Scaling of detonation velocity in cylinder and slab geometries for ideal, insensitive and non-ideal explosives

Abstract

Experiments were conducted to characterize the detonation phase-velocity dependence on charge thickness for two-dimensional detonation in condensed-phase explosive slabs of PBX 9501, PBX 9502 and ANFO. In combination with previous diametereffect measurements from a cylindrical rate-stick geometry, these data permit examination of the relative scaling of detonation phase velocity between axisymmetric and two-dimensional detonation. We find that the ratio of cylinder radius (R) to slab thickness (T) at each detonation phase velocity (D 0 ) is such that R(D 0 )/T(D 0 ) < 1. The variation in the R(D 0 )/T(D 0 ) scaling is investigated with two detonation shock dynamics (DSD) models: a lower-order model relates the normal detonation velocity to local shock curvature, while a higher-order model includes the effect of front acceleration and transverse flow. The experimentally observed R(D 0 )/T(D 0 ) (<1) scaling behaviour for PBX 9501 and PBX 9502 is captured by the lower-order DSD theory, revealing that the variation in the scale factor is due to a difference in the slab and axisymmetric components of the curvature along the shock in the cylindrical geometry. The higher-order DSD theory is required to capture the observed R(D 0 )/T(D 0 ) (<1) scaling behaviour for ANFO. An asymptotic analysis of the lower-order DSD formulation describes the geometric scaling of the detonation phase velocity between the cylinder and slab geometries as the detonation phase velocity approaches the Chapman-Jouguet value.

Cylinder test wall velocity profiles and product energy for an ammonium nitrate and aluminum explosive

“…This late-time heat release increases as the scale of the test is increased, presumably because larger tests maintain higher product temperatures during expansion. This mechanism has been suggested for other non-ideal explosives, including ammonium nitrate-fuel oil (ANFO) blends [3]. Differences in energy output between the 50.8 mm and 76.2 mm test were smaller than those between the 12.7 mm and 25.4 mm tests, indicating that specific energy release as a function of diameter follows a schedule of diminishing returns.…”

“…This well-known phenomenon is referred to as the diameter effect. Non-ideal explosives are much more sensitive to confinement and diameter effects, exhibiting increased detonation velocity and confiner-acceleration performance with increased charge diameter and confinement [1][2][3]. This difference in behavior is due to the fact that ideal explosives react promptly, releasing more energy before the sonic surface, while the slower reactions in non-ideal explosives may continue behind the sonic surface.…”

Ultrafast Fiber Bragg Grating Interrogation for Sensing in Detonation and Shock Wave Experiments

“…The CFBG position uncertainty is determined by the scatter level in the data of Figure 9 and can be estimated as ±200 $\mathsf{\mu }$m. The accepted value for a PBX-9501 detonation velocity in a rectangular slab is 8.80 mm/$\mathsf{\mu }$s [20]. Table 3 is a compilation of the extracted detonation velocity taking the entire dataset for each diagnostic.…”

Geometry effects on detonation in vapor-deposited hexanitroazobenzene (HNAB)

“…[9] Their form for diameter effect data can be applied to films of effectively infinite width by substituting radius with thickness: [1,2,10] …”

“…Detonation failure experiments are typically conducted in a cylindrical geometry owing to symmetry considerations as well as fabrication considerations of the confining tube and cylindrical explosive pellets that make up the charge. Departures from cylindrical geometries include the two-dimensional slab configuration, [1,2] and the three-dimensional wedge configuration. [3,4] In a slab configuration, detonation losses to confinement arising from varying width-to-thickness ratio are specific to each explosive; with increasing ratio resulting in an eventual symmetry increase from a three-dimensional charge to a two-dimensional "infinite" slab.…”