On the geometrical scaling of hydrocarbon detonation dynamics

Abstract

The present communication examines the geometrical scaling of highly unstable detonations by extending the authors’ very recent methodology to analyze the dynamics of hydrocarbon detonations in three-dimensional (3D) circular tubes and two-dimensional (2D) narrow channels. With the effective induction zone length as the normalization scale, dynamics of detonations in each hydrocarbon mixture can be successfully unified, irrespective of the geometry sizes. In terms of these unified dynamics of detonations subject to boundary-layer-induced curvature losses, the experiments have been demonstrated to be in excellent agreement with the theoretically expected geometrical scaling of 2:1 between 3D and 2D geometries. This experimentally confirmed perfect geometrical scaling contributes to the community good news that, even for the intractable highly unstable detonations, their macro-scale behaviors shall permit quasi-steady 1D modelling while neglecting the multi-dimensional cellular structures. Furthermore, these unified dynamics were demonstrated to show no dependence on fuel-oxidizer equivalence ratios and as well the argon dilutions, whose universality appears to be governed by the effective activation energy rather than the well-known detonation instability of mixtures.