The Evolution of the Velocity-Curvature-Acceleration Relationship with Activation Energy for Unstable Gaseous Detonations

Abstract

Gaseous detonations are being evaluated for use in pressure-gain combustors for engine and turbine technologies. A key issue is that gaseous detonations are unstable, exhibiting a cellular instability that locally modifies the shock shape and velocity. To accurately predict the detonation evolution through a detonation combustor, it is critical to bound the magnitude of these instabilities. The detonation shock front paths along a cellular cycle for a given mixture were previously shown to form a unique three-dimensional surface composed of the local shock velocity, curvature, and acceleration using analysis concepts from detonation shock dynamics. The effect of activation energy on this surface is numerically explored in the present study. Instabilities are observed to become more irregular with increasing activation energy, eventually exhibiting at least two disparate length scales that allow smaller cells to exist inside larger cells. Increasing activation energy was also found to increase the span of normal velocities, to increase the rate of cellular shock velocity decay, and to decrease the final velocities in the cellular cycle. The velocity-curvature-acceleration surfaces for all mixtures studied had two distinct regimes of cellular propagation, which are proposed to correspond to coupled and decoupled modes of shock-driven combustion.