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A methodology to develop predictive simplified kinetics schemes (one-step/three-step chain-branching) is presented in which detonation velocity-curvature (D − κ) curves computed with detailed thermochemistry are used as the fitting target aiming to capture the turning point of the curve (κ crit). This was motivated by the similar trend observed between the κ crit values obtained using the simplified schemes of Taileb et al. (2020), fitted using conventional methods, and the critical reactive layer heights for detonation propagation under yielding confinement (h crit) reported by the same authors. Both updated schemes satisfactorily reproduce the target D − κ curves and are used to (re)compute multidimensional cellular detonations propagating in channels and confined by inert layers. Simulations show a much better agreement with the results obtained with detailed kinetics for the detonation flow fields, cell sizes distributions, and h crit. Moreover, it is observed that the average curvatures of the computed fronts are in line with those predicted by the D − κ formulation, providing supporting evidence of the applicability of reduced order models for fast and inexpensive estimates of detonation limiting behaviors in safety studies. Novelty and Significance Statement The novelty of this research lies in proposing and testing an alternative methodology to determine the kinetics parameters of simplified kinetics schemes (1 − step and 3 − step) so that these retain the predictive capabilities of detailed kinetics. This is achieved by using detonation velocity-curvature curves (D − κ) as a fitting target. Conventional fitting procedures, such as targeting ignition delay times and/or matching ZND profiles have been shown to perform poorly in previous research. The new methodology shows significant improvements in the prediction of dynamic detonation parameters in ideal detonations such as cell sizes distributions, as well as in the prediction of the critical reactive layer heights for detonation propagation under yielding confinement (h crit); a canonical configuration of interest to propulsion and industrial safety. For the latter, the new methodology yields h crit for H 2 -O 2 detonations of h crit = 12 mm instead of 24 mm (with conventional methods), and h crit = 8 mm instead of 20 mm , for the 1-step and 3-step models, respectively. The D κ results are much closer to those obtained with detailed kinetics ( h crit = 6 mm) and to the experimental measurements ( h crit = 4. 6 mm). The methodology is generic to be applied to any mixture of interest. [ABSTRACT FROM AUTHOR]

The propagation of low-Lewis-number premixed flames is analyzed in a partially confined Hele-Shaw chamber formed by two parallel plates separated a distance h apart. An asymptotic-numerical study can be performed for small gaps compared to the flame thickness δ T. In this narrow-channel limit, the problem formulation simplifies to a quasi-2D description in which the velocity field is controlled by dominant viscous effects. After accounting for conductive heat losses through the plates in our formulation, we found that the reaction front breaks into one or several isolated flame cells where the temperature is large enough to sustain the reaction, both in absence and in presence of buoyancy effects. Under these near-limit conditions, the isolated flame cells either travel steadily or undergo a slow random walk over the chamber in which the reacting front splits successively to form a tree-like pathway, burning only a small fraction of the fuel before reaching the end of the chamber. The production of quasi-2D circular or comet-like flames under specific favorable conditions is demonstrated in this paper, with convection, conductive heat losses and differential diffusion playing an essential role in the formation of the isolated one and two-headed flame cells. [ABSTRACT FROM AUTHOR]

Abstract An experimental study of methane, propane and dimethyl ether (DME) premixed flames propagating in a quasi-two-dimensional Hele-Shaw cell placed horizontally is presented in this paper. The flames are ignited at the open end of the combustion chamber and propagate towards the closed end. Our experiments revealed two distinct propagation regimes depending on the equivalence ratio of the mixture as a consequence of the coupling between the heat-release rate and the acoustic waves. The primary acoustic instability induces a small-amplitude, of around 8 mm, oscillatory motion across the chamber that is observed for lean propane, lean DME, and rich methane flames. Eventually, a secondary acoustic instability emerges for sufficiently rich (lean) propane and DME (methane) flames, inducing large-amplitude oscillations in the direction of propagation of the flame. The amplitude of these oscillations can be as large as 30 mm and drastically changes the outline of the flame. The front then forms pulsating finger-shaped structures that characterize the flame propagation under the secondary acoustic instability. The experimental setup allows the recording of the flame propagation from two different points of view. The top view is used to obtain accurate quantitative information about the flame propagation, while the lateral view offered a novel three dimensional perspective of the flame that gives relevant information on the transition between the two oscillatory regimes. The influence of the geometry of the Hele-Shaw cell and of the equivalence ratio on the transition between the two acoustic-instability regimes is analyzed. In particular, we find that the transition to the secondary instability occurs for values of the equivalence ratio ϕ above (below) a critical value ϕ c for propane and DME (methane) flames. In all the tested fuels, the transition to the secondary instability emerges for values of the Markstein number M below a critical value M c. The critical Markstein number varies with the gap size h formed by the two horizontal plates that bound the Hele-Shaw cell. As h is reduced, the critical Markstein number is shifted towards larger values. [ABSTRACT FROM AUTHOR]

The influence of ozone on quasi-steady curved detonations was numerically studied in stoichiometric H 2 -air and DME-O 2 (-CO 2) mixtures with 0 % , 0.1 % and 1 % O 3 addition. Detonation speed - curvature (D - κ) relations were determined for both fuels. The H 2 -air mixture has one critical point related to high-temperature chemistry whereas the DME-O 2 (-CO 2) mixture has two critical points, one sustained by high-temperature chemistry, and the other supported by low-temperature chemistry. O 3 addition significantly increases the curvature at all the critical points by speeding up both high- and low-temperature chemistry. Two mechanisms were found to be responsible for the results. First, O 3 addition increases the rate of reaction initiation by fast decomposition to provide O radical via O 3 (+M) = O 2 + O (+M). The dominant reaction with fuel therefore changes from a fuel + OH/CH 3 radical chain propagation reaction to a fuel + O radical chain branching reaction during the initial stage, which establishes the radical pool more rapidly. Second, O 3 influences the reaction pathways. For H 2 -air with 1 % O 3 , H + O 3 = O 2 + OH becomes the most important reaction for OH radical and heat generation during the initial stage. For DME-O 2 -CO 2 , O 3 changes the respective contributions of competing low-temperature chemistry reactions, i.e. CH 3 OCH 2 = CH 2 O + CH 3 vs. CH 3 OCH 2 + O 2 = CH 3 OCH 2 O 2 and CH 2 OCH 2 O 2 H = 2CH 2 O + OH vs. CH 2 OCH 2 O 2 H + O 2 = O 2 CH 2 OCH 2 O 2 H. The change of dominant reactions either enhances (0.1% of O 3) or eliminates (1% O 3) the negative temperature coefficient behavior. Our study contributes to the detailed understanding of the thermo-chemical impact of ozone on detonation limits. [ABSTRACT FROM AUTHOR]

The problem of the steady propagation of detonation waves with friction losses is revisited including detailed kinetics. The derived formulation is used to study the influence of chemical modeling on the steady solutions and reaction zone structures obtained for stoichiometric hydrogen-oxygen. Detonation velocity - friction coefficient (D − c f) curves, pressure, temperature, Mach number, thermicity and species profiles are used for that purpose. Results show that both simplified kinetic schemes considered (i.e., one-step and three-step chain-branching), fitted using standard methodologies, failed to quantitatively capture the critical c f values obtained with detailed kinetics; moreover one-step Arrhenius chemistry also exhibits qualitative differences for D / D C J ≤ 0.55 due to an overestimation of the chemical time in this regime. An alternative fitting methodology for simplified kinetics is proposed using detailed chemistry D − c f curves as a target rather than constant volume delay times and ideal Zel'dovich-von Neumann-Döring profiles; this method is in principle more representative to study non-ideal detonation propagation. The sensitivity of the predicted critical c f value, c f , crit , to the detailed mechanisms routinely used to model hydrogen oxidation was also assessed; significant differences were found, mainly driven by the consumption/creation rate of the HO 2 radical pool at low postshock temperature. [ABSTRACT FROM AUTHOR]

Two types of three-step chain-branching kinetics for gaseous hydrogen–oxygen detonation quenching are proposed. The reaction rates dependency on density and pressure, as well as the change in molecular weight are included and fitted to results of detailed chemistry not only along the Hugoniot curve but also behind transverse waves. The trend of induction and reaction times and reduced activation energy of zero-dimensional constant pressure combustion process as well as the induction, reaction lengths, and peak thermicity of the ZND model are focused on in the calibration procedure. One model (3SM-I) is designed to model the ideal detonation whereas the other (3SM-N) focuses on the D n − κ curve during calibration, i.e. the detonation velocity-mean front curvature curves, aiming to capture the non-idealities. The predictive ability using the proposed models is evaluated in a detonation transmission configuration, a layer of ▪ mixture being confined by N 2 , in determining the critical height, reactive layer height at which detonation transmission is not possible. Both approaches get closer to the critical height from detailed chemistry. With the present set of model parameters, 3SM-I is better than 3SM-N for prediction of critical height. Moreover, borrowing analytical ignition criteria and wave hierarchy approach, the comparison of various chemical models that are able to recover the critical height suggests that the slope of the D n − κ curve, linked with the chemical response to losses, is the first key parameter for the critical height determination. In addition, the dynamics of the extinction near criticality such as appearance of transverse detonation and quenching distance from 3SM-I are in very good agreement with that of detailed chemistry due to better estimation of the chemical features along the Hugoniot curve and behind transverse waves. The present study provides a guideline to get simplified chemical models from detailed chemistry for predictive simulations. Novelty and significance statement The novelty of research is two-fold. The first is to provide general guideline to get simplified models from detailed chemistry for the simulation of detonation extinction with improved predictive ability. The tested configuration was that of a stoichiometric hydrogen–oxygen mixture semi-confined by nitrogen. The evolution of the induction, reaction times, and the maximum thermicity were used as fitting targets for our 3-step model. Furthermore, they were evaluated not only at the post-shock states along the Hugoniot curve, but also behind the transverse waves, keystones of the cellular structure. Second, borrowing analytical ignition criteria and wave hierarchy approach, the comparison of different chemical models that were able to recover the critical height suggested that the slope of the normal velocity–curvature curve was the first key parameter for the critical height determination. Moreover, the dynamics of extinction near criticality, and quenching distance depended on the reaction rate dependency on density and pressure. [ABSTRACT FROM AUTHOR]