Laser-initiated conical detonation wave for supersonic combustion

Preliminary theoretical studies are undertaken of the feasibility of an air-breathing supersonic combustor based on a stabilized, conically configured, oblique detonation wave. The conical wave is the result of the interaction of a train of spherical detonation waves, each directly initiated by a very rapidly repeatedly pulsed laser, which is tightly focused on a fixed site (taken to be the origin of coordinates) in a steady, uniform, supersonic stream of combustible gaseous mixture. Downwind of the Chapman-Jouguet detonation is a supersonic, isentropic, inviscid flow. This expansional flow is selfsimilar and describable entirely in terms of the spherical polar angle theta (where theta = 0 is the axis of symmetry downwind of the nonintrusive energy-deposition site, and theta = beta, (pi/2) > beta > 0, identifies the locus of the conical detonation wave). The combustor is idealized as a circular-cross-section pipe upwind of the axial position where the conical detonation wave interacts with the wall. Downwind of this axial position, the reacted-gas flow is no longer selfsimilar, and we seek to identify a not-impractically-long, small-drag-incurring, axisymmetric nozzle configuration such that the method-of-characteristics-computed pressure field at the nozzle-exit plane is nearly uniform at the ambient-atmosphere value.