Acoustic timescale characterisation of symmetric and asymmetric multidimensional hot spots

Abstract

In this work, two-dimensional hot spots are modelled by combining a linear temperature gradient with a constant temperature plateau. This approach retains the simplicity of a linear temperature gradient, but captures the effects of a local temperature maximum of finite size. Symmetric and asymmetric plateau regions are modelled using both rectangular and elliptical geometries. A one-step Arrhenius reaction for H₂–air is used to model the reactive mixture. Plateaus with different ratios of excitation to acoustic timescales, spanning two orders of magnitude, are simulated. Even with clear differences in behaviour between one and two dimensions, the a priori prescribed hot spot timescale ratio is shown to characterise the 2-D gasdynamic response. The relationship between one and two dimensions is explored using asymmetric plateau regions. It is shown that 1-D behaviour is recovered over a finite time. Furthermore, the duration of this 1-D behaviour is directly related to the asymmetry of the plateau.

Keywords:

• multidimensional hot spot
• detonation initiation
• acoustic timescale
• temperature gradient
• thermal stratification

Additional information

Funding

The research reported in this paper is partially supported by the HPC equipment purchased through: NSF MRI [grant number CNS 1229081]; NSF CRI [grant number 1205413].