Chapman-Jouguet Deflagration Research Articles

Model for Chapman-Jouguet deflagrations in open ended tubes with varying vent ratios

We present a gas dynamic model for Chapman-Jouguet deflagrations driving a shock in tubes or congested configurations with rear venting. The model extends the previous work of Chue, Clarke and Lee (Proc. Roy. Soc. 1993) to include rear venting. Two models are formulated, one for a perfect gas with constant heat of combustion, and the second by assuming chemical equilibrium in the product gases and temperature dependent specific heats. In the presence of rear venting, much slower flames and shock strengths are generated; these are controlled by the vent ratio, which reduces the post shock strength and speed of the gas convecting the flame forward. Calculation results are presented for small hydrocarbon-air and hydrogen-air deflagrations. The results of the model are found in good agreement with the critical deflagration speed measured experimentally in large scale weakly confined congested experiments for auto-ignition insensitive mixtures. This suggests that flames in these experiments have reached their maximum Chapman-Jouguet deflagration speed prior to transition. We present a time scale estimate for flame acceleration and auto-ignition behind reflected shocks. For sensitive mixtures for which the flame acceleration time is longer than the auto-ignition time (hydrogen, acetylene), limited experimental evidence indicate transition to detonation at critical speeds lower than the CJ deflagration condition. The time scale ratio thus provides the conditions for which reaching the CJ deflagration condition can be taken as a necessary condition for DDT.

Chapman–Jouguet deflagration criteria and compressibility dynamics of turbulent fast flames for turbulence-induced deflagration-to-detonation transition

This work characterizes the compressibility dynamics in turbulent fast flames for a range of turbulent flame speeds. These turbulent fast flames experience increased effects of compressibility through the formation of strong shocks and may develop a runaway acceleration combined with a pressure buildup that leads to turbulence induced deflagration-to-detonation transition (tDDT). Simultaneous high-speed particle image velocimetry, OH* chemiluminescence, schlieren, and pressure measurements are used to examine the reacting flow field and flame dynamics. We examine flames with turbulent flame speeds ranging from 100 to 600 m/s. At lower turbulent flame speeds, the flame is not able to produce favorable background conditions for deflagration-to-detonation transition (DDT) onset, and thus flame compressibility and turbulence amplification are less dominant, resulting in a weaker acoustic coupling between the flame and compressed region. As the turbulent burning velocities exceed the Chapman–Jouguet deflagration speed, favorable background conditions are produced, as we observe flame-generated shocks and flame-generated turbulence with higher turbulent velocities and larger turbulent scales. At this regime, the flame is categorized to be at the runaway transition regime that leads to tDDT.

The evolution of fast turbulent deflagrations to detonations

We use advanced experimental techniques to explore turbulence-induced deflagration-to-detonation transition (tDDT) in hydrogen–air mixtures. We analyze the full sequence of turbulent flame evolution from fast deflagration-to-detonation using simultaneous direct measurements of pressure, turbulence, and flame, shock, and flow velocities. We show that fast turbulent flames that accelerate and develop shocks are characterized by turbulent flame speeds that exceed the Chapman–Jouguet deflagration speed in agreement with the tDDT theory and direct numerical simulation (DNS) results. Velocity and pressure evolutions are provided to detail the governing mechanisms that drive turbulent flame acceleration. Turbulent flame speeds and fluctuations are examined to reveal flow field characteristics of the tDDT process. This work contributes to the understanding of fundamental mechanisms responsible for spontaneous initiation of detonations by fast turbulent flames.

Modeling of Thermonuclear Fusion Flames: Parametric Transition to Detonation

ABSTRACT The paper is concerned with the identification of the key mechanisms controlling deflagration-to-detonation transition in a stellar medium. The issue of thermal runaway triggered by positive feedback between the advancing flame and the flame-driven precompression is discussed in the framework of a one-dimensional flame-folding model. The paper is an extension of the authors’ previous study dealing with the non-stoichiometric fusion, , kinetics (Phys.Rev.E, 103(2021)) over physically more relevant, , kinetics. Despite this change the runaway effect endures. The mean velocity of the pretransition flame does not reach the threshold of Chapman–Jouguet deflagration.

Spontaneous runaway of fast turbulent flames for turbulence-induced deflagration-to-detonation transition

One of the fundamental mechanisms for detonation initiation is deflagration-to-detonation transition (DDT). This research experimentally explores the runaway condition for highly turbulent fast flames before DDT, which are characterized by extremely high turbulent flame speeds. Such fast turbulent flames experience increased effects of compressibility and may develop a runaway acceleration combined with a pressure buildup that leads to a turbulence-induced DDT (tDDT) mechanism that has been recently reported. The flame dynamics and the associated reacting flow field are characterized using simultaneous high-speed particle image velocimetry, OH* chemiluminescence, pressure measurements, and schlieren imaging. We study the flow-field conditions for runaway acceleration of fast turbulent flames and effects of compressibility on the evolution of these flames. The locally measured turbulent flame speed is found to be greater than that of a Chapman–Jouguet deflagration speed, which places the flame in the runaway transition regime that would eventually lead to a detonation.

Numerical investigation of three deflagration-to-detonation transition conditions related to the velocity of the spontaneous reaction wave

In this work, the deflagration-to-detonation transition (DDT) process in a tube filled with quiescent and stoichiometric hydrogen/oxygen mixture is numerically simulated by a detailed chemical reaction model together with a high-resolution adaptive mesh refinement (AMR) mesh system. Then the flow field is analyzed in detail. It is found that for the onset of detonation in a DDT process there are three essential conditions related to the velocity of the spontaneous reaction wave DSpRW. The first condition is that on a hot spot the DSpRW should be slower than the speed of the Chapman–Jouguet (CJ) detonation wave DCJ to make sure that a spontaneous shock wave could arise originating from the spontaneous reaction wave. The spontaneous shock wave and the spontaneous reaction wave have conspicuous positive correlation to accelerate the spontaneous reaction wave to be faster than the local sound speed, which is the second DDT condition. With this condition the spontaneous reaction wave could catch up with its associated spontaneous shock wave and implement a coupling of the gasdynamics and the chemical energy release. This process is in line with Lee's SWACER idea, while throughout the process the spontaneous reaction wave propagates mainly through the Zel'dovich's reactivity gradients mechanism. Meanwhile, the gas velocity Vg is also essential to maintain the above two conditions and the resultant velocity meets the relation ∥DSpRW+Vg∥≥DCJ, which is the third condition. Distinctly this settles the wave speed gap between deflagration and detonation. More importantly, gas velocity plays an important role especially for the pressure build-up. The most important expressive differences between CJ deflagration and CJ detonation are the gas velocities of both the reactants and products as well as the pressure build-up. When these three relations successfully trigger a DDT and get a detonation wave, they still hold in the resulting detonation wave. They are delicately inherited as the inherent characters of the (detonation) wave. Formerly they are preconditioning-sustaining in the DDT process, and now they become self-sustaining in the detonation wave. Besides, the important role of the progress ratio of the induction period ε is emphasized for a spontaneous propagation.

Parametric transition from deflagration to detonation in stellar medium.

The nature of thermonuclear explosions of white-dwarf stars is a fundamental astrophysical issue, the first principle interpretation of which is still commonly regarded as an unresolved problem. There is a general consensus that stellar explosions are a manifestation of the deflagration-to-detonation transition of an outward propagating self-accelerating thermonuclear flame subjected to instability-induced corrugations. A similar problem arises in unconfined terrestrial flames where a positive feedback mechanism leading to the pressure runaway has been identified. The present study is an application of this finding to the stellar environment. Notwithstanding a substantial modification of the equation of state the runaway effect endures. Approaching the runaway point the pretransition flame may stay perfectly subsonic, which challenges the view that to ensure the transition the flame should cross the threshold of Chapman-Jouguet deflagration.

Deflagration to detonation transition in fast flames and tracking with chemical explosive mode analysis

In the context of vapour cloud explosion, the flame acceleration process can lead to conditions promoting deflagration to detonation transition (DDT), potentially leading to increased damages in accidental scenarios. This study focuses on this phenomenon by performing simulations of detonation reinitiation for fast flames in the Chapman–Jouguet deflagration regime. It is obtained experimentally by the attenuation of an incident detonation by an array of obstacles. A primary objective of the paper is to demonstrate the ability of the numerical model to reproduce the major experimental trends, namely the variation of the reinitiation propensity for different initial pressures and blockage ratios (BRs). Chemical explosive mode analysis (CEMA) is also adapted to the context of this study, in order to identify locally the propagation regime and to provide insights on the reinitiation mechanism. An a priori validation of the CEMA methodology is first performed on relevant canonical one-dimensional configurations. Subsequently, ensembles of five realizations are computed at different initial pressures and BRs and compared to experimental data. They are shown to reproduce the major observed trends in terms of detonation reinitiation length with respect to the operating conditions, with significant variability from one realization to another. In addition, the reinitiation mechanism is also found to be consistent with experimental observations and a previous numerical study of the same configuration. The CEMA methodology adapted to this context is able to identify locally the different propagation regimes, and to track the highly reactive zones that coherently couple with transverse pressure perturbations, leading to the formation of a strongly reacting kernel which eventually triggers the detonation reinitiation.

Influence of initial pressure on hydrogen/air flame acceleration during severe accident in NPP

Flame acceleration (FA) and explosion of hydrogen/air mixtures remain key issues for severe accident management in nuclear power plants. Empirical criteria were developed in the early 2000s by Dorofeev and colleagues, providing effective tools to discern possible FA or DDT (Deflagration-to-Detonation Transition) scenarios. A large experimental database, composed mainly of middle-scale experiments in obstacle-laden ducts at atmospheric pressure condition, has been used to validate these criteria. However, during a severe accident, the high release rate of steam and non-condensable gases into the containment can result in pressure increase up to 5 bar abs. In the present work, the influence of the unburnt gas initial pressure on flame propagation mechanisms was experimentally investigated. Premixed hydrogen/air mixtures with hydrogen concentration close to 11% and 15% were considered. From the literature, we know that these flames are supposed to accelerate up to Chapman-Jouguet deflagration velocity in long obstacle-laden tubes at initial atmospheric conditions. Varying the pressure in the fresh gas in the range 0.6–4 bar, no effects on the flame acceleration phase were observed. However, as the initial pressure was increased, we observed a decrease in the flame velocity close to the end of the tube. The pressure increase due to the combustion reaction was found to be proportional to the initial pressure according to adiabatic isochoric complete combustion.

Uniform formula for the riemann solutions of a scalar combustion model

In this paper, we construct a uniform formula for the Riemann solutions of the simplified Chapman-Jouguet model. Firstly, we define a new functional, and then, we obtain that the Riemann solutions can be expressed by the maximum value point of this functional, while Riemann solutions may contain some of strong detonation waves, Chapman-Jouguet detonation waves and contact discontinuities. Finally, Chapman-Jouguet deflagration waves are also discussed.

Pulsating instability and self-acceleration of fast turbulent flames

A series of three-dimensional numerical simulations is used to study the intrinsic stability of high-speed turbulent flames. Calculations model the interaction of a fully resolved premixed flame with a highly subsonic, statistically steady, homogeneous, isotropic turbulence. The computational domain is unconfined to prevent the onset of thermoacoustic instabilities. We consider a wide range of turbulent intensities and system sizes, corresponding to the Damköhler numbers Da = 0.1 − 6.0. These calculations show that turbulent flames in the regimes considered are intrinsically unstable. In particular, we find three effects. (1) Turbulent flame speed, ST, develops pulsations with the observed peak-to-peak amplitude STmax/STmin>10 and a characteristic time scale close to a large-scale eddy turnover time. Such variability is caused by the interplay between turbulence, which continuously creates the flame surface, and highly intermittent flame collisions, which consume the flame surface. (2) Unstable burning results in the periodic pressure build-up and the formation of pressure waves or shocks, when ST approaches or exceeds the speed of a Chapman-Jouguet deflagration. (3) Coupling of pressure gradients formed during pulsations with density gradients across the flame leads to the anisotropic amplification of turbulence inside the flame volume and flame acceleration. Such process, which is driven by the baroclinic term in the vorticity transport equation, is a reacting-flow analog of the mechanism underlying the Richtmyer-Meshkov instability. With the increase in turbulent intensity, the limit-cycle instability discussed here transitions to the regime described in our previous work, in which the growth of ST becomes unbounded and produces a detonation.

Combining Discrete Equations Method and Upwind Downwind-Controlled Splitting for non-reacting and reacting two-fluid computations: Two dimensional case

This work deals with impermeable and permeable interfaces and the design of numerical strategies allowing multi-dimensional propagation of these interfaces on general unstructured grids. The numerical context is the (Reactive) Discrete Equations Method (DEM/RDEM) for the Baer–Nunziato type non-equilibrium multiphase model allowing a diffused interface, and meanwhile preserving the global conservation, which is of fundamental importance for studying long term combustion phenomena in large-scale geometries. Another advantage of RDEM for combustion lies in its ability to compute both deflagration and detonation, provided an appropriate reactive Riemann solver is inserted within the method. The present paper is a sequel to the recent publication (Tang et al., 2014) [35] where an anti-diffusive approach and an original Upwind Downwind-Controlled Splitting method (UDCS) were combined with the 1D formulation of the DEM and RDEM. The method successfully developed in 1D for computing inert interfaces (e.g. impermeable water gas shock tube problem) and flame interfaces (e.g. Chapman–Jouguet deflagration and strong detonation wave) with excellent robustness and accuracy properties is extended here to two dimensional problems. The proposed low- and anti-diffusive versions of the multi-D UDCS strategy form an original contribution to the modeling of multifluid flows on unstructured grids. This multi-D extension relies on a general derivation of the Downwind Factors involved in the formulation of UDCS. In particular, the proposed UDCS anti-diffusive algorithm represents a new alternative to the “Extended–Vofire” solver (Faucher and Kokh, 2013) [15] for unstructured meshes. Numerical experiments performed for non-reacting gas–gas and liquid–gas shock bubble interactions as well as for a model combustion problem demonstrate the combination of DEM/RDEM with UDCS yields excellent robustness/accuracy properties. Some remaining issues linked to the modeling of flame propagation in multi-dimensional cases are eventually discussed.

Combining Discrete Equations Method and upwind downwind-controlled splitting for non-reacting and reacting two-fluid computations: One dimensional case

The Discrete Equations Method (DEM) (Abgrall and Saurel, 2003) relies on integrating the solutions of interface problems over a two-phase control volume with these solutions provided by Riemann solvers. The method was next extended to reacting flows (RDEM) by Le Métayer et al. (2005). The objective of the present work is to compute high speed combustion waves in a robust and accurate way using RDEM. Several ingredients need to be implemented within the RDEM framework to achieve this goal and they are successively assessed on non-reacting interface problems using DEM and on reacting flows using RDEM. These ingredients are: the anti-diffusive approach developed in Després and Lagoutière (2002), the Large Time Step generalization of Godunov’s method proposed by LeVeque and an original upwind downwind-controlled spitting method (UDCS). Numerical experiments performed on one-dimensional non-reacting (water gas shock tube problem) and reacting (Chapman–Jouguet deflagration, strong detonation wave) flows demonstrate the combination of DEM/RDEM with UDCS and the anti-diffusive approach yields excellent robustness and accuracy properties.

The perturbation on initial binding energy for a Majda-CJ combustion model

We investigate the perturbed Riemann problem for a scalar Chapman–Jouguet combustion model – the perturbation on initial binding energy. Under the entropy conditions, we obtain the unique solutions in a neighbourhood of the origin (t > 0) on the (x, t) plane. It is found that, for some cases, the perturbed Riemann solutions are essentially different from the corresponding Riemann solutions. That is, the perturbation may transform a Chapman–Jouguet detonation into a strong detonation or a weak deflagration following a shock wave; a strong detonation into a weak deflagration following a shock wave; a Chapman–Jouguet deflagration into a weak deflagration.

Quasi-steady stages in the process of premixed flame acceleration in narrow channels

The present paper addresses the phenomenon of spontaneous acceleration of a premixed flame front propagating in micro-channels, with subsequent deflagration-to-detonation transition. It has recently been shown experimentally [M. Wu, M. Burke, S. Son, and R. Yetter, Proc. Combust. Inst. 31, 2429 (2007)]10.1016/j.proci.2006.08.098, computationally [D. Valiev, V. Bychkov, V. Akkerman, and L.-E. Eriksson, Phys. Rev. E 80, 036317 (2009)]10.1103/PhysRevE.80.036317, and analytically [V. Bychkov, V. Akkerman, D. Valiev, and C. K. Law, Phys. Rev. E 81, 026309 (2010)]10.1103/PhysRevE.81.026309 that the flame acceleration undergoes different stages, from an initial exponential regime to quasi-steady fast deflagration with saturated velocity. The present work focuses on the final saturation stages in the process of flame acceleration, when the flame propagates with supersonic velocity with respect to the channel walls. It is shown that an intermediate stage may occur during acceleration with quasi-steady velocity, noticeably below the Chapman-Jouguet deflagration speed. The intermediate stage is followed by additional flame acceleration and subsequent saturation to the Chapman-Jouguet deflagration regime. We elucidate the intermediate stage by the joint effect of gas pre-compression ahead of the flame front and the hydraulic resistance. The additional acceleration is related to viscous heating at the channel walls, being of key importance at the final stages. The possibility of explosion triggering is also demonstrated.

Gas Compression Moderates Flame Acceleration in Deflagration-to-Detonation Transition

The effect of gas compression at the developed stages of flame acceleration in smooth-wall and obstructed channels is studied. We demonstrate analytically that gas compression moderates the acceleration rate, and we perform numerical simulations within the problem of flame transition to detonation. It is shown that flame acceleration undergoes three distinctive stages: (1) initial exponential acceleration in the incompressible regime, (2) moderation of the acceleration process due to gas compression, so that the exponential acceleration state goes over to a much slower one, (3) eventual saturation to a steady (or statistically steady) high-speed deflagration velocity, which may be correlated with the Chapman–Jouguet deflagration speed. The possibility of deflagration-to-detonation transition is demonstrated.

Chemical Energy Release in Several Recently Discovered Detonation and Deflagration Flows

Several recent experiments on complex detonation and deflagration flows are analyzed in terms of the chemical energy release required to sustain these flows. The observed double cellular structures in detonating gaseous nitromethane–oxygen and NO2–fuel (H2, CH4, and C2H6) mixtures are explained by the amplification of two distinct pressure wave frequencies by two exothermic reactions, the faster reaction forming vibrationally excited NO* and the slower reaction forming highly vibrationally excited N2**. The establishment of a Chapman-Jouguet (C-J) deflagration behind a weak shock wave, the C-J detonation established after a head-on collision with a shock front, and the C-J detonation conditions established in reactive supersonic flows are quantitatively calculated using the chemical energy release of a H2 + Cl2 mixture. For these three reactive flows, these calculations illustrate that different fractions of the exothermic chemical energy are used to sustain steady-state propagation. C-J detonation calculations on the various initial states using the CHEETAH chemical equilibrium code are shown to be in good agreement with experimental detonation velocity measurements for the head-on collision and supersonic flow detonations.

Flame acceleration in channels with obstacles in the deflagration-to-detonation transition

It was demonstrated recently in Bychkov et al. [Bychkov et al., Phys. Rev. Lett. 101 (2008) 164501], that the physical mechanism of flame acceleration in channels with obstacles is qualitatively different from the classical Shelkin mechanism. The new mechanism is much stronger, and is independent of the Reynolds number. The present study provides details of the theory and numerical modeling of the flame acceleration. It is shown theoretically and computationally that flame acceleration progresses noticeably faster in the axisymmetric cylindrical geometry as compared to the planar one, and that the acceleration rate reduces with increasing Mach number and thereby the gas compressibility. Furthermore, the velocity of the accelerating flame saturates to a constant value that is supersonic with respect to the wall. The saturation state can be correlated to the Chapman–Jouguet deflagration as well as the fast flames observed in experiments. The possibility of transition from deflagration-to-detonation in the obstructed channels is demonstrated.

Different stages of flame acceleration from slow burning to Chapman-Jouguet deflagration

Numerical simulations of spontaneous flame acceleration are performed within the problem of flame transition to detonation in two-dimensional channels. The acceleration is studied in the extremely wide range of flame front velocity changing by 3 orders of magnitude during the process. Flame accelerates from realistically small initial velocity (with Mach number about 10(-3)) to supersonic speed in the reference frame of the tube walls. It is shown that flame acceleration undergoes three distinctive stages: (1) initial exponential acceleration in the quasi-isobaric regime, (2) almost linear increase in the flame speed to supersonic values, and (3) saturation to a stationary high-speed deflagration velocity. The saturation velocity of deflagration may be correlated with the Chapman-Jouguet deflagration speed. The acceleration develops according to the Shelkin mechanism. Results on the exponential flame acceleration agree well with previous theoretical and numerical studies. The saturation velocity is in line with previous experimental results. Transition of flame acceleration regime from the exponential to the linear one, and then to the constant velocity, happens because of gas compression both ahead and behind the flame front.

On the stability of subsonic thermal fronts

The stability of subsonic thermal fronts against corrugation is analyzed and an exact dispersion relation is obtained taking into account the compressibility of the gas. For heat fronts, this dispersion equation has an unstable root (Ωex) corresponding to the Landau–Darrieus unstable mode (Ω0) modified by the compressional effects. In particular, the exact solution shows a conspicuous maximum very close to the value of the intake Mach number M1 at which a Chapman–Jouguet deflagration wave behind the heat front is formed. Cooling fronts are stable for corrugation-like disturbances. A maximum damping as well as a maximum in the frequency occur at a value of M1 depending on the value of the normalized cooling q.