Effect of Curvature on the Neutral Stability Boundary for Cellular Gaseous Detonations

For one-step Arrhenius reactions, a significant volume of work has been conducted on establishing the neutral stability boundaries for two-dimensional cellular instabilities to develop from a one-dimensional Zeldovich-von Neumann-Doring wave (ZND) structure in rigid channels. In the one-step model, for fixed ratio of specific heats, the boundary is characterized by variations in the heat release and activation energy. What has not been studied to date is how the aforementioned neutral stability boundary is affected when the reference steady wave is curved. Here, we examine the shift in the rigid channel 2D neutral stability boundary that occurs when semi-confined flows are considered. Specifically, we consider an inert bounding mixture that is not confining for the detonation, i.e., in a steady flow, the flow at the inert boundary is sonic. Then, for a fixed channel width and heat release, we reduce the activation energy until the detonation becomes stable with a well-defined detonation driving zone (DDZ) structure. We examine the change in the neutral stability boundary for multiple channel widths, demonstrating that curved detonations have a significant effect on the neutral stability boundary for cellular flows.