On the self-similarity of diffracting gaseous detonations and the critical channel width problem

TL;DR

This paper develops a mathematical model to predict the critical channel width for detonation quenching in gaseous detonations, validated by experiments and simulations, enhancing understanding of detonation diffraction and arrest mechanisms.

Contribution

It introduces a closed-form model combining shock dynamics and strain rate criteria to accurately predict critical channel widths for detonation transmission.

Findings

Model accurately predicts critical channel width for detonation transmission.

Good agreement with experimental and simulation data.

Provides a theoretical framework for detonation control in pipes.

Abstract

One strategy for arresting propagating detonation waves in pipes is by imposing a sudden area enlargement, which provides a rapid lateral divergence of the gases in the reaction zone and attenuates the leading shock. For sufficiently small tube diameter, the detonation decays to a deflagration and the shock decays to negligible strengths. This is known as the critical tube diameter problem. In the present study, we provide a closed form model to predict the detonation quenching for 2D channels. Whitham's geometric shock dynamics, coupled with a shock evolution law based on shocks sustained by a constant source obtained by the shock change equations of Radulescu, is shown to capture the lateral shock dynamics response to the failure wave originating at the expansion corner. A criterion for successful detonation transmission to open space is that the lateral strain rate provided by the failure wave not exceed the critical strain rate of steady curved detonations. Using the critical lateral strain rate obtained by He and Clavin, a closed form solution is obtained for the critical channel opening permitting detonation transmission. The predicted critical channel width is found in very good agreement with our recent experiments and simulations of diffracting H$_2$/O$_2$/Ar detonations.