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Transport Properties in Gases at High Temperature and Low Pressure: Comparison of Kinetic Theory with Direct Simulation Monte Carlo

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Abstract

Expressions for the transport coefficients obtained from the Gross-Jackson and the Chapman–Enskog methods are used to derive explicit relations incorporating the internal energy of the molecules for pure polyatomic gases and for binary mixtures of gases. Various coefficients such as the binary diffusion, thermal conductivity, and the viscosity coefficients and the thermal diffusion factor are calculated and a comparison with the direct simulation Monte Carlo (DSMC) method is carried out. The results show that the contribution of the internal energy is important and cannot be neglected.

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Abbreviations

b :

Impact parameter

\({c_p^{\rm rot}}\) :

Molecular specific heat of rotation, J · K−1

\({c_p^{\rm vib}}\) :

Molecular specific heat of vibration, J · K−1

dtm :

Time step, s

d p , d q :

Diameter of molecule p or q, m

D pq :

Coefficient of diffusion in a binary gas mixture, m2 · s−1

[D pq ]N=L :

Lth-order approximation of D pq , m2 · s−1

\({D_p^{\rm T} ,D_q^{\rm T}}\) :

Coefficient of thermal diffusion, kg · m−1 · s−1

[D T]N=L :

Lth-order approximation of DT, kg · m−1 · s−1

D pp :

Coefficient of self diffusion, m2 · s−1

g pq :

Relative velocity vector of the colliding molecules, m · s−1

\({I_{ij}^{kl}}\) :

Differential collision cross section, m2

(j p )N=3 :

Flux vector, kg · m−2 · s−1

k :

Boltzmann constant, \({k = 1.38 \times 10^{-23}\;{J} \cdot {K}^{-1}}\)

Kn :

Knudsen number

K tot :

Total coefficient of thermal conductivity, W · m−1 · K−1

K trans :

Translational thermal conductivity, W · m−1 · K−1

K rot :

Rotational thermal conductivity, W · m−1 · K−1

K vib :

Vibrational thermal conductivity, W · m−1· K−1

k T :

Thermal diffusion ratio

m p , m q :

Mass of molecule p or q, kg

m pq :

Reduced mass of molecules p and q, kg

N :

Total number of molecules

n :

Total number density, m−3

n p , n q :

Number density of species p and q, m−3

P :

Pressure, N · m−2

q :

Heat flux vector, W · m−2

Q :

Total collision cross section, m2

r :

Intermolecular separation, m

r :

Position vector, m

T :

Temperature, K

v p :

Diffusion velocity of species p, m · s−1

X p , X q :

Mole fraction of species p or q

\({Z_p^{\rm rot}}\) :

Rotational relaxation collision number for molecule p

\({Z_p^{\rm vib}}\) :

Vibrational relaxation collision number for molecule p

α pq :

Parameter for VSS potential

α T :

Thermal diffusion factor

Γ :

Euler’s Gamma function

γ :

Dimensionless relative velocity vector

λ :

Mean free path, m

\({\varphi (r)}\) :

Intermolecular potential

\({\varphi}\) :

Azimuthal angle, radian

μ :

Shear viscosity, kg · m−1 · s−1

ν :

Collision rate, s−1

Ω :

Solid angle of diffusion, steradian

\({{\bf \Omega}_{pq}^{({l,s})}}\) :

Collision integral

ρ :

Density, kg · m−3

ω p , ω q :

Temperature exponent of the viscosity coefficient for VSS or VHS potentials

χ :

Deflection angle, radian

θ r :

Characteristic temperature of rotational mode, K

θ v :

Characteristic temperature of vibrational mode, K

τ :

Viscosity stress tensor, N · m−2

int:

Internal modes

p,q :

Particular molecular species

ref:

Reference value

trans:

Translational modes

rot:

Rotational modes

vib:

Vibrational modes

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Authors and Affiliations

  1. Laboratoire de Physico-Chimie des Surfaces, Université de Skikda, Skikda, Algeria

    D. Omeiri

  2. Laboratoire de Physique des Lasers, Université d’ Annaba, B.P. 12, Annaba, 23000, Algeria

    D. E. Djafri

Authors
  1. D. Omeiri
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  2. D. E. Djafri
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Omeiri, D., Djafri, D.E. Transport Properties in Gases at High Temperature and Low Pressure: Comparison of Kinetic Theory with Direct Simulation Monte Carlo. Int J Thermophys 31, 1111–1130 (2010). https://doi.org/10.1007/s10765-010-0771-3

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  • DOI: https://doi.org/10.1007/s10765-010-0771-3

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