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.