Convert NASA 9 coefficients to NASA 7 coefficients from CEA

[Clayton Fox]

Dear Cantera community,

I need to generate my own NASA coefficients for species with the same temperature ranges.   For example 300 to 1000 and 1000 to 6000. 

I am looking at using the thermo build tool from CEA (https://www.grc.nasa.gov/www/CEAWeb/ceaThermoBuild.htm) which is suggested on the cantera website (here)   


For H, this produces:

COEFFICIENTS FOR FITTED THERMODYNAMIC FUNCTIONS


      H                 D0(H2):Herzberg,1970. Moore,1972. Gordon,1999.                
       3 g 6/97 H   1.00    0.00    0.00    0.00    0.00 0      1.00794     217998.828
          200.000  1000.000 7 -2.0 -1.0  0.0  1.0  2.0  3.0  4.0  0.0         6197.428
       0.000000000E+00 0.000000000E+00 2.500000000E+00 0.000000000E+00 0.000000000E+00
       0.000000000E+00 0.000000000E+00 0.000000000E+00 2.547370801E+04-4.466828530E-01
         1000.000  6000.000 7 -2.0 -1.0  0.0  1.0  2.0  3.0  4.0  0.0         6197.428
       6.078774250E+01-1.819354417E-01 2.500211817E+00-1.226512864E-07 3.732876330E-11
      -5.687744560E-15 3.410210197E-19 0.000000000E+00 2.547486398E+04-4.481917770E-01
         6000.000 20000.000 7 -2.0 -1.0  0.0  1.0  2.0  3.0  4.0  0.0         6197.428
       2.173757694E+08-1.312035403E+05 3.399174200E+01-3.813999680E-03 2.432854837E-07
      -7.694275540E-12 9.644105630E-17 0.000000000E+00 1.067638086E+06-2.742301051E+02

 
For the first temperature range I have highlighted in yellow where the 9 coefficients are located.  From inspection of the equations for the 9 and 7 NASA polynomials,  It seems If I want to make a NASA 7 polynomial from this then I need

to ignore the first two numbers of the CEA output.  And I highlighted in Green a value which we ignore and do not count towards either NASA 9 nor NASA 7. Is there anyone who can confirm this or has used this method in a similar

fashion?  Is there an alternative method to generate just 7 coefficients?

Thanks in advance.

-Clayton

[Ray Speth]

Clayton,

Except in the case where the first two coefficients are zero, you can't just ignore them when trying to generate a 7-coefficient polynomial. You would need to generate a new fits for the two 7-coefficient polynomials. But in any case, you can use the 9-coefficient polynomials with Cantera, so I'm not sure why you would need to do this.

Also, the online ThermoBuild tool actually prints spaces where you have highlighted in green, clearly indicating that that position does not contain a polynomial coefficient.

Regards,

Ray

[Clayton Fox]

Dear Ray, thank you for your response. 

I have a multi step reaction from Muller et al. where the second step is:

X + 11 O2  => P

where X= 3C2H4 + CH3 + H, and P = 7 CO2 + 8 H20.

The issue in cantera is how to accurately model this in a .cti file.

I originally tried to  model it in cantera like this:

But its not correct, (the units will of course not work out) as K needs to be kmol/m3-s. 

This step should actually be modeled as:


now the published units of A=2x10^12 actually work out, and its important for the "orders" of the concentrations to match to work with their published data. 
 
So now the issue is coming up with thermo data for a species called X.  We determined the best way to get thermo data is to add the respective coefficients to make the combined species,


 e.g. for the first NASA coefficient:  a1_{X} = 3* a1_{C2H4} + a1_{CH3} + a1_{H} , and so on.  


This is fine for species X, as its relatively easy to get the thermo data for at the same temperature range, 

However, Muller et al, have another species which I have only have thermo data for 7-coefficents.
it occurs in their 3rd step (the reveres reaction)

I = F + 2 O2. 

where I = HO2R''O + H2O.  I need to make thermo data for species I, 

I have the thermo data for HO2R''O from a detailed mech by LLNL (Mehl et. al. 2011)  for a very specific temperature range, but its only 7 coefficients.  I would need to make water at those 7 coefficients with the same temperature range in order to add them. 

[Ray Speth]

Clayton,

I would think the easiest approach would be to generate 9-coefficient polynomials for your pseudospecies, since you can create 9-coefficient polynomials from 7-coefficient polynomials by just setting the first two coefficients of the 9-coefficient polynomials to zero.

Regards,

Ray