The velocity and specific entropy of the Chapman–Jouguet (CJ) detonation are shown to remain invariant for initial-state families that each satisfy a common pressure–temperature dependence. Arbitrary reference states define distinct dependences and thereby distinct invariant values. The analysis yields additional properties that, in particular, allow the CJ state — including the adiabatic exponent — to be determined from the CJ velocity alone, without requiring an equation of state for the detonation products. For gaseous stoichiometric explosives with ideal detonation products, numerical calculations using detailed chemical equilibrium support the invariance to within O(10−2)% and the additional CJ properties to within O(10−1)%. For four organic liquid explosives, the predicted CJ pressures are approximately 20% higher than the available experimental values, highlighting both the difficulty of obtaining the experimental data required to calibrate empirical equations of state for detonation products from CJ properties and the physical limitations of the hydrodynamic modeling framework — namely, single-phase inviscid fluids. This invariance may represent a particular manifestation of a more general property of hyperbolic systems and their characteristic surfaces.Novelty and Significance StatementThe novelty lies in an invariance property of the Chapman–Jouguet (CJ) detonation: both the detonation velocity and the specific entropy of the detonation products remain constant under the same appropriately chosen variations in initial temperature and pressure. In particular, this allows the CJ state — including the adiabatic exponent — to be determined from the CJ velocity alone, without requiring an equation of state for the detonation products. The significance lies, first, in a fundamental contribution to detonation physics that may extend to other hyperbolic phenomena; second, in highlighting the limitation ofthe inviscid homogeneous-fluid model when calibrating empirical equations of state for detonation products from measured detonation properties

This work analyzes the interaction between non-equilibrium plasma and detonation. The aim is to enhance the detonability of gaseous mixtures by reducing the detonation cell width through dissociation of a fresh gas mixture by plasma action. The experiments were performed in a square-section detonation tube, and the diagnostic tools used were ICCD chemiluminescence imaging, soot-plate recording, dynamic pressure sensors, and back current shunt technique. The results show that the application of a nanosecond plasma ahead of a self-sustained detonation reduces the cell width by a factor of about 2 in H2:O2:Ar, 2 :O 2 :Ar, H2:O2, 2 :O 2 , CH4:H2:O2:Ar 4 :H 2 :O 2 :Ar and CH4:O2:Ar 4 :O 2 :Ar mixtures for initial pressures between 100 and 200 mbar. A parametric study of plasma properties focused on the effect of the initial pressure on the deposited energy and homogeneity. A kinetic mechanism was proposed to estimate the dissociation effect of plasma chemistry on the fresh combustible mixture. The obtained densities of atoms produced in the plasma were used as input parameters to calculate the thermicity and temperature profiles of the detonation reaction zone according to the Zel'dovich-von Neumann-D & ouml;ring model. The reduction factor of the ZND characteristic chemical length is about the same as the experimental cell widths, i.e. 2. This combination of experiments and calculations substantiates the relationship between plasma parameters, ZND chemical lengths, and detonation cell widths and, thus, demonstrates the possibility of controlling detonability using a nanosecond discharge. Novelty and significance The novelty is the first experimental demonstration that the action of a non-equilibrium plasma on a fresh combustible mixture can instantaneously produce enough atomic species ahead of a self-sustained detonation front to reduce by about half the mean width of the cells that structure the detonation reaction zone in gases. The significance is that a nanosecond discharge is now proven to be a means of controlling detonability, here considered as the ability of a detonation to propagate in a device of given transverse dimensions, since the smaller the cells, the higher the detonability.

We study the transient dynamics of three-dimensional detonation cells when the detonation front is subjected to weak expansion due to the diffraction from a straight channel to a diverging channel. We focus on the effect of the cross-sectional shape, namely square or round, using diverging channels with the same initial cross-sectional area of 16 cm ^2 as the straight channels and the same expansion rate. The reactive mixture is 2 H_2 + O_2 + 2 Ar at the initial pressure of 20 kPa and temperature of 294 K, and we use the sooted-foil technique to record the cellular dynamics. The mean cell widths first increase from different initial values, which depend on the cross-sectional shape and then decrease to stabilize at the same value independent of the shape but larger than the initial values. We use a relation of detonation dynamics between the velocity, total curvature and acceleration of the average detonation front to interpret successfully, albeit qualitatively, all the experimental trends. This sensitivity thus makes these experimental data a reliable basis for high-resolution numerical simulations capable of handling three-dimensionality and detailed chemical kinetics mechanisms. Defining a significative mean width of detonation cells requires constant cross-sectional tubes of size and length sufficiently large. Inductively, representing three-dimensional cells requires more statistical descriptors than a single mean width.

The efficiency gain of rotating detonation depends on several loss factors related to the chamber geometry, the injection principle, the propellants and their mass flow rates, and the equivalence ratio. Numerical simulation can help quantify these losses, and this work presents a Large Eddy Simulation (LES) of rotating detonation in an annular chamber and its validation against experiments. The simulation captured the mixing processes, the overall dynamics of the detonation, the deflagration, and the burnt gas expansion. The injection device was numerically designed to ensure partial premixing of the propellants before injection into the chamber. The chamber had a length of 110 mm, an outer diameter of 80 mm, and a radial width of 10 mm. The mixture consisted of gaseous CH4 and O2 with an equivalence ratio of 1.2 and a mass flow rate of 160 g/s. Combustion kinetics was modeled using a skeletal mechanism with 62 reactions and 16 species. The boundary conditions were adiabatic slip walls. The results reproduce well the detonation velocity (within 1% deviation) and the pressure variation behind the wave. The simulated OH* chemiluminescence compares well with experimental high-speed imaging of the outlet and side of the chamber. The simulation results indicate that 65% of the propellant mass is well mixed in front of the wave whereas 15% of the mixture is burned by deflagration. They show that CH4 and O2 do not axially stratify because they have similar injection dynamics between periodic perturbations induced by the rotating detonation. Good propellant mixing and low deflagration losses explain the high experimental detonation velocity, about 90% of DCJ, and a high combustion efficiency of 98%. These agreements between the computational and experimental results indicate that the simulation is capable of capturing the physical scales relevant to RDC operation and producing reliable results for RDC design.

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.

This experimental and numerical work reports on the dynamical behaviour of a shock in an inert gas at the concave wall of a hollow circular chamber. The gas in the chamber was air or He + O_2 + 2 Ar at initial pressures p_ c0 ranging from 2 to 12 kPa and initial temperature T 0 =288 K. The shock was generated using a detonation driven shock tube. The shock dynamics were characterized through high-speed shadowgraph recordings and high-resolution numerical simulations. For each gas and p_c0 , the experiments evidenced the formation of a Mach reflection along the wall and identified a range of initial pressures for which this configuration rotates with constant stem heights and constant velocities larger than those at the chamber entry. The numerical simulations were capable of capturing the dynamics quantitatively. These results extend to inert gases our previous work with a reactive gas for which we reported on the possibility of a steadily rotating overdriven Mach detonation. The steadiness range is narrower with the inert gases, likely because of the smaller initial pressure ratios at the chamber entry and lower support from the subsonic flow behind the shock. The initial support in the reactive case was more efficient because the discontinuities at the chamber entry were self-sustained Chapman–Jouguet detonations. Further investigations of these Mach rotating regimes should rely only on specific experiments and numerical simulations, for example, on the effect of the chamber dimensions, because of the complex non-dimensional formulation of the problem.

We present a model for predicting a representative width for the three-dimensional irregular patterns observed on the front views of cellular detonation fronts in reactive gases. Its physical premise is that the cellular combustion process produces the same burnt mass per unit of time as the average planar steady Zel'dovich-von Neuman-Döring (ZND) process. The transverse waves of irregular cells are described as a stochastic system subject to a stationary ergodic process, considering that the distributions of the patterns should have identical temporal and statistical average properties. Graph theory then defines an ideal cell whose grouping is equivalent to the actual 3D cellular front, geometric probabilities determine the mean burned fraction that parameterizes the model, and ZND calculations close the problem with the time-position relationship of a fluid element in the ZND reaction zone. The model is limited to detonation reaction zones whose only ignition mechanism is adiabatic shock compression, such as those of the mixtures with H2, C3H8 or C2H4 as fuels considered in this work. The comparison of their measured and calculated widths shows an agreement better than or within the accepted experimental uncertainties, depending on the quality of the chemical kinetic scheme used for the ZND calculations. However, the comparison for CH4:O2 mixtures shows high overestimates, indirectly confirming that the detonation reaction zones in these mixtures certainly include other ignition mechanisms contributing to the combustion process, such as turbulent diffusion. In these situations, the cell widths on longitudinal soot recordings have a very large dispersion, so a mean width may thus not be a relevant detonation characteristic length. The model is easily implementable as a post-process of ZND profiles and provides rapid estimates of the cell width, length and reaction time.

This experimental work investigates the possibility to non-dimensionalize the limits and the distances of the deflagration-to-detonation transition process (DDT). The deflagration was ignited using jets of hot gases generated by the impact of a Chapman–Jouguet detonation on a multi-perforated plate. The tube was 1 m long with a square cross section $$40\times 40$$   mm $$^2$$ . The reactive mixtures were the stoichiometric compositions of hydrogen, methane, and oxygen ( $$1-x$$ ) $$\hbox {H}_2 + x\hbox {CH}_4 + 1/2(1 + 3x)\hbox {O}_2$$ with the composition parameter x ranging from 0 to 1. The initial pressure $$p_0$$ was varied from 12 to 35 kPa, and the initial temperature was 294 K. The widths of the detonation cells and the conditions and distances for DDT were obtained as functions of x, $$p_0$$ , the thickness of the plate, and the number and diameter of its perforations. The cell width was used as the reference length. The non-dimensional DDT distances correlate well with the non-dimensional number representing the surface re-ignition effect in the form of a concave increasing function. The non-dimensional DDT limits appear to be independent of the surface dissipation phenomena in the perforations. These trends are found to be independent of the regularity of the detonation cells. DDT processes are very dependent on the system configuration and the ignition conditions, but our analysis suggests that the proper selection of non-dimensional numbers based on the system characteristics can predict the DDT limits and distances to a reasonable approximation.

The notions of regularity and characteristic width of detonation cells are revisited based on crossed analyses of experimental front-view and longitudinal recordings obtained with the soot-plate technique. Tubes with cross-sections of different shapes, namely round, triangular and square, but the same surface area of 16 cm(2), are used to detonate the stable mixture 2H(2) + O-2 + 2Ar with the initial pressure p(0) varying from 15 kPa to 100 kPa and the initial temperature T-0 = 294 K. The longitudinal recordings show the well-known regular arrangements for this mixture for all cross-section shapes and p(0), but the front -view recordings show irregular patterns except for the square shape and low-enough p(0). There are fewer cells in the round tube, more in the square one, and their average widths and relative differences de-crease with increasing p(0). All front-view cell patterns become irregular and independent of the cross-section shapes with increasing p(0). The cellular dynamics at the walls of a tube is thus not representative of that on the whole detonation front, and longitudinal soot traces alone are not sufficient for describing the cellular structure. An analysis based on graph theory proposes that a tessellation of regular hexagons can model a large set of irregular front-view cells. A cell count on an experimental front-view recording thus defines an average cell width and an intrinsic but high minimum error for this width. Its resulting large sensitivity to the parameters of a simple Arrhenius rate of chemical progress indicates that detailed schemes of chemical kinetics and more advanced conceptual tools than a single length are necessary for characterizing the three-dimensional structures of detonation cells. The Voronoi tessellation supplemented with a physical criterion for the surface density of randomly-distributed point sources could rep-resent a step forward. (C) 2022 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

The dynamics of detonation transmission from a straight channel into a curved chamber was investigated numerically and experimentally as a function of initial pressure (10 kPa <= p(0) <= 26 kPa) in an argon diluted stoichiometric H-2-O-2 mixture. Numerical simulations considered the two-dimensional reactive Euler equations with detailed chemistry; hi-speed schlieren and OH* chemiluminescense were used for flow visualization. Results show a rotating Mach detonation along the outer wall of the chamber and the highly transient sequence of events (i.e. detonation diffraction, re-initiation attempts and wave reflections) that precedes its formation. An increase in pressure, from 15 kPa to 26 kPa, expectedly resulted in detonations that are less sensitive to diffraction. The decoupling location of the reaction zone and the leading shock along the inner wall determined where transition from regular reflection to a rather complex wave structure occurred along the outer wall. This complex wave structure includes a rotating Mach detonation (stem), an incident decoupled shock-reaction zone region, and a transverse detonation that propagates in pre-shocked mixture. For lower pressures, i.e. <= 10 kPa, the detonation fails shortly after ignition. However, the interaction of the decoupled leading shock with the curved section of the chamber results in detonation initiation behind the inert Mach stem. Thereafter, the evolution was similar to the 15 kPa case. Simulations and experiments qualitatively and quantitatively agree indicating that the global dynamics in this configuration is mostly driven by the geometry and initial pressure, and not by the cellular structure in highly compressed regions. (C) 2020 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

In a former work, the effect of a volumetric nanosecond discharge at decreasing the detonation cell size was demonstrated experimentally. The experiments were performed under non-optimal conditions for plasma homogeneity. The present work is a paremetric study that aims at optimizing these experimental conditions. An electrode system was installed in a tube to produce a double-pulse discharge with high deposited energy ahead of the detonation front. The amplitude of the high-voltage pulses, the gas mixture and pressure were optimized so that the plasma filled the entire interelectrode space. The analysis of the detonation cell size with and without plasma generation was performed via the sooted-plate technique. Production of atoms and radicals in the discharge triggered combustion chemistry and decreased the ignition delay time. At these optimal conditions, the detonation cell size was thus reduced by a factor of 2, while passing through the region of the discharge.

While most of the work carried out by the detonation team at Institute Pprime in Poitiers is essentially fundamental, a part of it aims at assessing the potential of specific applications at low technology readiness levels (≤ 3); those relating to propulsion have been developed for nearly 30 years. This presentation will summarize four including fundamental and/or applied contributions to (i) the combustion regimes behind a hypersonic oblique shock, (ii) flames and detonations in cryogenic H2-O2 gaseous mixtures, (iii) propulsive performance of pulsed detonations, and (iv) rotating detonations in annular chambers with constant or increasing cross section.

The effect of a volumetric nanosecond discharge on detonation cell size was demonstrated experimentally in a detonation tube test rig. The experiments were performed in CH4:O-2:Ar=1:2:2 and CH4:O-2:Ar:H-2=3:7:8:2 mixtures, at 180 mbar and 120 mbar respectively and ambient temperature. The plasma was generated by two consecutive pulses of -50 and -32 kV amplitude on the high-voltage electrode and 25 ns pulse duration. The analysis of the detonation cell size with and without plasma generation was performed via sooted-plate technique. The detonation cell size was reduced by a factor of 1.5-3, while passing through the region of the discharge. (C) 2020 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

The effect of a volumetric nanosecond discharge on detonation cell size was demonstrated experimentally in a detonation tube test rig.The experiments were performed in CH 4 :O 2 :Ar=1:2:2 mixture, at initial pressure 180 mbar and ambient temperature.The detonation wave was initiated in a 3.6-m long, 50 × 50-mm 2 square cross section tube, and entered the measuring section where the electrode system was installed to produce a double-pulse discharge ahead of the detonation front.The triggering of the discharge was synchronized with the arrival of the detonation front to the diagnostic chamber.The plasma was generated by two consecutive pulses of -50 and -32 kV amplitude on the high-voltage electrode and 25 ns pulse duration.It was shown that the plasma fills the entire interelectrode space.The analysis of the detonation cell size with and without plasma generation was performed via sooted-plate technique.Production of atoms and radicals in the discharge triggered combustion chemistry decreasing the ignition delay time.As a result, the detonation cell size was reduced by a factor of 1.5 -2, while passing through the region of the discharge.

This experimental work reports on detonation behaviors in a curved chamber without inner wall after diffraction of a ChapmanJouguet (CJ) detonation from a straight channel tangent to the chamber outer wall. The upper and lower faces of the chamber receive either soot foils for recording the history of the transmission dynamics, or optical windows for schlieren high-speed visualizations. Tests were carried out with the stoichiometric propane-oxygen mixture at initial temperature T-0 = 288 K and initial pressures ranging between 8 kPa and 15 kPa. The primary observation is the existence of an initial pressure range (812 kPa) for which, after diffraction transients, a Mach detonation can rotate normal to the outer wall with a constant angular velocity such that the normal front velocity at the wall is larger than the CJ value. The height of the Mach front decreases and its tangential velocity increases with increasing initial pressure. This overdriven detonation results from the irregular reflection of the initially-oblique front as the outer wall tilts with respect to the front, similarly to shock propagation in a continuously-converging channel. The Mach triple-point moves away from the wall and stabilizes its trajectory parallel to the wall. This Mach front shows detonation cells parallel to the wall with a constant mean width very small compared to that on the initial CJ front. A detonation can thus smoothly propagate in a curved chamber without center body, though the Mach front does not sweep the entire equivalent cross-section of the chamber. These observations are consistent with experimental results for RDE chambers without center body, or with linearly-increasing cross sections, that show improved properties of rotating detonation, compared to chambers with constant cross sections. This supports the interest of further studies on the hollow-chamber configuration of RDEs. (C) 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.