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

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, effectively allowing accurate isentrope determination for any cylinder test. The isentrope derived from a PBX 9502 cylinder test with compressible motion is shown to agree well with a reference isentrope. The errors associated with the one-dimensional flow assumption are also quantified. The incompressible case model can be used to estimate case shape and velocity from a given isentrope, providing a maximum fragment velocity. (C) 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.