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.     

Strain rates,flow patterns and flame surface densities in hydrodynamically unstable,weakly turbulent premixed flames

Recent numerical and experimental studies have unveiled a potentially marked difference between the laminar as well as turbulent propagation of premixed flames exhibiting Darrieus–Landau (DL) (or hydrodynamic) instabilities from flames for which instabilities are inhibited. In this study we utilize two-dimensional numerical simulations of slot burner flames as well as experimental Propane–Air Bunsen flames to analyse differences in turbulent propagation, strain rate and induced flow patterns of hydrodynamically stable and unstable flames. We also investigate the effects of hydrodynamic instability on quantities which are directly related to reaction rate closure models, such as flame surface density and stretch factor. A clear enhancement of turbulent flame speed can be observed for unstable flames, generally mitigated at higher turbulence intensity, which is attributed to a flame area increase induced by the characteristic cusp-like DL-induced corrugation, absent in stable flames, which occurs concurrently and in synergy with turbulent wrinkling. Unstable flames also exhibit, both numerically and experimentally, a different correlation between strain rate and flame curvature and are observed to give rise to a channeling of the induced flow in the fresh mixture. Conditionally averaged flame surface density is also observed to attain smaller values in unstable flames, as a result of the thicker turbulent flame brush, indicating that closure models should incorporate instability-related parameters in addition to turbulence-related parameters.     

Characteristic patterns of thermodiffusively unstable premixed lean hydrogen flames

Large-scale two-dimensional numerical simulations of thermodiffusively unstable, lean, premixed hydrogen flames have been performed using detailed finite rate chemistry to analyze flame intrinsic scales. The simulations feature a long integration time and large domain sizes to rule out effects of confinement on the dynamics of the flame front. For sufficiently large domain sizes, the total consumption speed of the flame is found to become independent of the domain size. An assessment of the characteristic scales of the flame front corrugation reveals the existence of a smallest and a largest flame intrinsic length scale. The smallest length manifests itself by local cusps, which lead to the formation of characteristic cells along the flame front. Their size is remarkably close to the most unstable wavelength predicted by a linear stability analysis of the flame front evolution in the linear regime. Independently of the domain size, a specific largest flame intrinsic structure, here referred to as flame finger, emerges from the interaction of multiple small-scale cusps. Thermodiffusively unstable flames are found to periodically form and destroy these flame fingers, but the formation of a global cusp that is known to emerge for purely hydrodynamically unstable flames is suppressed. The finite size of the largest scale fingers is explained by an instability in their movement. As they proceed towards the unburnt mixture, they tend to tilt and move laterally, thereby eventually being incorporated again by the rest of the flame. This behavior arises from the interaction of the flame fingers and the diverging velocity field ahead of them. Finally, the effect of equivalence ratio and unburnt gas temperature is investigated showing that flame fingers are found to develop only in case of a thermodiffusively unstable flame.     

Cellular instabilities of expanding hydrogen/propane spherical flames at elevated pressures: theory and experiment

An experimental and theoretical investigation of the onset of cellular instabilities on spherically expanding flames in mixtures of hydrogen and propane in air at elevated pressures was conducted. Critical conditions for the onset of instability were measured and mapped out over a range of pressures and mixture compositions. An asymptotic theory of hydrodynamic and diffusional-thermal cell development on flames in mixtures comprised of two scarce fuels burning in air was also formulated. Predicted values of Peclet number, defined as the flame radius at the onset of instability normalized by the flame thickness, were shown to compare favorably with the experimentally measured values.     

Effects of cryogenic temperature on premixed hydrogen/air flame propagation in a closed channel

As a carbon-free fuel, hydrogen has received significant attention recently since it can help enable low-carbon-economy. Hydrogen has very broad flammability range and very low minimum ignition energy, and thereby there are severe safety concerns for hydrogen transportation and utilization. Cryo-compressed hydrogen is popularly used in practice. Therefore, it is necessary to investigate the combustion properties of hydrogen at extremely low or cryogenic temperatures. This study aims to assess and interpret the effects of cryogenic temperature on premixed hydrogen/air flame propagation and acceleration in a thin closed channel. Different initial temperatures ranging from normal temperature (T₀ = 300 K) to cryogenic temperature (T₀ = 100 K) are considered. Both one- and two-dimensional hydrogen/air flames are investigated through transient simulations considering detailed chemistry and transport. It is found that when the initial temperature decreases from T₀ = 300 K to T₀ = 100 K, the expansion ratio and equilibrium pressure both increase substantially while the laminar flame speeds relative to unburned and burned gasses decrease moderately. The one-dimensional flame propagation is determined by laminar flame speed and thereby the combustion duration increases as the initial temperature decreases. However, the opposite trend is found to happen to two-dimensional flame propagation, which is mainly controlled by the flame surface area increase due to the no-slip side wall constraint and flame instability. Based on the change in flame surface area, three stages including the initial acceleration, steady burning and rapid acceleration are identified and investigated. It is demonstrated that the large expansion ratio and high pressure rise at cryogenic temperatures can significantly increase the flame surface area in early stage and promote both Darrieus-Landau instability (hydrodynamic instability) and Rayleigh-Taylor instability in later stage. These two instabilities can substantially increase the flame surface area and thereby accelerate flame propagation in hydrogen/air mixtures at cryogenic temperatures. The present study provides useful insights into the fundamental physics of hydrogen flames at extremely low temperatures, and is closely related to hydrogen safety.     

On polyhedral structures of lean methane/hydrogen Bunsen flames: Combined experimental and numerical analysis

In premixed flame propagation of lean hydrogen or hydrogen-enriched blends, both hydrodynamic and thermo-diffusive instabilities are governing the flame front shape and affect its propagation velocity. As a result, different types of cellular patterns can occur along the flame front in a laminar scenario. In this context, an interesting phenomenon is the formation of polyhedral flames which can be observed in a Bunsen burner. It is the objective of this work to systematically characterize the polyhedral structures of premixed methane/hydrogen Bunsen flames in a combined experimental and numerical study. A series of lean flames with hydrogen content varying between 20 and 85% at two equivalence ratios is investigated. The experiments encompass chemiluminescence imaging together with Planar Laser-induced Fluorescence (PLIF) measurements of the OH radical. Characteristic cell sizes are quantified from the experiments and related to the characteristic length scales obtained from a linear stability analysis. In the experiments, it is observed that the cell sizes at the base of the polyhedral Bunsen flames decrease almost linearly with hydrogen addition and only a weak dependence on the equivalence ratio is noted. These trends are well reflected in the numerical results and the length scale comparison further shows that the wavelength with the maximum growth rate predicted by the linear stability analysis is comparable to the cell size obtained from the experiment. The correlation between the experimental findings and the linear stability analysis is discussed from multiple perspectives considering the governing time and length scales, furthermore drawing relations to previous studies on cellular flames.     

稀甲烷/氢气预混湍流传播火焰实验研究

本文采用定容湍流燃烧弹获取了稀甲烷/氢气/空气在强湍流条件下的火焰发展历程,研究了湍流火焰在负马克斯坦数条件下的传播特性.结果表明,湍流火焰呈现自相似传播特性,即使在强湍流条件下,湍流传播火焰仍然会受到不稳定性的影响.并且随着马克斯坦数的减小,不稳定性对湍流传播火焰的影响增强。同时,本文获得一种新的湍流燃烧速度拟合公式,包含了负马克斯坦数条件下不稳定性对湍流燃烧速度的影响。     

Large eddy simulation of piloting effects on turbulent swirling flames

Pilot flames, created by additional injectors of pure fuel, are often used in turbulent burners to enhance flame stabilization and reduce combustion instabilities. The exact mechanisms through which these additional rich zones modify the flame anchoring location and the combustion dynamics are often difficult to identify, especially when they include unsteady hydrodynamic motion. This study presents Large Eddy Simulations (LES) of the reacting flow within a large-scale gas turbine burner for two different cases of piloting, where either 2 or 6% of the total methane used in the burner is injected through additional pilot flame lines. For each case, LES shows how the pilot fuel injection affects both flame stabilization and flame stability. The 6% case leads to a stable flame and limited hydrodynamic perturbations in the initial flame zone. The 2% case is less stable, with a small-lift-off of the flame and a Precessing Vortex Core (PVC) in the cold stabilization zone. This PVC traps some of the lean cold gases issuing from the pilot passage stream, changes the flame stabilization point and induces instability.     

Detailed simulation of laser-induced ignition,spherical-flame acceleration,and the origins of hydrodynamic instability

Ignition of a lean hydrogen–oxygen premixture by focused-laser-induced breakdown and subsequent three-dimensional expanding-flame instabilities are simulated in high detail. Both diffusive–thermal and hydrodynamic (Darrieus–Landau) instabilities are active and accelerate the flame expansion. The fluid is a partially-ionized gas in local thermodynamic equilibrium with detailed kinetics and transport models, starting from initial conditions from an auxiliary simulation based on a two-temperature local thermodynamic non-equilibrium model. After the decay of the initial laser-induced plasma, the r ～ t^1.5 growth in time of the flame radius matches theory and experimental observations. Based on hydrodynamic theory for spherical-flame propagation, a global Karlovitz number is defined as the ratio of the hydrodynamic to flame-distortion time scales. It initially increases during the diffusive–thermal instability stage, then with the onset of significant baroclinic torque, this trend reverses, with vorticity production becoming the dominant mechanism of instability.     

How fast can we burn, 2.0

We review the state of the art in measurements and simulations of the behavior of premixed laminar and turbulent flames, subject to differential diffusion, stretch and curvature. The first part of the paper reviews the behavior of premixed laminar flames subject to flow stretch, and how it affects the accuracy of measurements of unstrained laminar flame speeds in stretched and spherically propagating flames. We then examine how flow field stretch and differential diffusion interact with flame propagation, promoting or suppressing the onset of thermodiffusive instabilities. Secondly, we survey the methodology for and results of measurements of turbulent flame speeds in the light of theory, and identify issues of consistency in the definition of mean flame speeds, and their corresponding mean areas. Data for methane at a single operating condition are compared for a range of turbulent conditions, showing that fundamental issues that have yet to be resolved for Bunsen and spherically propagating flames. Finally, we consider how the laminar flame scale response of flames to flow perturbations interacting with differential diffusion leads to very different outcomes to the overall sensitivity of the burning rate to turbulence, according to numerical simulations (DNS). The paper concludes with opportunities for future measurements and model development, including the perennial recommendation for robust archival databases of experimental and DNS results for future testing of models.     

Stabilization, propagation and instability of tribrachial triple flames

A tribrachial (or triple) flame is one kind of edge flame that can be encountered in nonpremixed mixing layers, consisting of a lean and a rich premixed flame wing together with a trailing diffusion flame all extending from a single point. The flame could play an important role on the characteristics of various flame behaviors including lifted flames in jets, flame propagation in two-dimensional mixing layers, and autoignition fronts. The structure of tribrachial flame suggests that the edge is located along the stoichiometric contour in a mixing layer due to the coexistence of all three different types of flames. Since the edge has a premixed nature, it has unique propagation characteristics. In this review, the propagation speed of tribrachial flames will be discussed for flames propagating in mixing layers, including the effects of concentration gradient, velocity gradient, and burnt gas expansion. Based on the tribrachial edge structure observed experimentally in laminar lifted flames in jets, the flame stabilization characteristics including liftoff height, reattachment, and blowout behaviors and their buoyancy-induced instability will be explained. Various effects on liftoff heights in both free and coflow jets including jet velocity, the Schmidt number of fuel, nozzle diameter, partial premixing of air to fuel, and inert dilution to fuel are discussed. Implications of edge flames in the modeling of turbulent nonpremixed flames and the stabilization of turbulent lifted flames in jets are covered.     

Turbulent propagation of premixed flames in the presence of Darrieus–Landau instability

We investigate the role played by hydrodynamic instability in the wrinkled flamelet regime of turbulent combustion, where the intensity of turbulence is small compared to the laminar flame speed and the scale large compared to the flame thickness. To this end the Michelson–Sivashinsky (MS) equation for flame front propagation in one and two spatial dimensions is studied in the presence of uncorrelated and correlated noise representing a turbulent flow field. The combined effect of turbulence intensity, integral scale, and an instability parameter related to the Markstein length are examined and turbulent propagation speed monitored for both stable planar flames and corrugated flames for which the planar conformation is unstable. For planar flames a particularly simple scaling law emerges, involving quadratic dependence on intensity and a linear dependence on the degree of instability. For corrugated flames we find the dependence on intensity to be substantially weaker than quadratic, revealing that corrugated flames are more resilient to turbulence than planar flames. The existence of a threshold turbulence intensity is also observed, below which the corrugated flame in the presence of turbulence behaves like a laminar flame. We also analyze the conformation of the flame surface in the presence of turbulence, revealing primary, large-scale wrinkles of a size comparable to the main corrugation. When the integral scale is much smaller than the characteristic corrugation length we observe, in addition to primary wrinkles, secondary small-scale wrinkles contaminating the surface. The flame then acquires a multi-scale, self-similar conformation, with a fractal dimension, for one-dimensional flames, plateauing at 1.23 for large intensities. The existence of an intermediate integral scale is also found at which the turbulent speed is maximized. When two-dimensional flames are subject to turbulence, the primary wrinkling patterns give rise to polyhedral-cellular structures which bear a very close resemblance to those observed in experiments on hydrodynamically unstable expanding spherical flames.     

Impact of the gravity field on stability of premixed flames propagating between two closely spaced parallel plates

The stability of a planar flame front propagating between two parallel adiabatic plates inclined at an arbitrary angle is investigated in the frame of narrow-channel approximation. It is demonstrated that buoyancy forces can suppress the hydrodynamic (Darrieus–Landau) and cellular (diffusive-thermal) instabilities for sufficiently large value of the gravity parameter for the case of downward-propagating flames. The stability analysis reveals that in the case of oscillatory diffusive-thermal instability, the flame front cannot be stabilized in the similar way. Finally, the stability results are compared satisfactorily with unsteady numerical simulations.     

Measurements of burning velocities of dimethyl ether and air premixed flames at elevated pressures

Laminar burning velocities of dimethyl ether (DME) and air premixed flames at elevated pressures up to 10 atm were measured by using a newly developed pressure-release type spherical bomb. The measurement system was validated using laminar burning velocities of methane–air flames. A comparison with the previous experimental data shows an excellent agreement and demonstrates the accuracy and reliability of the present experimental system. The measured flame speeds of DME–air flames were compared with the previous experimental data and the predictions using the full and reduced mechanisms. At atmospheric pressure, the measured laminar burning velocities of DME–air flames are in reasonable agreement with the previous data from spherical bomb method, but are much lower than both predictions and the experimental data of the PIV based counterflow flame measurements. The laminar burning velocities of DME–air flames at 2, 6, and 10 atm were also measured. It was found that flame speed decreases considerably with the increase of pressure. Moreover, the measured flame speeds are also lower than the predictions at high pressures. In addition, experiments showed that at high pressures the rich DME–air flames are strongly affected by the hydrodynamic and thermal-diffusive instabilities. Markstein lengths and the overall reaction order at different equivalence ratios were extracted from the flame speed data at elevated pressures. Sensitivity analysis showed that reactions involving methyl and formyl radicals play an important role in DME–air flame propagation and suggested that systematic modification of the reactions rates associated with methyl and formyl formations are necessary to reduce the discrepancies between predictions and measurements.     

Large scale effects in weakly turbulent premixed flames

In this study we numerically investigate large scale premixed flames in weakly turbulent flow fields. A large scale flame is classified as such based on a reference hydrodynamic lengthscale being larger than a neutral (cutoff) lengthscale for which the hydrodynamic or Darrieus–Landau (DL) instability is balanced by stabilizing diffusive effects. As a result, DL instability can develop for large scale flames and is inhibited otherwise. Direct numerical simulations of both large scale and small scale three-dimensional, weakly turbulent flames are performed at constant Karlovitz and turbulent Reynolds number, using two paradigmatic configurations, namely a statistically planar flame and a slot Bunsen flame. As expected from linear stability analysis, DL instability induces its characteristic cusp-like corrugation only on large scale flames. We therefore observe significant morphological and topological differences as well as DL-enhanced turbulent flame speeds in large scale flames. Furthermore, we investigate issues related to reaction rate modeling in the context of flame surface density closure. Thicker flame brushes are observed for large scale flames resulting in smaller flame surface densities and overall larger wrinkling factors.     

Effect of Soret diffusion on lean hydrogen/air flames at normal and elevated pressure and temperature

The influence of Soret diffusion on lean premixed flames propagating in hydrogen/air mixtures is numerically investigated with a detailed chemical and transport models at normal and elevated pressure and temperature. The Soret diffusion influence on the one-dimensional (1D) flame mass burning rate and two-dimensional (2D) flame propagating characteristics is analysed, revealing a strong dependency on flame stretch rate, pressure and temperature. For 1D flames, at normal pressure and temperature, with an increase of Karlovitz number from 0 to 0.4, the mass burning rate is first reduced and then enhanced by Soret diffusion of H₂ while it is reduced by Soret diffusion of H. The influence of Soret diffusion of H₂ is enhanced by pressure and reduced by temperature. On the contrary, the influence of Soret diffusion of H is reduced by pressure and enhanced by temperature. For 2D flames, at normal pressure and temperature, during the early phase of flame evolution, flames with Soret diffusion display more curved flame cells. Pressure enhances this effect, while temperature reduces it. The influence of Soret diffusion of H₂ on the global consumption speed is enhanced at elevated pressure. The influence of Soret diffusion of H on the global consumption speed is enhanced at elevated temperature. The flame evolution is more affected by Soret diffusion in the early phase of propagation than in the long run due to the local enrichment of H₂ caused by flame curvature effects. The present study provides new insights into the Soret diffusion effect on the characteristics of lean hydrogen/air flames at conditions that are relevant to practical applications, e.g. gas engines and turbines.     

Lean or ultra-lean stretched planar methane/air flames

Lean premixed combustion has potential advantages of reducing pollutants and improving fuel economy. In some lean engine concepts, the fuel is directly injected into the combustion chamber resulting in a distribution of lean fuel/air mixtures. In this case, very lean mixtures can burn when supported by hot products from more strongly burning flames. This study examines the downstream interaction of opposed jets of a lean-limit CH₄/air mixture vs. a lean H₂/air flame. The CH₄ mixtures are near or below the lean flammability limit. The flame composition is measured by laser-induced Raman scattering and is compared to numerical simulations with detailed chemistry and molecular transport including the Soret effect. Several sub-limit lean CH₄/air flames supported by the products from the lean H₂/air flame are studied, and a small amount of CO₂ product (around 1% mole fraction) is formed in a “negative flame speed” flame where the weak CH₄/air mixture diffuses across the stagnation plane into the hot products from the H₂/air flame. Raman scattering measurements of temperature and species concentration are compared to detailed simulations using GRI-3.0, C₁, and C₂ chemical kinetic mechanisms, with good agreement obtained in the lean-limit or sub-limit flames. Stronger self-propagating CH₄/air mixtures result in a much higher concentration of product (around 6% CO₂ mole fraction), and the simulation results are sensitive to the specific chemical mechanism. These model-data comparisons for stronger CH₄/air flames improve when using either the C₂ or the Williams mechanisms.     

Suppression of self-excited thermoacoustic instabilities by convective-acoustic interference

In this paper we demonstrate direct suppression of self-excited thermoacoustic instabilities over a range of operating conditions using targeted convective-acoustic interference. Premixed hydrogen enriched methane-air flames were confined in a cylindrical pipe resulting in self-excited instabilities that corresponded to the quarter wave mode of the pipe. To suppress the instability, the phenomenon of lock-in (synchronisation) between the acoustic mode and vortex shedding from a set of cylinders placed upstream was used to produce destructive interference and suppress the self-excited modes. This was done by varying the location of the cylinders to control the convective time-delay between the convective and acoustic modes so that their combined effect on the flame response was tuned to suppress the global fluctuation of the heat release rate. This leads to a reduction in the limit-cycle amplitude and stable operation without a significant change to the flame structure. Measurements were taken over a wide range of equivalence ratios to demonstrate that the method is capable of stabilising the system for all conditions. Using a methodology which relies on time-delays related to hydrodynamic instability, rather than flame-related parameters, enables its application to fuel-flexible systems, often designed to operate within a wide range of power outputs.