Figure 2. Schematic illustration of the typical computational mesh for the fluid and solid of the gas turbine combustor configured to combust propane for the reduction of nitrogen oxides emissions by heterogeneous catalysis.
Steady-steady simulations are performed, unless otherwise stated. The fluid density is calculated using the ideal gas law. The fluid viscosity, specific heat, and thermal conductivity are calculated from a mass fraction weighted average of species properties, and the specific heat of each species is calculated using a piecewise polynomial fit of temperature. The wall thermal conductivity and exterior convective heat loss coefficient are taken as independent parameters to understand how important thermal management is. The heat flux at the wall-fluid interface is computed using Fourier’s law and continuity in temperature and heat flux links the fluid and solid phases. The left and right edges of the wall are assumed to be insulated. Newton’s law of cooling is used at the outer edge of the wall. Computations are performed using meshes with varying nodal densities to determine the optimum node spacing and density that would give the desired accuracy and minimize computation time. As the mesh density increases, there is a convergence of the solution. The coarsest mesh fails to accurately capture the inflection point at the ignition point and the maximum temperature. Solutions obtained with meshes consisting of a few million nodes are reasonably accurate. The gas phase is assumed to be in quasi-steady-state. The walls are transiently modeled using energy diffusion and radiation. The gas phase is modeled using the forms of the momentum, energy, and species equations. To solve the conservation equations, a segregated solution solver with an under-relaxation method is used. The segregated solver first solves the momentum equations, then solves the continuity equation, and updates the pressure and mass flow rate. The energy and species equations are subsequently solved and convergence is checked. The latter is monitored through both the values of the residuals of the conservation equations and the difference between subsequent iterations of the solution. Numerical convergence is in general difficult because of the inherent stiffness of the chemistry as well as the disparity between the wall and the fluid heat conductivities. In order to assist convergence and compute extinction points, natural parameter continuation is implemented. The calculation time varies for these problems, depending on the initial guess as well as the parameter set.