Abstract:The present work revisits the problem of modelling the real gaseous detonation dynamics at the macro-scale by simple steady one-dimensional (1D) models. Experiments of detonations propagating in channels with exponentially expanding cross-sections (exponential horns) were conducted in the H 2 /O 2 /Ar reactive system. Steady detonation waves were obtained at the macroscale, with cellular structures characterized by reactive transverse waves. For all the mixtures studied, the dependence of the mean detonation s… Show more
“…From the instantaneous flow fields, these regions were seen to be thin non-reactive tails in the gas between the leading shock front and the transverse waves due to the lower temperature, which were reported numerically by Gamezo et al. (2000) and observed experimentally by Xiao & Radulescu (2020) in a hydrogen–oxygen–argon mixture. Figure 15.The 2-D flow fields of the projected Lagrangian values in the position where the Lagrangian particles experienced the maximum thermicity in 2––7Ar mixture.…”
Section: Resultssupporting
confidence: 66%
“…There are regions in the cellular structure where the Lagrangian particles did not complete the induction process (figures 15, 16). From the instantaneous flow fields, these regions were seen to be thin non-reactive tails in the gas between the leading shock front and the transverse waves due to the lower temperature, which were reported numerically by Gamezo et al (2000) and observed experimentally by Xiao & Radulescu (2020) in a hydrogen-oxygen-argon mixture.…”
Section: Dispersion In Induction Time Scalesupporting
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.
“…From the instantaneous flow fields, these regions were seen to be thin non-reactive tails in the gas between the leading shock front and the transverse waves due to the lower temperature, which were reported numerically by Gamezo et al. (2000) and observed experimentally by Xiao & Radulescu (2020) in a hydrogen–oxygen–argon mixture. Figure 15.The 2-D flow fields of the projected Lagrangian values in the position where the Lagrangian particles experienced the maximum thermicity in 2––7Ar mixture.…”
Section: Resultssupporting
confidence: 66%
“…There are regions in the cellular structure where the Lagrangian particles did not complete the induction process (figures 15, 16). From the instantaneous flow fields, these regions were seen to be thin non-reactive tails in the gas between the leading shock front and the transverse waves due to the lower temperature, which were reported numerically by Gamezo et al (2000) and observed experimentally by Xiao & Radulescu (2020) in a hydrogen-oxygen-argon mixture.…”
Section: Dispersion In Induction Time Scalesupporting
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.
“…The present study addresses whether a curvature based prediction of critical transmission is compatible with experiments in weakly unstable detonations and can quantitatively predict the critical diffraction conditions. of such weakly unstable cellular hydrogen detonations at low pressure, which are characterized by much longer reaction zones as compared to induction zones, can be well captured by the predictions of the ZND model with curvature 23 and neglect of the cellular structure. It is thus of interest to verify whether the diffraction process in these same mixtures can be equally well predicted by neglecting the influence of the cellular structure for these conditions using a critical curvature criterion, as suggested by Lee 22 .…”
Section: Introductionmentioning
confidence: 79%
“…This resolution of 7 µm corresponds to 40 to 90 grid points in the induction length (depending on pressure), which is well above usual recommendations. Given that low pressure hydrogen detonations have reaction zones longer than the induction zones by an order of magnitude, and halfreaction zone lengths 2-3 times larger than the induction zone length 23 , our effective resolution is on the order of 100 to 200 grid points per half reaction length. For reference, the recently reported state of the art simulations of Shi, Uy, and Wen 10 used only 24 grid points per half reaction length, a limitation imposed by the lack of AMR.…”
Section: Numerics and Experimentsmentioning
confidence: 99%
“…23 in slowly enlarging channels has shown that the quasi-steady dynamics arXiv:2105.04481v1 [physics.flu-dyn] 10 May 2021…”
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.
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