Thermal Flame Thickness Research Articles

LES of Premixed Turbulent Combustion Using Filtered Tabulated Chemistry

The filtered tabulated chemistry (FTACLES) approach utilizes data from pre-tabulated explicitly filtered 1D flame profiles for closure of the LES-filtered transport terms. Different methodologies are discussed to obtain a suitable progress variable c from detailed chemistry calculations of a methane/air flame. In this context, special focus is placed on the analytical modeling of the reaction source term using series of parameterized Gaussians. For increasing effective filter sizes in LES (i.e. including the flame thickening) the precise shape of the reaction rate profile becomes less and less relevant. In particular, it is shown that for one-step chemistry, a single Gaussian is sufficient to derive an explicitly expressible 1D flame profile with a prescribed laminar flame speed and thermal flame thickness. The resulting artificial flame profile is shown to have similarities with profiles based on carbon chemistry and detailed reaction mechanisms. Next, the behavior of the filtered c-transport equation is analyzed and several possible closure methods are compared for a wide range of filter widths. It is shown that the unclosed contribution of the filtered diffusion term can be combined with the subgrid convection term, thus simplifying the FTACLES formulation. The model is implemented in OpenFOAM and validated in 1D for a variety of LES filter sizes in combination with artificial flame thickening. A power-law-based wrinkling model is modified for use with artificial flame thickening and combined with the FTACLES model to enable 3D simulations of a premixed turbulent Bunsen burner. The comparison of 3D Large Eddy Bunsen flame simulations at increasing levels of turbulence intensity shows a good match to experimental results for most investigated cases. In addition, the results are mostly insensitive to the variation of the mesh size.

Effects of Pressure and Characteristic Scales on the Structural and Statistical Features of Methane/Air Turbulent Premixed Flames

In this study, the highly nonlinear and multi-scale flame-turbulence interactions prevalent in turbulent premixed flames are examined by using direct numerical simulation (DNS) datasets to understand the effects of increase in pressure and changes in the characteristic scale ratios at high pressure. Such flames are characterized by length-scale ratio (ratio of integral length scale and laminar thermal flame thickness) and velocity-scale ratio (ratio of turbulence intensity and laminar flame speed). A canonical test configuration corresponding to an initially laminar methane/air lean premixed flame interacting with decaying isotropic turbulence is considered. We consider five cases with the initial Karlovitz number of 18, 37, 126, and 260 to examine the effects of an increase in pressure from 1 to 10 atm with fixed turbulence characteristics and at a fixed Karlovitz number, and the changes to characteristic scale ratios at the pressure of 10 atm. The increase in pressure for fixed turbulence characteristics leads to enhanced flame broadening and wrinkling due to an increase in the range of energetic scales of motion. This further manifests into affecting the spatial and state-space variation of thermo-chemical quantities, single point statistics, and the relationship of heat-release rate to the flame curvature and tangential strain rate. Although these results can be inferred in terms of an increase in Karlovitz number, the effect of an increase in pressure at a fixed Karlovitz number shows differences in the spatial and state-space variations of thermo-chemical quantities and the relationship of the heat release rate with the curvature and tangential strain rate. This is due to a higher turbulent kinetic energy associated with the wide range of scales of motion at atmospheric pressure. In particular, the magnitude of the correlation of the heat release rate with the curvature and the tangential strain rate tend to decrease and increase, respectively, with an increase in pressure. Furthermore, the statistics of the flame-turbulence interactions at high pressure also show sensitivity to the changes in the characteristic length- and velocity-scale ratios. The results from this study highlight the need to accurately account for the effects of pressure and characteristic scales for improved modeling of such flames.

Combustion Performance of the Premixed Ammonia-Hydrogen-Air Flame in Porous Burner

ABSTRACT Flame stability and pollutant emission performances of a porous burner fueled with ammonia/hydrogen blend were investigated numerically in this study. In this regard, a 2D solver based on finite volume method was developed in order to simulate reacting flow and heat transfer modes through a porous medium. Combustion characteristics in terms of porous structure, equivalence ratio and fuel component were studied and the pollutant emission trends were discussed. Flame stability limit was observed to be extended with increasing equivalence ratio regardless to ammonia fraction. Results proved that addition of ammonia in the fuel blend reduced the flame stability limits and thermal flame thickness but led to the enhanced NO emission. Increasing equivalence ratio led to a decrease in thermal flame thickness under fuel-lean conditions while it caused that the thickness of flame zone to be increased slightly under fuel-rich conditions. It was found that flame stability limits were extended as the mean pore diameter of the porous medium increased. The maximum amounts of NO concentration were achieved at stoichiometric conditions while, NO emission increased as equivalence ratio increased at fuel-lean conditions and it decreased as equivalence ratio increased at rich combustion regimes.

Simple criterion of importance of laminar flame instabilities in premixed turbulent combustion of mixtures characterized by low Lewis numbers.

By (i) highlighting the mitigation effect of strain rates on laminar flame instabilities and (ii) comparing peak growth rates of laminar flame instabilities with strain rates generated by small-scale turbulent eddies, a simple criterion of importance of the influence of the instabilities on an increase in premixed flame surface area in turbulent flows is suggested. The criterion implies that, even in lean hydrogen-air mixtures, laminar flame instabilities can significantly affect the flame area only in weak or moderate turbulence (the Karlovitz number defined using laminar flame speed, thermal flame thickness, and Kolmogorov time scale is on the order of 10 or less under room conditions).

Characteristics of Premixed Flames of Hot and Diluted Mixtures

ABSTRACT Internal recirculation of product gases and mixing with fresh reactants, to form a hot and diluted combustible mixture, has been demonstrated to result in lower pollutant emissions. With sufficient amount of product gas recirculation, the mixture can reach above its auto-ignition temperature with low oxygen mass fractions (<4 wt%), resulting in distributed reactions instead of a flame. Some of the technologies with this feature are Moderate or Intense Low oxygen Dilution (MILD) combustion, FLameless OXidation (FLOX) and Colorless Distributed Combustion (CDC). However, if the amount of product gas recirculation is not enough and the auto ignition condition is not reached, premixed reactants of the hot and diluted mixture can be established. In this study, characteristics of such hot and diluted mixtures is studied which include the ignition delay time and the flame attributes such as laminar flame speed, S L and thermal flame thickness, . A perfectly stirred reactor (PSR) using the hot and diluted mixture as the inlet was further examined to simulate the main combustor and combustion efficiency η, and CO and NOx emissions were obtained. The investigations are performed at different product gas recirculation amounts , equivalence ratios ϕ and operating pressures P, using chemical kinetic simulations. The thermo-chemical state of the recirculated product gases was obtained using a PSR with varying residence times (τ) to simulate different “burntness” levels (smaller τ simulates lower “burntness” level). The hot and diluted mixture temperature is higher, while oxygen and fuel mole fraction are lower for higher ξ, ϕ, P, and τ. Radical species’ mole fraction is higher for higher ξ, ϕ, and lower P, τ. Lower is observed for higher ξ, ϕ, P and smaller τ. Higher S L is observed for higher ξ, ϕ and lower P. Lower is observed for higher ξ, ϕ and P. S L and are found to be higher or lower with variation in τ, depending on ξ, ϕ and P, owing to variation in temperature and radicals’ concentration. Higher η is observed for higher ξ, P, lower ϕ, τ, and higher residence time of gases (τ reac ) inside the main combustor. Lower CO is observed with increase in ξ, P and decrease in τ, while exhaust NOx increases with ϕ and mostly remains unchanged with increase in ξ, while inconsistent trends are observed with change in P and τ.

Investigation of the generalization capability of a generative adversarial network for large eddy simulation of turbulent premixed reacting flows

In the past decades, Deep Learning (DL) frameworks have demonstrated excellent performance in modeling nonlinear interactions and are a promising technique to move beyond physics-based models. In this context, super-resolution techniques may present an accurate approach as subfilter-scale (SFS) closure model for Large Eddy Simulations (LES) in premixed combustion. However, DL models need to perform accurately in a variety of physical regimes and generalize well beyond their training conditions. In this work, a super-resolution Generative Adversarial Network (GAN) is proposed as closure model for the unresolved subfilter-stress and scalar-flux tensors of the filtered reactive Navier–Stokes equations solved in LES. The model trained on a premixed methane/air jet flame is evaluated a-priori on similar configurations at different Reynolds and Karlovitz numbers. The GAN generalizes well at both lower and higher Reynolds numbers and outperforms existing algebraic models when the ratio between the filter size and the Kolmogorov scale is preserved. Moreover, extrapolation at a higher Karlovitz number is investigated indicating that the ratio between the filter size and the thermal flame thickness may not need to be conserved in order to achieve high correlation in terms of SFS field. Generalization studies obtained on substantially different flame conditions indicate that successful predictive abilities are demonstrated if the generalization criterion is matched. Finally, the reconstruction of a scalar quantity, different from that used during the training, is evaluated, revealing that the model is able to reconstruct scalar fields with large gradients that have not been explicitly used in the training. The a-priori investigations carried out assess whether out-of-sample predictions are even feasible in the first place, providing insights into the quantities that need to be conserved for the model to perform well between different regimes, and represent a crucial step toward future embedding into LES numerical solvers.

Large eddy simulation of the dynamics of lean premixed flames using global reaction mechanisms calibrated for CH4–H2 fuel blends

The effects of hydrogen addition on the flame dynamics of a bluff-body stabilized methane–hydrogen turbulent flame are studied with large eddy simulation (LES). The LES is carried out with the thickened flame model and global kinetic mechanisms calibrated for the methane–hydrogen mixtures. Conjugate heat transfer is included in the LES to consider a proper wall temperature while the flame shape changes with hydrogen addition. A data-based calibration of the global mechanisms is done with a methodology based on reproducing the net species production rates computed with a detailed kinetic mechanism. An improvement in this methodology is proposed to increase its accuracy and reliability. The calibrated mechanisms accurately describe the variation of the laminar flame speed and the thermal flame thickness with hydrogen addition and equivalence ratio in a freely propagating premixed flame. The variations of the consumption speed and the thermal flame thickness with the strain rate in a symmetric counterflow premixed flame are also well predicted. The numerical simulations reproduce the transition from V- to M-shape flame induced by hydrogen addition, and the axial distribution of the heat release agrees with the experimental measurements of OH chemiluminescence. The unit impulse response and the flame transfer function are computed from the LES data using system identification (SysID). The flame transfer functions show a remarkable agreement with the experimental data, demonstrating that the LES-SysID approach using properly calibrated global mechanisms can predict the response of turbulent methane–hydrogen flames to velocity fluctuations. A comparison of the unit impulse response for the various hydrogen additions is presented, and the effect of hydrogen in the flow–flame interaction of the burner evaluated is discussed.

Superadiabatic small-scale combustors: Asymptotic analysis of a two-step chain-branching combustion model

An asymptotic study for a counterflow burner consisting of thin channels with heat exchange is proposed. The focus is made on the cases of ultra lean burning using a model of a two-step chain-branching chemistry. The ratio of the channel length to the thermal flame thickness is used as a natural large parameter. Then, the solution is constructed by the method of asymptotic expansions using this parameter. Finally, the obtained asymptotic for the flame position is satisfactorily compared with the exact solution of the problem. These explicit results have a clear advantage in that they facilitate considerably the parametric analysis. It is demonstrated that combustion of mixtures below the flammability limit can be carried out in the considered systems.

Relations Between Statistics of Three-Dimensional Flame Curvature and its Two-Dimensional Counterpart in Turbulent Premixed Flames

The relations between the actual flame curvature probability density function (PDF) evaluated in three-dimensions and its two-dimensional counterpart based on planar measurements have been analytically derived subject to the assumptions of isotropy and statistical independence of various angles and two-dimensional curvature. These relations have been assessed based on Direct Numerical Simulation (DNS) databases of turbulent premixed (a) statistically planar and (b) statistically axisymmetric Bunsen flames. It has been found that the analytically derived relation interlinking the PDFs of actual three-dimensional curvature and its two-dimensional counterpart holds reasonably well for a range of curvatures around the mean value defined by the inverse of the thermal flame thickness for different turbulence intensities across different combustion regimes. The flame surface is shown to exhibit predominantly two-dimensional cylindrical curvature but there is a significant probability of finding saddle type flame topologies and this probability increases with increasing turbulence intensity. The presence of saddle type flame topologies affects the ratios of second and third moments of two-dimensional and three-dimensional curvatures. It has been demonstrated that the ratios of second and third moments of two-dimensional and three-dimensional curvatures cannot be accurately predicted based on two-dimensional measurements. The ratio of the third moments of two-dimensional and three-dimensional curvatures remains positive and thus the qualitative nature of curvature skewness can still be obtained based on two-dimensional curvature measurements. As the curvature skewness is often taken to be a marker of the Darrius-Landau instability, the conclusion regarding the presence of this instability can potentially be taken from the two-dimensional curvature measurements.

Scalar gradient and flame propagation statistics of a flame-resolved laboratory-scale turbulent stratified burner simulation

A bluff-body stabilised turbulent jet flame burning in a stratified mode of combustion for fuel-lean methane/air mixtures is investigated by a flame-resolved simulation. A tabulated chemistry approach based on premixed flamelet generated manifolds (PFGM) accounts for thermochemistry. The computations are performed for a grid-resolution of 100 µm, sufficient to resolve the thermal flame thickness. The look-up table is generated with a mixture-averaged diffusivity assumption and the preferential diffusion fluxes are included in the simulation, using an efficient method without increasing the dimensionality of the manifold. The predicted mean and RMS quantities are found to be in good agreement with the experiment. The investigation focuses on the comparison of the combustion behaviour of the upstream locations close to the inlet with weak mixture fraction gradients to the downstream locations away from the inlet with strong mixture fraction gradients. Statistical analysis of the diffusion terms within the flame revealed that the preferential diffusion remains significant near the inlet, in the recirculation zone over the bluff-body. The structure of the stratified flame in downstream locations is statistically analysed in terms of displacement speed and scalar gradients by comparing against the corresponding quantities in upstream locations with weak mixture fraction gradients. It is shown that the displacement speed is statistically different between the flames under weak or strong mixture fraction gradients due to the influence of molecular diffusion and reaction rate components. However, increased curvature effects and cross-dissipation component also play a role. Finally, scalar dissipation and cross-dissipation rates of the mixture fraction fluctuation and the reaction progress variable fluctuation within the flame-brush are investigated, and their closure approaches are discussed.

The effect of pressure on the hydrodynamic stability limit of premixed flames

The effect of pressure on the hydrodynamic stability limits of lean methane–air premixed flames is investigated with Direct Numerical Simulation based on multi-step chemistry and using a simplified one-step chemistry formulation. The dependency on pressure p of the cut-off length scale λc, that separates stable from unstable wavelengths of the initial perturbation, is computed for a number of different conditions. An increase of pressure causes a significant decrease of the cut-off length, as observed already in previous simulations and experiments. However, this decrease cannot be ascribed only to the decreased flame thickness due to elevated pressures, but the cut-off is reduced significantly even if normalized by either the thermal flame thickness ℓT or the diffusive flame thickness ℓD. For the conditions analyzed, the cut-off can be well approximated by the power-law λc∝p−0.8, while the thermal and diffusive flame thicknesses, in accordance with previous experiments, are proportional and scale as ℓT∝ℓD∝p−0.3. Therefore, the non-dimensional cut-off scales as λc/ℓT∝λc/ℓD∝p−0.5. This behavior is linked to the increase of the Zeldovich number with pressure, caused by higher inner layer temperatures at higher pressures, which is a result of increased importance of chain termination reactions. The same behavior is observed also in a one-step chemistry approach if the Zeldovich number, appearing explicitly in the one-step model equations, is varied with pressure according to the results from multi-step chemistry. The analysis is extended to the non-linear phase of the instability, when typical strong cusps are observed on the flame surface, simulating a two-dimensional slot burner for different pressures; it is confirmed that the same pressure effects are observed also in more complex settings and in the non-linear regime.

Algebraic Flame Surface Density Modelling of High Pressure Turbulent Premixed Bunsen Flames

Performance of representative algebraic flame surface density (FSD) models have been a-priori assessed based on a direct numerical simulation database consisting of four turbulent premixed Bunsen flames at four different pressure levels. Results indicate that for a given resolution of the flame front, the considered algebraic FSD closures perform in a qualitatively similar manner irrespective of pressure variation. However, for a given computational mesh, the performance deteriorates as flame thickness decreases with increasing pressure. Additionally, the contribution of the subgrid scale surface-filtered density-weighted tangential diffusion component of the displacement speed tends to increase with pressure increment, further complicating the modelling of FSD. Further analysis also indicate that the inner cut-off scale normalized by the thermal flame thickness increases with increasing pressure, possibly due to the presence of Darrieus–Landau instability which is more likely to occur at higher pressure due to a larger ratio of hydrodynamic length scale to thermal flame thickness.

Three-dimensional pore-scale numerical simulation of methane-air combustion in inert porous media under the conditions of upstream and downstream combustion wave propagation through the media

Abstracts Porous media combustion of lean and ultra-rich methane-air mixtures was numerically studied using the approach when the process is simulated at the pore scale with explicit consideration of the three-dimensional porous structure and interstitial flow with thermal interaction between fluid and solid phases including the detailed chemical kinetics model and solid-to-solid radiation. The geometrical model of the packed bed was generated synthetically by simulation of particles falling under gravity force. A novel workflow for a randomly packed bed meshing at the pore scale was used to avoid the point contact problem. The results demonstrate that the model predicts a thermal nonequilibrium and heat recuperation mechanism in the combustion wave in the low-velocity regime correctly. The inhomogeneous structure of the porous media leads to large spatial variation of the process parameters such as velocity and temperature. It was shown that radiation makes a significant contribution to heat transfer in the region of a large temperature gradient. Radiative heat flux is transferred through the bed via radiation layer-by-layer due to restricted mutual visibility of the opaque particles. The mixture composition has a significant impact on the heat release rate and wave velocity and direction as well as thermal flame thickness and exhaust gas composition. At the macro scale, the mode of combustion wave propagation is quasi-steady whereas at the pore scale with little time steps the unsteady effects can be observed. Different subregions of the flame front propagate with not equal velocity, stand or accelerate depending on the local flow and porous matrix inhomogeneity. For the lean mixture the oscillatory regime of propagation was detected and analyzed.

Investigation of the premixed methane–air combustion through the combined porous-free flame burner by numerical simulation

Combustion process of the premixed methane–air in a novel combined porous-free flame burner was investigated numerically. Two-dimensional model considering nonequilibrium thermal condition between the gas and solid phases was used and the combustion was simulated using reduced GRI 3.0 multistep chemical kinetics mechanism. To examine the validity of the implemented numerical model, the burner was manufactured and tested. Good agreement between the numerical results and experimental data were observed. Thermal flame thickness, flame stability limit, and thermal efficiency were discussed. Multimode heat transfer in the porous medium including convection, radiation, and conduction were quantified and perused. Results showed that the thermal thickness of laminar free flame established in the perforated portion of the burner was considerably less than thickness of submerged flame stabilized in the porous medium. Predicted results suggested that the flame stability limit was augmented in the combined burner compared to the burner with full porous foam. Analyses of the heat balance showed that the thermal efficiency of the combined porous-free flame burner was less than thermal efficiency of the full porous burner. Comparison of the full porous burner with the novel combined porous-free flame burner demonstrated that the combined burner caused higher stability limits and lower thermal efficiencies.

Optimized single-step (OSS) chemistry models for the simulation of turbulent premixed flame propagation

A simple and efficient triple-optimization procedure (TOP) is introduced to determine single-step chemistry model parameters. The cornerstone of the proposed approach lies in the introduction of a fictive (or virtual) chemical species, the physical characteristics of which are set to recover some essential properties of combustion and flames. Special emphasis is presently placed on the capability of such a global kinetic scheme to recover three parameters that are recognized as the most influential in terms of turbulence–chemistry interactions and turbulent premixed combustion regimes. These parameters are (i) the burnt gases temperature Tb, which settles the value of the thermal expansion factor τ=(Tb−Tu)/Tu, (ii) the propagation velocity SL0, which is mandatory to reproduce the flame dynamics, and (iii) the laminar premixed flame thickness δL0. In practice, the thermochemical properties of the fictive species (hereafter denoted by AΦ) are set to account for the impact of dissociation effects and partial oxidation of the fuel, i.e., presence of species other than H2O and CO2 in the burnt gases, which allows to recover a satisfactory estimate of Tb. The value of the pre-exponential factor associated to the single-step Arrhenius law is also optimized to reproduce the laminar flame propagation velocity. Finally, the transport characteristics are determined to recover a satisfactory estimate of the thermal flame thickness. The method is general in its principles and quite easy to implement. It is applicable to any couple of fuel and oxidizer. Attention is focused on the application of the method to any stoichiometry but it is also shown that the influence of both pressure and fresh reactants temperature can be recovered. The performance of the resulting optimized single step (OSS) chemistry models are assessed through a direct comparison with detailed chemistry results. Computations of one-dimensional laminar flames are performed with the OSS model using the Cantera software for a wide range of pressure levels, fresh reactant temperatures, and equivalence ratios. Obtained results do show that the flame propagation velocity is correctly reproduced for the whole range of parameters, with a maximum value recovered in the vicinity of stoichiometry, a decrease towards rich conditions, and a satisfactory pressure dependence. Burnt gases temperature as well as thermal flame thickness values are also in excellent agreement with those issued from the reference detailed kinetics models. The OSS model is then used to perform direct numerical simulation (DNS) computations of flame kernel growths in both laminar and turbulent conditions. The comparison of obtained OSS results with detailed chemistry computations further confirms the relevance and performance of the proposed methodology.

Effects of Turbulence on Ignition of Methane–Air and n-Heptane–Air Fully Premixed Mixtures

ABSTRACTWe performed direct numerical simulations (DNS) for the two-dimensional (2D) turbulent ignition of ultra-lean methane–air and n-heptane–air mixtures with a high exhaust gas recirculation (EGR) rate at high pressure to determine the ignition criteria and ignition delay time. We defined an initial high-temperature region as an ignition kernel and conducted one-dimensional preliminary DNS to determine the ignition criteria in terms of the ignition source energy and the thermal conduction from the ignition kernel during the induction period. Additionally, we analyzed the 2D DNS results to clarify the influence of the turbulent strain rate on the ignition delay time and the mechanism by which the turbulence influences the establishment of the ignition kernel. We observed that the distribution of eddies and the strain rate in the high-temperature region influences the success or failure of the ignition process and, therefore, the ignition delay time. The ignition delay time increases proportionally to the square of strain rate averaged in the high concentration region of the intermediate species during the induction period. This suggests that the ignition in a turbulent field is based on the balance between the influence of a locally averaged strain rate in the preheating region and the chemical (flame) time scale. Based on these observations, a simple model for the ignition delay time was constructed based on the mean strain rate in the high concentration region of the intermediate species during the induction period. The strain rate averaged in the high concentration region of the intermediate species was normalized by using the laminar burning velocity and the laminar thermal flame thickness. Additionally, the ignition delay time was normalized by the ignition delay time of the corresponding laminar case, yielding the same ignition model/criterion for both examined fuels, which could be extended to other mixtures.

Experimental and Theoretical Study of Combustion under Elevated Pressure within Porous Inert Media

AbstractGas combustion occurring within porous inert media (PIM) results in intensified heat and mass transfer in comparison to free laminar combustion. This leads to considerably lower emissions of pollutant species, that is, NOx and CO, larger flame stability range, lower thermo‐acoustic instabilities, gradual response to operative changes, and geometric flexibility of design. In this work, experiments were carried out to describe the influence of flow rate, pressure, temperature, and air‐to‐fuel ratio on the flame stability within PIM at nearly adiabatic conditions. The macroscopic thermal flame thickness and the burning velocity were calculated from measured temperature profiles and flow rates. As the main result, it was observed that the pressure effect on the burning velocity can differ considerably from that of laminar free flames, that is, the increase of pressure can positively affect the burning velocity. The obtained results were supported by theoretical modeling. A new model to average the species production rates in a volume‐averaged numerical model was proposed. The model considered spatial deviations of temperature and mass fractions along the cross‐sectional area using presumed probability density functions. Using this new model, results of burning velocities and profiles of average temperature were satisfactorily predicted when compared to experimental results shown here. Furthermore, easy‐to‐use tools for porous burner design were formulated and validated.

Dynamics and Morphology of Premixed Flame Propagation in Channels: Effects of the Lewis Number and Thermal Boundary Conditions

Equidiffusive combustion is a model, which is widely employed in analytical and computational studies, including those on premixed flame acceleration. However, realistic combustible mixtures are oftentimes far from the stoichiometry, being thereby strongly non-equidiffusive and thus requiring extra analyses. The present work addresses this demand by means of the computational simulations of the basic fully-compressible hydrodynamic and combustion equations. Specifically, here we focus on the non-equidiffusive flames at various thermal boundary conditions, including adiabatic or isothermal walls of the channels. A detailed parametric study is performed, with the key parameters of the problem being the Lewis number, Le, taken in the range 0.2 ≤ Le ≤ 2.0, the thermal expansion factor Θ, being 5 ≤ Θ ≤ 8, and the flame propagation Reynolds number, Re = R/PrLf, where Lf is the thermal flame thickness and Pr the Prandtl number. We used Re in the range 5 ≤ Re ≤ 30. It is shown that while Θ ~ 8 flames tend to accelerate exponentially in channel with adiabatic, nonslip walls; acceleration moderates to a linear trend for Θ ~ 5. Moreover, with the isothermal walls, acceleration moderates (with hot walls) or even terminates (with cold walls). Furthermore, it is found that a non-unity Le influences the flame dynamics notably in both adiabatic and isothermal channels. Namely, Le &lt; 1 flames get extra strong corrugation and thereby spread much faster than equidiffusive ones. In contrast, Le &gt; 1 flames are thickened and propagate slower.

Different Trends of Premixed Flame Propagation in Obstructed Channels with both Ends Open

Premixed flames accelerate extremely fast and may even trigger a detonation when propagating in semi-open obstructed channels (here one end of a channel is closed; the flame is ignited at the closed end and propagates towards the open one). However, industrial pipes often have both ends open, with a flame ignited at one the ends. The present work is devoted to this configuration. Specifically, premixed flame propagation through a comb-shaped array of obstacles, in-built in a two-dimensional (2D) channel of half-width R with both ends open, is studied by solving fully-compressible hydrodynamic and combustion equations with Arrhenius chemical kinetics. The channels of half-widths R/Lf = 12, 24, 36 (Lf is the thermal flame thickness) are considered, with various blockage ratios, α = 1/3, 1/2, 2/3, for each R. It is found that in the relatively narrow channels, R/Lf =12 and 24, the instantaneous total burning rate oscillates with time for all α considered, with the oscillation period and amplitude varying with R and α. In fact, such an oscillating regime resembles that observed previously in unobstructed channels with both ends open. The oscillations can potentially be treated as fluctuations around a quasi-steady solution. In contrast, in a wider channel, R/Lf = 36, the oscillations are terminated soon, followed by flame acceleration, which is weaker (though similar) to that in semi-open channels. The results support the recent experiment, modelling and theory yielding steady or quasi-steady flame propagation prior to the onset of flame acceleration in obstructed pipes with both ends open.

Effect of Nonequidiffusivity on Flame Acceleration in Obstructed Channels

The mechanism of ultrafast acceleration of a premixed flamefront propagating in a channel equipped with a “tooth-brush”-shaped array of tightly-packed obstacles has been revealed and quantified, analytically, and validated by means of the computational simulations [Bychkov et al., Phys. Rev. E (2008) 164501]. However, the Bychkov theory and modeling employed various simplifications, including that of equidiffusive combustion, where the thermal-to-mass diffusivities ratio (the Lewis number, Le) is unity. Nevertheless, real flames are usually nonequidiffusive, which is addressed in the present work. Specifically, the impact of Le, in the range 0.2 ≤ Le ≤ 2.0, on flame acceleration in obstructed channels is investigated by means of the extensive numerical simulation of the reacting flow equations with fully-compressible hydrodynamics and Arrhenius chemical kinetics. A detailed parametric study is performed for the blockage ratio (BR) in the range 1/3~2/3, the spacing between the obstacles being dz/R = 1/4~1/2, and the channel width D in the range 48 ≤ D/Lf ≤ 96, where Lf is the thermal flame thickness. A key role of Le is shown in all considered cases. Specifically, due to a flamefront thickening, the Le &gt; 1 flames accelerate slower as compared to the equidiffusive ones. In contrast, the Le &lt; 1 flames acquire stronger distortion of the front shape and thereby accelerate much faster than the equidiffusive flames. We relate the latter effect to the onset of the diffusional-thermal combustion instability.