Solving Combustion Problems Using The First And Second Laws Of Thermodynamics Simultaneously

This paper describes a unified approach of the first and second laws of thermodynamics for solving combustion problems. By modeling the products of combustion as an ideal gas mixture, minimization of Gibbs free energy principle is implemented by the use of chemical equilibrium constants together with the conservation of energy principle. The combustion of hydrogen with oxygen as oxidizer is considered. Newton-Raphson method is used for solving the resulting set of nonlinear algebraic equations in the model. Several case studies that were performed are discussed and recommendations on how this approach can be implemented in thermodynamics textbooks are presented. Introduction In most elementary engineering thermodynamics textbooks[1-4], there are several standard types of problems considered dealing with combustion/chemical reactions, and chemical equilibrium. In the typical combustion problems considered, there is usually sufficient information about the composition of the combustion products or sufficient information for determining the composition of the combustion products from a simple conservation of mass principle. With this information, the application of first law of thermodynamics is straightforward or requires trial and error solution for combustion product temperature. In the typical chemical equilibrium problems considered, the combustion product temperature is provided and the composition of the combustion products is then determined by the use of chemical equilibrium constants. Usually the chemistry mechanism is kept to a minimum complexity with dissociation reactions to radicals occurring at high temperatures being mostly ignored. Some exceptions can be found, see Ref. 1 for example, in which a single dissociation reaction was considered and the equilibrium composition and adiabatic flame temperature are determined simultaneously from first and second laws of thermodynamics. These types of problems are very important in propulsion systems where at system level design, it is very desirable to predict the equilibrium composition as well as the equilibrium temperature (equilibrium flame temperature) of the products of combustion. In addition, a parametric study of the rate of cooling required for the combustor is also desirable. This requires the combination of the first law consideration with the minimization of Gibbs free energy. Proceedings of the 2004 American Society for Engineering Education Annual Conference & Exposition Copyright © 2004, American Society for Engineering Education P ge 9.109.1 In this paper, this approach has been used for modeling the combustion of hydrogen with oxygen using a simple chemistry mechanism in which four dissociation reactions have been considered with the products of combustion being composed of , , , , , and O H 2 2 H 2 O OH O H . The schematic diagram the problem is depicted in Fig. 1. The products of combustion are assumed to form an ideal gas mixture. The mathematical model is obtained by applying the first law of thermodynamics for steady flow case together with chemical equilibrium for the products of combustion, which follows from the second law of thermodynamics. The chemical equilibrium, which is equivalent to minimization of Gibbs free energy, which has been used in codes such as CEA[5], has been implemented by the use of chemical equilibrium constants. In what follows, the mathematical model for stoichiometric case as well as oxygen rich (lean mixture) and fuel rich (rich mixture) cases are presented and the solution procedure is discussed.