Figure 1. Schematic illustration of the highly exothermic reactor with a
catalytic heat-recirculating reaction chamber. The thick arrows indicate
the direction of flow, whereas the thin arrows indicate the direction of
heat transfer. All external surfaces exposed to the surroundings are
subjected to convective and radiative heat losses. Symmetry allows the
simulation of only half of each system.
The highly exothermic reactor is illustrated schematically in Figure 2
with a catalytic single-channel reaction chamber. The catalytic
single-channel micro-combustors are modeled as parallel plates of
infinite width. For the single-channel combustor, this is a simple
geometry, consisting of two walls coated with a catalytically active
washcoat. This geometry is used here for comparison purposes. The
physical properties of the combustor solid structure, such as the
density, specific heat, and wall thermal conductivity, are assumed
constant, whereas all fluid properties are temperature-dependent.
Specifically, the gaseous species-specific heat is computed using a
piecewise polynomial fit of temperature, whereas temperature-dependent
species transport properties in the gas phase, such as the species
thermal conductivity and viscosity, are computed using the kinetic
theory of ideal gases. Fluid transport properties, such as the fluid
thermal conductivity, specific heat, and viscosity, are computed by a
mass-fraction-weighted average of species properties, depending on the
local mixture temperature and composition. The fluid density is
determined from the ideal gas law for the local mixture temperature,
pressure, and composition. Uniform profiles for the species mass
fractions, gas temperature, and axial velocity are specified at the
inlet. No-slip boundary conditions are used for both velocity components
at the fluid-solid interfaces. A symmetry boundary condition is used to
model half of each system where symmetry exists. At the symmetry plane
and the outlet, the transverse velocity is set to zero and zero gradient
Neumann boundary conditions are used for all other scalars, namely the
normal derivatives are set to zero. It is important to note that once
the reaction zone shifts approximately past half the length of the
combustor, the boundary conditions at the exit may no longer describe
the system properly. As a result, the blowout critical conditions are
less accurate. To overcome the accuracy problem for a fixed combustor
length, one needs to experimentally measure the exit conditions and
impose them as boundary conditions.