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.