Low Order Modeling for the Dynamics of Spray Flames

Spray flames are commonly used in aviation and land-based power-generation combustors. In order to model and understand combustion instabilities, system modeling tools use acoustic networks to capture the acoustic mode shapes and frequencies, especially those of the unstable modes. A critical piece is the model for the flame dynamics. A large body of work exists for modeling the dynamics of premixed and diffusion flames, with limited focus on spray flames. Prior work in the literature presented extensions to the Schvab-Zeldovich formulation by introducing the droplet phase through a mixture fraction that couples with the gaseous mixture fraction through vaporization physics. While several coupling mechanisms have been identified for thermoacoustic instabilities, a mechanism unique to spray flames is the dynamics of spray injection, oscillatory evaporation and atomization. This results in new control parameters related to a Damkohler number for vaporization, oscillatory droplet physics, spray injection, to name a few. First, we present results from this formulation within a linear framework for the global flame response to oscillatory spray and velocity dynamics. Furthermore, we assess the suitability of this reduced order framework against detailed Large Eddy Simulations from a model combustor. The formulation can be extended to study the non-linear flame response to build Flame Describing Functions, that can then be used in acoustic network tools to capture limit-cycles.