Nonlinear non-stationary equation describing evolution of weakly curved premixed flames with arbitrary gas expansion, subject to the Landau-Darrieus instability, is derived. The new equation respects all the conservation laws to be satisfied across the flame front, as well as correctly takes into account influence of vorticity, generated in the flame, on the flame front structure and flame velocity. Analytical solutions of the derived equation are found.
The influence of the small scale ``cellular'' structure of premixed flames on their evolution at larger scales is investigated. A procedure of the space-time averaging of the flow variables over flame cells is introduced. It is proved that to the leading order in the flame front thickness, the form of dynamical equations for the averaged gas velocity and pressure, as well as of jump conditions for these quantities at the flame front, is the same as in the case of a zero-thickness flame propagating in an ideal fluid at constant velocity with respect to the fuel, equal to the adiabatic velocity …
The problem of burning of high-velocity gas streams in channels is revisited. Previous treatments of this issue are found to be incomplete. It is shown that despite relative smallness of the transversal gas velocity, it plays crucial role in determining flame structure. In particular, it is necessary in formulating boundary conditions near the flame anchor, and for the proper account of the flame propagation law. Using the on-shell description of steady anchored flames, a consistent solution of the problem is given. Equations for the flame front position and gas-velocity at the front are obtai…
The problem of non-perturbative description of stationary flames with arbitrary gas expansion is considered. On the basis of the Thomson circulation theorem an implicit integral of the flow equations is constructed. With the help of this integral, a simple explicit expression for the vortex mode of the burnt gas flow near the flame front is obtained. Furthermore, a dispersion relation for the potential mode at the flame front is written down, thus reducing the initial system of bulk equations and jump conditions for the flow variables to a set of integro-differential equations for the flame fr…
Spark ignition and subsequent flame propagation in a premixed, fuel-lean (equivalence ratio of 0.4) H2-N2O mixture are shown in this fluid dynamics video. High-speed schlieren photography was used to visualize the flame propagation and the complex instabilities that developed on the flame surface. The instabilities are a result of the competition between diffusive processes at the flame front and hydrodynamic instability.
Evolution of fuel droplet evaporation zone and its interaction with the propagating flame front are studied in this work. A general theory is developed to describe the evolutions of flame propagation speed, flame temperature, droplet evaporation onset and completion locations in ignition and propagation of spherical flames. The influences of liquid droplet mass loading, heat exchange coefficient (or evaporation rate) and Lewis number on spherical spray flame ignition are studied. Two flame regimes are considered, i.e., heterogeneous and homogeneous flames, based on the mixture condition near t…
The complete set of hydrodynamic equations for a corrugated flame front is reduced to a system of coordinate-free equations at the front using the fact that vorticity effects remain relatively weak even for corrugated flames. It is demonstrated how small but finite flame thickness may be taken into account in the equations. Similar equations are obtained for turbulent burning in the flamelet regime. The equations for a turbulent corrugated flame are consistent with the Taylor hypothesis of stationary external turbulence.
Reported in the paper are results of unsteady three-dimensional direct numerical simulations of laminar and turbulent, lean hydrogen-air, complex-chemistry flames propagating in forced turbulence in a box. To explore the eventual influence of thermo-diffusive instability of laminar flames on turbulent burning velocity, (i) a critical length scale Λn that bounds regimes of unstable and stable laminar combustion is numerically determined by gradually decreasing the width Λ of computational domain until a stable laminar flame is obtained and (ii) simulations of turbulent flames are performed by v…
The fractal scaling properties of turbulent premixed flame fronts have been investigated and considered for modelling sub-grid scales in the Large-Eddy-Simulation framework. Since the width of such thin reaction fronts cannot be resolved into the coarse mesh of LES, the extent of wrinkled flame surface contained in a volume is taken into account. The amount of unresolved flame front is estimated via the "wrinkling facto" that depends on the definition of a suitable fractal dimension and the scale at which the fractal scaling is lost, the inner cut-off length εi. In this context, the present st…
Shock flame interactions are fundamental problems in many combustion applications ranging from flame acceleration to flame control in supersonic propulsion applications. The present paper seeks to quantify the rate of deformation of the flame surface and burning velocity caused by the interaction and to clarify the underlying mechanisms. The interaction of a single shock wave with a cellular flame in a Hele-Shaw shock tube configuration was studied experimentally, numerically, and theoretically. A mixture of stoichiometric hydrogen-air at sub-atmospheric pressure was chosen such that large cel…
G-equations are level-set type Hamilton-Jacobi partial differential equations modeling propagation of flame front along a flow velocity and a laminar velocity. In consideration of flame stretching, strain rate may be added into the laminar speed. We perform finite difference computation of G-equations with the discretized strain term being monotone with respect to one-sided spatial derivatives. Let the flow velocity be the time-periodic cellular flow (modeling Rayleigh-Bénard advection), we compute the turbulent flame speeds as the asymptotic propagation speeds from a planar initial flame fron…
Steady propagation of premixed flames in straight channels is studied numerically using the on-shell approach. A first numerical algorithm for solving the system of nonlinear integro-differential on-shell equations is presented. It is based on fixed-point iterations and uses simple (Picard) iterations or the Anderson acceleration method that facilitates separation of different solutions. Using these techniques, we scan the parameter space of the problem so as to study various effects governing formation of curved flames. These include the thermal gas expansion and the finite-front-thickness ef…
Premixed flames propagating in horizontal tubes are observed to take on shape convex towards the fresh mixture, which is commonly explained as a buoyancy effect. A recent rigorous analysis has shown, on the contrary, that this process is driven by the balance of vorticity generated by a curved flame front with the baroclinic vorticity, and predicted existence of a regime in which the leading edge of the flame front is concave. We report first experimental realization of this regime. Our experiments on ethane and n-butane mixtures with air show that flames with an inflection point on the front …
The problem of non-perturbative description of stationary flames with arbitrary gas expansion is considered. A general method for deriving equations for the flame front position is developed. On the basis of the Thomson circulation theorem an implicit integral of the flow equations is constructed. With the help of this integral the flow structure near the flame front is determined, and a closed system of equations for the flame front position and a set of auxiliary quantities is obtained. This system is shown to be quasi-local, and its transverse representation is found. This representation al…
Premixed flames propagating within small channels show complex combustion phenomena that differ from flame propagation at conventional scales. Available experimental and numerical studies have documented stationary/non-stationary and/or asymmetric modes that depend on properties of the incoming reactant flow as well as channel geometry and wall temperatures. The present work seeks to illuminate mechanisms leading to symmetry-breaking and limit cycle behavior that are fundamental to these combustion modes. Specifically, four cases of lean premixed methane/air combustion -- two equivalence ratio…
The morphology of flame fronts propagating in reactive systems comprised of randomly positioned, point-like sources is studied. The solution of the temperature field and the initiation of new sources is implemented using the superposition of the Green's function for the diffusion equation, eliminating the need to use finite difference approximations. The heat released from triggered sources diffuses outward from each source, activating new sources and enabling a mechanism of flame propagation. Systems of $40000$ sources in a $200$ by $200$ two-dimensional domain were tracked using computer sim…
Spark ignition of ethanol droplet/vapor/air mixture is studied with a Eulerian-Eulerian method and detailed chemical mechanism. The flame kernel-droplet interaction is quantified with an evaporation completion front (ECF). Two categories of spray flames can hence be defined based on the relative location between the ECF and flame front, i.e., homogeneous and heterogeneous spray flames. An element-based equivalence ratio (ER) at the flame front (flame ER for short) is introduced to measure the gas composition in evaporating sprays. For overall fuel-lean mixtures, quasi-stationary spherical flam…
Data from a three-dimensional Direct Numerical Simulation of a turbulent premixed Bunsen flame at a low global Lewis number are analyzed to address the effects of the curvature on the local flame front. For this purpose, the chemical kinetics is modeled according to a reduced scheme, involving 5 reactions and 7 species, to mimic a H$_{2}$/Air flame at equivalence ratio $ϕ=0.5$. An increase of the local temperature and reaction rate is found for fronts elongated into the fresh gases (concave), while local quenching is observed for fronts elongated in the opposite direction (convex), i.e. toward…
Recent complex-chemistry direct numerical simulations of lean hydrogen-air flames propagating in forced turbulence in a box were continued by switching-off the turbulence forcing. Results show that a decrease in burning velocity U_T(t), caused by the turbulence decay, is reversed when the turbulence becomes weak and a peak of U_T(t) appears, with the peak magnitudes and associated Karlovitz numbers being similar in two different cases. These results (i) are attributed to activation of laminar flame instabilities, which have been suppressed by intense turbulence, and (ii) are argued to indicate…
An unconfined strongly swirled flow is investigated to study the effect of hydrogen addition on upstream flame propagation in a methane-air premixed flame using Large Eddy Simulation (LES) with a Thickened Flame (TF) model. A laboratory-scale swirled premixed combustor operated under atmospheric conditions for which experimental data for validation is available has been chosen for the numerical study. In the LES-TF approach, the flame front is resolved on the computational grid through artificial thickening and the individual species transport equations are directly solved with the reaction ra…
The renormalization ideas of self-similar dynamics of a strongly turbulent flame front are applied to the case of a flame with realistically large thermal expansion of the burning matter. In that case a flame front is corrugated both by external turbulence and the intrinsic flame instability. The analytical formulas for the velocity of flame propagation are obtained. It is demonstrated that the flame instability is of principal importance when the integral turbulent length scale is much larger than the cut off wavelength of the instability. The developed theory is used to analyse recent experi…
We study the effect of thermal noise on the propagation speed of a planar flame. We show that this out of equilibrium greatly amplifies the effect of thermal noise to yield macroscopic reductions in the flame speed over what is predicted by the noise-free model. Computations show that noise slows the flame significantly. The flame is modeled using Navier Stokes equations with appropriate diffusive transport terms and chemical kinetic mechanism of hydrogen/oxygen. Thermal noise is modeled within the continuum framework using a system of stochastic partial differential equations, with transport …
The problem of non-perturbative description of unsteady premixed flames with arbitrary gas expansion is solved in the two-dimensional case. Considering the flame as a surface of discontinuity with arbitrary local burning rate and gas velocity jumps given on it, we show that the front dynamics can be determined without having to solve the flow equations in the bulk. On the basis of the Thomson circulation theorem, an implicit integral representation of the gas velocity downstream is constructed. It is then simplified by a successive stripping of the potential contributions to obtain an explicit…
(Abridged) 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. 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 develops pulsations with the …
The dynamics of two-dimensional thin premixed flames is addressed in the framework of mathematical models where the flow field on either side of the front is piecewise incompressible and vorticity-free. Flames confined in channels with asymptotically-straight impenetrable walls are considered. Beside a few free propagations along straight channels, attention is focused on flames propagating against high-speed flows and positioned near a round central obstacle, or near two symmetric bumps protruding inward. Combining conformal maps and Green's functions, a regularised generalisation of Frankel'…
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…
Neural networks (NN) are implemented as sub-grid flame models in a large-eddy simulation of a single-injector liquid-propellant rocket engine with the aim to replace a look-up table approach. The NN training process presents an extraordinary challenge. The multi-dimensional combustion instability problem involves multi-scale lengths and characteristic times in an unsteady flow problem with nonlinear acoustics, addressing both transient and dynamic-equilibrium behaviors, superimposed on a turbulent reacting flow with very narrow, moving flame regions. Accurate interpolation between the points o…
In this experimental study on a laboratory-scale turbulent annular combustor with sixteen swirl-stabilized burners, we study the flame-flame and flame-acoustic interactions during different dynamical states associated with the longitudinal mode of the combustor. We simultaneously measure the acoustic pressure and CH* chemiluminescence emission of the flame using a high-speed camera. Upon increasing the equivalence ratio, the combustor undergoes the following sequence of transition: combustion noise (CN) to low amplitude longitudinal thermoacoustic instability (TAI) through the state of intermi…
The early stages of flames propagation in tubes with no-slip walls and the inversion of the flame front from a convex shape directed towards unburned gas to a concave shape with a cusp directed to the burned gas, known as a tulip flame, was investigated for closed and half-open tubes by solving the fully compressible reactive Navier-Stokes equations with a one-step Arrhenius chemical model for the highly reactive hydrogen/air and slowly reacting methane/air mixtures. The development of the tulip flame in hydrogen/air obtained in simulations with a one-step Arrhenius model was compared with sim…
The problem of linear stability of confined V-flames with arbitrary gas expansion is addressed. Using the on-shell description of flame dynamics, a general equation governing propagation of disturbances of an anchored flame is obtained. This equation is solved analytically for V-flames in high-velocity channel streams. It is demonstrated that dynamics of flame disturbances in this case is controlled by the memory effects associated with vorticity generated by the curved front. The perturbation growth rate spectrum is determined, and explicit analytic expressions for the eigenfunctions are give…
A new optical technique based on light-matter interaction is devised in-house to detect thermo-acoustic disturbances generated after ignition and during propagation of a premixed flame front in a half open channel. The technique involves passing a polarized laser light through a medium whose density or refractive index varies due to the passage of acoustic waves and/or flame front and then capturing the leaked depolarised light through an analyser by a photo-detector. The technique is applied to combustor involving premixed flame propagation and tulip inversion. The thermo-acoustic signals and…
A modified Thickened Flame (TF) model based on Large Eddy Simulation methodology is used to investigate premixed combustion and the model predictions are evaluated by comparing with the piloted premixed stoichiometric methane-air flame data (Chen et al., 1996) for Reynolds numbers Re = 24,000 (flame F3) and Re=52,000 (flame F1). The basic idea of Thickened-Flame approach is that the flame front is artificially thickened to resolve on the computational LES grid while keeping the laminar flame speed ( ) constant. The artificially thickening of the flame front is obtained by enhancing the molecul…
An experimental study of methane, propane and dimethyl ether (DME) pre-mixed flames propagating in a quasi-two-dimensional Hele-Shaw cell placed horizontally is presented in this paper. The flames are ignited at the open end of the combustion chamber and propagate towards the closed end. Our experiments revealed two distinct propagation regimes depending on the equivalence ratio of the mixture as a consequence of the coupling between the heat-release rate and the acoustic waves. The primary acoustic instability induces a small-amplitude, of around 8 mm, oscillatory motion across the chamber th…
The present work investigates forced ignition and oscillating propagation of spray flame in a mixture of fine ethanol droplets and air. Eulerian-Eulerian method with two-way coupling is used and detailed chemical mechanism is considered. Different droplet diameters and liquid fuel equivalence ratios (ER) are studied. The evaporation completion front (ECF) is defined to study the interactions between the evaporation zone and flame front. The gas composition at the flame front is quantified through an effective ER. The results show that the kernel trajectory is considerably affected by droplet s…
This work is dedicated to the analysis of the delicate details of the effect of upstream velocity fluctuations on the flame propagation speed. The investigation was carried out using the Sivashinsky model of cellularisation of hydrodynamically unstable flame fronts. We identified the perturbations of the steadily propagating flames which can be significantly amplified over finite periods of time. These perturbations were used to model the effect of upstream velocity fluctuations on the flame front dynamics and to study a possibility to control the flame propagation speed.
This study aims to build a theoretical model to describe the ignition process of spherical spray flame laden with fuel droplets under overall fuel-lean condition. Two characteristic fronts are introduced to reveal where the evaporation starts and ends in the ignition process. The results demonstrate that the flame has been strengthened with extra fuel droplet adding while the minimum ignition energy (MIE) is decreased. The evolution of the two evaporation fronts in the flame kernel and propagating branches has also be revealed coupled with the evaporation zone length.
Rocket engine combustors are prone to transverse instabilities that are characterized by large amplitude high frequency oscillations in the acoustic pressure and the heat release rate. We study the coupled interaction between the acoustic pressure and the CH* intensity oscillations in a 2D multi-element self-excited model rocket combustor during the transition from a stable state to thermoacoustic instability through intermittency. We show the emergence of synchronization between these oscillations from desynchronization through intermittent phase synchronization during the onset of thermoacou…
The problem of premixed flame propagation in wide horizontal tubes is revisited. Employing the on-shell description of flames with arbitrary gas expansion, a nonlinear second-order differential equation for the front position of steady flame is derived. Solutions to this equation, obtained numerically, reveal two distinct physical regimes of laminar flame propagation controlled by the strong baroclinic effect. They differ by the front shape and flame speed, the ratio of the total consumption rates in the two regimes being 1.4 to 1.8, depending on the value of the gas expansion coefficient. Com…
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…
Rayleigh-Taylor (RT) unstable flames are a key component of Type Ia and Iax supernovae explosions, but their complex hydrodynamics is still not well understood. These flames are affected not only by the RT instability, but also by the turbulence it generates. Both processes can increase the flame speed by stretching and wrinkling the flame. This makes it hard to choose a subgrid model for the flame speed in full star Type Ia or Iax simulations. Commonly used subgrid models get around this difficulty by assuming that either the RT instability or turbulence is dominant and sets the flame speed. …
The dynamics of flame propagation in systems with infinite Lewis number and spatially discretized sources of heat release is examined, which is applicable to the combustion of suspensions of fuel particles in air. The system is analyzed numerically using a one-dimensional heat equation with a source term for the reaction progress variable, which is specified to have zero diffusivity, and the model reveals a spectrum of flame-propagation regimes. For the case of a switch-type reaction rate and homogeneous media (continuous regime), the flame propagates steadily at a velocity in agreement with a…
The present study employs a linear global stability analysis to investigate buoyancy-induced flickering of axisymmetric laminar jet diffusion flames as a hydrodynamic global mode. The instability-driving interactions of the buoyancy force with the density differences induced by the chemical heat release are described in the infinitely fast reaction limit for unity Lewis numbers of the reactants. The analysis determines the critical conditions at the onset of the linear global instability as well as the Strouhal number of the associated oscillations in terms of the governing parameters of the p…
This paper shows the importance of considering the thermal state of a combustor to investigate or predict its thermoacoustic stability. This aspect is often neglected or regarded as less important than the effect of the operating parameters, such as thermal power or equivalence ratio, but under certain circumstances it can have a dramatic influence on the development of the instabilities. The paper presents experimental results collected from a combustor featuring a lean swirl-stabilized flame exhibiting thermoacoustic instability at some operating conditions. It is shown that this instability…
Direct Numerical Simulation of Thermoacoustically Unstable Flames Via Non-Drifting Acoustic Delay Characteristic Boundary Conditions
School of Engineering, University of Manchester（曼彻斯特大学工程学院）；Department of Mathematics, University of Manchester（曼彻斯特大学数学系）；School of Engineering, Cardiff University（卡迪夫大学工程学院）
The Lagrangian point of view is adopted to study turbulent premixed combustion. The evolution of the volume fraction of combustion products is established by the Reynolds transport theorem. It emerges that the burned-mass fraction is led by the turbulent particle motion, by the flame front velocity, and by the mean curvature of the flame front. A physical requirement connecting particle turbulent dispersion and flame front velocity is obtained from equating the expansion rates of the flame front progression and of the unburned particles spread. The resulting description compares favorably with…
Axisymmetric simulations of a liquid rocket engine are performed using a delayed detached-eddy-simulation (DDES) turbulence model with the Compressible Flamelet Progress Variable (CFPV) combustion model. Three different pressure instability domains are simulated: completely unstable, semi-stable, and fully stable. The different instability domains are found by varying the combustion chamber and oxidizer post length. Laminar flamelet solutions with a detailed chemical mechanism are examined. The $β$ Probability Density Function (PDF) for the mixture fraction and Dirac $δ$ PDF for both the press…
Analytical treatment of premixed flame propagation in vertical tubes with smooth walls is given. Using the on-shell flame description, equations describing quasi-steady flame with a small but finite front thickness are obtained and solved numerically. It is found that near the limits of inflammability, solutions describing upward flame propagation come in pairs having close propagation speeds, and that the effect of gravity is to reverse the burnt gas velocity profile generated by the flame. On the basis of these results, a theory of partial flame propagation driven by the gravitational field …
A theory of flame propagation in curved channels is developed within the framework of the on-shell description of premixed flames. Employing the Green function appropriate to the given channel geometry, an implicit integral representation for the burnt gas velocity is constructed. It is then used to derive an explicit expression for rotational component of the gas velocity near the flame front by successive separation of irrotational contributions. We prove that this separation can be performed in a way consistent with boundary conditions at the channel walls. As a result, the unknown irrotati…
