The role of duct thickness on the quenching process of premixed flame propagation

The propagation of premixed laminar flame in ducts of circular cross-section considering a thermal-diffusive model is investigated numerically. Heat losses by conduction to the channels walls are taken into account using the thermally thin wall regime. The effects and the relationship between thickness and diameter of the tube with the flame speed propagation are studied and the quenching condition is obtained as a function of the heat-loss parameter. The mathematical model employs the axisymmetric energy and species equations. The calculations are based on a two-step chemistry, with an Arrhenius, energetically neutral, radical production reaction followed by an exothermic radical recombination reaction. For large values of the heat-loss parameter, the wall temperature is close to the free stream temperature and all the heat losses through the wall are convected away. No heat feedback occurs. On the other hand, for small values of the heat-loss parameter, a feedback mechanism occurs by transferring heat from the burned gas to the fresh mixture along the tube wall. For values of the heat-loss parameter of order unity, the heat feedback mechanism is able to sustain the flame propagation and the quenching condition disappears, producing an almost planar flame front as the propagation velocity reduces. For this two-step reaction mechanism, the radical species behaviour at the duct walls seems to have negligible effect on the quenching process.     

Measurements of three-dimensional mean flame surface area ratio in turbulent premixed Bunsen flames

A data processing scheme with particular emphasis on proper flame contour smoothing is developed and applied to measure the three-dimensional mean flame surface area ratio in turbulent premixed flames. The scheme is based on the two-sheet imaging technique such that the mean flame surface area ratio is an average within a window covering a finite section of the turbulent flame brush. This is in contrast to the crossed-plane tomograph technique which applies only to a line. Two sets of Bunsen flames have been investigated in this work with the turbulent Reynolds number up to 4000 and the Damköhler number ranging from less than unity to close to 10. The results show that three-dimensional effects are substantial. The measured three-dimensional mean flame surface area ratio correlates well with a formula similar to the Zimont model for turbulent burning velocity but with different model constants. Also, the mean flame surface area ratio displays a weak dependency on turbulence intensity but a strong positive dependency on the turbulence integral length scale.     

Structure and propagation of two-dimensional,partially premixed,laminar flames in diesel engine conditions

We investigate the influence of inflow velocity (V_in) and scalar dissipation rate (χ) on the flame structure and stabilisation mechanism of steady, laminar partially premixed n-dodecane edge flames stabilised on a convective mixing layer. Numerical simulations were performed for three different χ profiles and several V_in (V_in = 0.2 to 2.5m/s). The ambient thermochemical conditions were the same as the Engine Combustion Network’s (ECN) Spray A flame, which in turn represents conditions in a typical heavy duty diesel engine. The results of a combustion mode analysis of the simulations indicate that the flame structure and stabilisation mechanism depend on V_in and χ. For low V_in the flame is attached. Increasing V_in causes the high-temperature chemistry (HTC) flame to lift-off, while the low-temperature chemistry (LTC) flame is still attached. A unique speed S_R associated with this transition is defined as the velocity at which the lifted height has the maximum sensitivity to changes in V_in. This transition velocity is negatively correlated with χ. Near $V_{in}=S_R$ a tetrabrachial flame structure is observed consisting of a triple flame, stabilised by flame propagation into the products of an upstream LTC branch. Further increasing the inlet velocity changes the flame structure to a pentabrachial one, where an additional HTC ignition branch is observed upstream of the triple flame and ignition begins to contribute to the flame stabilisation. At large V_in, the LTC is eventually lifted, and the speed at which this transition occurs is insensitive to χ. Further increasing V_in increases the contribution of ignition to flame stabilisation until the flame is completely ignition stabilised. Flow divergence caused by the LTC branch reduces the χ at the HTC branches making the HTC more resilient to χ. The results are discussed in the context of identification of possible stabilisation modes in turbulent flames.     

Numerical study of transient evolution of lifted jet flames: partially premixed flame propagation and influence of physical dimensions

Three-dimensional (3D) unsteady Reynolds-averaged Navier–Stokes simulations of a spark-ignited turbulent methane/air jet flame evolving from ignition to stabilisation are conducted for different jet velocities. A partially premixed combustion model is used involving a correlated joint probability density function and both premixed and non-premixed combustion mode contributions. The 3D simulation results for the temporal evolution of the flame's leading edge are compared with previous two-dimensional (2D) results and experimental data. The comparison shows that the final stabilised flame lift-off height is well predicted by both 2D and 3D computations. However, the transient evolution of the flame's leading edge computed from 3D simulation agrees reasonably well with experiment, whereas evident discrepancies were found in the previous 2D study. This difference suggests that the third physical dimension plays an important role during the flame transient evolution process. The flame brush's leading edge displacement speed resulting from reaction, normal and tangential diffusion processes are studied at different typical stages after ignition in order to understand the effect of the third physical dimension further. Substantial differences are found for the reaction and normal diffusion components between 2D and 3D simulations especially in the initial propagation stage. The evolution of reaction progress variable scalar gradients and its interaction with the flow and mixing field in the 3D physical space have an important effect on the flame's leading edge propagation.     

Size distribution and morphology of nascent soot in premixed ethylene flames with and without benzene doping

Particle size distribution functions of nascent soot formed in four burner-stabilized, premixed ethylene-oxygen-argon flames were studied in a spatially resolved manner by online sampling/scanning mobility particle sizer. Particle morphology was analyzed by atomic force microscopy (AFM) of substrate-deposited samples. Two of the four flames were doped with benzene. An aerosol electrometer is introduced to extend the lower detection limit to around 1.5 nm in diameter. The results show that the bimodal behavior of particle size is applicable to all premixed ethylene flames studied. The variation of the size distribution from flame to flame is conclusively attributed to flame temperature variation. Under the condition of an equal carbon concentration, benzene doping leads to negligible changes in the characteristics of the size distribution. For all flames studied, AFM observations show that nascent soot is liquid-like and spreads extensively upon impact on a substrate surface.     

Flame propagation speed and Markstein length of spherically expanding flames: Assessment of extrapolation and measurement techniques

Laminar burning velocities are of great importance in many combustion models as well as for validation and improvement of chemical kinetic schemes. Determining laminar burning velocities with high accuracy is quite challenging and different approaches exist. Hence, a comparison of existing methods measuring and evaluating laminar burning velocities is of interest. Here, two optical diagnostics, high speed tomography and Schlieren cinematography, are simultaneously set up to investigate methods for evaluating laminar flame speed in a spherical flame configuration. The hypothesis to obtain the same flame propagation radii over time with the two different techniques is addressed. Another important aspect is the estimation of flame properties, such as the unstretched flame propagation speed and Markstein length in the burnt gas phase and if these are estimated satisfactorily by common experimental approaches. Thorough evaluation of the data with several extrapolation techniques is undertaken. A systematic extrapolation approach is presented to give more confidence into results generated experimentally. The significance of the linear extrapolation routine is highlighted in this context. Measurements of spherically expanding flames are carried out in two high-pressure, high-temperature, constant-volume vessels at RWTH in Aachen, Germany and at ICARE in Orleans, France. For the discussion of the systematic extrapolation approach, flame speed measurements of methane / air mixtures with mixture Lewis numbers moderately away from unity are used. Conditions were varied from lean to rich mixtures, at temperatures of 298–373 K, and pressures of 1 atm and 5 bar.     

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.     

Effects of compression and stretch on the determination of laminar flame speeds using propagating spherical flames

The effects of flow compression and flame stretch on the accurate determination of laminar flame speeds at normal and elevated pressures using propagating spherical flames at constant pressure or constant volume are studied theoretically and numerically. The results show that both the compression-induced flow motion and flame stretch have significant impacts on the accuracy of flame speed determination. For the constant pressure method, a new method to obtain a compression-corrected flame speed (CCFS) for nearly constant pressure spherical bomb experiments is presented. Likewise, for the constant volume method, a technique to obtain a stretch-corrected flame speed (SCFS) at elevated pressures and temperatures is developed. The validity of theoretical results for both constant pressure and constant volume methods is demonstrated by numerical simulations using detailed chemistry for hydrogen/air, methane/air, and propane/air mixtures. It is shown that the present CCFS and SCFS methods not only improve the accuracy of the flame speed measurements significantly but also extend the parameter range of experimental conditions. The results can be used directly in experimental measurements of laminar flame speeds.     

Generalized analytical expressions for the burning velocity in a combustion model with non-constant transport coefficients and several specific heats

We derive new expressions to estimate the burning velocity of a laminar gas flame in a simplified combustion model based on a one-step single reaction with transport coefficients (mass and heat) depending on temperature, and species with different specific heats. These new expressions generalize the bounds and approximations previously derived by Williams, von Karman, Zeldovich and Frank-Kamenetskii, Benguria and Depassier, and the matching asymptotic expansion method in a two zone model. The comparison of the flame speed predicted by these new analytical expressions with that numerically simulated by the full combustion model for a large variety of cases allows us to determine their range of validity. The upper bound based on the Benguria and Depassier method provides very good approximations for the actual propagation speed of combustion flames, being substantially better than the asymptotic method used in the recent papers.     

Numerical study of strongly-nonlinear regimes of steady premixed flame propagation. The effect of thermal gas expansion and finite-front-thickness effects

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 effects, namely flame stretch, curvature, and compression. In particular, flame compression is demonstrated to have a profound influence on the flame, strongly affecting the dependence of its propagation speed on the channel width b. Specifically, the solutions found exhibit a sharp increase of flame speed with channel width. Under weak flame compression, this increase commences at b/λ_c ≈ 2 ～ 3, where λ_c is the cutoff wavelength, but this ratio becomes significantly larger as the flame compression grows. The results obtained are also used to identify limitations of the analytical approach based on the weak-nonlinearity assumption, and to revise the role of noise in flame evolution.     

Effect of inlet flow turbulence on the combustion instability in a premixed backward-facing step combustor

This paper reports the effect of inlet flow turbulence intensity on the combustion instability characteristics in a backward facing step combustor. The inlet turbulence intensity is varied by a turbulence generator. Unsteady pressure measurements and OH* chemiluminescence images are recorded over a wide range of operating conditions at different inlet turbulence intensities. The study shows an early onset of instability at low turbulence level, i.e., higher turbulence postpones the onset of instability to higher Reynolds number Re and/or higher equivalence ratio Φ. The early onset of instability in the Re and Φ parameter spaces is due to the change in system parameters such as flame speed and size of the recirculation zone downstream of the step at different turbulence levels. Further, the onset is characterized as subcritical bifurcation. At low Re, the hysteresis zone width is small for low turbulence levels and it is large at higher turbulence levels; and at higher Re, the hysteresis width remains constant at all turbulence levels. Investigation of instability characteristics reveals that there are momentary slippages from limit cycle orbit into brief silent regimes in an intermittent manner. The frequency of occurrence of the momentary silent regimes increases with reduction in turbulence, indicating that higher turbulence helps in maintaining the system in a stable limit cycle orbit. High-speed chemiluminescence imaging reveals the necessity of the vortex rollup in the recirculation zone to grow up to the top wall by dilatation from the heat release for the onset of instability. Considerations of the effect of turbulence on both the flame speed and the recirculation zone size together explain all the observed bifurcation trends. These results suggest that inlet flow turbulence should not just be considered as background noise. The turbulence effects on both the flame and flow should be considered in predicting the instability characteristics.     

Influence of pressure on near nozzle flow field and soot formation in laminar co-flow diffusion flames

Soot formation from combustion devices, which tend to operate at high pressure, is a health and environmental concern, thus investigating the effect of pressure on soot formation is important. While most fundamental studies have utilised the co-flow laminar diffusion flame configuration to study the effect of pressure on soot, there is a lack of investigations into the effect of pressure on the flow field of diffusion flames and the resultant influence on soot formation. A recent work has displayed that recirculation zones can form along the centreline of atmospheric pressure diffusion flames. This present work seeks to investigate whether these zones can form due to higher pressure as well, which has never been explored experimentally or numerically. The CoFlame code, which models co-flow laminar, sooting, diffusion flames, is validated for the prediction of recirculation zones using experimental flow field data for a set of atmospheric pressure flames. The code is subsequently utilised to model ethane-air diffusion flames from 2 to 33 atm. Above 10 atm, recirculation zones are predicted to form. The reason for the formation of the zones is determined to be due to increasing shear between the air and fuel steams, with the air stream having higher velocities in the vicinity of the fuel tube tip than the fuel stream. This increase in shear is shown to be the cause of the recirculation zones formed in previously investigated atmospheric flames as well. Finally, the recirculation zone is determined as a probable cause of the experimentally observed formation of a large mass of soot covering the entire fuel tube exit for an ethane diffusion flame at 36.5 atm. Previously, no adequate explanation for the formation of the large mass of soot existed.     

Effect of fuel/air ratio and aromaticity on the molecular weight distribution of soot in premixed n-heptane flames

Soot growth from inception to mass-loading is studied in a wide range of molecular weights (MW) from 10⁵ to 10¹⁰u by means of size exclusion chromatography (SEC) coupled with on-line UV-visible spectroscopy. The evolution of MW distributions of soot is also numerically predicted by using a detailed kinetic model coupled with a discrete-sectional approach for the modeling of the gas-to-particle process. Two premixed flames burning n-heptane in slightly sooting and heavily sooting conditions are studied. The effect of aromatic addition to the fuel is studied by adding n-propylbenzene (10% by volume) to n-heptane in the heavily sooting condition. A progressive reduction of the MW distribution from multimodal to unimodal is observed along the flames testifying the occurrence of particle growth and agglomeration. These processes occur earlier in the aromatic-doped n-heptane flame due to the overriding role of benzene on soot formation which results in bigger young soot particles. Modeled MW distributions are in reasonable agreement with experimental data although the model predicts a slower coagulation process particularly in the slightly sooting n-heptane flame. Given the good agreement between model predictions and experiments, the model is used to explore the role of fuel chemistry on MW distributions. Two flames of n-heptane and n-heptane/n-propylbenzene in heavily sooting conditions with the same temperature profile and inert dilution are modeled. The formation of larger soot particles is still evident in the n-heptane/n-propylbenzene flame with respect to the n-heptane flame in the same operating conditions of temperature and dilution. In addition the model predicts a larger formation of molecular particles in the flame containing n-propylbenzene and shows that soot inception occurs in correspondence of their maximum formation thus indicating the importance of molecular growth in soot inception.     

Effect of electric fields on reattachment and propagation speed of tribrachial flames in laminar coflow jets

The effects of electric fields on the reattachment of lifted flames have been investigated experimentally in laminar coflow jets with propane fuel by applying high voltages to the fuel nozzle. In case of AC, the frequency has also been varied. Results showed that reattachment occurred at higher jet velocity when applying the AC voltages, thus the stabilization limit of attached flames was extended by the AC electric field. Higher voltage and lower frequency of the AC were found to be more effective. On the contrary, the effect of DC was found to be minimal. To understand the early onset of the reattachment with the AC, occurring at higher jet velocity, the influence of AC electric fields on the propagation speed of tribrachial flame edge was investigated during the transient reattachment processes. The propagation speed increased reasonably linearly with the applied AC voltage and decreased inversely to the distance between the flame edge and the nozzle electrode. Consequently, the enhancement in the propagation speed of tribrachial flame edge was correlated well with the electric field intensity, defined as the applied AC voltage divided by the distance.     

A comparative study of nanoparticles in premixed flames by scanning mobility particle sizer, small angle neutron scattering, and transmission electron microscopy

Scanning mobility particle sizer (SMPS) and transmission electron microscopy (TEM) studies were conducted for TiO₂ and soot particles. The TiO₂ particles were produced from a premixed stagnation ethylene-oxygen-argon flame (? = 0.36) doped with titanium tetraisopropoxide. Soot was generated from a burner-stabilized premixed ethylene-oxygen-argon flame (? = 2.5). The close agreement among SMPS, TEM, and X-ray diffraction results for TiO₂ nanoparticles demonstrates that the probe sampling/mobility measurement technique is accurate for on-line analysis of the size distribution of particles as small as 3 nm in diameter. In the case of soot, notable disagreement between the SMPS and TEM sizes was found and attributable to the fact that the soot taken from the flame studied herein is liquid-like and that upon deposition on the TEM grid, the primary particles do not retain their sphericity. This interpretation is supported by measurements with photo ionization aerosol mass spectrometry, small angle neutron scattering, and thermocouple particle densitometry.     

Flame propagation in narrow horizontal channels: Impact of the gravity field on the flame shape

In this paper, we study the effect of gravity, or buoyancy forces, on the structure of flames propagating in horizontal channels. It is shown that there are two mechanisms for the appearance of non-symmetric flames. The first, more obvious, is related to buoyancy, when a hotter gas of lower density tends to be located in the upper half of the channel. However, there is a second mechanism associated with the intrinsic flame instabilities, which also can cause the loss of flame symmetry. This mechanism can, at certain values of the parameters, act in the opposite direction, when hotter gases are enclosed in the lower part of the channel. In this case, two stable non-symmetric solutions may exist in the presence of gravitational forces and the establishment of one or another configuration depends on the initial conditions. The stability of these solutions is demonstrated by time-dependent computations.     

A DNS study of the physical mechanisms associated with density ratio influence on turbulent burning velocity in premixed flames

Data obtained in 3D direct numerical simulations of statistically planar, 1D weakly turbulent flames characterised by different density ratios σ are analysed to study the influence of thermal expansion on flame surface area and burning rate. Results show that, on the one hand, the pressure gradient induced within a flame brush owing to heat release in flamelets significantly accelerates the unburned gas that deeply intrudes into the combustion products in the form of an unburned mixture finger, thus causing large-scale oscillations of the burning rate and flame brush thickness. Under the conditions of the present simulations, the contribution of this mechanism to the creation of the flame surface area is substantial and is increased by σ, thus implying an increase in the burning rate by σ. On the other hand, the total flame surface areas simulated at σ = 7.53 and 2.5 are approximately equal. The apparent inconsistency between these results implies the existence of another thermal expansion effect that reduces the influence of σ on the flame surface area and burning rate. Investigation of the issue shows that the flow acceleration by the combustion-induced pressure gradient not only creates the flame surface area by pushing the finger tip into the products, but also mitigates wrinkling of the flame surface (the side surface of the finger) by turbulent eddies. The latter effect is attributed to the high-speed (at σ = 7.53) axial flow of the unburned gas, which is induced by the axial pressure gradient within the flame brush (and the finger). This axial flow acceleration reduces the residence time of a turbulent eddy in an unburned zone of the flame brush (e.g. within the finger). Therefore, the capability of the eddy for wrinkling the flamelet surface (e.g. the side finger surface) is weakened owing to a shorter residence time.     

Guided propagation in a step-index, multi-mode fiber: effect of index difference variation on allowable TM propagation constants

The effect of variation of core and cladding index difference, Δn=n_core−n_cladding, on allowable values for the guided mode transverse magnetic propagation constants within a step-index, multi-mode optical fiber is investigated. We use a iterative computational technique to calculate the propagation constants for modes inside and outside the core that satisfy the boundary conditions contained within the characteristic eigen-equation for the TM field components. Evidence of a strong dependence of the allowable propagation constants on changes of Δn is shown.     

The differential diffusion effect of the intermediate species on the stability of premixed flames propagating in microchannels

The propagation of premixed flames in adiabatic and non-catalytic planar microchannels subject to an assisted or opposed Poiseuille flow is considered. The diffusive–thermal model and the well-known two-step chain-branching kinetics are used in order to investigate the role of the differential diffusion of the intermediate species on the spatial and temporal flame stability. This numerical study successfully compares steady-state and time-dependent computations to the linear stability analysis of the problem. Results show that for fuel Lewis numbers less than unity, Le_F < 1, and at sufficiently large values of the opposed Poiseuille flow rate, symmetry-breaking bifurcation arises. It is seen that small values of the radical Lewis number, Le_Z, stabilise the flame to symmetric shape solutions, but result in earlier flashback. For very lean flames, the effect of the radical on the flame stabilisation becomes less important due to the small radical concentration typically found in the reaction zone. Cellular flame structures were also identified in this regime. For Le_F > 1, flames propagating in adiabatic channels suffer from oscillatory instabilities. The Poiseuille flow stabilises the flame and the effect of Le_Z is opposite to that found for Le_F < 1. Small values of Le_Z further destabilise the flame to oscillating or pulsating instabilities.