“…2022; Crane et al. 2023). Figure 2.The 2-D instantaneous flow fields in 2H–O–7Ar mixture: ( a ) temperature; ( b ) thermicity; ( c ) maximum pressure.Figure 3.The 2-D instantaneous flow fields in 2H–O mixture: ( a ) temperature; ( b ) thermicity, ( c ) maximum pressure.…”
Two-dimensional numerical simulations with the particle tracking method were conducted to analyse the dispersion behind the detonation front and its mean structure. The mixtures were 2H
$_2$
–O
$_2$
–7Ar and 2H
$_2$
–O
$_2$
of increased irregularity in ambient conditions. The detonation could be described as a two-scale phenomenon, especially for the unstable case. The first scale is related to the main heat release zone, and the second where some classical laws of turbulence remain relevant. The dispersion of the particles was promoted by the fluctuations of the leading shock and its curvature, the presence of the reaction front, and to a lesser extent transverse waves, jets and vortex motion. Indeed, the dispersion and the relative dispersion could be scaled using the reduced activation energy and the
$\chi$
parameter, respectively, suggesting that the main mechanism driving the dispersion came from the one-dimensional leading shock fluctuations and heat release. The dispersion within the induction time scale was closely related to the cellular structure, particles accumulating along the trajectory of the triple points. Then, after a transient where the fading transverse waves and the vortical motions coming from jets and slip lines were present, the relative dispersion relaxed towards a Richardson–Obukhov regime, especially for the unstable case. Two new Lagrangian Favre average procedures for the gaseous detonation in the instantaneous shock frame were proposed and the mean profiles were compared with those from Eulerian procedure. The characteristic lengths for the detonation were similar, meaning that the Eulerian procedure gave the mean structure with a reasonable accuracy.
“…2022; Crane et al. 2023). Figure 2.The 2-D instantaneous flow fields in 2H–O–7Ar mixture: ( a ) temperature; ( b ) thermicity; ( c ) maximum pressure.Figure 3.The 2-D instantaneous flow fields in 2H–O mixture: ( a ) temperature; ( b ) thermicity, ( c ) maximum pressure.…”
Two-dimensional numerical simulations with the particle tracking method were conducted to analyse the dispersion behind the detonation front and its mean structure. The mixtures were 2H
$_2$
–O
$_2$
–7Ar and 2H
$_2$
–O
$_2$
of increased irregularity in ambient conditions. The detonation could be described as a two-scale phenomenon, especially for the unstable case. The first scale is related to the main heat release zone, and the second where some classical laws of turbulence remain relevant. The dispersion of the particles was promoted by the fluctuations of the leading shock and its curvature, the presence of the reaction front, and to a lesser extent transverse waves, jets and vortex motion. Indeed, the dispersion and the relative dispersion could be scaled using the reduced activation energy and the
$\chi$
parameter, respectively, suggesting that the main mechanism driving the dispersion came from the one-dimensional leading shock fluctuations and heat release. The dispersion within the induction time scale was closely related to the cellular structure, particles accumulating along the trajectory of the triple points. Then, after a transient where the fading transverse waves and the vortical motions coming from jets and slip lines were present, the relative dispersion relaxed towards a Richardson–Obukhov regime, especially for the unstable case. Two new Lagrangian Favre average procedures for the gaseous detonation in the instantaneous shock frame were proposed and the mean profiles were compared with those from Eulerian procedure. The characteristic lengths for the detonation were similar, meaning that the Eulerian procedure gave the mean structure with a reasonable accuracy.
“…In the studied cases, the threshold value is 1.4-2 times the characteristic cell size under the same mixture condition. It is worth noting that a real three-dimensional detonation structure is very complex, involving irregularity and inhomogeneity of the detonation cell (Pintgen et al 2003;Crane et al 2023), which may lead to greater fluctuations of the threshold than that in the current simulations. For case F, the sizes of cell samples at various radii are closer to the fitted line due to the more uniform distribution.…”
Section: Detonation Cell Diverging and Coalescencementioning
Two-dimensional simulations are conducted to investigate the direct initiation of cylindrical detonation in hydrogen/air mixtures with detailed chemistry. The effects of hotspot condition and mixture composition gradient on detonation initiation are studied. Different hotspot pressures and compositions are first considered in the uniform mixture. It is found that detonation initiation fails for low hotspot pressures and the critical regime dominates with high hotspot pressures. Detonation is directly initiated from the reactive hotspot, whilst it is ignited somewhere beyond the non-reactive hotspots. Two cell diverging patterns (i.e. abrupt and gradual) are identified and the detailed mechanisms are analysed. Moreover, cell coalescence occurs if many irregular cells are generated initially, which promotes the local cell growth. We also consider non-uniform detonable mixtures. The results show that the initiated detonation experiences self-sustaining propagation, highly unstable propagation and extinction in mixtures with a linearly decreasing equivalence ratio along the radial direction, i.e. 1 → 0.9, 1 → 0.5 and 1 → 0. Moreover, the hydrodynamic structure analysis shows that, for the self-sustaining detonations, the hydrodynamic thickness increases at the overdriven stage, decreases as the cells are generated and eventually becomes almost constant at the cell diverging stage, within which the sonic plane shows a ‘sawtooth’ pattern. However, in the detonation extinction cases, the hydrodynamic thickness continuously increases, and no ‘sawtooth’ sonic plane can be observed.
“…Numerical simulations get around the difficulty of the assumptions on the fluid dynamics by running the computation long enough so that the small perturbations from the initial conditions have stabilized into statistically identical detonation cells given the boundary conditions. However, they still require large computational resources and reliable chemical kinetic schemes, e.g., (Crane, et al, 2022), to realistically account for the fundamental interplay of inviscid compressibility, chemical kinetics, and tube cross-section shape even for the simple propagation of cellular detonation. Nevertheless, considering that most practical problems also include ignition, quenching, heat transfer and deflagration, numerical simulation should be the preferred tool for a coherent combination that includes at least diffusive effects.…”
Section: Local Instabilities: Detonation Cellsmentioning
Propulsion systems based on the constant-pressure combustion process have reached maturity in terms of performance, which is close to its theoretical limit. Technological breakthroughs are needed to develop more efficient transportation systems that meet today’s demands for reduced environmental impact and increased performance. The Rotating Detonation Engine (RDE), a specific implementation of the detonation process, appears today as a promising candidate due to its high thermal efficiency, wide operating Mach range, short combustion time and, thus, high compactness. Following the first proofs of concept presented in the 1960s, the last decade has seen a significant increase in laboratory demonstrators with different fuels, injection techniques, operating conditions, dimensions and geometric configurations. Recently, two flight tests of rocket-type RDEs have been reported in Japan and Poland, supervized by Professors Kasahara (Nagoya University) and Wolanski (Warsaw University), respectively. Engineering approaches are now required to design industrial systems whose missions impose efficiency and reliability constraints. The latter may render ineffective the simplified solutions and configurations developed under laboratory conditions. This requires understanding the fundamentals of detonation dynamics relevant to the RDE and the interrelated optimizations of the device components. This article summarizes some of the authors’ experimental and numerical work on fundamental and applied issues now considered to affect, individually or in combination, the efficiency and reliability of the RDE. These are the structure of the detonation reaction zone, the detonation dynamics for rotating regimes, the injection configurations, the chamber geometry, and the integration constraints.
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