Bug in the modified Eucken method of Modelica.Media.IdealGases.Common.Functions.thermalConductivityEstimate

[finback-at]

I don’t have the original paper, but 3 linked documents below show that the modified Eucken correlation is

    (Lambda * M)/(eta * Cv) = 1.32 + 177 * (R/Cv).

R is the universal gas constant and Cv is heat capacity at mol. Units of them are “J/(mol.K)” and this equation is a dimensionless factor.

Last term is rewritten to,

    1.77*(R/Cv) = 1.77/(Cv/R) = 1.77/((Cp-R)/R) = 1.77/(Cp/R - 1.0)

Cp in Modelica.Media.IdealGases.Common.Functions.thermalConductivityEstimate is specific heat capacity “J/(kg.K)” and should be converted.

   Cp [J/(kg.K)] ->  Cp * data.MM [J/(mol.K)]

This last term should be

   1.77 / ((Cp * data.MM / Modelica.Constants.R) - 1.0).

Modified Eucken method equation in Modelica.Media.IdealGases.Common.Functions.thermalConductivityEstimate is

  eta*(Cp - data.R)*(1.32 + 1.77/((Cp/Modelica.Constants.R) - 1.0))

I think it should be corrected to,

  eta*(Cp - data.R)*(1.32 + 1.77/(((Cp*data.MM/Modelica.Constants.R) - 1.0)).

I checked this corrected equation for the cases of N2 and CH4 and those show better agreement with data of NIST Chemistry WebBook.

Links,. www.geocities.jp/penguinitis2002/study/note/gas_property.pdf eq. (16) https://ws680.nist.gov/publication/get_pdf.cfm?pub_id=914943 eq. (11) https://pdfs.semanticscholar.org/550c/f570367b409c3e947bac864dc4f88f2c86ba.pdf eq.(2)

Best regards Amane Tanaka amane@amane.to

[beutlich]

Thank you for the issue report with concrete analysis. Can you please check, if this is already resolved in MSL v3.2.3-rc.1, particularily by ef8359f75cf9ad6fdd071e3559023ebeffaacdf3 for #2377?

[thorade]

In the function Modelica.Media.IdealGases.Common.Functions.thermalConductivityEstimate variables have following units: Cp has unit J/kg.K MM has unit kg/mol data.R has unit J/kg.K Modelica.Constants.R has unit J/mol.K lambda has W/m.K eta has unit Pa/s

So, I think your analysis is correct, and the same equation can correctly be written in mass-based or mol-based units. Here, both are mixed incorrectly, and that happened maybe because the same name R was used for mass-based and mol-based gas constant.

2438 suggests to use R for mol-based universal gas constant and R_specific=R/MM for mass-based substance specific gas constant.

Note @HansOlsson : Should Dymola 2019 unit checking catch this?

[hubertus65]

The analysis is correct, and is not the first time the double use of R as shorthand for both mass and mole based units has led to errors. I am a bit baffled that unit checking did not catch this. Maybe it is not doen in functions? Note that this would change regression results (if there are any for this particular function, probably not).

[HansOlsson]

Note @HansOlsson : Should Dymola 2019 unit checking catch this?

With default settings it will not be caught.

The problem is that it is inside a function and you have the two constants 1.32 and 1.77 messing up the unit-checking (they are unit-less, but in general we are relaxed for such constants).

The tickets #2376 #2377 #2379 were created by being less strict, but not in functions.

If we also are less strict for functions it would be detected but so will all functions in Modelica.SIunits.Conversions. There is a proposal from Francesco about improving unit-checking, I will have to investigate if that would detect this issue and no others.

[thorade]

@HansOlsson and @casella Could you point me to the proposal for better unit checking?

[HansOlsson]

The original proposal with discussion was in https://github.com/modelica/ModelicaSpecification/issues/2127 However, the conclusion was to rework it - and little progress has been made.

As for the extended unit-checking possibilities in Dymola I would need time to dig up details on exactly what they are and what they do, but it might be that we should use that as a start - as it has found a number of tricky unit issues without finding too many false positives.