Progress variable Chemical Thermodynamic

The example reactions considered in this section all have the property that the number of reactions is less than or equal to the number of chemical species. Thus, they are examples of so-called simple chemistry (Fox, 2003) for which it is always possible to rewrite the transport equations in terms of the mixture fraction and a set of reaction-progress variables where each reaction-progress variablereaction-progress variable —> depends on only one reaction. For chemical mechanisms where the number of reactions is larger than the number of species, it is still possible to decompose the concentration vector into three subspaces (i) conserved-constant scalars (whose values are null everywhere), (ii) a mixture-fraction vector, and (iii) a reaction-progress vector. Nevertheless, most commercial CFD codes do not use such decompositions and, instead, solve directly for the mass fractions of the chemical species. We will thus look next at methods for treating detailed chemistry expressed in terms of a set of elementary reaction steps, a thermodynamic database for the species, and chemical rate expressions for each reaction step (Fox, 2003). 

Unless the progress variable A can be controlled, the thermodynamic functions cannot be determined at all possible compositions. This is necessary in order for the general discussion of equilibrium criteria to be operationally meaningful. The rigorous thermodynamic theory of chemical equilibrium does not apply to reactions of the type N2O4 2NO2 since neither component can be isolated. 

The Chemkin gas-phase subroutine library provides the evaluation of information about species, reactions, gas constants and units, equations of state, mole-mass conversion, thermodynamic properties, chemical production rates, equilibrium constants, rate of progress variables, and sensitivity parameters, along with the appropriate derivatives of the above quantities. 

For a discussion of progress variables and chemical equilibria see, e.g., F. T. Wall, Chemical Thermodynamics, 3rd ed. (San Francisco Freeman, 1974), Chapter 10. The pressure dependence of k in single-step reactions is usually small this problem is treated by C. A. Eckart, Ann. Rev. Phys. Chem. 23,239 (1972). Gas-phase unimolecular reaction, for which A is a sensitive function of p, is not a single-step process (Section 5.4). 

Another reaction variable, sometimes called the efficiency of the reaction, suggests itself when the progress of the reaction is limited by the >ositiun of chemical equilibrium. When the thermodynamic variables arc such that A cannot reach its maximum value but will approach its equilibrium... 

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