The role of viscous stress in heating of the fuel mixture in deflagration-to-detonation transition in tubes is studied both analytically and numerically. The analytical theory is developed in the limit of low Mach number; it determines temperature distribution ahead of an accelerating flame with maximum achieved at the walls. The heating effects of viscous stress and the compression wave become comparable at sufficiently high values of the Mach number. In the case of relatively large Mach number, viscous heating is investigated by direct numerical simulations. The simulations were performed on the basis of compressible Navier-Stokes gas-dynamic equations taking into account chemical kinetics. In agreement with the theory, viscous stress makes heating and explosion of the fuel mixture preferential at the walls. The explosion develops in an essentially multi-dimensional way, with fast spontaneous reaction spreading along the walls and pushing inclined shocks. Eventually, the combination of explosive reaction and shocks evolves into detonation.
The problem of deflagration-to-detonation transition in an unconfined environment is revisited. With a freely expanding self-accelerating hydrogen-oxygen flame as an example, it is shown that deflagration-to-detonation transition is indeed possible provided the flame is large enough. The transition occurs prior to merging of the flame with the flame-supported precursor shock. The pre-transition flame does not reach the threshold of CJ-deflagration. Numerical simulations employed are based on the recently developed pseudo-spectral method with time and space adaptation.
The study on deflagration-to-detonation transition (DDT) is very important because this mechanism has relevance to safety issues in industries, where combustible premixed gases are in general use. However, the quantitative prediction of DDT is one of the major unsolved problems in combustion and detonation theory to date. In this paper, the DDT process is studied theoretically and the critical condition is given by a concise theoretical expression. The results show that a deflagration wave propagating with about 60% Chapman-Jouguet (C-J) detonation velocity is a critical condition. This veloci…
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 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…
Dynamics of ethylene autoignition and Deflagration-to-Detonation Transition (DDT) in a one-dimensional shock tube are numerically investigated using a skeletal chemistry including 10 species and 10 reactions. Different combustion modes are investigated through considering various premixed gas equivalence ratios (0.2 to 2.0) and incident shock wave Mach numbers (1.8 to 3.2). Four ignition and DDT modes are observed from the studied cases, i.e., no ignition, deflagration combustion, detonation after reflected shock and deflagration behind the incident shock. For detonation development behind the…
We study experimentally fast flames and their transition to detonation in mixtures of methane, ethane, ethylene, acetylene, and propane mixtures with oxygen. Following the interaction of a detonation wave with a column of cylinders of varying blockage ratio, the experiments demonstrate that the fast flames established are Chapman-Jouguet deflagrations, in excellent agreement with the self-similar model of Radulescu et al. (2015). The experiments indicate that these Chapman-Jouguet deflagrations dynamically restructure and amplify into fewer stronger modes until the eventual transition to deton…
In this article effect of radiation preheating of unburnt mixture by propagating deflagration front is studied from the viewpoint of its ability to form a promoting temperature gradient and trigger transition to detonation. First, we investigate the effect of radiation preheating of the unburnt mixtures, when they are traveling through the wrinkles on the flame surface, in order to estimate a possibility of significant temperature rise. Subsequently, numerical simulations of a simplified mathematical model are carried out. They demonstrate plausibility of the proposed mechanism of the deflagra…
The deflagration-to-detonation transition (DDT) process is of great importance to both combustion theory and industry safety. In this study, the propagating mechanism of Chapman-Jouguet (C-J) deflagration is studied. Firstly, three models are put forth to decouple the C-J detonation front. These three models are (a) to introduce an expansion parameter into the one-dimensional energy equation, (b) to increase the activation energy of the chemical reaction model and (c) to decouple the shock wave from the flame front by artificial method. The C-J deflagration is obtained after the C-J detonation…
The general relation between ignition and deflagration analyses was studied theoretically and computationally. Simple analysis showed that the temporal evolutions of normalized fuel mass fraction and the normalized temperature in a 0D homogeneous ignition are equivalent to the spatial evolutions of those in a 1D laminar premixed flame at Lewis number of unity if a spatio-temporal transformation of the flame is applied. Furthermore, computations showed that the degree of reduction in normalized fuel mass fraction in the preheat zone was found to be in the following order: when the Lewis number …
In the current study, the influence of turbulent mixing and local reaction rates on deflagration to detonation transition (DDT) was investigated using a state-of-the-art large eddy simulation (LES) strategy. Specifically, detonation attenuation by a porous medium, and the subsequent re-initiation for methane-oxygen, a moderately unstable mixture, was considered. The purpose of the investigation was to validate the numerical strategy with previous experimental observations, and to determine what specific roles turbulent mixing and shock compression have on flame acceleration during the final st…
The present paper seeks to determine the mechanism of flame acceleration and transition to detonation when a turbulent flame preceded by a shock interacts with a single obstruction in its path, taken as a cylindrical obstacle or a wall in the present study. The problem is addressed experimentally in a mixture of propane-oxygen at sub-atmospheric conditions. The turbulent flame was generated by passing a detonation wave through a perforated plate, yielding flames with turbulent burning velocities 10 to 20 larger than the laminar values and incident shock Mach numbers ranging between 2 and 2.5. …
In this study we examine influence of the radiation heat transfer on the combustion regimes in the mixture, formed by suspension of fine inert particles in hydrogen gas. The gaseous phase is assumed to be transparent for the thermal radiation, while the radiant heat absorbed by the particles is then lost by conduction to the surrounding gas. The particles and gas ahead of the flame is assumed to be heated by radiation from the original flame. It is shown that the maximum temperature increase due to the radiation preheating becomes larger for a flame with lower velocity. For a flame with small …
One of the most important and difficult parts of constructing a multidimensional numerical simulation of flame acceleration and deflagration-to-detonation transition (DDT) in a reacting flow is finding a reliable and affordable model of the chemical and diffusive properties. For simulations of realistic scenarios, full detailed chemical models are computationally prohibitive. In addition, they are usually inaccurate for high-temperature and high-pressure shock-laden flows. This paper presents a general approach for developing an automated procedure to determine the reaction parameters for a si…
It was demonstrated recently in 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…
We study a flame propagating in the gaseous combustible mixture with suspended inert particles. The gas is assumed to be transparent for the radiation emitted by the combustion products, while particles absorb and re-emit the radiation. Thermal radiation heats the particles, which in turn transfer the heat to the surrounding gaseous mixture by means of heat conduction, so that the gas temperature lags that of the particles. We consider different scenarios depending on the spatial distribution of the particles, their size and the number density. In the case of uniform distribution of the partic…
The nature of type Ia supernovae (SNIa) - thermonuclear explosions of white dwarf stars - is an open question in astrophysics. Virtually all existing theoretical models of normal, bright SNIa require the explosion to produce a detonation in order to consume all of stellar material, but the mechanism for the deflagration-to-detonation transition (DDT) remains unclear. We present a unified theory of turbulence-induced DDT that describes the mechanism and conditions for initiating detonation both in unconfined chemical and thermonuclear explosions. The model is validated using experiments with ch…
The current work examines regimes of the hydrogen-oxygen flame propagation and ignition of mixtures heated by radiation emitted from the flame. The gaseous phase is assumed to be transparent for the radiation, while the suspended particles of the dust cloud ahead of the flame absorb and reemit the radiation. The radiant heat absorbed by the particles is then lost by conduction to the surrounding unreacted gaseous phase so that the gas phase temperature lags that of the particles. The direct numerical simulations solve the full system of two phase gas dynamic time-dependent equations with a det…
Multidimensional numerical simulations of a homogeneous, chemically reactive gas were used to study ignition, flame stability, and deflagration-to-detonation transition (DDT) in a supersonic combustor. The configuration studied was a rectangular channel with a supersonic inflow of stoichiometric ethylene-oxygen and a transimissive outflow boundary. The calculation is initialized with a velocity in the computational domain equal to that of the inflow, which is held constant for the duration of the calculation. The compressible reactive Navier-Stokes equations were solved by a high-order numeric…
The paper is concerned with identification of the key mechanisms controlling deflagration-to-detonation transition in 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, $fuel \to products$, kinetics (Phys.Rev.E, 103(2021)) over physically more relevant, $fuel+fuel \to products$, kinetics. Despite this change the runaway effect endures. …
Deflagration-to-detonation transition (DDT) can occur in environments ranging from experimental and industrial systems to astrophysical thermonuclear (type Ia) supernovae explosions. Substantial progress has been made in explaining the nature of DDT in confined systems with walls, internal obstacles, or pre-existing shocks. It remains unclear, however, whether DDT can occur in unconfined media. Here we use direct numerical simulations (DNS) to show that for high enough turbulent intensities unconfined, subsonic, premixed, turbulent flames are inherently unstable to DDT. The associated mechanis…
The present work investigates the structure of fast supersonic turbulent flames typically observed as precursors to the onset of detonation. These high speed deflagrations are obtained after the interaction of a detonation wave with cylindrical obstacles. Two mixtures having the same propensity for local hot spot formation were considered, namely hydrogen-oxygen and methane-oxygen. It was shown that the methane mixture sustained turbulent fast flames, while the hydrogen mixture did not. Detailed high speed visualizations of nearly two-dimensional flow fields permitted to identify the key mecha…
We show experimentally and numerically that when a weak shock interacts with a finger flame in a narrow channel, an extremely efficient mechanism for deflagration to detonation transition occurs. This is demonstrated in a 19-mm-thick channel in hydrogen-air mixtures at pressures below 0.2 atm and weak shocks of Mach numbers 1.5 to 2. The mechanism relies primarily on the straining of the flame shape into an elongated alligator flame maintained by the anchoring mechanism of Gamezo in a bifurcated lambda shock due to boundary layers. The mechanism can increase the flame surface area by more than…
This experimental study addresses the re-initiation mechanism of detonation waves following the Mach reflection of a shock-flame complex. The detonation diffraction around a cylinder is used to reproducibly generate the shock-flame complex of interest. The experiments are performed in methane-oxygen. We use a novel experimental technique of coupling a two-in-line-spark flash system with a double-frame camera in order to obtain microsecond time resolution permitting accurate schlieren velocimetry. The first series of experiments compares the non-reactive sequence of shock reflections with the r…
The problem of engine unstart of scramjets has not been resolved. In this paper, the mechanism of engine unstart is discussed from the point of view of shock/shock interaction and deflagration-to-detonation transition. The shock/shock interaction leads to the nonlinear, transient and discontinuous process of the supersonic combustion flow field. This process is similar to the deflagration-to-detonation transition process. If the velocity of pre-combustion shock wave is faster than the velocity in the isolator, it will propagate upstream and cause the engine unstart. The C-J detonation velocity…
The non-monotonic profile of temperature is to be considered in the context of combustion inside tubes or thermonuclear flames, which may accelerates to become detonation waves. This transition is known as deflagration-to-detonation transition. Focusing on this point, we extend the study of adiabatic flames, which assumes zero temperature gradient at the burned-side edge of a flame front, to the case of non-zero temperature gradient by introducing compression zone behind the front. Such a treatment has been performed in the previous work based on the ignition temperature approximation. In that…
Spray detonation in n-heptane two-phase mixtures is simulated using Eulerian Lagrangian method. Two-dimensional configuration is considered, and the effects of droplet diameter and liquid equivalence ratio on detonation propagation, structure, and dynamics are investigated. The results show that the average detonation propagation speed first increases and then decreases as liquid equivalence ratio changes, and the speed peaks at higher liquid equivalence ratio for larger droplets. The triple points and transverse detonations vaporize or aerodynamically expel the droplets from their trajectorie…
The aim of this work is to identify and explain the necessary conditions required for an energetic explosion of a Chandrasekhar-mass white dwarf. We construct and analyze weakly compressible turbulence models with nuclear burning effects for carbon/oxygen plasma at a density expected for deflagration-to-detonation transition (DDT) to occur. We observe formation of carbon deflagrations and transient carbon detonations at early times. As turbulence becomes increasingly inhomogeneous, sustained carbon detonations are initiated by the Zel'dovich reactivity gradient mechanism. The fuel is suitably …
In the present work we compare reliability of several most widely used reduced detailed chemical kinetic schemes for hydrogen-air and hydrogen-oxygen combustible mixtures. The validation of the schemes includes detailed analysis of 0D and 1D calculations and comparison with experimental databases containing data on induction time, equilibrium temperature, composition of the combustion products, laminar flame speed and the flame front thickness at different pressures. 1D calculations are carried out using the full gasdynamical system for compressible viscous thermal conductive multicomponent mi…
Type I X-ray bursts are thermonuclear burning events which occur on the surfaces of accreting neutron stars. Burning begins in a localised 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…
We show that converging spherical and cylindrical shock waves may ignite a detonation wave in a combustible medium, provided the radius at which the shocks become strong exceeds a critical radius, R_c. An approximate analytic expression for R_c is derived for an ideal gas equation of state and a simple (power-law-Arrhenius) reaction law, and shown to reproduce the results of numerical solutions. For typical acetylene-air experiments we find R_c~0.1 mm (spherical) and R_c~1 mm (cylindrical). We suggest that the deflagration to detonation transition (DDT) observed in these systems may be due to …
Thermal radiation of the hot combustion products usually does not influence noticeably the flame propagating through gaseous mixture. the situation is changed drastically in the presence even small concentration of particles, which absorb radiation, transfer the heat to the surrounding unburned gaseous mixture by means of heat conduction, so that the gas phase temperature in front of the advancing flame lags that of the particles. It is shown that radiative preheating of unreacted mixture ahead of the flame results in a modest increase of the advancing flame velocity for a highly reactive gase…
Two-dimensional wedge-stabilized oblique detonations in stoichiometric and fuel-lean H2/O2/Ar mixtures with water mists are studied with Eulerian-Lagrangian method. The effects of water droplet mass flow rate on flow and chemical structures in the induction zone, as well as physical / chemical roles of water vapor, are investigated. The results show that the oblique detonation wave (ODW) can stand in a range of water mass flow rates for both stoichiometric and fuel-lean mixtures. With increased droplet mass flow rate, the deflagration front in the induction zone is distorted and becomes zigzag…
Since detonation is the only established theory that allows rapid burning producing a high pressure that can be sustained in open areas, the generally accepted opinion was that the mechanism explaining the high rate of combustion in dust explosions is deflagration-to-detonation transition. We propose a theoretical substantiation of an alternative mechanism explaining the origin of the secondary explosion producing high speeds of combustion and high overpressures in unconfined dust explosions. We show that the clustering of dust particles in a turbulent flow ahead of the advancing flame gives r…
