Entropy Generation during Head-On Interaction of Premixed Flames with Inert Walls within Turbulent Boundary Layers

The statistical behaviours of different entropy generation mechanisms in the head-on interaction of turbulent premixed flames with a chemically inert wall within turbulent boundary layers have been analysed using Direct Numerical Simulation data. The entropy generation characteristics in the case of head-on premixed flame interaction with an isothermal wall is compared to that for an adiabatic wall. It has been found that entropy generation due to chemical reaction, thermal diffusion and molecular mixing remain comparable when the flame is away from the wall for both wall boundary conditions. However, the wall boundary condition affects the entropy generation during flame-wall interaction. In the case of isothermal wall, the entropy generation due to chemical reaction vanishes because of flame quenching and the entropy generation due to thermal diffusion becomes the leading entropy generator at the wall. By contrast, the entropy generation due to thermal diffusion and molecular mixing decrease at the adiabatic wall because of the vanishing wall-normal components of the gradients of temperature and species mass/mole fractions. These differences have significant effects on the overall entropy generation rate during flame-wall interaction, which suggest that combustor wall cooling needs to be optimized from the point of view of structural integrity and thermodynamic irreversibility.     

Effects of gas compressibility on the dynamics of premixed flames in long narrow adiabatic channels

We examine the dynamics of premixed flames in long, narrow, adiabatic channels focusing, in particular, on the effects of gas compressibility on the propagation. Recognising the importance of the boundary conditions, we examine and compare three cases: flame propagation in channels open at both ends, where the pressure must adjust to the ambient pressure at both ends and the expanding gas is allowed to leave the channel freely, and flame propagation in channels that remain closed at one of the two ends, where the burned/unburned gas remains trapped between the flame and one of the two walls. Earlier studies have shown that a flame accelerates when travelling down a narrow channel as a result of the combined effects of wall friction and thermal expansion. In the present work we show that compressibility effects enhance the transition to fast accelerating flames in channels open at both ends and in channels closed at the ignition end. In both situations, the accelerating flames could reach values that, depending on the effective Mach number, are as large as fifty times the laminar flame speed. In contrast, when the channel is closed at the far end, the acceleration is limited and the propagation speed is damped as the flame approaches the far boundary. Moreover, we show that, in channels closed at their ignition end, the flame in sufficiently long channels evolves into a steadily propagating compression-driven flame. The propagation speed of these flames depends exponentially on the constant-volume equilibrium temperature, which is higher than the (constant pressure) adiabatic flame temperature, and is therefore larger than for ordinary isobaric flames. Fast propagating compression waves cannot emerge in channels that remain open at their ignition end because of the reduced pressure forced by the open boundary.     

A numerical study on extinction behaviour of laminar micro-diffusion flames

We conducted a numerical study on the fluid dynamic, thermal and chemical structures of laminar methane–air micro flames established under quiescent atmospheric conditions. The micro flame is defined as a flame on the order of one millimetre or less established at the exit of a vertically-aligned straight tube. The numerical model consists of convective–diffusive heat and mass transport with a one-step, irreversible, exothermic reaction with selected kinetics constants validated for near-extinction analyses. Calculations conducted under the burner rim temperature 300 K and the adiabatic burner wall showed that there is the minimum burner diameter for the micro flame to exist. The Damköhler number (the ratio of the diffusive transport time to the chemical time) was used to explain why a flame with a height of less than a few hundred microns is not able to exist under the adiabatic burner wall condition. We also conducted scaling analysis to explain the difference in extinction characteristics caused by different burner wall conditions. This study also discussed the difference in governing mechanisms between micro flames and microgravity flames, both of which exhibit similar spherical flame shape.     

微尺度扩散火焰特性的数值解析

本文以均匀空气流中圆管形成的甲烷射流扩散火焰为对象,用数值解析的方法研究了微尺度扩散火焰的火焰结构和燃烧特性。燃烧反应采用甲烷/空气一步总包反应,喷管壁面采用绝热条件。在Re一定情况下,改变喷口尺寸和喷口流速考察了微扩散火焰的结构和火焰熄灭的尺度效应。数值结果表明,随着喷口直径的增大,微火焰的上方出现回流; Re=12条件下,在喷口直径=0.07 mm时存在熄灭极限;稳定燃烧区的最小发热率约为0.5 W;微尺度条件下,Da数对火焰结构和火焰的熄灭有一定的影响。     

Flamelet structure in turbulent premixed swirling oxy-combustion of methane

Two key flame macrostructures in swirling flows have been observed in experiments of oxy-combustion (as well as air-combustion); as the equivalence ratio is raised, the flame moves from being stabilized on just the inner shear layer (Flame III) to getting stabilized on both the inner and outer shear layers (Flame IV). We report results of an LES investigation of two different inlet oxy-fuel mixtures, in a turbulent swirling flow at $\text{Re}=20,000,$ that capture these two macrostructures. Previous work on the effects of heat loss have mostly focused on its impact on macro-scale observations. In this paper, we examine how heat loss impacts the flame microstructures as well for these two macrostructures. For both flames, the flamelet structure, as represented by a scatter plot of the normalized fuel concentration against the normalized temperature, depends on whether the combustor walls are adiabatic or non-adiabatic. For the adiabatic case, the flamelets of both macrostructures behave like strained flames. When wall heat transfer is included, Flame III microstructure is more bimodal. Since this flame extends farther downstream and part of it propagates along the walls, heat transfer has a greater impact on it’s microstructure. These results show that heat loss impacts not just the macro properties of the flame such as its shape or interactions with the wall, but also fundamentally changes its internal structure. Scatter plots of the turbulent flames are constructed and compared to different 1D laminar flame profiles (e.g., strained or with heat loss), and comparisons suggest the important role of the wall thermal boundary conditions in the accurate simulations of combustion dynamics and interpretations of experimental data, including data reduction and scaling.     

The role of spontaneous waves in the deflagration-to-detonation transition in submillimetre channels

Flame acceleration and transition to detonation in submillimetre two-dimensional planar and three-dimensional square channels were simulated by solving the compressible reactive Navier–Stokes equations. A simplified chemical–diffusive model was used to describe the diffusive transport and chemical reaction of a highly reactive mixture, such as stoichiometric ethylene and oxygen in 2D and 3D channels. The walls of the channels were modelled as no-slip and adiabatic. The initial flame acceleration and precursor shock formation were consistent with earlier results. Viscous dissipation in the boundary layer heats the reactants, which have been compressed by the precursor shock. The strength of the precursor shock and the amount of viscous dissipation increase until the temperature of the boundary layer is high enough to ignite the reactants. This produces a spontaneous wave, which, in most of the cases considered, initiates the detonation. The spontaneous wave first forms where the flame attaches to the wall in the planar channels, and forms at the corner where two walls meet in the square channels. In a separate study, the boundary layer also ignited in a computation for a circular tube containing a mixture hydrogen and oxygen represented by a detailed chemical reaction mechanism. The formation of spontaneous waves to the extent studied appears to be robust, and is relatively insensitive to channel geometry, fuel and oxidiser mixture, and the level of detail in the chemical–diffusive models used.     

Heat recirculation effects on flame propagation and flame structure in a mesoscale tube

Heat recirculation effects on flame propagation and flame structure are theoretically and experimentally examined in a mesoscale tube as the simplest model of heat-recirculating burners. Solutions for steady propagation are obtained using a one-dimensional two-temperature approximation. The results show that the low heat diffusivities of common solid materials permit significant heat recirculation through the wall only for a slowly-propagating condition, otherwise the flame behaves almost like a freely-propagating nonadiabatic flame. This limited heat recirculation sharply pinches and stretches two well-known branches of the freely-propagating nonadiabatic flame, resulting in the appearance of two slow-propagation branches. On the upper slow-propagation branch flames can reach superadiabatic temperatures and on the lower one, which is stretched from the classical unstable lower branch, flames can be stable. As the tube inner diameter decreases, another burning regime appears where flames are barely sustained by the heat recirculation. Further reduction of the tube inner diameter makes no flame exist. It is also revealed that a flame in a mesoscale tube has two length scales, i.e. the conventional flame thickness and a convective preheat zone thickness, and that the latter should be much larger than the former for significant heat recirculation. It is theoretically predicted that a heat-recirculating, even superadiabatic, flame with positive propagation velocity against the gas flow can exist in a mesoscale tube. It is also found that a flame transition from one branch to another in a given tube is well described by only one dimensionless parameter. Finally, these theoretical results show good qualitative agreements with experiments, especially for the transition behaviours.     

Travelling waves in a radiation-combustion free-boundary model for flame propagation

We study a combustion-radiation model which models premixed flames propagating in a gaseous mixture with inert dust. This model combines diffusion of mass and temperature with reaction at the flame front. We choose a free boundary model to describe the propagating flames and take a linearized approximation to model the radiation, but we keep a nonlinear reaction term which is temperature dependent. The radiative transfer of thermal energy emitted and absorbed by dust is modelled using the Eddington equation. We analyse the bifurcation diagram of the travelling wave solution curve. In a specific parameter plane, travelling waves are given by a single smooth curve which is parameterized by the flame temperature.     

Flame–wall interaction effects on the flame root stabilization mechanisms of a doubly-transcritical LO2/LCH4 cryogenic flame

High-fidelity numerical simulations are used to study flame root stabilization mechanisms of cryogenic flames, where both reactants (O₂ and CH₄) are injected in transcritical conditions in the geometry of the laboratory scale test rig Mascotte operated by ONERA (France). Simulations provide a detailed insight into flame root stabilization mechanisms for these diffusion flames: they show that the large wall heat losses at the lips of the coaxial injector are of primary importance, and require to solve for the fully coupled conjugate heat transfer problem. In order to account for flame–wall interaction (FWI) at the injector lip, detailed chemistry effects are also prevalent and a detailed kinetic mechanism for CH₄ oxycombustion at high pressure is derived and validated. This kinetic scheme is used in a real-gas fluid solver, coupled with a solid thermal solver in the splitter plate to calculate the unsteady temperature field in the lip. A simulation with adiabatic boundary conditions, an hypothesis that is often used in real-gas combustion, is also performed for comparison. It is found that adiabatic walls simulations lead to enhanced cryogenic reactants vaporization and mixing, and to a quasi-steady flame, which anchors within the oxidizer stream. On the other hand, FWI simulations produce self-sustained oscillations of both lip temperature and flame root location at similar frequencies: the flame root moves from the CH₄ to the O₂ streams at approximately 450 Hz, affecting the whole flame structure.     

Numerical studies of curved stationary flames in wide tubes

The nonlinear problem of the propagation of curved stationary flames in tubes of different widths is studied by means of direct numerical simulation of the complete system of hydrodynamic equations including thermal conduction, viscosity, fuel diffusion and chemical kinetics. While only a planar flame can propagate in a narrow tube of width smaller than half of the cut–off wavelength determined by the linear theory of the hydrodynamic instability of a flame front, in wider tubes stationary curved flames propagate with velocities considerably larger than the corresponding velocity of a planar flame. It is shown that only simple ‘single-hump’ slanted stationary flames are possible in wide tubes, and ‘multi–hump’ flames are possible in wide tubes only as a nonstationary mode of flame propagation. The stability limits of curved stationary flames in wider tubes and the secondary Landau–Darrieus instability are investigated. The dependence of the velocity of the stationary flame on the tube width is studied. The analytical theory describes the flame reasonably well when the tube width does not exceed some critical value. The dynamics of the flame in wider tubes is shown to be governed by a large–scale stability mechanism resulting in a highly slanted flame front. In wide tubes, the skirt of the slanted flame remains smooth with the length of the skirt and the flame velocity increasing progressively with the increase of the tube width above the second critical value. Results of the analytical theory and numerical simulations are discussed and compared with the experimental data for laminar flames in wide tubes.     

Dynamics and stability of premixed hydrogen-air flames in square microchannels with wall temperature gradients

The dynamics and stability of premixed hydrogen-air flames in square microchannels with heated walls were investigated through three-dimensional direct numerical simulations. The inlet velocity and equivalence ratio were 1.5 m/s and 0.5. The effect of the wall temperature gradient characteristics on the flame dynamics and stability was examined varying the width and location of the wall temperature gradient for a channel height of 1.5 mm. Five distinct flame modes were observed at different wall temperature profiles: flame with repetitive extinction-ignition (FREI), pulsating flame, laterally oscillating flame, spinning flame, and steady flame modes. Furthermore, transitions between these flame modes were observed for specific inflow and boundary conditions. The effect of the channel height on the flame stability was investigated by varying the channel height from 1.0 mm to 1.677 mm for a fixed wall temperature gradient. As the channel height was increased, four of the flame modes, namely, FREI, laterally oscillating flame, spinning flame, and steady flame modes appeared sequentially. To determine whether this sequential appearance was associated with the variation of the wall heat loss, the maximum wall temperature was changed by small amounts. For a lower wall temperature, the laterally oscillating flame mode transitioned to the FREI mode, and for a higher wall temperature, unstable flame modes such as the FREI and laterally oscillating flame modes disappeared, resulting in stable flame.     

Nonlinear equation for curved nonstationary flames and flame stability

A time-dependent nonlinear equation for a nonstationary curved flame front of an arbitrary expansion coefficient is derived under the assumptions of a small but finite flame thickness and weak nonlinearity. On the basis of the derived equation, stability of two-dimensional curved stationary flames propagating in tubes with ideally adiabatic and slip walls is studied. The stability analysis shows that curved stationary flames become unstable for sufficiently wide tubes. The obtained stability limits are in a good agreement with the results of numerical simulations of flame dynamics and with semiqualitative stability analysis of curved stationary flames. Possible outcomes of the obtained instability at the nonlinear stage are discussed. The instability may result in extra wrinkles at a flame front close to the stability limits and in self-turbulization of the flame far from the limits. The self-turbulization can also be interpreted as a fractal structure. The fractal dimension of a flame front and velocity of a self-turbulized flame are evaluated.     

Inward-propagating cylindrical flames under different ignition conditions

Inward-propagating cylindrical flames are studied numerically by high-resolution simulations using a one-step Arrhenius kinetics. Emphasis is placed on the effect of shock waves on the flame propagation by setting initial ignition conditions with and without shock wave. It is found that without initial shock wave, the inward-propagating flame propagates initially at a constant speed, while in the later stage of the propagation, it shows a small-amplitude oscillatory motion. When the shock wave initially introduced is medium, a large-amplitude oscillatory motion is caused by the interaction of shock waves with the inward-propagating flame. Moreover, autoignition occurs at the center and develops outwardly into a cellular flame. However, as the introduced shock wave is strong, autoignition created at the center evolves outwardly a cellular detonation.     

Combustion waves in a model with chain branching reaction and their stability

In this paper the travelling wave solutions in the adiabatic model with the two-step chain branching reaction mechanism are investigated both numerically and analytically in the limit of equal diffusivity of reactant, radicals and heat. The properties of these solutions and their stability are investigated in detail. The behaviour of combustion waves are demonstrated to have similarities with the properties of non-adiabatic one-step combustion waves in that there is a residual amount of fuel left behind the travelling waves and the solutions can exhibit extinction. The difference between the non-adiabatic one-step and adiabatic two-step models is found in the behaviour of the combustion waves near the extinction condition. It is shown that the flame velocity drops down to zero as the extinction condition is reached. Prospects of further work are also discussed.     

Strong flame acceleration and detonation limit of hydrogen-oxygen mixture at cryogenic temperature

A series of experiments were carried out in a closed tube at cryogenic temperature (77 K) for hydrogen-oxygen mixtures. Flame propagation speed and overpressure were measured by optical fibers and pressure sensors, respectively. The first and second shock waves were captured in the cryogenic experiments, although the shock waves always precede the flames in all cases indicating the absence of stable detonation. However, strong flame acceleration was observed for all situations, which is consistent with the prediction by expansion ratio and Zeldovich number. Besides, the tube diameter and length are also critical for flame acceleration to supersonic. All the flames in this work accelerate drastically reaching the C-J deflagration state. But at 0.4 atm, only fast flame is formed, while at higher initial pressures, the flame further accelerates to a galloping mode manifesting a near-limit detonation, which could be indicated by the stability parameter $\chi$.     

Effect of flame retardants on side-wall quenching of partially premixed laminar flames

A combined experimental and numerical investigation of partially premixed laminar methane-air flames undergoing side-wall quenching (SWQ) is performed. A well-established SWQ burner is adapted to allow the seeding of the main flow with additional gaseous products issued from a (secondary) wall inlet close to the flame’s quenching point. First, the characteristics of the partially premixed flame that quenches at the wall are assessed using planar laser-induced fluorescence measurements of the OH radical, and a corresponding numerical simulation with fully-resolved transport and chemistry is conducted. A boundary layer of enriched mixture is formed at the wall, leading to a reaction zone parallel to the wall for high injection rates from the wall inlet. Subsequently, in a numerical study, the wall inflow is mixed with dimethylmethylphosphonat (DMMP), a phosphor-based flame retardant. The DMMP addition allows the assessment of the combined effects of heat loss and flame retardants on the flame structure during flame-wall interaction. With an increasing amount of DMMP in the injected mixture, the flame stabilizes further away from the wall and shows a decrease in the local heat-release rate. Thereby, the maximum wall heat flux is significantly reduced. That results in a lower thermal load on the quenching wall. The flame structure analysis shows an accumulation of the intermediate species HOPO at the wall similar to the CO accumulation during the quenching of premixed flames without flame retardant addition. The study shows how the structure of a partially premixed flame is influenced by a wall that releases either additional fuel or a mixture of fuel and flame retardant. The insights gained from the canonical configuration can lead to a better understanding of the combined effects of flame retardants and heat losses in near-wall flames.     

Characterization of symmetric to non-symmetric flamefront transition in slender microchannels

The purpose of the present work is to analyze propagating two-dimensional flames confined in slender semi open channels, where the combustion process takes place towards the closed end. The study focuses on the calculation of the growth rate of the transition from symmetric to non-symmetric flames propagation identified by Jiménez et al. [1].The combustion cell is initially filled with a stoichiometric mixture of fuel and air at standard conditions. Ignition is induced close to the open end of the channel under planar and gaussian profiles in temperature and species mass fractions which activate a sustained combustion process. The gases inside the chamber, initially stagnant, are accelerated due to the heat generated in the chemical reactions, leading to the development of lateral boundary layers, so that the hot gases exit the channel following a Poiseuille velocity profile. This transverse flow velocity differences are accommodated by means of a symmetric tulip shape formed after a short initial transient.Acoustic waves generated in the ignition process, keep travelling along the channel, bouncing at the walls and interacting with the flame during all the combustion process. Additionally, the flame structure, curved by Darrieus-Landau instability, interacts with the pressure waves triggering small amplitude oscillations (primary oscillation mode), which under certain conditions can transition to higher amplitude oscillations (secondary mode).This transition is observed to be highly dependent not only on the cell geometry, but also in the initial conditions generated by the ignition procedure.The aim of this work is to improve the understanding of this process, complementing the work of Jiménez et al. [1], and to characterize the effect of the channel width in this transition.     

Numerical study of sporadic combustion waves in straight channels of different diameters

The dynamics of flames propagating in straight channels filled with a stationary low-Lewis-number premixed gas mixture is studied numerically. A method for determining the propagation velocity of a sporadic combustion wave consisted of separate flame spots is proposed. Dependencies of the sporadic combustion wave propagation velocity, the residual fuel concentration and the number of flame spots on the channel size and the value of radiation heat losses are obtained. Analysis of numerical results show that for the channels of diameter exceeding some value the number of separate cup-like fragments constituting sporadic combustion wave is proportional to the channel cross-sectional area. At smaller diameters, the number of flame spots changes insignificantly and is one or two. It is shown that one of the universal characteristics of the sporadic combustion wave depending only on mixture properties but independent on system geometry is the area necessary to accommodate one reacting spot. Flame velocity which is another fundamental combustion characteristic is found to be almost independent on channel size starting from some critical diameter. This diameter, however, depends on mixture properties or radiative heat loss intensity and corresponds to the sporadic flame containing from several to ten reacting spots. Thus, the main properties of sporadic combustion waves in wide channels can be determined by numerical modeling of the flame propagation in the relatively narrow channels in which the flame consists of 1–10 cup-like fragments.     

Detonation development in hydrogen/air mixtures inside a closed chamber: role of a cold wall

Detonation development from a hot spot has been extensively studied, where ignition occurs earlier than that in the surrounding mixtures. It has also been reported that a cool spot can induce detonation for large hydrocarbon fuels with Negative Temperature Coefficient (NTC) behavior, since ignition could happen earlier at lower temperatures. In this work we find that even for hydrogen/air mixtures without NTC behaviors, a cold wall can still initiate and promote detonation. End-wall reflection of the pressure wave and wall heat loss introduce an exothermic center outside the boundary layer, and then autoignitive reaction fronts on both sides may evolve into detonation waves. The right branch can be further strengthened by appropriate temperature gradient near the cold wall, and exhibits different dynamics at various initial conditions. The small excitation time and the large diffusivity of hydrogen provide the possibility for detonation development within the limited space between the autoignition kernel and the cold wall. Moreover, detonation may also develop near the flame front, which may or may not co-exist with detonation waves from the cold wall. Correspondingly, wall heat flux evolution exhibits different responses to detailed dynamic structures. Finally, we propose a regime diagram describing different combustion modes including normal flame, autoignition, and detonation from the wall and/or the reaction front. The boundary of normal flame regime qualitatively agrees with the prediction by the Livengood-Wu Integral method, while the detonation development from both the end wall and the reaction front observes Zel'dovich mechanism. Compared to hydrocarbons, hydrogen is resistant to knock onset but it is more prone to superknock development. The latter mode becomes more destructive in the presence of wall heat loss. This study isolates and identifies the role of wall heat loss on a potential mechanism for superknock development in hydrogen-fueled spark-ignition engines.