Figure 1. Physical representation of the gas turbine combustor
configured to combust propane for the reduction of nitrogen oxides
emissions by heterogeneous catalysis.
Complex modeling methods and algorithms are required for the gas turbine
combustor due not only to the complex geometry but also the complex
physicochemical processes involved. It is therefore essential to reduce
the complexity of the model through use of certain simplifying
assumptions. Steady-state analyses are performed, variations in reactor
pressure and temperature are determined in accordance with the ideal gas
law. The model is implemented in computational fluid dynamics software
to obtain the solution of the problem. Computational fluid dynamics is
used to describe a broader range of calculations for a wide variety of
scientific and engineering applications. Thermodynamics is an important
consideration in many of these applications. It relates internal energy
to temperature, which affects the flow of heat. Further sources of heat
include thermal radiation and chemical reactions, in particular
combustion. Heat transfer may involve conduction in solid materials,
coupled with the fluid flow, known as conjugate heat transfer. A modern
definition of computational fluid dynamics would be the prediction of fluid
motion and forces by computation using numerical analysis, generally
extended to include heat, thermodynamics, chemistry and solids.
Numerical analysis provides many methods and algorithms that are
suitable for computational fluid dynamics. The methods include finite
volume, finite element and finite difference, which calculate the
distributions of properties, for instance, pressure, velocity and
temperature, over regions of space which are usually fixed. Alternative
methods attribute properties to particles represented by points in
space, whose motions are calculated. To perform the calculation first
requires a description of the problem by the domain occupied by the
fluid, equations that represent the fluid behavior in terms of properties
such as pressure and velocity, and conditions at the boundary of the fluid domain and initially within the domain for the fluid properties.
The typical computational mesh for the fluid and solid of the gas turbine
combustor configured to combust propane is illustrated schematically in
Figure 2 for the reduction of nitrogen oxides emissions by heterogeneous
catalysis. A computational fluid dynamics simulation begins with a
solution domain which specifies a region of space of a particular
geometric shape, in which fluid dynamics equations are solved. The
process of mesh generation subdivides the solution domain into a mesh of
small volumes. The computational mesh consists of about 600,000 nodes in
total for the fluid and solid of the gas turbine combustor. A
computational fluid dynamics analysis is carried out on the mesh. A mesh
independence test is performed to assure independence of the solution to
the problem. The specification of boundary conditions is one of the most
challenging tasks in setting up a computational fluid dynamics
simulation. The range of possible boundary conditions is endless, to
cover all of the potential applications and physics. Velocity inlet
boundary conditions are used to define the velocity properties of the
flow at the inlet boundary of the fluid region. A uniform velocity
profile is specified at the flow inlet. The temperature of the mixture
is prespecified at the flow inlet. Under-relaxation is a general method
used to improve solution convergence by limiting the amount that a
variable changes during a solution step. The computational fluid
dynamics calculations may take days in order to arrive at a reasonably
accurate solution, using fine grids of the gas turbine combustor, due to
the time-consuming nature of the model. 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.