Solution algorithms traditionally used for CFD simulation are designed to efficiently solve the Navier-Stokes equations, where fluid transport dominates and source terms are relatively small and not closely coupled from equation to equation. Species are solved one at a time over the solution domain. These algorithms are not well-designed to address species production and consumption due to chemical reactions.

In chemically reacting flow systems, there are large disparities in time-scales between the transport (~1.E-3 seconds) and the kinetics (~1.E-6 seconds) processes. Accurate prediction of the chemical state using existing algorithms would require that the time step for all equations be small enough to capture the kinetic time scales, increasing the cost of solution to ~3 orders of magnitude greater than when no chemistry is present with the same number of species (that is, equations) being solved in the system.

In the traditional approach, the species conservation equation is solved one species at a time, keeping all others fixed. However, the species are inherently closely coupled to each other and to temperature due to the kinetics interaction of the species and the exponential dependence of kinetic rates on temperature. Thus, the onespecies-at-a-time solution method causes each species to easily become out of sync with the other species during an iteration loop. This results in instabilities, non-convergence, or a practical limit of time step (for transient simulations) or relaxation factors (for steady-state) to very small values. Figure 2.1: Typical method for solving mass, momentum, energy, and species equations in commercial computational fluid dynamics illustrates this traditional approach.

This situation is particularly acute when the system involves "stiff kinetics," where there is a large disparity in the magnitude of reaction rates and in the magnitude of species concentrations. Examples of stiff kinetics include ignition, flames, and catalytic light-off conditions.

Trace species can have large non-linear effects on major species through chemical reactions. Therefore, accuracy of species calculations over a wide range of species fractions is very important. In such cases, tolerances must be set and adhered to rigorously. In addition, some reactions may have estimated reaction rates that are not temperature dependent, in most cases. In these cases it can be difficult if not impossible to numerically resolve all of the important time scales without very close coupling between the species.

For steady-state systems, a traditional CFD approach uses transient or time-stepping to get to a steady state, with time steps set as large as possible and under-relaxation factors often set to less than one to damp out instabilities during convergence. Steady state is then defined as the time at which things are not changing any more in the system as a function of time. This transient approach can be inefficient due to the small time steps required to keep species in sync and also the small relaxation factors required to keep the simulation stable.

For laminar reacting flows, molecular diffusion between reacting species can play a critical role in determining the chemical state and the fluxes in the system. Here, the overall mass conservation from species diffusion is often handled in an ad-hoc, non mass-conserving way. Properties can vary at every location in the solution grid but are often represented as constants. Accurate representation of diffusion terms requires calculation of molecular-scale diffusion properties that depend on the local chemical state and on the gradients of that state in the system. Neglect of these effects can lead to very inaccurate results and poor mass conservation in some cases. Poor mass conservation can lead to non-convergence or un-physical results.

Finally, boundary conditions applied to conservation equations for chemical species in CFD typically do not consider the surface state. The chemical and thermodynamic state of a solid surface can strongly affect the interaction between the gas and the surface, especially when catalytic reactions or material deposition takes place. Surface coverage (the chemical identity of the surface, or the identity of molecules that are chemically or physically bound to the surface) affects reactions through competition of gas-phase species for sites, preference of species to react with one adsorbed species over another, and the actual value of the rates for a given reaction through modification of the surface thermodynamic state. Production and destruction of fluid-phase species at the surface must match the flux transported (through convection or diffusion or other means) to that surface. Self-consistency between species surface losses are important for stable convergence. Total mass balance must adjust for net surface mass exchange (for example, deposition or etch). A non-zero velocity at surfaces may result, contrary to the assumption in most cases of a zero velocity condition between a gas and a surface. This non-zero velocity ("Stefan flow") arises due to net deposition or etching at the surface and must be included for proper conservation of mass in the system.