An analytic method for two-dimensional wall motion and product isentrope from the detonation cylinder test

Abstract

The cylinder test provides a measurement of detonation product's ability to perform work on adjacent material. Historically, direct numerical simulation has been required to derive the product energy content and isentrope from experiments of cylinder expansion driven by detonation products. One-dimensional analytic methods have not been able to accurately recover these parameters when the cylinder motion is compressible, exhibiting shocks. For incompressible cylinder motion, analytic one-dimensional approximations more accurately recover the isentrope, but still only approximate the two-dimensional cylinder motion and energy. This work provides a fully two-dimensional model that recovers the exact outer cylinder shape from experimental measurements. The inner cylinder shape and product isentrope are also exactly recovered in the limit of incompressible case motion. An alternate methodology also approximates the inner case shape and isentrope for compressible case motion, e↵ectively allowing accurate isentrope determination for any cylinder

The detonation cylinder test: Determination of full wall velocity and shape from a single velocimetry probe with an arbitrary angle

“…Detonation of the explosive results in high pressure products that accelerate and expand the metal wall ( Figure 1). The velocity of the wall at standard locations can be used to infer the Gurney energy [1,2], while a combination of the wall position and acceleration history yields the isentrope of the detonation products [3,4,5]. Computational fluid dynamics (CFD) simulations can also be used, in an iterative fashion, to reconstruct the product isentrope.…”

“…These data were then once or twice differentiated to compute Gurney energies [1] or product isentropes [4]. However, the streak camera measurement technique does not yield sufficient resolution to accurately resolve the compressible ringing motion of the wall, which for most combinations of ideal explosives and standard copper confinement, can persist for wall pressures as low as 1 GPa [5]. Models that do not capture this compressible motion will generally underestimate the product pressure in this compressible region [4].…”

An analytical approach to obtaining JWL parameters from cylinder tests

“…Given in the form Quantity {Minimum, Maximum, Energy release hydro-code value}, the analytical isentropes produced a detonation pressure, P CJ {38. 4 (all values are quoted in GPa). The differences between the predicted energies from the analytical and hydro-code isentropes increase as the cylinder expands, as implied by Fig.…”

“…Analytical methods of determining JWL parameters from cylinder tests have been previously discussed by Taylor [2], Hill [3] and Jackson [4]. The method described here determines JWL parameters using an analytical technique, building on work previously carried out by Taylor and Hill.…”

The measured temperature and pressure of EDC37 detonation products

“…The results of the cylinder test can then be used to obtain the pressure-volume relationship for the expanding detonation products; this can be done directly [1][2][3][4] as is the case in this work or indirectly using hydrocodes [5,6]. In addition to the usually measured wall expansion and VoD the temperature of the detonating products was also measured.…”