Detonation propagation in annular arcs of condensed phase explosives

Abstract

We present a numerical study of detonation propagation in unconfined explosive charges shaped as an annular arc (rib). Steady detonation in a straight charge propagates at constant speed but when it enters an annular section, it goes through a transition phase and eventually reaches a new steady state of constant angular velocity. This study examines the speed of the detonation wave along the annular charge during the transition phase and at steady state, as well as its dependence on the dimensions of the annulus. The system is modeled using a recently proposed diffuse-interface formulation which allows for the representation of a twophase explosive and of an additional inert material. The explosive considered is the polymer-bonded TATB-based LX-17 and is modeled using two JWL equations of state and the Ignition and Growth reaction rate law. Results show that steady state speeds are in good agreement with experiment. In the transition phase, the evolution of outer detonation speed deviates from the exponential bounded growth function suggested by previous studies. We propose a new description of the transition phase which consists of two regimes. The first is caused by local effects at the outer edge of the annulus and leads to a dependence of outer detonation speed on angular position along the arc. The second regime is induced by effects originating from the inner edge of the annular charge and leads to the deceleration of the outer detonation until steady state is reached. The study concludes with a parametric study where the dependence of the steady state and the transition phase on the dimensions of the annulus is investigated.

A diffuse interface model of reactive-fluids and solid-dynamics

“…Figure 2 shows the r 0 = 20 mm confined and unconfined test for reference. The tests also show good qualitative agreement with previous numerical rate stick tests, such as Ioannou et al [19], the strong confinement case of Banks et al [2] and Michael and Nikiforakis [25].…”

“…The results are non-dimensionalised following the procedure in Ioannou et al [19]. Here, quantities are nondimensionalised using the CJ (Chapman-Jouguet) detonation velocity, D CJ , for LX-17 and a reference time:…”

A Diffuse Interface Model of Reactive-fluids and Solid-dynamics

“…This contrasts the mixed approach used by both Schoch et al [33] and Michael and Nikiforakis [23] Figure 2 shows the results of several confined and unconfined rate stick tests with comparison against experiment [34]. The results are non-dimensionalised following the procedure in Ioannou et al [17]. The results show good agreement with the experimental values, validating the reactive part of the model.…”

“…The explosive's products and reactants are governed by the JWL equation-of-state previously outlined. The reactants have the parameters A = 7.781×10 13 Pa, B = −5.031×10 9 Pa, R 1 = 11.3, R 2 = 1.13, Γ = 0.8938, C V = 1305.5 Jkg −1 K −1 and the products have the parameters A = 14.8105 × 10 11 Pa, B = 6.379 × 10 10 Pa, R 1 = 6.2, R 2 = 2.2, Γ = 0.5, C V = 524.9 Jkg −1 K −1 [35,36,17]. The detonation energy is given by Q = 3.94 × 10 6 Jkg −1 .…”

Three-dimensional simulations of detonation propagation in circular tubes: Effects of jet initiation and wall reflection

“…Controlling the propagation mechanism of the detonation wave [25][26][27] is another key issue for having a reliable and efficient detonation-based propulsion system. Several propagation modes have been observed in quiescent mixtures in the detonation of a circular tube, such as the spinning, twoheaded, and multi-headed modes.…”