Self-Consistent Effective Binary Diffusion in Multicomponent Gas Mixtures

Abstract

The correct treatment of diffusion in multicomponent gas mixtures requires solution of a linear system of equations for the diffusive mass fluxes relative to the mass-averaged velocity of the mixture. Effective binary diffusion approximations are often used to avoid solving this system. These approximations are generally internally inconsistent in the sense that the approximate diffusion fluxes do not properly sum to zero. The origin of this inconsistency is identified, and a general procedure for removing it is presented. This procedure applies equally to concentration, forced, pressure, and thermal diffusion, either separately or in combination. It is used to obtain a self-consistent effective binary diffusion approximation in which the diffusive mass fluxes properly sum to zero and all four types of diffusion are simultaneously accounted for. Multicomponent diffusion in gasesMulticomponent diffusion in gases is governed by the equations [1] Z(WAE/)(«j-«0 = ei (/ = !,-~,JV),(1) j where N is the number of species or components in the mixture, n £ is the specific velocity of species ι, x t is the mole fraction of species i, D tj is the binary diffusivity for the pair (r,y), and the driving forces G t are given by (2) *

Modeling of Shock Tunnel Aeroheating Data on the Mars Science Laboratory Aeroshell

“…The self-consistent effective binary diffusion method [20] is used to compute the species diffusion coefficients. This method allows for the variations in species diffusion coefficients to be accurately modeled without sacrificing the requirement that the diffusion velocities sum identically to zero, and has been shown [21] to accurately model the true multicomponent diffusion velocities.…”

Numerical Assessment of Data in Catalytic and Transitional Flows for Martian Entry

“…Transport properties are appropriately modeled in DPLR for this type of flow 17,18 using the binary collision-integral based mixing rules from Gupta, et al 19 . Diffusion coefficients are modeled using the self-consistent effective binary diffusion (SCEBD) method 20 . Turbulence models available in the DPLR code currently include the Baldwin-Lomax 0-equation model 21 , the Spalart-Allmaras model 1-equation model 22 , and the Shear Stress Transport (SST) 2-equation model 23 each with corrections for compressibility effects 24,25 .…”

Heat and mass transfer at sublimation of a single chromium (III) and zirconium (IV) β-diketonate particle in the inert gas mixture

“…Simplified models based on the concept of effective diffusion coefficient are more economically efficient, but often have a limited scope of application. One of the most effective models of multicomponent diffusion is Ramshaw model [6], which is used in this work. The diffusion flux of each component of the mixture is determined by correlations below:…”