High resolution GPU-based flow simulation of the gaseous methane-oxygen detonation structure

A gaseous detonation is a combustion-driven, compressible wave propagating at supersonic speeds. Experimental visualizations and numerical simulations confirm that detonation waves have a complex, multi-dimensional, cellular structure generated by various gasdynamic interactions (Ohyagi et al. 2000; Ng and Zhang 2012). Except in special combustible mixtures (such as argon-diluted mixtures) with a ‘‘laminar’’ detonation front and regular cellular pattern, the fine-scale cellular structure of unstable detonations remains difficult to describe due to its turbulent nature with large hydrodynamic fluctuations and unreacted pockets (Gamezo et al. 1999; Radulescu et al. 2005). Fundamentally, it is desirable to determine a characteristic length scale for the unstable cellular detonation so as to correlate with other detonation dynamic parameters such as direct initiation energy or detonability limits (Lee and Radulescu 2005). Numerical simulations of cellular detonations have been performed since the 1980s, see Ng and Zhang (2012) and references therein. The detonation model is generally the reactive Euler equations with one-step chemical kinetics. This model has proven useful in capturing the salient features of cellular detonations: the triple-wave configuration at the leading front and the unburned pockets within the detonation structure. However, despite advanced numerical techniques like adaptive mesh refinement (AMR), previous simulations suffer from a lack of numerical resolution to properly reveal the hydrodynamic instabilities and pressure wave interactions within or behind the irregular detonation structure. These instabilities have recently been found to be essential in the propagation mechanism of detonations (Radulescu et al. 2005; Kiyanda and Higgins 2013) and a large number of computation cells at the detonation front are inevitably required to resolve the structure (Mahmoudi and Mazaheri 2011; Kessler et al. 2011; Mazaheri et al. 2012). In this paper, high-resolution numerical simulations are reported to elucidate the dynamics of unstable gaseous methane-oxygen detonations. Comparisons of the numerical detonation structure with experimental photography are presented. The computation is performed using graphic processing units (GPU). The computational Cartesian geometry used makes the many GPU cores convenient to perform computations leading to significant speed-ups over a conventional CPU (Vanka 2013). GPU computing allows the use of a high-resolution mesh throughout the complete domain. It eliminates the use of AMR and, hence, any possible adaptive grid-induced, numerical artifacts.