1. Introduction
Combustion is a chemical reaction between substances, usually including oxygen and usually accompanied by the generation of heat and light in the form of flame [1, 2]. The rate or speed at which the reactants combine is high, in part because of the nature of the chemical reaction itself and in part because more energy is generated than can escape into the surrounding medium, with the result that the temperature of the reactants is raised to accelerate the reaction even more [3, 4]. Combustion encompasses a great variety of phenomena with wide application in industry, the sciences, professions, and the home, and the application is based on knowledge of physics, chemistry, and mechanics; their interrelationship becomes particularly evident in treating flame propagation [5, 6]. Combustion, with rare exceptions, is a complex chemical process involving many steps that depend on the properties of the combustible substance. It is initiated by external factors such as heat, light, and sparks [7, 8]. The reaction sets in as the mixture of combustibles attains the ignition temperature. The combustion spreads from the ignition source to the adjacent layer of gas mixture; in turn, each point of the burning layer serves as an ignition source for the next adjacent layer, and so on. Combustion terminates when equilibrium is achieved between the total heat energies of the reactants and the total heat energies of the products [9, 10]. Most reactions terminate when what is called thermal equilibrium has been attained, namely when the energy of the reactants equals the energy of the products.
The complexity of the combustion reaction mechanism and the rapidly varying temperatures and concentrations in the mixture make it difficult and often impossible to derive an equation that would be useful for predicting combustion phenomena over wide temperature and concentration ranges. Instead, use is made of empirical expressions derived for specific reaction conditions [11, 12]. In addition to chemical reactions, physical processes that transfer mass and energy by diffusion or convection occur in gaseous combustion. In the absence of external forces, the rate of component diffusion depends upon the concentration of the constituents, pressure, and temperature changes, and on diffusion coefficients [13, 14]. The latter are either measured or calculated in terms of the kinetic theory of gases. The process of diffusion is of great importance in combustion reactions, in flames, that is, in gaseous mixtures, and in solids or liquids. Diffusion heat transfer follows a law stating that the heat flux is proportional to the temperature gradient [15, 16]. The coefficient of proportionality, called the thermal conductivity coefficient, is also measured or calculated in terms of the kinetic theory of gases, like the diffusion coefficient. Convective transport of mass and energy may be accounted for by buoyant forces, external forces, and turbulent and eddy motions. Convection is in the main responsible for the mixing of gases. Flame combustion is most prominent with fuels that have been premixed with an oxidant, either oxygen or a compound that provides oxygen, for the reaction [17, 18]. The temperature of flames with this mixture is often several thousand degrees. The chemical reaction in such flames occurs within a narrow zone several micrometers thick [19, 20]. This combustion zone is usually called the flame front. Dilution of the burning mixture with an inert gas, such as helium or nitrogen, lowers the temperature and, consequently, the reaction rate [21, 22]. Great amounts of inert gas extinguish the flame, and the same result is achieved when substances that remove any of the active species are added to the flame [23, 24]. Conditions must be such that the flame is fixed at the burner nozzle or in the combustion chamber [25, 26]. This positioning is required in many practical uses of combustion. Various devices, such as pilot flames and recirculation methods, are designed for this purpose.
A number of combustion systems promote partial conversion of a fuel followed by complete combustion of that fuel in a downstream combustion zone [27, 28]. These methods generally comprise introducing a fuel and air mixture into a combustion zone wherein a portion of the fuel has been partially reacted prior to entering the combustion zone. Such partial reaction may be promoted chemically, catalytically, or by any other conventional means depending upon each particular application [29, 30]. As the partially reacted fuel and air mixture are introduced into a region of the combustion zone, as with a dump, a flame is established to promote complete combustion of the fuel within the fuel and air mixture. Flame stabilization is a common problem in these combustion systems [31, 32]. A flame will propagate through a fuel-air mixture only when certain conditions prevail. Initially, a minimum percentage of fuel must be present within the fuel-air mixture to make the fuel-air mixture flammable, namely the lean flammability limit. Similarly, a maximum percentage of fuel must be present within the fuel-air mixture wherein greater than this percentage will prevent burning, namely the rich flammability limit. The flammability range of a fuel-air mixture is that range of the percentage of fuel within the fuel-air mixture between the lean flammability limit and the rich flammability limit [33, 34]. The stoichiometry of a fuel-air mixture contributes to its flammability range [35, 36]. A stoichiometric fuel-air mixture composition contains sufficient oxygen for complete combustion thereby releasing all the latent heat of combustion of the fuel [37, 38]. The strength of a fuel-air mixture composition typically is expressed in terms of its equivalence ratio. The equivalence ratio is the actual fuel-air ratio divided by stoichiometric fuel-air ratio. For example, an equivalence ratio of one represents a stoichiometric fuel-air mixture composition. An equivalence ratio less than one represents a lean mixture and an equivalence ratio less great than one represents a rich mixture.
Pressure and temperature contribute to the flammability range of fuel-air mixtures. Typically, with increases in pressure, the rich flammability limit is extended thereby extending the flammability range of the fuel-air mixture. Temperature, on the other hand, partially defines the flammability range of fuel-air mixtures [39, 40]. The lowest temperature at which a flammable fuel-air mixture can be formed, based upon the vapor pressure of the fuel at atmospheric pressure, is the flash point of that fuel-air mixture [41, 42]. Within the flammability range of a fuel-air mixture, at temperatures exceeding the flash point of the fuel-air mixture, auto-ignition of the fuel vapor occurs. Auto-ignition generally occurs at or slightly above the stoichiometric fuel-air mixture composition. The time interval between the mixing of the fuel-air mixture such that it is combustible and the auto-ignition of that fuel-air mixture is known as the auto-ignition delay time [43, 44]. One reason that flame stabilization is required in combustion systems is to prevent the flame front from moving upstream from the combustion zone toward the source of fuel, namely a flashback. During a flashback event, the heat of combustion moves upstream and may damage numerous structures within the fuel and air mixing region of the combustor. Flashback may occur due to auto-ignition of a fuel-air mixture caused by a residence time of the fuel-air mixture in a region upstream of the combustion zone that exceeds the auto-ignition delay time of that fuel-air mixture at the temperature and pressure of that region [45, 46]. Flame stabilization also is dependent upon speed of the fuel-air mixture entering the combustion zone where propagation of the flame is desired [47, 48]. A sufficiently low velocity must be retained in the region where the flame is desired in order to sustain the flame. A region of low velocity in which a flame can be sustained can be achieved by causing recirculation of a portion of the fuel-air mixture already burned thereby providing a source of ignition to the fuel-air mixture entering the combustion zone. However, the fuel-air mixture flow pattern, including any recirculation, is critical to achieving flame stability.
In gas turbines, compressed air enters the combustion chamber where it mixes with the fuel. The expanding combustion products impart their energy to the turbine blades. However, flammable mixtures of most fuels are normally burned at relatively high temperatures, which inherently results in the formation of substantial emissions of nitrogen oxides. In the case of gas turbine combustors, the formation of nitrogen oxides can be greatly reduced by limiting the residence time of the combustion products in the combustion zone. However, even under these circumstances, undesirable quantities of nitrogen oxides are nevertheless produced. Additionally, limiting such residence time makes it difficult to maintain stable combustion even after ignition. The present study relates to the design of gas turbine combustors for the reduction of nitrogen oxides emissions by heterogeneous catalysis. More particularly, the present study is directed to an improved method for more efficiently operating a catalytically supported thermal combustion gas turbine system, and at the same time provide low emissions of unburned hydrocarbons, carbon monoxide, and nitrogen oxides. The present study is focused primarily upon at least a portion of the thermal combustion of the fuel takes place in the expansion zone of the gas turbine to counteract the cooling effect of the expansion of the gases. Natural parameter continuation is performed by moving from one stationary solution to another. A critical point is denoted as the solution to the problem when a turning point is reached. Knowledge of critical parameters gains a fundamental understanding of the essential factors affecting the stability of the catalytically supported thermal combustion process. The critical parameters are useful as the design guides associated with the gas turbine combustor. The principal quantitative characteristic of a flame is its normal, or fundamental, burning velocity, which depends on the chemical and thermodynamic properties of the mixture and on pressure and temperature, under given conditions of heat loss. The burning velocity value ranges from several centimeters to even tens of meters per second. The dependence of the burning velocity on molecular structure, which is responsible for fuel reactivity, is known for a great many fuel-air mixtures. Steady-steady simulations are performed using computational fluid dynamics. The present study aims to provide an improved method for operating a gas turbine combustor by catalytically supported thermal combustion of carbonaceous fuel. Particular emphasis is placed upon the sustained combustion of at least a portion of fuel under essentially adiabatic conditions at a rate which surmounts the mass transfer limitation.