Steady detonation propagation in a circular arc: a Detonation Shock Dynamics model. (18th October 2016) - Short, Mark; Quirk, James J.; Meyer, Chad D.; Chiquete, Carlos
Abstract : We study the physics of steady detonation wave propagation in a two-dimensional circular arc via a Detonation Shock Dynamics (DSD) surface evolution model. The dependence of the surface angular speed and surface spatial structure on the inner arc radius (R_i ), the arc thickness (R_e-R_i, whereR_e is the outer arc radius) and the degree of confinement on the inner and outer arc is examined. We first analyse the results for a linearD_n –[STIX]x1D705 model, in which the normal surface velocityD_n=D_CJ(1-B[STIX]x1D705), whereD_CJ is the planar Chapman–Jouguet velocity, [STIX]x1D705 is the total surface curvature andB is a length scale representative of a reaction zone thickness. An asymptotic analysis assuming the ratioB/R_i1 is conducted for this model and reveals a complex surface structure as a function of the radial variation from the inner to the outer arc. For sufficiently thin arcs, where(R_e-R_i)/R_i=O(B/R_i), the angular speed of the surface depends on the inner arc radius, the arc thickness and the inner and outer arc confinement. For thicker arcs, where(R_e-R_i)/R_i=O(1), the angular speed does not depend on the outer arc radius or the outer arc confinement to the order calculated. It is found that the leading-order angular speed depends only onD_CJ andR_i, and corresponds to a Huygens limit (zero curvature) propagation model whereD_n=D_CJ, assuming a constant angular speed and perfect confinement on the inner arc surface. Having the normal surface speed depend on curvature requires the insertion of a boundary layer structure near the inner arc surface. This is driven by an increase in the magnitude of the surface wave curvature as the inner arc surface is approached that is needed to meet the confinement condition on the inner arc surface. For weak inner arc confinement, the surface wave spatial variation with the radial coordinate is described by a triple-deck structure. The first-order correction to the angular speed brings in a dependence on the surface curvature through the parameterB, while the influence of the inner arc confinement on the angular velocity only appears in the second-order correction. For stronger inner arc confinement, the surface wave structure is described by a two-layer solution, where the effect of the confinement on the angular speed is promoted to the first-order correction. We also compare the steady-state arc solution for a PBX 9502 DSD model to an experimental two-dimensional arc geometry validation test.