Transport Database description (View the transport data file)

The FFCM transport database originates from the database distributed in the Sandia Transport subroutine library [1].

The library is appended with selected pairs of diffusion coefficients from [2-7]. 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].

Within the framework of Sandia PREMIX [9] and similar codes, implementing these updates is quite straightforward. 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

$$\ln D_{ij}=d_0+d_1\ln T+d_2(\ln T)^2+d_3(\ln T)^3$$

Where $d_k$ (k=0, 3) is the polynomial coefficients (see Table 1 for selected pairs. 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 integrals [1,10]:

$$A_{ij}^*=\Omega_{ij}^{(2,2)}/(2\Omega_{ij}^{(1,1)})$$ $$B_{ij}^*=(5\Omega_{ij}^{(1,2)}-\Omega_{ij}^{(1,3)})/(3\Omega_{ij}^{(1,1)})$$ $$C_{ij}^*=\Omega_{ij}^{(1,2)}/(3\Omega_{ij}^{(1,1)})$$

The above ratios are also parameterized as

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

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.

Table 1. Summary of polynomial coefficients for updated binary diffusion coefficients and ratios of collision integrals

Pair			Dij					Aij*
	d0	d1	d2×102	d3×103	Ref.a	a0'	a1'×10	a2'×102	a3'×103
H-He	-9.6699	2.1002	-7.7060	5.4611	[2]	0.9300	0.8015	-0.9473	0.6346
H-Ar	-9.0511	1.6161	-0.2878	1.3054	[3]	0.6882	1.5342	-1.7700	0.8880
H-H2	-11.7498	3.1507	-25.7472	15.8916	[2]	0.6857	1.5339	-1.3674	0.3221
H-O2	-11.0410	2.4043	-10.2797	5.3264	[4]	1.2925	-1.8499	4.2710	-2.6082
H-N2	-13.2703	3.5187	-29.6649	16.4314	[5]	1.3387	-0.8545	0.9229	0.0441
H2-He	-12.7513	3.4244	-28.4726	15.9317	[2]	0.5953	2.0781	-2.4848	1.0013
H2-N2	-10.9994	2.2026	-8.1155	4.4061	[6]	1.3165	-1.3202	2.4162	-1.2026
H2-H2	-9.9610	2.0560	-6.4977	4.1368	[7]	1.3221	-1.2075	2.2047	-1.0596
N-H2	-11.0630	2.3500	-10.3715	5.8031	[4]	1.3158	-1.3458	2.4925	-1.1910
N-N2	-14.5098	3.2704	-22.4113	10.7044	[4]	1.2855	-2.0527	3.7964	-2.3074
O-O2	-14.6025	3.2905	-22.3516	10.6864	[4]	1.2983	-1.7305	3.6353	-2.0673
N2-N2	-16.5175	4.0527	-34.5936	16.7101	[6]	1.3530	-0.5405	-0.1134	0.5980
			Bij*					Cij*
	b0'	b1'×10	b2'×102	b3'×103		c0'	c1'×10	c2'×102	c3'×103
H-He	0.8764	1.0238	-1.4803	0.9880		1.0600	-0.5993	1.0265	-0.7345
H-Ar	0.6968	1.7158	-2.4357	1.3655		0.6703	1.1433	-1.5041	0.5188
H-H2	0.6780	1.3747	-1.1059	0.1658		0.6512	0.8216	-0.4389	-0.2736
H-O2	1.9927	-2.7220	2.0595	0.1644		1.2757	-2.2786	4.4500	-2.7462
H-N2	-2.2030	15.9160	-25.3394	13.6448		1.2562	-2.6882	5.5776	-3.4083
H2-He	0.6771	1.3579	-1.1425	0.1889		0.6519	0.8365	-0.4450	-0.2599
H2-N2	1.9423	-4.1911	6.7119	-3.3685		1.2907	-1.9301	3.3990	-1.9684
H2-H2	3.6314	-11.3979	16.9421	-8.1268		1.2981	-1.7814	2.9567	-1.7020
N-H2	6.9907	-25.9650	37.7202	-17.8856		1.2855	-2.0527	3.7964	-2.3074
N-N2	1.3147	-1.2582	2.0939	-0.9124		1.1853	-0.0110	-0.6790	0.8244
O-O2	9.9616	-39.5289	58.2753	-28.2893		1.2659	-2.4767	4.9470	-3.0093
N2-N2	3.6149	-10.8631	15.4819	-7.2344		1.2562	-2.6882	5.5776	-3.4083

^a The fits are based on diffusion coefficients directly taken from the referenced paper, or those computed using the potential functions given in the referenced paper.

 

The coefficients listed in the above table are appended to the transport database as follows:

We will be working with Reaction Design to implement the above formulations and transport parameters into ChemKin. In the meantime, a user has two options:

a) Delete the block after the “END” line and use the original transport database. For hydrogen-air mixtures at 1 bar pressure and 298 K unburned gas temperature, the thus-calculated laminar flame speed values are 3-4% lower than those using the updated transport database. For methane or other hydrocarbon flames, the updated diffusion coefficients produce little changes in the simulated laminar flame speed.

b) Write to Hai Wang to obtain a version of the ChemKin/TranFit/PreMix codes that works with the updated transport database.

References

[1]  Kee R, Dixon-Lewis G, Warnatz J, Coltrin M, Miller J. Sandia report SAND86-8246. Sandia National Laboratories, New Mexico. 1986.

[2]  Middha P, Yang B, Wang H. A first-principle calculation of the binary diffusion coefficients pertinent to kinetic modeling of hydrogen/oxygen/helium flames. Proc Combust Inst. 2002;29:1361-9.

[3]  Middha P, Wang H. First-principle calculation for the high-temperature diffusion coefficients of small pairs: The H-Ar case. Combust Theor Model. 2005;9:353-63.

[4]  Stallcop JR, Partridge H, Levin E. Effective potential energies and transport cross sections for atom-molecule interactions of nitrogen and oxygen. Phys Rev A. 2001;64:042722.

[5]  Stallcop JR, Partridge H, Walch SP, Levin E. H–N2 interaction energies, transport cross sections, and collision integrals. J Chem Phys. 1992;97:3431-6.

[6]  Stallcop JR, Partridge H, Levin E. Effective potential energies and transport cross sections for interactions of hydrogen and nitrogen. Phys Rev A. 2000;62:062709.

[7]  Stallcop JR, Levin E, Partridge H. Transport properties of hydrogen. J Thermophys Heat Transfer. 1998;12:514-9.

[8]  Paul P, Warnatz J. A re-evaluation of the means used to calculate transport properties of reacting flows. Symp (Int) Combust. 1998;27:495-504.

[9]  Kee, RJ, Grcar, JF, Smooke, MD, Miller JA. PREMIX: A Fortran Program for Modeling Steady Laminar One-Dimensional Premixed Flames, Sandia Report SAND85-8240, 1985.

[10]  Dixon-Lewis, G. Flame structure and flame reaction kinetics. II. Transport phenomena in multicomponent systems. Proc Roy Soc A 1968; 307: 111-35.