhkri
Date Added
2025-02-11
Date Last Modified
2025-02-11
File Size
236.74 kilobytes
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Rights
Redistribution rights reserved
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Evaluation of the polyatomic Boltzmann collision operator and comparison with experimental data for N2, O2, NO, CO, H2
by Milana Čolić, Vladimir Djordjić and Manuel Torrilhon
Evaluation of the polyatomic Boltzmann collision operator and comparison with experimental data for , , NO, CO,
by Milana Čolić, Vladimir Djordjić and Manuel Torrilhon
N
2
O
2
H
2
by Milana Čolić, Vladimir Djordjić and Manuel Torrilhon
We present a user-friendly notebook that, for a specific collision kernel of the Boltzmann operator, offers a possibility to check if derived transport coefficients recover experimental data.
In the background, the code does the following:
1. Lists experimental data for gases, , NO, CO, with constant specific heats (also called polytropic or calorically perfect) over a significant temperature range. Measurements are taken from the NIST Chemistry WebBook.
2.(i) Computes production terms of 14- and 17-moment equations by evaluating the quadratic Boltzmann collision operator. This evaluation procedure is based on the notebook Vladimir Djordjić, Milana Pavić-Čolić, Manuel Torrilhon, “Boltzmann Collision Operator for Polyatomic Gases” from the Notebook Archive (2021), https://notebookarchive.org/2021-05-607ilfo
2.(ii) Provides models for transport coefficients that depend on the parameters of the collision kernel in the Boltzmann operator. Transport coefficients we are considering are shear viscosity, heat conductivity (or equivalently Prandtl number) and bulk viscosity.
3. Concludes that experimental data can be matched if the system of equations { transport coefficient model = measured value of transport coefficient} can be solved in terms of the collision kernel parameters.
We test the procedure on the following collision kernels:
1. Initial collision kernel, from the paper Djordjić, Pavić-Čolić, Torrilhon, Consistent, explicit, and accessible Boltzmann collision operator for polyatomic gases, PRE, 2021
2. Extended collision kernel introduced in the paper Djordjić, Oblapenko, Pavić-Čolić, Torrilhon, Boltzmann collision operator for polyatomic gases in agreement with experimental data and DSMC method, Continuum Mech. Thermodyn., 2022.
Users are welcome to choose any other micro-reversible model, by changing the first line in 2.1 or 2.2. One needs to be careful in naming the parameters of the model.
In the background, the code does the following:
1. Lists experimental data for gases
N
2
O
2
H
2
2.(i) Computes production terms of 14- and 17-moment equations by evaluating the quadratic Boltzmann collision operator. This evaluation procedure is based on the notebook Vladimir Djordjić, Milana Pavić-Čolić, Manuel Torrilhon, “Boltzmann Collision Operator for Polyatomic Gases” from the Notebook Archive (2021), https://notebookarchive.org/2021-05-607ilfo
2.(ii) Provides models for transport coefficients that depend on the parameters of the collision kernel in the Boltzmann operator. Transport coefficients we are considering are shear viscosity, heat conductivity (or equivalently Prandtl number) and bulk viscosity.
3. Concludes that experimental data can be matched if the system of equations { transport coefficient model = measured value of transport coefficient} can be solved in terms of the collision kernel parameters.
We test the procedure on the following collision kernels:
1. Initial collision kernel, from the paper Djordjić, Pavić-Čolić, Torrilhon, Consistent, explicit, and accessible Boltzmann collision operator for polyatomic gases, PRE, 2021
2. Extended collision kernel introduced in the paper Djordjić, Oblapenko, Pavić-Čolić, Torrilhon, Boltzmann collision operator for polyatomic gases in agreement with experimental data and DSMC method, Continuum Mech. Thermodyn., 2022.
Users are welcome to choose any other micro-reversible model, by changing the first line in 2.1 or 2.2. One needs to be careful in naming the parameters of the model.
1. Experimental data from NIST Chemistry WebBook
Run Section
2. Derivation of models for transport coefficients for a specific collision kernel
Run Section
2.1 Initial model for collision kernel (cf. Djordjić, Pavić-Čolić, Torrilhon, PRE, 2021)
2.1 Initial model for collision kernel (cf. Djordjić, Pavić-Čolić, Torrilhon, PRE, 2021)
2.2 Extended model for collision kernel (cf. Djordjić, Oblapenko, Pavić-Čolić, Torrilhon, Continuum Mech. Thermodynamics, 2022)
2.2 Extended model for collision kernel (cf. Djordjić, Oblapenko, Pavić-Čolić, Torrilhon, Continuum Mech. Thermodynamics, 2022)
3. Determination of collision kernel parameters to match experimental data
Run Section
◼
The value of δ
◼
The value of ζ
◼
The values of other parameters depend on the choice of collision kernel
◼
Comparison consists in solving (the system of) equation(s) {Pr and/or = measured value} with respect to the parameters of the model.
ν
μ
Values (ω, η, ηf) of the Initial model
Values (ω, η, ηf) of the Initial model
◼
Computation
◼
Results for the Initial model
In[]:=
SetterBar[Dynamic[i],{1" ",2" ",3->" NO ",4->" CO ",5->" "}]SetterBar[Dynamic[j],{1" low pressure ",2" standard pressure "}]SetterBar[Dynamic[k],{1" shear viscosity temperature dependence ",2" thermal conductivity temperature dependence "}]SetterBar[Dynamic[l],{1" Prandtl number, 14-moment equations ",2" Prandtl number, 17-moment equations ",3->" ratio bulk to shear viscosity "}]"Exemplary values of Initial model parameters are: "Dynamic[Solution$Initial〚l,k,j,i〛]
N
2
O
2
H
2
Out[]=
N 2 | O 2 | NO | CO | H 2 |
Out[]=
low pressure | standard pressure |
Out[]=
shear viscosity temperature dependence | thermal conductivity temperature dependence |
Out[]=
Prandtl number, 14-moment equations | Prandtl number, 17-moment equations | ratio bulk to shear viscosity |
Out[]=
Exemplary values of Initial model parameters are:
Solution$Initial〚1,1,1,1〛
Values (ω, η, ηf, ζ0, ζf) of the Extended model
Values (ω, η, ηf, ζ0, ζf) of the Extended model
◼
Computation
◼
Results for the Extended model
In[]:=
Extended=SetterBar[Dynamic[i],{1" ",2" ",3->" NO ",4->" CO ",5->" "}]SetterBar[Dynamic[j],{1" low pressure ",2" standard pressure "}]SetterBar[Dynamic[k],{1" shear viscosity temperature dependence ",2" thermal conductivity temperature dependence "}]SetterBar[Dynamic[l],{1" Prandtl number, 14-moment equations ",2" Prandtl number, 17-moment equations ",3->" ratio bulk to shear viscosity "}]"Exemplary values of Extended model parameters are: "Dynamic[Solution$Extended〚l,k,j,i〛]
N
2
O
2
H
2
Out[]=
N 2 | O 2 | NO | CO | H 2 |
Out[]=
low pressure | standard pressure |
Out[]=
shear viscosity temperature dependence | thermal conductivity temperature dependence |
Out[]=
Prandtl number, 14-moment equations | Prandtl number, 17-moment equations | ratio bulk to shear viscosity |
Out[]=
Exemplary values of Extended model parameters are:
Solution$Extended〚1,1,1,1〛
4. Exemplary collision kernel parameters matching experimental data
Initial model, CO, low pressure, temperature dependence of shear viscosity, 14-moment equations.
Initial model, CO, low pressure, temperature dependence of shear viscosity, 14-moment equations.
In[]:=
Parameters={δ,ζ,ω,η,ηf};Panel[Transpose[{Parameters,Parameters/.Solution$Initial〚1,1,1,4〛}]//TableForm,"Physical values of the collision kernel parameters"]
Out[]=
Physical values of the collision kernel parameters | ||||||||||
|
Extended model, H2, standard pressure, temperature dependence of shear viscosity, 17-moment equations.
Extended model, , standard pressure, temperature dependence of shear viscosity, 17-moment equations.
H
2
In[]:=
Parameters={δ,ζ,ω,η,ηf,ζ0,ζf};Panel[Transpose[{Parameters,Parameters/.Solution$Extended〚2,1,2,5〛}]//TableForm,"Physical values of the collision kernel parameters"]
Out[]=
Physical values of the collision kernel parameters | ||||||||||||||
|
Cite this as: Milana Colic, Vladimir Djordjic, Manuel Torrilhon, "Evaluation of the polyatomic Boltzmann collision operator and comparison with experimental data for N2, O2, NO, CO, H2" from the Notebook Archive (2025), https://notebookarchive.org/2025-02-54nhkri
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