A Numerical and Analytical Study of Thermally Driven Combustion Oscillations in a Perfectly Stirred Reactor

The oscillatory behaviors of methane and hydrogen oxidation in a perfectly stirred reactor (PSR) are examined. The work explores the parameter spaces in which oscillatory combustion and ignition take place using heat transfer coefficient, mean residence time, and reactor wall temperatures as variables. An analytic model was developed using an eigenvalue analysis to determine the nature and stability of these oscillations. Both numerical and analytical studies suggest that combustion oscillations occur at the extinction turning point of the hysteresis curve or the boundary of combustion extinction. These oscillations are found to be driven by the coupling of the heat released from the reaction and the heat dissipation through the reactor wall, and these are unstable, which perhaps explains why they were never or rarely observed experimentally. In the case of hydrogen oxidation, we demonstrate the existence of two additional types of oscillations, namely, hybrid oscillation and oscillatory ignition, both of which occur at or near the turning point of ignition. These oscillations are stable and driven by detailed reaction kinetics. The numerical results for hydrogen oxidation were compared with previous experiments and found to be within $5K$ of the observed wall temperature where oscillations were observed.