State of Detonation Stability Theory and Its Application to Propulsion

We present an overview of the current state of detonation stability theory and discuss its implications for propulsion. The emphasis of the review is on the exact or asymptotic treatments of detonations, including various asymptotic limits that appear in the literature. The role that instability plays in practical detonation-based propulsion is of primary importance and is largely unexplored, hence we point to possible areas of research both theoretical and numerical, thatmight help improve our understanding of detonation behavior in propulsion devices. We outline the basic formulation of detonation stability theory that starts from linearized Euler equations, describe the algorithm of solution, and present an example that illustrates typical results. Nomenclature c = sound speed D = one-dimensional detonation speed D = shock velocity vector E = activation energy e = internal energy per unit mass including chemical energy f = degree of overdrive H = enthalpy flux across the shock k = transverse wave number k! = reaction rate constant M = local Mach number relative to the shock M = mass flux across the shock n = shock-attached frame axial coordinate n = unit normal to the shock P = momentum flux across the shock p = pressure Q = heat release per unit mass q = state vector t = unit tangent vector to the shock U = x component of particle velocity in steady shock frame U1 = x component of particle velocity in unsteady shock frame u = particle velocity vector in laboratory frame u1 = x component of particle velocity in laboratory frame u2 = y component of particle velocity v = specific volume x = laboratory frame axial coordinate y = transverse coordinate = perturbation growth rate = ratio of specific heats = reaction progress variable = density = thermicity = shock displacement from the steady position along x axis! = reaction rate