Finite rate chemistry

Mixture Fraction, Dissipation, and Finite-Rate Chemistry... 

One of the most challenging aspects of modeling turbulent combustion is the accurate prediction of finite-rate chemistry effects. In highly turbulent flames, the local transport rates for the removal of combustion radicals and heat may be comparable to or larger than the production rates of radicals and heat from combustion reactions. As a result, the chemistry cannot keep up with the transport and the flame is quenched. To illustrate these finite-rate chemistry effects, we compare temperature measurements in two piloted, partially premixed CH4/air (1/3 by vol.) jet flames with different turbulence levels. Figure 7.2.4 shows scatter plots of temperature as a function of mixture fraction for a fully burning flame (Flame C) and a flame with significant local extinction (Flame F) at a downstream location of xld = 15 [16]. These scatter plots provide a qualitative indication of the probability of local extinction, which is characterized... 

It is then no longer necessary to solve a transport equation for Y and the numerical difficulties associated with treating the first reaction with a finite-rate chemistry solver are thereby avoided. 

In (5.297), the interpolation parameter is defined separately for each component. Note, however, that unlike the earlier examples, there is no guarantee that the interpolation parameters will be bounded between zero and one. For example, the equilibrium concentration of intermediate species may be negligible despite the fact that these species can be abundant in flows dominated by finite-rate chemistry. Thus, although (5.297) provides a convenient closure for the chemical source term, it is by no means guaranteed to produce accurate predictions A more reliable method for determining the conditional moments is the formulation of a transport equation that depends explicitly on turbulent transport and chemical reactions. We will look at this method for both homogeneous and inhomogeneous flows below. 

For finite-rate chemistry, the concentration bounds will thus be time-dependent. As seen in Section 5.5, the dependence of the upper bounds of the reaction-progress variables on the mixture fraction is usually non-trivial. 

This will happen regardless of the magnitude of the mixing time k/e. Thus, it does not correspond to flame quenching at high scalar dissipation rates (small mixing time) seen in real flames with finite-rate chemistry. 

The reaction-progress vector is premixed in the sense that variations due to finite-rate chemistry will occur along iso-clines of constant mixture fraction. 

Pdf modeling of finite-rate chemistry effects in turbulent nonpremixed jet flames. 

Linear-eddy modelling of turbulent transport. Part 7. Finite rate chemistry and multi-stream mixing. Journal of Fluid Mechanics 240, 289-313. 

These approaches can be divided into two groups. In the first group, fast chemistry (approaches 1 and 2), it is assumed that the rate of chemical conversion is not kinetically controlled. The second group,finite rate chemistry (approaches 3-5), allows for kinetically controlled processes, in that restrictions are put on the chemical reaction rate. Below we discuss these different approaches in more detail. 

The assumption of fast chemistry is useful in systems with diffusion limitation. However, if the chemistry is kinetically limited or if the chemistry involves competing product channels, only finite rate chemistry provides a good representation. Finite rate chemistry can be represented on different levels of complexity, ranging from a single global reaction to a detailed reaction mechanism involving perhaps hundreds of species. These approaches are described in more detail in the following sections. 

Global Reactions The use of global or multi-step reactions to represent the chemistry in a reacting flow system may be a significant improvement compared to assumptions of fast reaction or chemical equilibrium. The use of global reactions such as in Eq. 13.2 is the simplest way to introduce finite rate chemistry. 

There are a number of possible approaches to the calculation of influences of finite-rate chemistry on diffusion flames. Known rates of elementary reaction steps may be employed in the full set of conservation equations, with solutions sought by numerical integration (for example, [171]). Complexities of diffusion-flame problems cause this approach to be difficult to pursue and motivate searches for simplifications of the chemical kinetics [172]. Numerical integrations that have been performed mainly employ one-step (first in [107]) or two-step [173] approximations to the kinetics. Appropriate one-step approximations are realistic for limited purposes over restricted ranges of conditions. However, there are important aspects of flame structure (for example, soot-concentration profiles) that cannot be described by one-step, overall, kinetic schemes, and one of the major currently outstanding diffusion-flame problems is to develop better simplified kinetic models for hydrocarbon diffusion flames that are capable of predicting results such as observed correlations [172] for concentration profiles of nonequilibrium species. 

We consider that equation (71) is solved first, prior to the study of equation (88). This may be done in principle if pD is independent of T and if changes in the solution T have a negligible influence on the fluid dynamics. Otherwise it is only a conceptual aid, and we cannot investigate directly the variation of T with space and time. We can, however, investigate the variation of T with Z and study the influence of finite-rate chemistry on this variation. This type of investigation is facilitated by introducing into (88) the variable Z as an independent variable, in a manner analogous to that of Crocco [185]. 

In the applications that have been discussed here, high rates of transport have, somewhat paradoxically, favored attainment of conditions under which analyses neglecting transport effects can be applied. The rapid transport helps to achieve conditions of uniformity, under which transport no longer is significant, and effects of finite-rate chemistry can be studied. This same kind of situation prevails in various other experiments, such as those employing a suitably designed turbulent-flow reactor [18], [19], [20]. In... 

With upstream stagnation conditions and (x) given, finite-rate chemistry may influence m by modifying throat conditions. This effect is not addressed here. 

So long as the finite-rate chemistry occurs in a single reactive-diffusive zone extending to the surface of the condensed phase, the analysis need not be restricted to a one-step reaction. Known mechanisms of homogeneous polymer degradation may be taken into account—for example, [45]. The results continue to be expressible in formulas that resemble equation (29) but that usually are somewhat more complicated. 

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