Simplified Expressions for the Transport Properties of Ionized Monatomic Gases

Abstract

Simplified theoretical expressions for the transport properties of ionized gas mixtures are derived within the framework of the Chapman—Enskog—Burnett method. The properties of equilibrium partially ionized argon are then computed with these expressions and compared with values obtained with the exact theory. Agreement is satisfactory.

Transport coefficients of high-temperature nitrogen

“…To the dominant In A term, these formulas in connection with the third approximation to AE, give the same results (for a completely ionized gas) as those obtained by the Spitzer-Harm expression derived from the Fokker-Planck equation (see [7]). …”

“…Finally the first and the third approximations of the Chapman-Enskog method have been utilized for computing the viscosity and the electrical conductivity [6,7]. The collision integrals necessary for the present calculations are essentially those of ref.…”

“…A shielded Coulomb potential has been used for calculating the collision integrals of charged-charged (including electron-electron) interactions. They appear in the form [7] where A = 2 d/bo is the ratio between the Debye lenght (d) and the average closest impact parameter bo.…”

“…The plasma has been assumed to consist of seven species N2, H2, N, H, N+, H+ and electrons, the concentration of which has been obtained in [5] [6,7] where the different terms represent the translational contribution due to the electrons (Â.E) and to the heavy components (AH), the reactive (£9 and internal (Â.inJ contributions.…”

Three-Dimensional Numerical Modeling of the Magnetohydrodynamic Augmented Propulsion Experiment

“…Fortunately, it turns out that all of the Q T ij l s , ( ) ( ) terms from equation (32) with l > 1 have coefficients proportional to a power of m 1 /m j (where 1 = electrons and j ≠ 1), can be neglected. 16 This leaves only values of Q ij 1 , which are the well-known momentum-transfer collision cross sections, which can be experimentally measured as a function of incident electron energy. 11,12 The integral in equation (32) takes the form of a half-range Gauss-Hermite polynomial, which is a special case of a Gauss-Laguerre integral equation, and can be solved using a 16-point Gauss-Laguerre quadrature (which is done in omega.f), essentially calculating the values of the average collision cross section for the selected species.…”