Chemical Equilibrium With Applications To Turbulent Reactive Flows

Chemical Equilibrium

For the purposes of this discussion, lets begin with a definition of chemical equilibrium. Chemical equilibrium is the state in which the composition has no net change over time. The composition $(\phi_\alpha)$ is defined by $\alpha$ species in terms of mole fractions $(X_\alpha)$, mass fractions $(Y_\alpha)$, or even mole numbers $(N_\alpha)$, having the relationships given below:

\begin{align} \phi_\alpha=X_\alpha=\frac{Y_\alpha M_{mix}}{M_\alpha}=\frac{N_\alpha}{N},~~~~\alpha=1,2,...,N_s \end{align}

where $M_\alpha$ and $M_{mix}$ denote the molecular weight of species $\alpha$ and of the mixture respectively, and $N_s$ denotes the number of species in the system. I will note here, that in our calculations of chemical equilibrium, presented in the next section, we are assuming that the temperature and pressure are specified and of constant value.

Since this discussion is presented with turbulent reactive flows and combustion in mind, we can make the following qualitative assumptions about the systems that we are interested in:

  • 1 phase only - gas phase - and this gas phase mixture is an ideal gas
  • Approximate temperature range of 300 K < T < 3000 K

These assumptions are very appropriate for most turbulent reactive flows, and will not be discussed further.

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