This describes an approach to estimate species critical properties from Lennard-Jones parameters,which can provide a convenient means for users to estimate non-ideal EoS interaction parameters where they are otherwise not known.
Motivation
At present, users implementing Cantera's non-ideal RedlichKwongMFTP thermo-phase class must provide, at minimum, two parameters (a and b) for each species (and up to N*(N+1) parameters, if cross-fluid a parameters are known). The same is true for the proposed PengRobinson class. For large mechanisms, this can be quite laborious/inconvenient. For select species, Cantera provides a database of critical properties (T_crit and P_crit), which can be used to calculate the required a and b coefficients if not provided. However, this provides no assistance for a great many minor species, radicals, etc.
Possible Solutions
A recent post on the Users' Group [1] refers to a paper [2] suggesting that we can use species Lennard Jones parameters (or possibly other interaction parameters, such as Stockamayer) as another means to estimate the critical properties (and therefore the species interaction parameters).
For the RedlichKwongMFTP class, the a and b coefficients are estimated as:
a_i = 5.55 * N^2 * eps_i * sigma_i^3 / m_i^2
and
b_i = 0.855 * N * sigma_i^3 / m_i
Where N is Avogadro’s number, sigma_i is the LJ molecular diameter, eps_i the LJ well depth, and m_i the molar mass of species i.
The article notes that, where known, the actual critical properties are a better means for estimating the interaction parameters. In the case where we want to generalize the routine for any range of non-ideal EoS, we can instead implement routines to estimate the critical properties, which we then use the calculate the desired parameters:
v_crit_i = 3.29 * N * sigma_i^3 / m_i
and
T_crit_i = 1.316 * eps_i / k
The meaning of k is not specifically listed in the reference[2], but one assumes that it is the Boltzmann constant.
Abstract
This describes an approach to estimate species critical properties from Lennard-Jones parameters,which can provide a convenient means for users to estimate non-ideal EoS interaction parameters where they are otherwise not known.
Motivation
At present, users implementing Cantera's non-ideal
RedlichKwongMFTPthermo-phase class must provide, at minimum, two parameters (aandb) for each species (and up toN*(N+1)parameters, if cross-fluidaparameters are known). The same is true for the proposed PengRobinson class. For large mechanisms, this can be quite laborious/inconvenient. For select species, Cantera provides a database of critical properties (T_critandP_crit), which can be used to calculate the requiredaandbcoefficients if not provided. However, this provides no assistance for a great many minor species, radicals, etc.Possible Solutions
A recent post on the Users' Group [1] refers to a paper [2] suggesting that we can use species Lennard Jones parameters (or possibly other interaction parameters, such as Stockamayer) as another means to estimate the critical properties (and therefore the species interaction parameters).
For the
RedlichKwongMFTPclass, theaandbcoefficients are estimated as:a_i = 5.55 * N^2 * eps_i * sigma_i^3 / m_i^2and
b_i = 0.855 * N * sigma_i^3 / m_iWhere
Nis Avogadro’s number,sigma_iis the LJ molecular diameter,eps_ithe LJ well depth, andm_ithe molar mass of speciesi.The article notes that, where known, the actual critical properties are a better means for estimating the interaction parameters. In the case where we want to generalize the routine for any range of non-ideal EoS, we can instead implement routines to estimate the critical properties, which we then use the calculate the desired parameters:
v_crit_i = 3.29 * N * sigma_i^3 / m_iand
T_crit_i = 1.316 * eps_i / kThe meaning of
kis not specifically listed in the reference[2], but one assumes that it is the Boltzmann constant.References [1] https://groups.google.com/g/cantera-users/c/DL9oD5kXrhI/m/8K-wsZ3OAQAJ
[2] V. Giovangigli, L. Matuszewski, F. Dupoirieux, "Detailed modeling of planar tran- scritical H2 –O2 –N2 flames," Combust. Sci. Technol. 15 (2) (2011) 141–182.