Deflagration Wave Research Articles

Electron-driven deflagration wave propagation in deuterium–tritium solid state by collective effect interaction of laser-driven block acceleration for fusion energy

Electron-driven deflagration wave propagation in deuterium–tritium solid state by collective effect interaction of laser-driven block acceleration for fusion energy

Predictions of flame acceleration, transition to detonation, and detonation propagation using the Chemical-Diffusive Model

This paper presents numerical simulations of the evolution of premixed flames in channels with obstacles using the Chemical-Diffusive Model (CDM) coupled to a compressible Navier-Stokes solver. The CDM is a parametric model for chemical reaction and diffusive transport, and it is calibrated to reproduce a set of properties of one-dimensional laminar flame and the Zel’dovich-Neumann-Döring (ZND) detonation. In this work, we use two different CDMs, one calibrated using the theoretical half-reaction distance of the ZND detonation and the other calibrated with the experimental detonation cell size, to simulate a stoichiometric hydrogen-air mixture and investigate flame acceleration, deflagration-to-detonation transition (DDT), and detonation propagation in obstacle-laden channels. As the channel geometry varies, both CDMs predict propagation of fast flames in the choking, quasi-detonation, and CJ-detonation regimes. When the channel width is much greater or smaller than the minimal scale requirement for the onset of DDT, both CDMs predict similar choked fast flames and CJ detonations. In cases where the channel widths are close to the critical conditions, deflagration waves are more likely to undergo DDT if the CDM is calibrated for the half-reaction distance, which produces smaller computed detonation cells than experiments. In numerical simulations of channels with the same geometries as prior experiments, using the cell size-constrained CDM improves predictions of DDT.

Physical and mathematical modeling of interaction of detonation waves with inert gas plugs

In the paper the physical and mathematical model for the description of the processes of transition, attenuation and suppression of detonation in hydrogen-air mixture in one- and two-dimensional formulation, taking into account reduced and detailed kinetics of chemical transformations in reactive gases, by inert gas plugs was proposed. On the basis of this model calculations of the interaction of plane (in one-dimensional formulation) and cellular (in two-dimensional formulation) detonation wave propagating in hydrogen-air mixture with layer of inert gases (argon, nitrogen, carbon dioxide) were performed. It was shown that depending on the type of isolating gas and the length of the plug various flow regimes were realized after the shock wave exits from the inert gas plug: a) reinitiation of detonation wave; b) suppression of the detonation wave with the formation of a deflagration wave at the end of the inert gas plug; c) suppression of the detonation wave with the combustion zone isolation by inert gas plug. The geometric limits of detonation (minimum inert gas plug length leads to detonation suppression with combustion zone isolation) for all three types of inert gas plugs were calculated. Comparison of the effectiveness of detonation suppression by various inert gas plugs shows that the carbon dioxide is more efficient for suppressing the detonation wave, i.e. geometric limits of detonation during interaction of detonation with carbon dioxide plug is smallest compared with other two types of plugs.

Ignition behavior and the onset of quasi-detonation in methane-oxygen using different end wall reflectors

The shock wave focusing technique is beneficial to the development of detonation-based engines, which can shorten the long run-up distance that is usually required for a detonation, reducing the weight of the detonation engine. In this work, we performed experiments using different end wall reflectors to facilitate the formation and intensity of the combustion wave in a stoichiometric methane-oxygen mixture diluted by argon. By changing shock wave intensity, the effects of the incident shock Mach number (Ma) on the ignition delay times in two reflectors are systematically investigated. The experimental results show that the conical reflector creates an abrupt pressure rise in the apex, resulting in a 64.5% rise in the acceleration of the reflected shock velocity compared with the planar reflector. The introduction of a conical reflector significantly shortens the ignition delay time by an order of magnitude and facilitates the amalgamation of the leading reflected shock wave and the subsequent combustion wave. The experimental results also illustrate that conical reflectors promote the formation of the second ignition. However, only a weak deflagration wave is formed in a planar reflector, and a strong deflagration wave and quasi-detonation wave are observed by using a conical reflector. Our observation sheds light on the mechanism of ignition modes induced by the shape of reflectors.

Enhancement of ethylene-air continuous rotating detonation in the cavity-based annular combustor

To investigate enhancement effects of cavity on continuous rotating detonation (CRD), extensive ethylene-air CRD tests are conducted in the cavity-based annular combustor. By varying the length-to-depth ratio (L/D) of cavity, five modes are distinguished and classified into three operating zones, I: Excessive Impact (deflagration and sawtooth wave); II: Proper Impact (single wave and co-rotating two-wave); III: Deficient Impact (counter-rotating two-wave). In the cavities with small L/D in zone I, excessive deflagration could inhibit the accumulation of combustible mixture, making detonation degenerate into deflagration. While the cavities with proper L/D in zone II could intensify CRD, resulting in a propagation mode transformation from counter-rotating two-wave to co-rotating mode. The added circumferential contact surface between the cavity-stabilized flame and combustible mixture is a key factor of cavity enhancement, which can pre-heat combustible mixture and reduce the detonation inducing time. Through the distribution of chemiluminescence intensity ratio, the intensity ratio peaks of deflagration and detonation are estimated to be in 40-50 mm and 20-30 mm downstream from the inlet respectively, indicating that detonation with proper cavities is accomplished in shorter distance. Overall, L/D=5.5 with the depth of 20 mm may be an optimized selection based on the evaluations of mode, reaction zone, and pressure.

Continuum and molecular dynamics simulations of pore collapse in shocked β-tetramethylene tetranitramine (β-HMX) single crystals

The collapse of pores plays an essential role in the shock initiation of high energy (HE) materials. When these materials are subjected to shock loading, energy is localized in hot-spots due to various mechanisms, including void collapse. Depending on the void size and shock strength, the resulting hot-spots may quench or evolve into a self-sustained deflagration wave that consequently can cause detonation. We compare finite element (FE) and non-reactive molecular dynamic (MD) simulations to study the formation of hot-spots during the collapse of an 80 nm size void in a β-tetramethylene tetranitramine energetic crystal. The crystal is shocked normal to the crystallographic plane (010), applying boundary velocities of 0.5 km/s, 1.0 km/s, and 2.0 km/s. The FE simulations capture the transition from viscoelastic collapse for relatively weak shocks to a hydrodynamic regime, the overall temperature distributions, especially at scales relevant for the initiation of HE materials, and the rate of pore collapse. A detailed comparison of velocity and temperature fields shows that the MD simulations exhibit more localization of plastic deformation, which results in higher temperature spikes but localized to small volumes. The void collapse rate and temperature field are strongly dependent on the plasticity model in the FE results, and we quantify these effects.

Unsupervised Learning-Based Multiscale Model of Thermochemistry in 1,3,5-Trinitro-1,3,5-triazinane (RDX).

The response of high-energy-density materials to thermal or mechanical insults involves coupled thermal, mechanical, and chemical processes with disparate temporal and spatial scales that no single model can capture. Therefore, we developed a multiscale model for 1,3,5-trinitro-1,3,5-triazinane, RDX, where a continuum description is informed by reactive and nonreactive molecular dynamics (MD) simulations to describe chemical reactions and thermal transport. Reactive MD simulations under homogeneous isothermal and adiabatic conditions are used to develop a reduced-order chemical kinetics model. Coarse graining is done using unsupervised learning via non-negative matrix factorization. Importantly, the components resulting from the analysis can be interpreted as reactants, intermediates, and products, which allows us to write kinetics equations for their evolution. The kinetics parameters are obtained from isothermal MD simulations over a wide temperature range, 1200-3000 K, and the heat evolved is calibrated from adiabatic simulations. We validate the continuum model against MD simulations by comparing the evolution of a cylindrical hotspot 10 nm in diameter. We find excellent agreement in the time evolution of the hotspot temperature fields both in cases where quenching is observed and at higher temperatures for which the hotspot transitions into a deflagration wave. The validated continuum model is then used to assess the criticality of hotspots involving scales beyond the reach of atomistic simulations that are relevant to detonation initiation.

Implementation of the Onsager Theorem to Evaluate the Speed of the Deflagration Wave.

While considering the deflagration regime, the thermal theory of combustion proposes that the mechanism of heat transfer from the flame exothermic zone to the front neighborhood reactants layer dominates the flame behavior. The introduction of the Fourier law allows a closed solution of the continuity and energy conservation equations to yield the burning velocity. It is, however, clear that this classical solution does not conform to the momentum equation. In the present work, instead of introducing the Fourier law, we suggest the introduction of a simplified version of the Onsager relationship, which accounts for the entropy increase due to the heat transfer process from the front layer to its successive layer. Solving for the burning velocity yields a closed solution that also definitely conforms to the momentum equation. While it is realized that the pressure difference across the flame front in the deflagration regime is very small, we believe that violating the momentum equation is intolerable. Quite a good fitting, similarly to the classic theory predictions, has been obtained between our predictions and some experimentally observed values for the propagation flame deflagration velocity, while here, the momentum equation is strictly conserved.

Explosive Nucleosynthesis in Near-Chandrasekhar Mass White Dwarf Models for Type Iax Supernovae: Dependence on Model Parameters

Abstract The recently observed diversity of Type Ia supernovae (SNe Ia) has motivated us to conduct the theoretical modeling of SNe Ia for a wide parameter range. In particular, the origin of Type Iax supernovae (SNe Iax) has been obscure. Following our earlier work on the parameter dependence of SN Ia models, we focus on SNe Iax in the present study. For a model of SNe Iax, we adopt the currently leading model of pure turbulent deflagration of near-Chandrasekhar mass C+O white dwarfs (WDs). We carry out two-dimensional hydrodynamical simulations of the propagation of the deflagration wave, which leaves a small WD remnant behind and ejects nucleosynthesis materials. We show how the explosion properties, such as nucleosynthesis and explosion energy, depend on the model parameters, such as central densities and compositions of the WDs (including the hybrid WDs), turbulent flame prescription, and initial flame geometry. We extract the associated observables in our models and compare with the recently discovered low-mass WDs with unusual surface abundance patterns and the abundance patterns of some SN remnants. We provide the nucleosynthesis yield tables for applications to stellar archeology and galactic chemical evolution. Our results are compared with the representative models in the literature.

Subgrid modeling of intrinsic instabilities in premixed flame propagation

This work is devoted to the investigation and subgrid-scale modeling of intrinsic flame instabilities occurring in the propagation of a deflagration wave. Such instabilities, of hydrodynamic and thermodiffusive origin, are expected to be of particular relevance in recent technological trends such as in the use of hydrogen as a clean energy carrier or as a secondary fuel in hydrogen enriched combustion. A dedicated set of direct numerical simulations is presented and used, in conjunction with coherent literature results, in order to develop scaling arguments for the propagation speed of self-wrinkled flames which are also supported by the outcomes of a weakly non-linear model, namely the Sivashinsky equation. The observed scaling is based on the definition of the number of unstable wavelengths in a reference hydrodynamic lengthscale, in other words the ratio between the neutral or cutoff lengthscale of intrinsic instabilities and the lateral domain of a planar flame. The scalings are then employed to develop an algebraic model for the wrinkling factor in the context of a flame surface density closure approach. An a-priori analysis shows that the model correctly captures the flame wrinkling caused by intrinsic instability at sub grid level. A strategy to include the developed self-wrinkling model in the context of a turbulent combustion model is finally discussed on the basis of the turbulence induced cut-off concept.

The precursor shock wave and flame propagation enhancement by CO2 injection in a methane-oxygen mixture

Successful initiation of a detonation in a confined combustor with limited length is a formidable task for designing the detonation-based engines, shortening the length for the run-up distance of a detonation greatly reduces the weight of the detonation engine, rendering the detonation propulsion become possible in the advanced aerospace propulsion systems. In this work, we proposed a new method that using a non-reactive gas jet (CO2) to facilitate the formation of the precursor shock wave and the flame propagation speed in a deflagration wave in a stoichiometric methane-oxygen mixture, by changing a series of the injection parameters, i.e., the initial pressure of mixture, the jet delay time, the jet pressure and its position, the effects of those parameters on the deflagration propagation are systematically investigated. The experimental results show that, the development processes of pressure rise are divided into two stages prior to the DDT: 1) slow deflagration stage, which characterized by two discrete shock waves named as the 1st shock wave and 2nd shock wave; 2) Fast deflagration stage, the two discrete waves merge into a strong precursor shock wave, and the velocities of precursor shock and flame achieve to the “quasi-detonation” state. The experimental results also illustrate that, introducing the CO2 jet in the first stage prior to the DDT promotes the formation of precursor shock wave and accelerates the flame speed, which speeds up the transformation of a detonation in a shorter distance. By comparing different jet parameter combinations, it is found that high jet pressure and long jet time increase the local concentration of CO2, which adversely affect the formation of a detonation. Thereby there exists an optimal condition of injection, whose injection pressure ratio is 15, jet delay time is 20 ms and jet position is found to be 0.6 m, those parameters are verified to have prominent detonation-enhancement effects on DDT, the underlying mechanisms for those optimal conditions are explored and explained in this study. This study provided new experimental evidences supporting the theory of turbulence-enhancement effect on the initiation of a detonation.

Role of dynamical compressive and shear loading on hotspot criticality in RDX via reactive molecular dynamics

Energy localization in hotspots due to shock-induced pore collapse is thought to be a critical process in the initiation of heterogeneous high-energy density materials. The dynamical collapse of porosity involves expansion, jetting, shearing, and recompression of the material surrounding the defect. While the resulting hotspots are known to result in deflagration waves that can lead to detonation, we lack the understanding of the relative potency of the various processes that occur during the collapse. We use molecular dynamics simulations with the reactive force field ReaxFF to characterize how uniaxial expansion/recompression, shear, and combinations thereof affect the formation and criticality of hotspots in RDX, 1,3,5-trinitro-1,3,5-triazine. We chose a planar pore configuration consisting of a 40 nm gap and independently control the relative amounts of compressive and shear shock loadings. We find that shear-dominated critical hotspots tend to be smaller but exhibit higher temperatures than uniaxial ones and involve longer reaction time scales. Interestingly, the chemical decomposition mechanisms are affected by the relative amount of dynamical shear and uniaxial loads.

Investigation of rotating detonation fueled by a methane–hydrogen–carbon dioxide mixture under lean fuel conditions

Rotating detonation combustor (RDC) operation is investigated under the main composition of the coal and supercritical water gasification process (a methane–hydrogen–carbon dioxide mixture), and air is selected as an oxidizer. Experiments are performed under four flow rates (79.1, 101.2, 125.8, and 158.2 g/s), and the equivalence ratio (ER) ranges from 0.23 to 0.87. The detonation delay time and propagation characteristics of the rotating detonation wave (RDW) are investigated, and the nonlinear time series analysis method is applied to the pressure signal using the wavelet entropy algorithm and phase space reconstruction. It is demonstrated that a decrease in the flow rate can increase the detonation delay time near the lean fuel boundary; however, the detonation delay time is affected only slightly when the ER is greater than 0.4. The ER significantly affects the wave velocity but is affected only slightly by the flow rate. Contrary to the wave velocity performance, the pressure of the RDW increases with the flow rate. The lean fuel boundary becomes wider when the flow rate increases. Five combustion modes are investigated: failure, fast deflagration, sawtooth wave, single-wave, and two-counter rotating wave modes. The fast deflagration and sawtooth wave modes may occur near the detonation operating boundary, and a higher flow rate tends to increase the occurrence probability of a multiwave mode. The phase space pattern and distribution of wavelet entropy can be used to distinguish the combustion modes intuitively.

Laminar Flame Speeds in Degenerate Oxygen–Neon Mixtures

Abstract The collapse of degenerate oxygen–neon cores (i.e., electron-capture supernovae or accretion-induced collapse) proceeds through a phase in which a deflagration wave (“flame”) forms at or near the center and propagates through the star. In models, the assumed speed of this flame influences whether this process leads to an explosion or to the formation of a neutron star. We calculate the laminar flame speeds in degenerate oxygen–neon mixtures with compositions motivated by detailed stellar evolution models. These mixtures include trace amounts of carbon and have a lower electron fraction than those considered in previous work. We find that trace carbon has little effect on the flame speeds, but that material with electron fraction has laminar flame speeds that are times faster than those at . We provide tabulated flame speeds and a corresponding fitting function so that the impact of this difference can be assessed via full star hydrodynamical simulations of the collapse process.

Nuclear Burning Wave Concept and Theoretical Approaches for its Description

After two major nuclear power plant accidents in Chernobyl (1986) and Fukushima (2011), one of the main requirements for the nuclear power engineering is the safety of the nuclear reactors in operation, as well as new nuclear power plants of the fourth generation, which are being developed now. One of such requirements is presence of the so-called “inherent safety” mechanism, which renders the uncontrolled reactor runaway impossible under any conditions, moreover, the implementation of such a mechanism should be ensured on the level of physical principles embedded in the reactor design. Another important problem of the nuclear power engineering is the need of the transition to the large-scale use of the fast-neutron breeder reactors, with which it would be possible to set up expanded reproduction of the nuclear fuel and by that means solve the problem of supplying humanity with relatively cheap energy for thousands of years. Moreover, at present an unresolved problem is the disposal of spent nuclear fuel containing radioactive nuclides with long half-lives, which presents a long-term danger to the ecology. One of the promising conceptions of the fast-neutron breeder reactor, which can, in the case of successful implementation, partially or even entirely solve the problems of the nuclear power engineering mentioned above, is the reactor that operates in the nuclear burning wave mode, which is also known as “Traveling wave reactor”, CANDLE and by some other names. This paper presents a short review of the main theoretical approaches used for description of such a physical phenomenon as slow nuclear burning (deflagration) wave in the neutron multiplication medium initially composed of the fertile material 238U or 232Th. A comparative analysis of the possibilities of different mathematical models for describing this phenomenon is performed, both for those based on the deterministic approach (i.e. solving neutron transport equations) and for models that use Monte Carlo methods. The main merits of the fast breeder reactor, working in the nuclear burning wave mode, and problems related to the practical realization of the considered concept are discussed.

Effects of Tangential Velocity in the Reactive Relativistic Riemann Problem

Abstract Type I X-ray bursts are thermonuclear burning events that occur on the surfaces of accreting neutron stars. Burning begins in a localized spot in the star’s ocean layer before propagating across the entire surface as a deflagration. On the scale of the entire star, the burning front can be thought of as discontinuity. To model this, we investigated the reactive Riemann problem for relativistic deflagrations and detonations and developed a numerical solver. Unlike for the Newtonian Riemann problem, where only the velocity perpendicular to the interface is relevant, in the relativistic case the tangential velocity becomes coupled through the Lorentz factor and can alter the waves present in the solution. We investigated whether a fast tangential velocity may be able to cause a deflagration wave to transition to a detonation. We found that such a transition is possible, but only for tangential velocities that are a significant fraction of the speed of light or for systems already on the verge of transitioning. Consequently, it is highly unlikely that this transition would occur for a burning front in a neutron star ocean without significant contributions from additional multidimensional effects.

Investigations on oblique detonations induced by a finite wedge in high altitude

In this paper, the characteristics of two-dimensional (2D) oblique detonation waves (ODWs) induced by finite wedges in high altitude are investigated numerically. The reactive Euler equations with a detailed chemical model are solved. This paper focuses on the effects of expansion waves and altitudes on ODW, including the initiation, wave structures, pressure and temperature distributions. Numerical results demonstrate that both the location of turning point from oblique wedge to horizontal wedge and the altitude influence the initiation characteristics of ODW. Then, the initiation criterion of ODW for finite wedges is proposed in this paper. As the characteristic length of induction zone LC (the length from the front point of oblique wedge to the front point of deflagration wave) and the characteristic length of oblique wedge LW satisfy the relationship LC/LW>1, the initiation of ODW occurs. When LC/LW<1, the initiation of ODW doesn't occur. This work would be significant to the designing of oblique detonation engines (ODE) in air-breathing hypersonic vehicle.

Research on parameter search of the worst operating condition for explosion overpressure in utility tunnels based on genetic algorithm

In this paper, the 2D numerical simulation model for the gas pipe tank of utility tunnels is established. Aiming at optimising the maximum overpressure produced by explosion in the gas pipe tank, in restricted conditions of vent position, pre-mixed gas concentration in the tank and ignition position, a method of parameter optimisation of the worst operating condition for explosion overpressure in the gas pipe tank of utility tunnels is proposed by combining computational fluid mechanics and genetic algorithm. The results show that genetic algorithm is feasible in searching the worst operating condition for explosion overpressure in the gas pipe tank of utility tunnels and can improve the searching efficiency significantly. Methane-air pre-mixed gas under the two conditions being both pre- and post-optimised can form deflagration phenomenon. The deflagration wave is the direct factor of the overpressure formed at the boundary of the model. Both the pressure and temperature imposed by the deflagration wave acting on the model boundaries have an evident increase compared with those before optimisation. The maximum overpressure is increased by 15% and the maximum temperature is increased by 7%.

Elementary Wave Interactions for the Simplified Combustion Model in Magnetogasdynamics

We investigate the elementary wave interactions for the simplified combustion model in magnetogasdynamics. Under the modified entropy conditions, we construct the unique solution and observe some interesting phenomena; such as, the combustion wave may be extinguished by the contact discontinuity or the shock wave. Especially, the transition between the detonation wave and the deflagration wave is also captured.

Thermoacoustic Instabilities in an Annular Rotating Detonation Combustor Under Off-Design Condition

Experiments are performed to investigate the combustion features in a laboratory-scale hydrogen ()/air annular rotating detonation combustor under the off-design condition of low air mass flow rates. The air mass flow rate is ranged from 10 to 115 g/s, and the overall equivalence ratio is ranged from 0.6 to 1.0. The unstable longitudinal pulsed deflagration (ULPD), rotating fast deflagration (RFD), and stable longitudinal pulsed deflagration (SLPD) are found to exist in the combustor according to the analysis of pressure traces obtained at different circumferential and axial positions. The RFD is such a combustion instability coupled with the first tangential acoustic mode, but it occurs very rarely. The propagation speed of the RFD waves is approximately 500 m/s, and the pressure wave amplitudes are as low as 0.2 MPa. The SLPD appears with stronger and periodic pressure oscillations, and it is coupled with the first longitudinal acoustic mode of the combustor. The ULPD found in the present experiment can be regarded as the longitudinal mode even though the main frequency band is wider. The pressure oscillations are very irregular in the ULPD situation, but they are traveling forward and backward along the axial direction of the combustor. The variation of the air mass flow rate has more influence on the oscillation intensity of the deflagration wave than the variation of the equivalence ratio. It is also found that the pressure oscillations in the air and hydrogen plenums are forced by the unstable combustion process in the annular combustor. The unchoked condition of the injectors contributes the system coupling of the combustor and plenum.