Inconsistency between TROE formula and code when T** is zero.

Cantera version

2.3.0

Operating System

Linux Ubuntu18.04 64bit

Python/MATLAB version

3.7

Expected Behavior

When T** is not given, the default value is 0.0, as description in https://cantera.org/science/reactions.html . Then the last term exp(-T**/T) ==1

Actual Behavior

When T** is not given, the last term exp(-T**/T) is ignored so this term is actually zero.

Steps to reproduce

1. With a very small T**

cti_def = '''
    ideal_gas(name='gas', elements='O H C',
              species='gri30:H CH2 CH3 O2 H2O CO2',
              reactions='all',
              options=['skip_undeclared_elements', 'skip_undeclared_species', 'skip_undeclared_third_bodies'],
              initial_state=state(temperature=2000, pressure=101325))
    #  Reaction 50
falloff_reaction( "H + CH2 (+ M) <=> CH3 (+ M)",
         kf = [6.00000E+14, 0, 0],
         kf0   = [1.04000E+26, -2.76, 1600],
         falloff = Troe(A = 0.562, T3 = 91, T1 = 5836, T2 = 1e-10))
'''
gas = ct.Solution(source=cti_def)
gas.TPX = 2000,1e6,[1,1,1,1,1,1]
gas.net_rates_of_progress
## output array([6.57248322e+10])

2. Without T**

cti_def = '''
    ideal_gas(name='gas', elements='O H C',
              species='gri30:H CH2 CH3 O2 H2O CO2',
              reactions='all',
              options=['skip_undeclared_elements', 'skip_undeclared_species', 'skip_undeclared_third_bodies'],
              initial_state=state(temperature=2000, pressure=101325))
    #  Reaction 50
falloff_reaction( "H + CH2 (+ M) <=> CH3 (+ M)",
         kf = [6.00000E+14, 0, 0],
         kf0   = [1.04000E+26, -2.76, 1600],
         falloff = Troe(A = 0.562, T3 = 91, T1 = 5836))
'''
gas = ct.Solution(source=cti_def)
gas.TPX = 2000,1e6,[1,1,1,1,1,1]
gas.net_rates_of_progress
## output array([2.8516357e+10])

Comment

According to CHEMKIN's source code and theory guide, this behavior of cantera is consistent with the implementation of CHEMKIN but it is inconsistent with the cantera's document, CHEMKIN's theory guide and Troe's paper.

However, I do not know which is correct. It may influence the behavior of Weiyao's 89 species, 683 reactions reduced mechanism for kerosene.

[bryanwweber]

@chengdi123000 Can you reproduce this behavior with the master branch?

[speth]

I don't think there are any relevant changes here between Cantera 2.3.0 and the current master branch.

There are two cases here, both of which have some issues. However, I have concerns with the validity of 0 or near-zero values for T**. The original paper by Troe states that "F_cent decreases from F_cent = 1 at 0 K with increasing temperatures, before it increases at very high temperatures". However, If T** is set to 0, then the low-temperature limit for F_cent is 2, not 1.

Case 1: T** omitted

• Cantera omits the term exp(T**/T) from the expression for F_cent.
• This is consistent with the implementation of Chemkin 2 and the Chemkin Input Manual
• This is not consistent with the Cantera "science" documentation.

Case 2: T** given as 0.0

• Cantera omits the term exp(T**/T) from the expression for F_cent. (same behavior as when T** is omitted)
• This is not consistent with the Cantera "science" documentation.
• This is not consistent with the implementation of Chemkin 2 and the Chemkin Input Manual

While the inconsistencies should be addressed, I think that we should warn if T** is specified as 0, since I suspect it is an error and what was intended is actually Cantera's current behavior of omitting the term.

I agree with @speth

In some mechanism in chemkin's format, the T** is assigned a very large negative number such as -10e30 to ensure the last term exp(T**/T) is essentially zero.

I think keeping consistency with CHEMKIN and modifying the description in document is the best approach to resolve this issue.

FYI, here is the description of TROE coefficients in Input Manual of CHEMKIN in ANSYS 18.2:

Defines the Troe pressure-dependent reaction rate (see Equation 3-31 of the ANSYS Chemkin-Pro Theory Manual). 

TROE must be followed by the slash-delimited 3 or 4 parameters α, T***, T*, and T**; 

the fourth parameter is optional and if omitted, the last term in Equation 3-31 is not used.

[speth]

I realized while looking at the warning added in #741 regarding this issue that there is an additional consideration of how this is handled by ck2cti and ck2yaml. ck2yaml silently drop the T2 parameter if a value of 0 is specified, the same as if it was not specified, while ck2cti preserves the zero.

So, in addition to warning about T** being specified as 0 at the time a Troe object is being instantiated (from whatever data source), we should probably also (a) warn about it in the converter scripts and (b) preserve the value as specified by the user.

[ischoegl]

This is an excellent point, and probably a philosophical question about ck2yaml: should the output be changed to pre-empt undesirable behavior or should it generate a literal conversion even if there are issues that will result in warnings? The discontinuities in the NASA polynomials raise a similar issue.

My own preference would be a literal translation. As long as ck2yaml preserves the zero, #741 would be a legitimate fix.

Edit ... I changed the ck2yaml behavior so a zero T2 value is preserved in #741

[bryanwweber]

I agree that a literal translation is the best approach. To the extent that the warnings generated by Cantera prompt people to improve their mechanisms, I'm happy to be the nagging voice for people 😁