Molecular diffusion of mass and energy predicted by ab initio potential energy surfaces for air components at high temperatures

The thermal conductivity and self-diffusion coefficients for molecular nitrogen and oxygen are investigated with the direct molecular simulation (DMS) technique using high-fidelity, ab initio potential energy surfaces. The DMS results are compared to available experimental data, and remarkable agreement is observed in all cases. Such comparisons are restricted to relatively low temperature, typically below 2000 K. For temperatures up to 10 000 K, the DMS data are also in excellent agreement with the corresponding transport properties obtained using kinetic theory based on collision integrals evaluated with simplified, point-particle interatomic potentials. An analysis of the Eucken approximation shows that the Eucken correction factor is based upon reasonably accurate assumptions, but a significant improvement can be obtained by properly accounting for the ratio of mass to momentum diffusion. Finally, it is shown that the DMS transport data for mass, momentum, and energy are consistent with kinetic theory across a wide range of temperatures, thus offering convincing evidence for the reliability of the methodologies employed for their determination.

Figure 1

Temperature gradients obtained by imposing a heat flux via Eq. (4) and corresponding density variations across the channel for pure molecular oxygen (a) at 2000 K and (b) at 8000 K.

Figure 2

(a) Evolution of mole fractions for pure molecular oxygen at 8000 K. ${\mathrm{O}}_2^{\alpha }$ and ${\mathrm{O}}_2^{\beta }$ are chemically identical but have been assigned a different computational label. (b) Corresponding diffusion coefficient from least-square fit of transient profiles.

Figure 3

Thermal conductivity of molecular nitrogen from DMS calculations using the MMP method. Comparison with the experimental data [25] and transport collision integrals models [30, 31].

Figure 4

Thermal conductivity of molecular oxygen from DMS calculations using the MMP method. Comparison with the experimental data [25] and transport collision integrals models [30, 31].

Figure 5

Thermal conductivity for a mixture of 22% ${\mathrm{O}}_2$ and 78% ${\mathrm{N}}_2$ by mole fraction from DMS calculations using the MMP method. Comparison with the experimental data [25] and the kinetic theory result of Gupta et al. [44].

Figure 6

Molecular nitrogen self-diffusion coefficient from DMS and comparison with experimental data [49, 50].

Figure 7

Molecular nitrogen self-diffusion coefficients from DMS and from transport collision integrals [30, 31, 51]: comparison at (a) low temperature and (b) over the entire temperature range considered in this work.

Figure 8

Molecular oxygen self-diffusion coefficients from DMS and from transport collision integrals [30, 31, 51]: comparison at (a) low temperature and (b) over the entire temperature range considered in this work.

Figure 9

(a) Temperature variation of the Eucken correction factor and (b) ratio of mass to momentum diffusion obtained from DMS transport data.

Figure 10

Kinetic theory prediction for molecular thermal conductivity coefficient from DMS transport data for mass ($D$) and momentum ($\eta$) diffusion.