Chapter 5: Gas-phase Species Transport Properties

In solving chemically reacting-flow problems, chemical production and destruction is often balanced by transport due to convection, diffusion, or conduction. In some cases, such as perfectly stirred reactors or plug-flow reactors, the determination of composition and temperature fields are assumed to be kinetically limited. In such cases, transport is assumed to be infinitely fast within the section of gas considered and the effects of transport properties can be neglected. In many other important cases, however, transport of species and energy can become rate limiting. Examples where transport properties play a key role in determining the gas state are laminar premixed and diffusion flames, as well as many chemical vapor deposition systems.

Characterizing the molecular transport of species, momentum, and energy in a multicomponent gaseous mixture requires the evaluation of diffusion coefficients, viscosities, thermal conductivities, and thermal diffusion coefficients. Although evaluation of pure species properties follows standard kinetic theory expressions, one can choose from a range of possibilities for evaluating mixture properties. Moreover, computing the mixture properties can be expensive, and depending on the use of the results, it is often advantageous to make simplifying assumptions to reduce the computational cost.

For most applications, gas mixture properties can be determined from pure species properties via certain approximate mixture averaging rules. However, there are some applications in which the approximate averaging rules are not adequate. Ansys Chemkin therefore addresses both the mixture-averaged approach and the full multicomponent approach to transport properties. The Transport package is designed for use with the Chemkin Thermodynamic Database and the Gas-phase Kinetics utilities. The multicomponent methods are based on the work of Dixon-Lewis [30] and the methods for mixture-averaged approach are reported in Warnatz [31] and Kee, et al [32].

The multicomponent formulation has several important advantages over the relatively simpler mixture formulas. The first advantage is accuracy. The mixture formulas are only correct asymptotically in some special cases, such as in a binary mixture, or in diffusion of trace amounts of species into a nearly pure species, or systems in which all species except one move with nearly the same diffusion velocity [33]. A second deficiency of the mixture formulas is that overall mass conservation is not necessarily preserved when solving the species continuity equations. To compensate for this shortcoming one has to apply some ad hoc correction procedure.[32] , [34] The multicomponent formulation guarantees mass conservation without any correction factors, which is a clear advantage. The only real deficiency of the multicomponent formulation is its computational expense. Evaluating the ordinary multicomponent diffusion coefficients involves inverting a matrix, and evaluating the thermal conductivity and thermal diffusion coefficients requires solving a system of algebraic equations, where is the number of species.

To maximize computational efficiency, Transport is structured to do a large portion of the calculations in a Pre-processor that provides information to Ansys Chemkin through a Linking File. Polynomial fits are thus computed a priori for the temperature-dependent parts of the kinetic theory expressions for pure species viscosities and binary coefficients. (The pure species thermal conductivities are also fit, but are only used in the mixture-averaged formulation.) The coefficients from the fit are passed to subroutines in the Transport Subroutine Library, which can be used to return either mixture-averaged properties or multicomponent properties. With this fitting procedure, expensive operations, such as evaluation of collision integrals, are only done once and not every time a property value is needed.