| Line 1: | Line 1: | ||
| − | + | = old janaf model = | |
| − | OpenFOAM uses the old janaf tables from which the temperature dependent values of Cp, H and S are valuated. Therefor the old janaf format uses 7 coefficients and 2 | + | OpenFOAM uses the old janaf tables from which the temperature dependent values of Cp, H and S are valuated. Therefor the old janaf format uses 7 coefficients and 2 polynomials for a lower and a higher temperature range. The old janaf tables are valid for temperatures up to 6000 K.<br><br> |
Cp(T) = R( a[1] + a[2]T + a[3]T^2 + a[4]T^3 + a[5]T^4 ) <br> | Cp(T) = R( a[1] + a[2]T + a[3]T^2 + a[4]T^3 + a[5]T^4 ) <br> | ||
H(T) = R( a[1]T + (a[2]T^2)/2 + (a[3]T^3)/3 + (a[4]T^4)/4 + (a[5]T^5)/5 + a[6] ) <br> | H(T) = R( a[1]T + (a[2]T^2)/2 + (a[3]T^3)/3 + (a[4]T^4)/4 + (a[5]T^5)/5 + a[6] ) <br> | ||
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ftp://ftp.technion.ac.il/pub/supported/aetdd/thermodynamics/THERM.DAT <br><br> | ftp://ftp.technion.ac.il/pub/supported/aetdd/thermodynamics/THERM.DAT <br><br> | ||
The old janaf model is implemented in the application "dieselFoam" and can be tested in the test case "aachenBomb".<br><br> | The old janaf model is implemented in the application "dieselFoam" and can be tested in the test case "aachenBomb".<br><br> | ||
| − | In OpenFOAM the same reader, which reads the thermodynamic data of the janaf table also contains the input data of the laminar viscosity. Therefor the | + | In OpenFOAM the same reader, which reads the thermodynamic data of the janaf table also contains the input data of the laminar viscosity. Therefor the Sutherland formula is used, which shows a linear increasing of the viscosity depending on the temperature. The input data is hard coded and describes the temperature dependent viscosity of pure nitrogen. In a case with nitrogen as environmental gas this could be an acceptable approximation, if there are no ionization processes. |
| − | + | = new janaf model = | |
| − | For some application the temperature range up to 6000 K is not sufficient. In an application containing plasma (e.g. arc welding) the temperature range could be up to 30000 K. Therefore the newer janaf model is needed which handles a larger temperature range up to 30000 K. The temperature dependent values of Cp, H and S are calculated with 3 | + | For some application the temperature range up to 6000 K is not sufficient. In an application containing plasma (e.g. arc welding) the temperature range could be up to 30000 K. Therefore the newer janaf model is needed which handles a larger temperature range up to 30000 K. The temperature dependent values of Cp, H and S are calculated with 3 polynomials using 9 coefficients.<br><br> |
Cp(T) = R( a[1]/T^2 + a[2]/T+ a[3] + a[4]T + a[5]T^2 + a[6]T^3 + a[7]T^4 ) <br> | Cp(T) = R( a[1]/T^2 + a[2]/T+ a[3] + a[4]T + a[5]T^2 + a[6]T^3 + a[7]T^4 ) <br> | ||
| − | H(T) = R( a[1]T + | + | H(T) = R( -a[1]/T + a[2]lnT + a[3]T + (a[4]T^2)/2 + (a[5]T^3)/3 + (a[6]T^4)/4 + (a[7]T^5)/5 + b[1] ) <br> |
| − | S(T) = R( a[1] lnT + a[ | + | S(T) = R( -a[1]/(2*T^2) - a[2]/T + a[3] lnT + a[4]T + (a[5]T^2)/2 + (a[6]T^3)/3 + (a[7]T^4)/4 + b[2] ) <br><br> |
| − | You can download an example for the | + | You can download an example for the new janaf table here: <br> |
| + | http://www.galcit.caltech.edu/EDL/public/thermo/thermo.inp <br><br> | ||
| + | For temperatures above 10000 K the Sutherland formula is not a good approximation anymore. The beginning ionization leads to an decreasing of the laminar viscostiy. Therefor a a transport model based on polynomials should be used instead. | ||
| + | |||
| + | == Implementation == | ||
Revision as of 12:14, 14 April 2011
1 old janaf model
OpenFOAM uses the old janaf tables from which the temperature dependent values of Cp, H and S are valuated. Therefor the old janaf format uses 7 coefficients and 2 polynomials for a lower and a higher temperature range. The old janaf tables are valid for temperatures up to 6000 K.
Cp(T) = R( a[1] + a[2]T + a[3]T^2 + a[4]T^3 + a[5]T^4 )
H(T) = R( a[1]T + (a[2]T^2)/2 + (a[3]T^3)/3 + (a[4]T^4)/4 + (a[5]T^5)/5 + a[6] )
S(T) = R( a[1] lnT + a[2]T + (a[3]T^2)/2 + (a[4]T^3)/3 + (a[5]T^4)/4 + a[7] )
You can download an example for the old janaf table here:
ftp://ftp.technion.ac.il/pub/supported/aetdd/thermodynamics/THERM.DAT
The old janaf model is implemented in the application "dieselFoam" and can be tested in the test case "aachenBomb".
In OpenFOAM the same reader, which reads the thermodynamic data of the janaf table also contains the input data of the laminar viscosity. Therefor the Sutherland formula is used, which shows a linear increasing of the viscosity depending on the temperature. The input data is hard coded and describes the temperature dependent viscosity of pure nitrogen. In a case with nitrogen as environmental gas this could be an acceptable approximation, if there are no ionization processes.
2 new janaf model
For some application the temperature range up to 6000 K is not sufficient. In an application containing plasma (e.g. arc welding) the temperature range could be up to 30000 K. Therefore the newer janaf model is needed which handles a larger temperature range up to 30000 K. The temperature dependent values of Cp, H and S are calculated with 3 polynomials using 9 coefficients.
Cp(T) = R( a[1]/T^2 + a[2]/T+ a[3] + a[4]T + a[5]T^2 + a[6]T^3 + a[7]T^4 )
H(T) = R( -a[1]/T + a[2]lnT + a[3]T + (a[4]T^2)/2 + (a[5]T^3)/3 + (a[6]T^4)/4 + (a[7]T^5)/5 + b[1] )
S(T) = R( -a[1]/(2*T^2) - a[2]/T + a[3] lnT + a[4]T + (a[5]T^2)/2 + (a[6]T^3)/3 + (a[7]T^4)/4 + b[2] )
You can download an example for the new janaf table here:
http://www.galcit.caltech.edu/EDL/public/thermo/thermo.inp
For temperatures above 10000 K the Sutherland formula is not a good approximation anymore. The beginning ionization leads to an decreasing of the laminar viscostiy. Therefor a a transport model based on polynomials should be used instead.
