Flame Strain Rate Research Articles

Steady laminar stagnation flow NH[formula omitted]-H[formula omitted]-air flame at a plane wall: Flame extinction limit and its influence on the thermo-mechanical stress and corrosive behavior of wall materials

The steady laminar stagnation flow flame of NH3-H2-air gas mixture stabilized at a plane wall is numerically investigated. Its interaction with the wall with the consideration of heat loss is the focus of this work. The numerical study of the combustion system is performed by using the full chemical mechanism and detailed transport model including the differential diffusion and Soret effect. The simulation of the solid mechanics is based on the theory of isotropic linear thermo-elasticity. With the numerical simulation, it will be discussed how the wall material would change the flame stability in terms of extinction limit, and how the combustion system such as mixture composition, flame strain rate, and pressure would vary the thermo-mechanical stresses in the solid wall and the corrosive behavior at the surface of the wall.

Non-periodic shear layer instabilities driving local extinction in premixed ramjet cavity flames

The local extinction characteristics of turbulent premixed ethylene-air flames are experimentally investigated in a high-speed cavity combustor to provide a full characterization of the temporally evolving non-periodic hydrodynamic instabilities that result in local extinction. The local flame extinction phenomenon is captured temporally using high-speed particle image velocimetry (PIV) and broadband chemiluminescence. The evolution of the flame topology, turbulent structures, and flame strain rate are analyzed through the extinction process to distinguish the turbulent shear layer mechanisms contributing to flame instabilities and extinction. A frequency analysis of the extinction event was performed and found the flame extinction to occur at non-periodic temporal intervals. A further wavelet decomposition revealed the presence of a non-periodic hydrodynamic instability in the shear layer causing extinction. The instability mechanism is related to the stability of vortex pairing in the shear layer, which were found to correspond to large-amplitude wave generation on the flame surface. In instances of flame extinction, the vortex pairs exhibit a core deformation from an elliptic instability mechanism, leading eventually to the shredding of the vortical cores, which is the primary mechanism for excessive turbulent flame strain and resulting extinction. Although the local flame extinction mechanism is driven from flame and shear layer interactions, the condition for local flame extinction to occur requires the flame to interact with an elliptical instability in the shear layer. The results can guide strategies to enhance combustion stability, performance, and efficiency.

A universal Karlovitz number to predict the lean blowoff limits of stabilized premixed flames

A Karlovitz number formulation is defined to predict the stability and lean blowoff (LBO) limits of premixed bluff-body flames. The Karlovitz number relies on a newly defined flame timescale as a representative chemical time, where the flame timescale is identified from experimental measurements of LBO of premixed, propane-air, bluff-body flames in the literature. The timescale is first defined as a function of the extinction strain rate across the premixed flame, and satisfies a criterion for LBO to occur when Ka ≥ 1. Theoretical analysis shows that the defined chemical timescale based on the extinction strain rate can be recast using unstretched laminar flame properties, and reveals a coupling between premixed flame (τpf) and extinction strain rate timescales (τesr) commonly used in literature. The new chemical timescale and the coupling between τpf and τesr is explored for a variety of premixed fuel-air mixtures including propane, methane, ethylene, ammonia, and hydrogen. The timescale definition is found to uphold for all fuels except for hydrogen, which required a Lewis number correction to account for the effects of enhanced mass diffusion. The timescale is also validated against a variety of LBO data within literature. When coupled with a flow timescale, defined as recirculation zone residence time, the chemical timescale is able to collapse the LBO data to a nominally uniform Karlovitz number near unity for a range of flameholder geometries and Reynolds numbers. However, adjusting the flow timescale to estimate the inverse of the flame strain rate at LBO shifted the compiled data to a collapsed value of Ka ≈ 1, thereby realizing a unified Karlovitz (or Damköhler) theory to predict LBO. The advantage of the new Karlovitz model is its ability to provide an a priori method to predict the stability and LBO limits of premixed flames based on appropriately defined timescales.

Extinction of buoyant turbulent non-premixed flames under reduced oxygen concentrations

Local and global extinction of 10 kW buoyant turbulent non-premixed flames of methane from a 13.7 cm diameter burner under oxygen concentrations (OCs) from 20.9 % to 12 % are investigated using a combination of OH* chemiluminescence imaging and exhaust-gas sampling. Local flame extinction, indicated by holes or discontinuities in the OH* images, is only observed at OC lower than 17 %. For OC below 16 %, large-scale turbulent flow dynamics causes rapid creation of large extinction holes that do not reclose, and the overall combustion efficiency (η) decreases rapidly as local extinction becomes more probable. Direct observation of local extinction in buoyant turbulent flames provides important physical insights and validation data for models of extinction and re-ignition by distinguishing their respective contributions to η. We observe that local extinction events are associated with large-scale flow features, leading us to hypothesize that extinction behavior correlates with resolved-scale strain rates from large-eddy simulation (LES) in excess of the laminar extinction limit. This idea is investigated by performing LES for the target flame, extracting strain-rate statistics on the flame surface, and comparing these to both the extinction limits for canonical counterflow diffusion flames and to the experimentally observed extinction behavior. Results show that the cumulative distribution of turbulent flame strain rates up to the laminar extinction limit closely follows the measured OC dependence of η. This approach to η works well for different OCs and other fuels such as propane and ethylene, which suggests great potential for the development of computationally efficient extinction models for fire suppression.

Pressure effects on reactivity and extinction of n-dodecane diffusion cool flame

Low-temperature combustion at high pressure has gained increasing interest owing to the growing demand for clean and efficient propulsion and energy systems. In particular, cool flame structure, extinction limits, and fuel reactivities at high pressure are critical in affecting the engine performance at near-limit conditions. This paper investigates the effects of pressure on the cool flame extinction limit, structure, radical index, reactivity, and oxygen concentration dependence by experiments, analysis, and modeling. A large n-alkane, namely n-dodecane (n-C12H26), is selected to study its diffusion cool flame dynamics and reactivity in a high-pressure counterflow burner up to 10 atm. The experimental results show that higher pressure increases the cool flame extinction strain rates, and that the pressure-weighted extinction strain rate (aP) is proportional to the square of pressure, P2. A scaling analysis explains the relationship between the dependence of flame structure, heat release rate, and pressure-weighted cool flame strain rate on pressure. Furthermore, radical indexes at different pressures are measured by isolating the thermal and transport effects from the chemical contribution to diffusion cool flame extinction. The radical index clearly shows that the low-temperature reactivity increases with pressure. In addition, due to the critical role of multiple oxygen addition reactions in low-temperature chemistry, the relationship between the cool flame extinction limit and the oxygen concentration is explored. It is found that the cool flame extinction limits are proportional to the nth power of the oxygen concentration, [O2]n, and increasing pressure leads to stronger extinction limit dependence (larger n) on the oxygen concentration. The present experiment and detailed kinetic analysis show clearly that increasing pressure promotes the low-temperature chemistry including the oxygen addition reactions, while the scaling analysis explains well the experimental results.

Influence of small-scale turbulence on internal flamelet structure

Direct numerical simulation data obtained from a highly turbulent (Kolmogorov length scale is less than a laminar flame thickness by a factor of about 20) lean hydrogen–air complex chemistry flame are processed, with the focus of the study being placed on flame and flow characteristics conditioned to instantaneous local values cFx,t of the fuel-based combustion progress variable. By analyzing such conditioned quantities, the following two trends are documented. On the one hand, magnitudes of fluctuations of various local flame characteristics decrease with increasing the combustion progress variable, thus implying that the influence of small-scale (when compared to the laminar flame thickness) turbulence on internal flamelet structure is reduced as the flow advance from unburned reactants to combustion products. On the other hand, neither local turbulence characteristics (conditioned rms velocities, total strain, and enstrophy) nor local characteristics of flame–turbulence interaction (flame strain rate) decrease substantially from the reactant side to the product side. To reconcile these two apparently inconsistent trends, the former is hypothesized to be caused by the following purely kinematic mechanism: residence time of turbulence within a large part of a local flamelet is significantly shortened due to combustion-induced acceleration of the local flow in the direction normal to the flamelet. This residence-time reduction with increasing cF is especially strong in the preheat zone (cF<0.3) and the residence time is very short for 0.3<cF<0.8. Therefore, small-scale turbulence penetrating the latter zone is unable to significantly perturb its local structure. Finally, numerical results that indirectly support this hypothesis are discussed.

Flame–Solid Interaction: Thermomechanical Analysis for a Steady Laminar Stagnation Flow Stoichiometric NH3–H2 Flame at a Plane Wall

While thermomechanical analyses in solid and combustion processes in the gas phase are intensively studied separately, their interaction is less investigated. On one hand, the combustion system can be affected by the solid as a result of, for example, the heat conduction. On the other hand, the high-temperature flame can induce the thermal load in the solid, which significantly affects the mechanical stress field in the material. This work focuses on the coupling between the solid and flame and the combustion-induced mechanical stress in the material. The influence of the solid on the flame structures and properties and also the influence of the flame on the thermomechanical behavior in the solid are investigated. A stagnation flow NH3–H2–air flame to a plane wall is considered as a representative model, which is simple but also realistic in many engineering conditions. It is mainly found that an increase of the flame strain rate leads to an increase of thermomechanical stress in the wall, and the system pressure improves the flame stability against extinction but enlarges the induced thermomechanical stress at the same time. Furthermore, it is observed that the hydrogen content in the gas mixture does not affect the thermomechanical stress in the wall if the flames with different hydrogen additions are imposed with the same strain rate. On the basis of various flame parameters, it is also shown that the solid would also flow plastically under certain conditions, such as high pressures. From the viewpoint of the wall, it is mainly shown that the flame stability against extinction can be improved using wall materials with larger heat conductivities.

A numerical investigation on the formation of NO2 and N2O in laminar counterflow methane/n-heptane dual fuel flames

To understand the fundamental mechanisms of nitrogen dioxide (NO2) and nitrous oxide (N2O) formation in natural gas-diesel dual fuel combustion, a numerical study on NO2 and N2O formation in laminar counterflow methane (CH4)/n-heptane (n-C7H16) dual fuel flames is conducted. The results indicate that NO2 accounts for a small part of total NOx formation. The NO2 emission index first increases and then decreases with increasing CH4 addition and increases monotonically with increasing flame strain rate. The NO2 emission indices by different reactions are identified and analyzed. It is revealed that a small amount of CH4 addition increases the NO2 emission index because of increased HO2 generation while a larger amount of CH4 addition decreases the NO2 emission index due to the reduced NO production. Besides, it is concluded that decreasing flame temperature is beneficial to the formation of NO2, which explains the monotonic increase of NO2 emission index with increasing flame strain rate. Little N2O is formed in CH4/n-C7H16 dual fuel flames compared to NO and NO2. The N2O emission index decreases with increasing CH4 addition and flame strain rate. However, the relatively change of N2O emission index is quite small compared to that of NO2 emission index.

Fluctuation and extinction of laminar diffusion flame induced by external acoustic wave and source

Acoustic wave can destabilize the flame and has a potential in firefighting, but the influences of the sound source and its frequency are still poorly understood. This work applies a loudspeaker to extinguish a laminar diffusion propane flame of 5–25 mm high, where the local sound frequency is 50–70 Hz and sound pressure is 0.8–3.2 Pa (92.0–104.1 dB). Results reveal a constant flame pulsating displacement at the extinction limit, independent of the sound environment used. Such a flame pulsating displacement is found to be caused by the motion of the speaker membrane (or diaphragm) and its induced wind, which could be two orders of magnitude larger than the displacement of the air that transmits acoustic wave. Thus, under the influence of sound source, a critical flame strain rate, stretched by the pulsating airflow, can be formulated to characterize the blow-off limit better than the local sound pressure. The sound source with a lower frequency can produce larger pulsating displacements of both membrane and flame, and thus promoting extinction. This work improves the understanding of flame dynamics under the external sound field and source, and it helps establish a scientific framework for acoustic-based fire suppression technologies.

Turbulence-Driven Blowout Instabilities of Premixed Bluff-Body Flames

Bluff-body flame instabilities are experimentally investigated under varying turbulence conditions during lean blowout. For all turbulence conditions, the blowout process is induced through a temporal reduction of the fuel flow rate to capture the flame-flow dynamics approaching blowout. Simultaneous high-speed particle image velocimetry (PIV), stereoscopic PIV, and C2*/CH* chemiluminescence imaging are employed, along with an independent CH* imaging system, to capture flame-flow instabilities. Proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) techniques are used to identify prominent flame oscillations and evaluate recurring spatiotemporal modes during blowout. The results reveal that the dominant flame oscillations and wrinkling characteristics are directly dependent on the turbulence conditions in the combustor. Specifically, the flame-flow oscillations are strongly coupled with the integral length scales, which were able to collapse the oscillation frequencies to a unified value. The turbulence-driven flame-flow oscillations are shown to largely impact the magnitude, temporal evolution, and oscillatory behavior of the flame strain rate. As the turbulence intensity is increased, the oscillation of the flame strain rate increases in frequency, making it more likely for localized extinctions to occur. Additionally, the magnitude of the flame strain rate increases at high turbulence intensities and accelerates the lean blowout process.

Modeling of Natural Gas Composition Effect on Low NOx Burners Operation in Heavy Duty Gas Turbine

Abstract This paper addresses the impact of natural gas composition on both the operability and emissions of lean premixed gas turbine combustion system. This is an issue of growing interest due to the challenge for gas turbine manufacturers in developing fuel-flexible combustors capable of operating with variable fuel gases while producing very low emissions at the same time. Natural gas contains primarily methane (CH4) but also notable quantities of higher order hydrocarbons such as ethane (C2H6) can also be present. A deep understanding of natural gas combustion is important to obtain the highest combustion efficiency with minimal environmental impact. For this purpose, Large Eddy Simulations of an annular combustor sector equipped with a partially premixed burner are carried out for two different natural gas compositions with and without including the effect of flame strain rate and heat loss resulting in a more adequate description of flame shape, thermal field, and extinction phenomena. Promising results, in terms of NOx, compared against available experimental data, are obtained including these effects on the flame brush modeling, enhancing the fuel-dependency under nonadiabatic condition.

Study on counterflow premixed flames using high concentration ammonia mixed with methane

In the present study, combustion characteristics of ammonia/methane were evaluated computationally utilizing counterflow premixed ammonia/methane/air flames at normal temperature and pressure conditions. Investigations were carried out over a wide range of flame strain rates, fuel blend compositions and equivalence ratios. Extinction characteristic results show that methane addition and equivalence ratio have significant impact on the extinction limits of the stretched flames. With more methane in the ammonia/methane fuel blends, the flame sustainability to high stretch rate substantially increases. Flame structures of the stretched flames were then investigated to have a deep insight into the combustion process of the ammonia/methane premixed combustion. Results show that temperature, heat release rate and important intermediate radicals of the flames are enhanced. However, the considerably increased carbon oxides and nitrogen oxides emissions suggest emission reduction is a key issue in the ammonia/methane combustion process. Pathway and sensitivity analyses reveal the chemistry of NOx emission characteristics of different ammonia/methane flames.

Coupling RSM with soot model for the study of soot formation in a momentum-dominated strained jet flames

This paper presents a comparison between the numerically determined soot volume fraction (SVF) in a momentum-dominated turbulent diffusion strained jet flames burning ethylene/hydrogen/nitrogen mixture in air with experimental results. The soot inception model used is based on the formation rate of two or three ring poly aromatic hydrocarbon with C6H6 as the soot precursor. Second-moment closure Reynolds stress method turbulent model is used in conjunction with the governing equation of mass, momentum and energy. The turbulent combustion kinetic chemistry interaction is modeled by choosing a chemical equilibrium non-premixed combustion model along with the species inlet diffusion probability density function (PDF). Soot radiation source term like P-1 radiation model is also included along with the turbulent combustion model. The soot turbulence interaction invoked uses single-variable PDF based on the temperature and mixture fraction (Z) for measurement of flame lift-off height, flame length and radiative heat loss. Equilibrium-based Lee soot oxidation model is chosen to estimate the hydroxyl (OH) and O2 species for the oxidation of soot particles. The numerical solutions for each of the experimental configurations are proposed by Mahmoud and co-workers for three different strained flames (4000 s−1, 7300 s−1, and 12,900 s−1). In each discretized finite volume cell, using a quadratic upstream interpolation for convective kinematics algorithm in spatial coordinate and time-bounded second-order accurate in temporal coordinate solution is obtained. All the above turbulence combustion interaction models are iterated with unit Courant–Friedrichs–Lewy condition. It is noted that the mixture fraction (Z) PDF used is very sensitive to the chosen turbulence combustion soot interaction models. Also, it is observed that the simulated outputs are in good agreement with the measured experimental data in terms of SVF, temperature both axially and radially. SVF increases with a decrease in the flame strain rate and shows the reverse trend in radially integrated soot volume reaction. In agreement with experiments, soot productivity shows a linear relationship in momentum-dominated flame with an increase in the strain rates for soot productivity, maximum mean SVF, exit Froude number, exit C2H4 flow rate.

Mechanisms of flame extinction and lean blowout of bluff body stabilized flames

Lean flame blowout is investigated experimentally within a high-speed combustor to analyze the temporal extinction dynamics of turbulent premixed bluff body stabilized flames. The lean blowout process is induced through fuel flow reduction and captured temporally using simultaneous high-speed particle imaging velocimetry (PIV) and CH* chemiluminescence. The evolution of the flame structure, flow field, and the resulting flame strain rate are analyzed throughout extinction to distinguish the physical mechanisms of blowout. The flame–vortex dynamics are found to be the main driving mechanism of flame extinction; namely, a reduction of the flame-generated vorticity coupled with an increase in the downstream shear layer vorticity. The vorticity dynamics are linked to hydrodynamic instabilities that vary as a function of the decreasing equivalence ratio. A frequency analysis is performed to characterize the dynamic changes of the hydrodynamic instability modes during flame extinction. Various bluff body inflow velocity regimes are investigated to further characterize the extinction instability modes. Both equivalence ratio and flow-driven instabilities are captured through a universal definition of the Strouhal number for the reacting bluff body flow. Finally, a Karlovitz number-based criterion is developed to consistently predict the onset of global extinction for the different inflow velocity regimes.

Characteristics of NOx emissions of counterflow nonpremixed water-laden methane/air flames

A computational investigation on the characteristics of nitrogen oxides (NOx) emissions for counterflow nonpremixed water (H2O)-laden methane (CH4)/air flames is conducted since a detailed observation of NOx formation for fuel having naturally high H2O vapor content is necessary. Using a detailed kinetic mechanism, NOx emissions are predicted for low and high flame strain rates (a), and the reaction paths are investigated. With H2O addition NOx emissions are reduced due to the chemical process as well as the thermal process such as diluting and cooling effects, the latter is more dominant than the former in NOx reduction, and the thermal and prompt NO mechanisms become less dominant for the chemical process. With increasing a, NOx emissions are also reduced, and it is mainly due to the thermal process. Reaction NH + O = NO + H in the prompt pathway is the major reaction step that results in reducing NO emissions via the chemical process due to H2O addition for both low- and high-stretched flames, though reaction N + OH = NO + H in the thermal pathway is also the major reaction step for the high-stretched flames. In addition, for the high-stretched flames the NO2 pathway in NO production becomes relatively more important with H2O addition.

Combustion characteristics of gaseous inverse O2/H2 coaxial jet flames in a single-element model combustor

To effectively design hydrogen (H2)/oxygen (O2) liquid rocket engines through understanding the combustion characteristics of H2/O2 bipropellants, fundamental studies for the bipropellants in different phases are needed. This study is focused on the combustion characteristics of inverse gaseous O2/H2 coaxial jet flames in a single-element model combustor as a preliminary step for succeeding studies of injection at different phases in the combustor, visualizing flame structure by direct imaging, OH∗ chemiluminescence and OH planar laser-induced fluorescence. With increasing Reynolds number (Re), the frequency of occurrence of the local flame extinction increases and the length of the disconnected OH reaction zone is extended. The OH layer thickness increases downstream, while it is almost constant where the local flame extinction occurs and decreases with increasing Re due to the enhanced strain and scalar-dissipation rates. The excessive flame wrinkledness increases the local flame strain rate and results in the local flame extinction, exhibiting the tendency of increasing and then decreasing flame surface density with increasing Re. The probability density function of OH intensity quantifies the fluctuation intensity of OH radicals and the possibility of the local flame extinction. A useful database is provided for modeling the combustion of H2/O2 bipropellants under different phases.

Effects of pressure on structure and extinction limits of counterflow nonpremixed water-laden methane/air flames

Structure and extinction limits of counterflow nonpremixed water (H2O)-laden methane (CH4)/air flames at various pressures are computationally investigated to better understand combustion processes of fuel having naturally high H2O (vapor) content under elevated pressures. Using a detailed kinetic mechanism and a statistical narrow-band radiation model, the flame structure and extinction limits are predicted for elevated pressures and a wide range of flame strain rates and compared with those at atmospheric pressure. Results show that with increasing pressure the maximum flame temperature increases and the extinction limits are generally extended due to the reduced amount of dissociation and the enhanced radiation reabsorption of H2O, indicating that flames can sustain more H2O vapor at elevated pressure. The concentration of active radicals and the flame thickness decrease with increasing pressure. The observed flammable range of the H2O to CH4 molar ratio at elevated pressures is comparable to that found in self-sustained combustion of CH4 hydrates at atmospheric pressure, and the chemical effects of H2O addition on flame structure are insignificant. Elevated pressure enhances the formation of soot precursors such as acetylene (C2H2), implying an opposite tendency from the water addition effects.

Local quenching phenomena of a lean premixed flat flame impinging with a pulsating air jet

Local quenching phenomena of a lean methane air premixed flat flame formed horizontally in a wall stagnating flow impinging with a pulsating air jet has been investigated experimentally. The burner system consists of 40mm inverted nozzle burner and a solid wall with 8mm diameter air jet placed in line vertically. The pulsating frequencies set up to 100Hz while the jet intensities generate up to 6 m/s by a loud speaker. Approximately '00mm disk shape flame front is curved by the pulsating air jet and the air jet impacting point is locally quenched. The fuel concentration of quenching start condition increases with increasing the intensity of air jet, because the increased jet intensity linked with the flame strain rate gain. For weak jet intensity range, the quenching hole becomes directly to develop the whole flame extinction. On the other hand, for moderate or strong jet condition, the flame can recover from the local quenching phenomena. In this condition, once the quenching hole creates, but the hole may close by the flame propagation or reigniting process. Then, the whole flame extinction limits are lower than no jet impacting condition depending on the circumstances.

Effects of ammonia substitution on extinction limits and structure of counterflow nonpremixed hydrogen/air flames

The potential of partial ammonia substitution to improve the safety of hydrogen use was evaluated computationally, using counterflow nonpremixed ammonia/hydrogen/air flames at normal temperature and pressure. The ammonia-substituted hydrogen/air flames were considered using a recent kinetic mechanism and a statistical narrow-band radiation model for a wide range of flame strain rates and the extent of ammonia substitution. The effects of ammonia substitution on the extinction limits and structure, including nitrogen oxide (NO x ) and nitrous oxide (N 2O) emissions, of nonpremixed hydrogen/air flames were investigated. Results show reduction of the high-stretch extinction (i.e., blow-off) limits, the maximum flame temperature and the concentration of light radicals (e.g., H and OH) with ammonia substitution in hydrogen/air flames, supporting the potential of ammonia as a carbon-free, clean additive for improving the safety of hydrogen use in nonpremixed hydrogen/air flames. For high-stretched flames, however, NO x and N 2O emissions substantially increase with ammonia substitution even though ammonia substitution reduces flame temperature, implying that chemical effects (rather than thermal effects) of ammonia substitution on flame structure are dominant. Radiation effects on the extinction limits and flame structure are not remarkable particularly for high-stretched flames.

The Problems of the Turbulent Burning Velocity

The paper reviews the practical problems in measuring a turbulent burning velocity that gives the mass rate of burning. These largely centre on identifying an appropriate flame surface to associate with the turbulent burning velocity, u t , and the density of the unburned mixture. Such a flame surface has been identified, in terms of the mean reaction progress variable, $\bar {c}$ , for explosive flame propagation in a fan-stirred bomb. Measurement of $\bar {c}$ makes possible an estimation of the flame surface density, Σ, from the relationship ${\it \Sigma} =k\bar {c}\left( {1-\bar {c}} \right)$ . It is shown that in such explosions, mass rates of burning derived from the measured total flame surface area agreed well with those found from the measured turbulent burning velocity. Flamelet considerations identify appropriate dimensionless correlating parameters for u t . As a result, correlations of turbulent burning velocity divided by the effective rms turbulent velocity, are plotted against the turbulent Karlovitz stretch factor, K, for different values of the Markstein number for flame strain rate, Masr. These plots cover a wide range of variables, including pressure and fuels, and are indicative of different regimes of turbulent combustion. At the lower values of K, there is some evidence of increases in u t and k due to high-frequency flame surface wrinkling arising from flame instabilities. These increase as Masr becomes more negative. It is found from the developed value of the mean flame surface density throughout the flame brush that, to a first approximation, an increase in u t for a given mixture is accompanied by a proportional increase in the volume of the brush. The analysis shows that the volume fraction of the turbulent flame brush that is reacting is quite small.