In the first part of this work, instability is correctly predicted for a Rijke tube with a new two-term acoustic forcing term derived from a one-dimensional flame dynamics model. The new two-term acoustic forcing term, which is comprised of the summation of chemical heat release rate and heat transfer due to convection, correctly predicts instability where older models of acoustic forcing based solely on chemical heat release rate incorrectly predicted stability. This stability analysis correctly predicts the inlet conditions of the instability in addition to the frequency of instability.

In the second part of this work, networks of dynamic well-stirred reactors are used to model qualitative behavior observed in turbulent combustion. First a model of dynamic well-stirred reactor is derived, and then several reactors are coupled together by recirculation. The dynamics of the various models are computed and assessed. The models exhibit interesting behavior that has been viewed experimentally including hysteresis and peaking in the dynamic response.