Why the MFix only calculate 5 coefficients of Cp but give 7 coefficents?

[chunlei]

Hi

I saw that MFiX uses polynomials to calculate the specific heat. I want to figure out how it works, and I found that there may be some conflicts.

Here is the example from the user guide:

where It shows the form of data to present the thermochemical data in MFiX
Note that it uses 7 coefficients for high temperature range and low temperature range, respectively.
So I guess the formula of Cp should be like this:

However, the user guide only present a1~a5, no a6 and a7.
Here is the what user guide said:

Then I go to find the source code to figure out whether the a6 and a7 are used or not.
Here is the source code:

model/thermochemical/read_thermochemical_mod.f

Here is the integration of Cp by T

and
Here is how it treats a6

The program defined the a6 and a7, but did not use it!

Looks like the MFiX source code does not use the a6 and a7!

Finally I read the PDF which explains the original database that MFiX used, i.e., Burcat & Russic
“Third millenium ideal gas and condensed phase thermochemical database for combustion (with update from active thermochemical tables)”

This is the website of Burcat database
http://garfield.chem.elte.hu/Burcat/burcat.html

In this PDF, it says:

and

I don’t know which equation it uses, but because there are 7 coefficients, I guess it uses eq. (7)

If so, there is a obvious contradiction between

(let us call this equation aaa)
and

Finally, let me conclude my question:

1. Which equation is true for MFiX when calculating Cp? eq (aaa) or eq (7)?

2. The “R” in the formula represents gas constant. Does it mean universal gas constant， i.e. 8.314J/molK? or the gas constant for specific gas, i.e., 8.314/(Molecular Weight)?

3. What is the unit of energy? cal or J?

---

my MFix version:19.3.1

[onlyjus]

a6 and a7 are constants of integration if you want to calculate H and S. These polynomials are also known as the Burcat or 7-coefficient NASA polynomials (also used by Chemkin, Cantera, etc). See Burcat’s website pdf, page 6, equation 1: http://garfield.chem.elte.hu/Burcat/Introduction.pdf

Cp/R = a1 + a2 T + a3 T^2 + a4 T^3 + a5 T^4

H/RT = a1 + a2 T /2 + a3 T^2 /3 + a4 T^3 /4 + a5 T^4 /5 + a6/T
    
S/R  = a1 lnT + a2 T + a3 T^2 /2 + a4 T^3 /3 + a5 T^4 /4 + a7

Note: there are newer 9-coefficient NASA polynomials which might be confusing you.

[chunlei]

THANKS
By the way, is the entropy “S” used in the MFiX? Where is S used？

[cgw]

The word “entropy” doesn’t occur anywhere in the MFiX source code, GUI, or documentation, so I think it’s safe to say that MFiX does not compute or use entropy.

[onlyjus]

Entropy is not used and the enthalpy is determined by integrating the Cp, so in reality MFiX is only using a1-a5.