Detonation Failure during Diffraction Marco Arienti, Joseph E. Shepherd CIT ASCI-ASAP FY01 Research Review October 22-23, 2001
cross-sections j = 0 density I II mass-fraction Decoupled Detonation in HMX(Eric Morano, FY00) pressure mass-fraction initial location ZND profile reflective VN II CJ Dirichlet reflective reflective I reflective Pressure-dependent reaction rate:
Idea: examine the problem of detonation failure in terms of decoupling of the reaction zone from the shock front (in the mean flow). • Note: most reaction rate laws are strongly temperature dependent. When decoupling occurs, shocked particles are prevented from undergoing thermal runaway. • In a corner-turning geometry, the expansion propagating from the corner induces a curvature in the undisturbed detonation front and may trigger decoupling.
Pressure field (z-axis) of failing detonation ideal gas and one-step Arrhenius chemistry • Examine the propagation of corner- generated expansionwaves. temperature isocontours corner
Adapt Skews’ construction for diffracting shock(Shultz & Shepherd, 2001) for hydrocarbon and hydrogen mixtures
Diagnostics & Modeling • Idea: follow a set of Lagrangian particles and perform “numerical dominant balance" of the terms contributing to the material derivative of temperature. • Cast Euler equation in reference frame attached to the shock (use Bertrand coordinates). • Track the detonation front and construct an intrinsic reference frame. • Express Lagrangian (material) derivative DT/Dt in this reference.
Generalization to 2D settings • Bertrand (or intrinsic coordinates) x and h.The local velocity of the front is: • In cylindrical coordinates:
Special case: cylindrical symmetry(Eckett & Shepherd, JFM 2000) • When evaluated in cylindrical (or spherical) symmetry, Eq. (4) loses N1, N2, N3, the divergence, the centripetal and the transverse derivative term. (4)
Analysis of detonation extinction in spherical symmetry Particle trajectory particle 10 fails to ignite time time time time
Axial shock decay model • When evaluated along the axis of symmetry, Eq. (4) loses N1, N2, N3, the centripetal and the transverse derivative term. • In previous investigations, Taylor-Sedov strong spherical blast similarity solution (modified for post-shock energy release) has been used to model the evolution of the detonation front after the corner disturbance has reached the centerline.