Reduced-Order Models for the Prediction of Unsteady Heat Release in Acoustically Forced Combustion

This work presents novel formulations for models describing acoustically forced combustion in three disjoint regimes; highly turbulent, laminar, and the moderately turbulent flamelet regime. Particular emphasis is placed on simplification of the models to facilitate analytical solutions while still reflecting real phenomenology. Each derivation is treated by beginning with general reacting flow equations, identifying a small subset of physics thought to be dominant in the corresponding regime, and making appropriate simplifications. Each model is non-dimensionalized and both naturally occurring and popular dimensionless parameters are investigated.

The well-stirred reactor (WSR) is used to characterize the highly turbulent regime. It is confirmed that, consistent with the regime to which it is ascribed for static predictions, the WSR is most appropriate to predict the dynamics of chemical kinetics. Both convection time and chemical time dynamics are derived as explicit closed-form functions of dimensionless quantities such as the Damk"ohler number and several newly defined parameters.

The plug-flow reactor (PFR) is applied to a laminar, burner stabilized flame, using a number of established approaches, but with new attention to developing simple albeit accurate expressions governing the flame's frequency response. The system is studied experimentally using a ceramic honeycomb burner, combusting a methane-air mixture, numerically using a nonlinear FEA solver, and analytically by exact solution of the simplified governing equations. Accurately capturing non-unity Lewis-number effects are essential to capturing both the static and the dynamic response of the flame. It is shown that the flame dynamics can be expressed solely in terms of static quantities.

Finally, a Reynolds-averaged flamelet model is applied to a hypothetical burner stabilized flame with homogeneous, isotropic turbulence. Exact solution with a simplified turbulent reaction model parallels that of the plug flow reactor closely, demonstrating a relation between static quantities and the flame frequency response. Comparison with published experiments using considerably more complex flame geometries yields unexpected similarities in frequency scale, and phase behavior. The observed differences are attributed to specific physical phenomena that were deliberately omitted to simplify the model's derivation.