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.