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.