On the Validity of the Constant Volume Assumption in Shock Tube Experiments

Abstract

Induction time is an important measurement obtained in shock tube experiments, for use in calibration or validation of chemical kinetic schemes. Typically, these times are taken as representative of spatially uniform, constant volume combustion induction times. The actual process that happens in the shock tube is clearly more complex, however. In a first approximation, the flow might be described as being one-dimensional, inviscid and reactive, behind an incident or reflected shock, although in reality, multi-dimensional and viscous effects will play a role [1, 2]. The constant volume assumption may yield good results when dealing with highly diluted mixtures at relatively high post-shock temperatures [3]. However in other circumstances, such as more reactive mixtures at low post-shock temperatures, strong spatial pressure gradients may be present, potentially leading to significant uncertainties or inaccuracies. Assessing the actual accuracy of the constant volume assumption or alternatively improving the means used in validating kinetic schemes will require at the very least a one-dimensional simulation of the reacting flow in shocked mixture. Although the required simulations are one-dimensional, they are not straightforward, because the initial conditions are singular in the sense that at the instant when chemistry is triggered by the passage of the shock into the reactive mixture, there is no simulation domain containing reactive mixture, and that domain subsequently grows as the shock propagates. We have developed techniques that handle these difficulties, mainly in the context of the deflagration-to-detonation scenario [4]. The full unsteady problem is described by the reactive Euler's equations, which are transformed from its original formulation, in which space x and time t are used as independent variables to $η${\thinspace}={\thinspace}x/t and t. This transformation effectively overcomes the non-existence of the initial physical domain. Chemistry is modeled using a three-step chain-branching mechanism originally proposed by Short & Quirk [5].