Modeling the Effects of Spray Number Density on the Global Heat Release Dynamics of Spray Flames

A large body of work exists for reduced order modeling of the response of premixed and gaseous diffusion flames, however, the focus on spray flames is limited. Recently, the author has presented reduced order models for the response of spray flames to velocity disturbances with a focus on both the flame shape and heat release. The model uses the classical Burke-Schumann diffusion flame configuration as a basis with the fuel introduced in the form of a spray of liquid droplets. The space-time dynamics in the model uses the fast-chemistry limit applied to the mixture fraction equation for both the gaseous and liquid phases. These equations are coupled through evaporation of the liquid droplets in effect resulting in an extension to the Schvab-Zeldovich formulation. 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. The results from this formulation present changes to the local and global flame dynamics due to oscillatory spray dynamics. More specifically, the model considers the dynamics of spray number density and its effects on both the local and global response of spray flames.