Method-of-characteristics model for a low-enthalpy, detonation-driven shock tube

Abstract

A reduced-order model for a detonation-driven shock tube was developed using the method of characteristics (MoC). The scope of this work was limited to calorically perfect slugs of gases. Effects of momentum and heat losses were included. The governing equations for inviscid, one-dimensional flow of a calorically perfect gas were simplified using MoC. These simplified equations represented and resolved various gasdynamic phenomena such as weak compressions, rarefactions, shocks, and contact surfaces. The momentum losses in the governing equations were estimated using established friction factors. Various empirical methods were explored to determine an appropriate heat-transfer model. Based on the expected ideal wave processes in a detonation-driven shock tube, MoC subroutines were assembled into a global algorithm representing detonation tube operation. To validate the results from the reduced-order model, experiments were carried out in a small-scale detonation tube. The experiments used nitrogen as the high-pressure driver gas, stoichiometric oxyhydrogen as the detonation driver gas, and nitrogen or helium as the driven gas. Comparison with experiments showed that the detonation tube model reasonably replicated detonation tube operation for all the experimental cases. Specifically, the decaying incident shock trajectory in the driven section was replicated well, and so was the peak pressure at the driven end wall. The quasisteady plateau pressure in the detonation driver was replicated reasonably, with experimental pressure traces showing earlier decay than MoC pressure traces. The wave system produced by the reflected shock wave–contact surface interaction in the driven section was also predicted accurately by the MoC model.