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OpenFOAM: sensible enthalpy/internal energy for a reactive case

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Old   August 15, 2022, 04:17
Default OpenFOAM: sensible enthalpy/internal energy for a reactive case
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Hi foamers,


I have a question regarding the calculation of the sensible enthalpy/interal energy.
I first start by explaining what I expect to see in the algorithem based on thermodynamic text books and after, I 'll compare it with the codes in OpenFoam.

For an inviscid/adiabatique reactive case exchanging no work with the environment, we have:
h^{0}_{\rm f,mixture} + c_{p,\text{mixture}} (T-T_{\rm ref})+\frac{u^{2}}{2} = \text{constant}

with h^{0}_{\rm f,mixture} = \sum h^{0}_{f,i} y_{i} where h^{0}_{f,i} and y_{i} are, respectively, the enthalpy of formation of species i and the mass fraction of species i. In the same way, c_{p,\text{mixture}} can be calculated;

c_{p,\text{mixture}} = \sum c_{p,i} y_{i}However, as the nature of species change in presence of chemical reactions, for enthalpy (the same applies for internal energy)
we HAVE to take a reference. The standard reference is T_{\rm ref} = 25°C and p_{\rm ref} = 1 atm. As such h, is calculated based on a reference value:

h(T,p) = h^{0}_{f}(T_{\rm ref},p_{\rm ref}) + c_{p} (T-T_{\rm ref})

Now, my question is how this reference temperature is considered in OpenFOAM (we know that the sensible enthalpy/interal energy do not change a lot with pressure). I cannot find any track of this reference temperature in OpenFOAM.

For instance, if we take a look at temperature calculation based on Newton’s method in src/thermophysicalModels/specie/thermo/thermo/thermoI.H, we have something as*:

T_{\rm new} = T_{\rm old} - [ hs(p_{\rm old},T_{\rm old}) - hs_{\rm fromTransportEqn}]/ c_{p}(p_{\rm old},T_{\rm old})

However, we know that:
hs_{\rm new}(p_{\rm new},T_{\rm new}) = c_{p,{\rm mixture}}(p_{\rm new},T_{\rm new}) (T_{\rm new} - T_{\rm ref})
hs_{\rm old}(p_{\rm old},T_{\rm old}) = c_{p,{\rm mixture}}(p_{\rm old},T_{\rm old}) (T_{\rm old} - T_{\rm ref})


Therefore:
hs_{\rm new}(p_{\rm new},T_{\rm new}) - hs_{\rm old}(p_{\rm old},T_{\rm old})
= c_{p,{\rm mixture}}(p_{\rm new},T_{\rm new}) (T_{\rm new} - T_{\rm ref})
- c_{p,{\rm mixture}}(p_{\rm old},T_{\rm old}) (T_{\rm old} - T_{\rm ref})

We know that c_{p,{\rm mixture}}(p_{\rm new},T_{\rm new}) is different from c_{p,{\rm mixture}}(p_{\rm old},T_{\rm old}) and we can NOT have the following simplification:

hs_{\rm new}(p_{\rm new},T_{\rm new}) - hs_{\rm old}(p_{\rm old},T_{\rm old}) = c_{p,\text{mixture}}(p_{\rm old},T_{\rm old}) (T_{\rm new} - T_{\rm old})

to deduce:

T_{\rm new} = T_{\rm old} + [hs_{\rm new}(p_{\rm new},T_{\rm new}) - hs_{\rm old}(p_{\rm old},T_{\rm old})]/c_{p,{\rm mixture}}(p_{\rm old},T_{\rm old})


I would be grateful if someone could explain that to me. Am I missing a step here?

P.S.: I read carefully http://caefn.com/openfoam/temperature-calculation and tried to search a lot on different forums. But, I could not find my answer there.

* that expression is coming from Temperature calculation from sensible internal energy .

Last edited by mkhm; August 15, 2022 at 07:05.
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inviscid flow, openfaom, reacting flow, sensible heat transfer, sensibleenthalpy

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