The equations governing steady, isobaric, quasi-one-dimensional flame propagation are discussed in this chapter. These equations pertain to the following two Ansys Chemkin Reactor Models:

Many practical combustors, such as internal combustion engines, rely on premixed flame propagation. Moreover, burner-stabilized laminar premixed flames are often used to study chemical kinetics in a combustion environment. Such flames are effectively one-dimensional and can be made very steady, facilitating detailed experimental measurements of temperature and species profiles. Also, laminar flame speed is often used to characterize the combustion of various fuel-oxidizer combinations and in determining mixture flammability limits. Therefore, the ability to model chemical kinetics and transport processes in these flames is critical to flammability studies, interpreting flame experiments, and to understanding the combustion process itself. Examples of the use of flame modeling to interpret experimental observations and to verify combustion chemistry and pollution formation can be found in Miller, et al. [97], [98], [99].

The Premixed Flame Models solve the set of governing differential equations that describe the flame dynamics using implicit finite difference methods, as well as, a combination of time-dependent and steady-state methods. The solver algorithm employed automates coarse-to-fine grid refinement as a means to enhance the convergence properties of the steady-state approach and as a means to provide optimal mesh placement.

The Burner-stabilized Flame Model is the one most often used for analyzing species profiles in flame experiments, where the mass flow rate through the burner is known. The user has two options for the burner-stabilized flame—one where the temperature profile is known and one in which the temperature profile is determined by the energy conservation equation. Often the temperatures are obtained from experiment. In this case, only the species transport equations are solved. In many flames there can be significant heat losses to the external environment, which are of unknown or questionable origin and thus are difficult to model. However, since the chemistry depends strongly on temperature, it is essential to know the temperatures accurately in order to draw conclusions about the chemical kinetics behavior. If a temperature profile can be measured accurately, it is often better to use this measurement than the temperature profile obtained by solving an energy conservation equation. For cases where the heat losses are known to be negligible, the application can solve a burner-stabilized flame problem in which the temperatures are determined from the energy conservation equation. Comparing these two problem types for the burner-stabilized model may also provide some indication of the heat losses.

The Flame-speed Calculation Model involves a freely propagating flame. This configuration is used to determine the characteristic flame speed of the gas mixture at specified pressure and inlet temperature. In this case there are no heat losses (by definition) and thus the temperatures should be computed from the energy equation. Flame speed depends, in part, on the transport of heat, and predicting the temperature distribution is an integral part of the flame speed calculation.