Transport database in FFCM-2

The table below lists the transport properties for all 96 species in FFCM-2.

Table of Contents

1. Chemkin transport database
2. Binary transport database
3. References

Chemkin transport database

The FFCM transport database originates from the Sandia Transport subroutine library ¹. The table below lists the parametrization of transport coeffcients used in FFCM-2.

• Geometry: an index indicating the geometrical configuration of the molecule; 0: monatomic atom, 1: linear, 2: nonlinear.
• $\epsilon/k_B$: the Lennard-Jones potential well depth, unit in Kelvins.
• $\sigma$: the Lennard-Jones collision diameter, unit in Angstroms.
• $\mu$: the dipole moment, unit in Debye. A Debye is 10$^{-18}$ cm $^{3/2}$ erg$^{1/2}$.
• $\alpha$: the polarizability, unit in cubic Angstroms.
• $Z_{rot}$: the rotational relaxation collision number at 298K.

Binary transport database

In the current FFCM-2 release, the binary transport coefficients are not considered. In FFCM-1, however, the transport library is appended with selected pairs of diffusion coefficients from ²$^{,}$³$^{,}$⁴$^{,}$⁵$^{,}$⁶$^{,}$⁷. These are mostly pairs involving light species (H and H₂). For these species, the repulsive part of the Lennard-Jones (L-J) 12-6 potential function is known to be too stiff to accurately model diffusion coefficients at high temperatures ⁸. For this reason, the diffusion coefficients of relevant, key pairs should be directly modeled without resorting to the use of tabulated L-J 12-6 collision integrals, as discussed in ²${,}$³. Selected pairs of diffusion coefficients in the form of polynomial coefficients are adopted. These coefficients are obtained from the potential functions directly calculated from high-level quantum chemistry and quantum scattering calculations. The temperature dependence of binary diffusion coefficients at 1 atm is parameterized as

\[\begin{equation} \ln D_{ij}=d_0+d_1\ln T+d_2(\ln T)^2+d_3(\ln T)^3 \end{equation}\]

where $d_k$ (k=0,1,2,3) is the polynomial coefficients. For the mixture-averaged transport formulation, the above polynomial is sufficient for simulations. The multi-component transport formulation as well as the computation of thermal diffusion ratio in both transport formulations, however, requires the input of the ratios of collision integrals¹:

\[\begin{align} A_{ij}^* &= \Omega_{ij}^{(2,2)}/(2\Omega_{ij}^{(1,1)}) \\ B_{ij}^* &= (5\Omega_{ij}^{(1,2)}-\Omega_{ij}^{(1,3)})/(3\Omega_{ij}^{(1,1)}) \\ C_{ij}^* &= \Omega_{ij}^{(1,2)}/(3\Omega_{ij}^{(1,1)}) \end{align}\]

The above ratios are also parameterized as

\[\begin{align} A_{ij}^* &= a_0+a_1\ln T_{ij}^*+a_2(\ln T_{ij}^*)^2+a_3(\ln T_{ij}^*)^3 \\ B_{ij}^* &= b_0+a_1\ln T_{ij}^*+b_2(\ln T_{ij}^*)^2+b_3(\ln T_{ij}^*)^3 \\ C_{ij}^* &= c_0+c_1\ln T_{ij}^*+c_2(\ln T_{ij}^*)^2+c_3(\ln T_{ij}^*)^3 \end{align}\]

where $a_k$, $b_k$, and $c_k$ (k=0, 3) are the polynomial coefficients whose values are found also in Table 1, $T_{ij}^{*}$ is the reduced temperature $T_{ij}^{*} =kT/\varepsilon_{ij}$ and $\varepsilon_{ij}$ is the well depth. When implementing non-L-J potentials for the key pairs, however, $T_{ij}^{*}$ is undefined. Therefore, the tabulated coefficients for $A_{ij}^{*}$, $B_{ij}^{*}$, and $C_{ij}^{*}$ were calculated for the actual temperature $T_{ij}$ instead, and special handling was added for these coefficients in the transport data interpreter code. These polynomials can be implemented to both Cantera codes and ChemKin PREMIX codes. For example, the set_binary_diff_coeffs_polynomial and set_collision_integral_polynomial subroutines in the latest version of Cantera (version 2.6.0) are useful.

References

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