Thermal Flame Thickness Research Articles

Multiscale analysis of turbulence-flame interaction in premixed flames

Multiscale analysis of turbulence–flame interaction is performed using direct numerical simulation (DNS) data of premixed flames. Bandpass filtering method is used to educe turbulent eddies of various sizes and their vorticity and strain rate fields. The vortical structures at a scale of Lω are stretched strongly by the most extensional principal strain rate of eddies of scale 4Lω, which is similar to the behaviour in non-reacting turbulence. Hence, combustion does not influence the physics of vortex stretching mechanism. The fractional contribution from eddies of size Ls to the total tangential strain rate is investigated. The results highlight that eddies larger than two times the laminar flame thermal thickness contributes predominantly to flame straining and eddies smaller than 2δth contributes less than 10% to the total tangential strain rate for turbulence intensities, from u′/sL=1.41 to u′/sL=11.25, investigated here. The cutoff scale identified through this analysis is larger than the previous propositions and the implication of this finding to subgrid scale premixed combustion modelling is discussed.

Nonlinear evolution of 2D cellular lean hydrogen/air premixed flames with varying initial perturbations in the elevated pressure environment

This paper reports on studies of cellular instability of lean hydrogen/air laminar premixed flames with an equivalence ratio of 0.6 at a 5 atm and a 25 atm pressure. Numerical simulations employing a detailed chemical kinetics mechanism and detailed transport properties are carried out to simulate the initial linear growth of instability as well as the nonlinear evolution of flames. At the initial linear growth stage, the amplitude of the initial sinusoidal shaped flame front grows exponentially. Later on, in the nonlinear evolution stage the flame front develops into a cellular surface with wavelengths and amplitudes different from its initial ones. At higher pressures, hydrodynamic instability is enhanced, due to smaller flame thermal thickness; the flame fronts are more chaotic. Chaotic flame fronts are captured during the nonlinear evolution stage and it is shown that the evolution is very sensitive to initial perturbations. Two phenomena in the nonlinear evolution process are observed, mode-lock and preferential choice of modes. Both of these appear in connection with the initial disturbances to the flame front. Sensitivity of the numerical results to numerical schemes and the computational setups is examined.

The influence of spatial discreteness on the thermo-diffusive instability of flame propagation with infinite Lewis number

The dynamics of flame propagation in systems with infinite Lewis number and spatially discretized sources of heat release is examined, which is applicable to the combustion of suspensions of fuel particles in air. The system is analyzed numerically using a one-dimensional heat equation with a source term for the reaction progress variable, which is specified to have zero diffusivity, and the model reveals a spectrum of flame-propagation regimes. For the case of a switch-type reaction rate and homogeneous media (continuous regime), the flame propagates steadily at a velocity in agreement with analytical solutions. As the sources are spatially concentrated into δ-function-like sources, propagation approaches the discrete regime with a fixed period between ignition of the sources, for which an analytic solution is also available for validation. When the source term is governed by an Arrhenius rate and the activation energy is increased beyond the stability boundary, the flame begins to exhibit a long-wavelength (4–5 times the thermal flame thickness) oscillation characteristic of the thermo-diffusive instability, in good agreement with prior stability analysis. When spatial discreteness is introduced, a competition is observed between the long-period oscillations of the thermo-diffusive instability and the pulsations associated with the rapid heat release of the concentrated sources. Interestingly, the presence of spatial discreteness is able to excite higher modes (period doubling and chaotic solutions) of the thermo-diffusive instability, suggesting that the introduction of discreteness may have an influence qualitatively similar to that of increasing activation energy. Relevance of the model parameters to experimental systems is then discussed.

Assessment of dynamic closure for premixed combustion large eddy simulation

Turbulent piloted Bunsen flames of stoichiometric methane–air mixtures are computed using the large eddy simulation (LES) paradigm involving an algebraic closure for the filtered reaction rate. This closure involves the filtered scalar dissipation rate of a reaction progress variable. The model for this dissipation rate involves a parameter βc representing the flame front curvature effects induced by turbulence, chemical reactions, molecular dissipation, and their interactions at the sub-grid level, suggesting that this parameter may vary with filter width or be a scale-dependent. Thus, it would be ideal to evaluate this parameter dynamically by LES. A procedure for this evaluation is discussed and assessed using direct numerical simulation (DNS) data and LES calculations. The probability density functions of βc obtained from the DNS and LES calculations are very similar when the turbulent Reynolds number is sufficiently large and when the filter width normalised by the laminar flame thermal thickness is larger than unity. Results obtained using a constant (static) value for this parameter are also used for comparative evaluation. Detailed discussion presented in this paper suggests that the dynamic procedure works well and physical insights and reasonings are provided to explain the observed behaviour.

A Numerical Investigation on Characteristics of Turbulent Premixed Flame in Porous Media

Abstract A numerical study on the turbulent combustion in porous media is conducted based on 2D staggered cylinders using the eddy dissipation concept model (EDC) with emphasis on characteristics of the turbulent premixed flame. The results show that as the velocity increases, the sheet of laminar flame is stretched and distorted gradually. A burned island forms at the recirculating zone due to the entrainment. Based on the parameter study, it is find that turbulent kinetic energy gradually decay after the reaction taking place. The pseudo thermal flame thickness is less than the length scale of a representative elementary volume. The Damkohler number at quasi-steady state is in the order of 10, indicating that the flame is in the flamelet regime.

Investigation on the thermal flame thickness for lean premixed combustion of low calorific H2/CO mixtures within porous inert media

The lean premixed combustion of hydrogen and carbon monoxide (H2/CO) mixtures within a porous inert media model-burner was investigated for ranges of H2/CO volumetric ratios from 2 to 4, inert volumetric concentrations in the fuel stream from 85% to 90%, thermal loads of 400kW/m2 (2kW) and 1000kW/m2 (5kW), constant reactants temperature of 673K and an equivalence ratio of ϕ=0.5. Experimental measurements and numerical predictions of temperature profiles and temperature gradients along the axial center-line of the combustion zone are presented and the thermal flame thickness is estimated and analyzed for the effect of thermal load, inert components in the fuel stream and H2/CO ratios. The adopted numerical model uses a volume-averaged approach and solves both the gas- and solid-phase energy balances explicitly and accounts for the radiative heat transport in the solid-phase. The thermal flame thickness results are compared with the respective laminar free flame values and differences between the flame thickness of free flames and flames inside a porous inert media are discussed.

Scalar dissipation rate modelling for Large Eddy Simulation of turbulent premixed flames

The statistical behaviours of scalar dissipation rate (SDR) in the context Large Eddy Simulations (LES) of turbulent premixed combustion have been analysed using a simplified chemistry based Direct Numerical Simulations (DNS) data of a turbulent V-flame. The filter size dependence of the SDR is analysed in detail and it has been demonstrated that the filtered reaction rate can be satisfactorily closed using the Favre filtered SDR provided the filter width, Δ, remains greater than the thermal flame thickness, δth. Due to the close relation between the SDR and generalised Flame Surface Density (FSD), the dependence of the FSD on filter size has also been addressed. It has been found that a fractal dimension based power-law model satisfactorily captures the global and local behaviours of the generalised FSD in the context of LES. The fractal dimension and the inner cut-off scale for flame surface based on the volume-averaged value of the FSD are found to be in good agreement with previous analytical, experimental and DNS studies. The ratio of the volume-integrated filtered value of density-weighted SDR to its resolved component exhibits a power-law in terms of Δ with an inner cut-off scale scaling with δth. A power-law based model with a global exponent and inner cut-off scale is found to be insufficient to capture the local variations of SDR possibly due to its multi-fractal nature. An algebraic model for SDR, which was originally proposed for Reynolds Averaged Navier Stokes simulations, has been extended here for LES, which is found to satisfactorily capture both the global and local behaviours of SDR.

Premixed flame extinction in narrow channels with and without heat recirculation

The conditions that lead to the extinction of a premixed flame propagating along a channel of height 2h1∼δT are studied using the thermo-diffusive approximation, with δT=DT/SL, DT and SL representing, respectively, the thermal flame thickness, the thermal conductivity and the planar flame speed.It is found that flame propagation is greatly affected by conductive heat losses to the wall ∂T/∂n=b˜(T-T0), where n denotes the transverse distance to the wall, T and T0 are, respectively, the fluid’s and wall’s temperature and b˜ is the heat transfer parameter. The sensitivity of the flame to heat losses grows as the channel narrows, leading to complete flame extinction at extremely small values of b˜=b˜c.As a way to overcome flame quenching at the walls, Lloyd and Weinberg [1] proposed the recirculation of part of the heat stored in the exhaust gases to preheat the cold combustible mixture. In order to understand the flame dynamics in the presence of heat recirculation, we analyze the problem of two parallel channels with a combustible mixture and an inert fluid moving in opposite directions, with maximum velocities m1 and m2 respectively, and where heat exchange is permitted through the common wall separating both channels. It is shown that flame extinction occurs if the velocity ratio m2/m1 is outside the range m2/m1∈[m21,minm21.max], where the limiting values m21,min and m21.max are obtained numerically for a given set of parameters. The amplitude of this range depends, mainly, on the Damkhöler number d=[h1/(DT/SL)]2, quantity that represents the ratio between the channel’s height h1 and the thermal flame thickness DT/SL. It is shown that heat recirculation is capable of extending combustion to very small h1, but there is still a minimum value of the Damkhöler number dmin below which combustion is not possible. The evolution of dmin is computed numerically to give values as small as d=0.0025 for a given combination of the geometric parameters of the problem. The maximum flame temperature computed in the parallel channel configuration rises above the adiabatic flame temperature Te due to the effect of the heat recirculation. This effect becomes more significant as d is reduced, leading to maximum temperatures close to T≃1.4Te in very narrow channels.

Spatial correlation of heat release rate and sound emission from turbulent premixed flames

The two-point spatial correlation of the rate of change of fluctuating heat release rate is central to the sound emission from open turbulent flames, and a few attempts have been made to address this correlation in recent studies. In this paper, the two-point correlation and its role in combustion noise are studied by analysing direct numerical simulation (DNS) data of statistically multi-dimensional turbulent premixed flames. The results suggest that this correlation function depends on the separation distance and direction but, not on the positions inside the flame brush. This correlation can be modelled using a combination of Hermite–Gaussian functions of zero and second order, i.e. functions of the form (1-Ax2)e-Bx2 for constants A and B, to include its possible negative values. The integral correlation volume obtained using this model is about 0.2δL3 with the length scale obtained from its cube root being about 0.6δL, where δL is the laminar flame thermal thickness. Both of the values are slightly larger than the values reported in an earlier study because of the anisotropy observed for the correlation. This model together with the turbulence-dependent parameter K, the ratio of the root-mean-square (RMS) value of the rate of change of reaction rate to the mean reaction rate, derived from the DNS data is applied to predict the far-field sound emitted from open flames. The calculated noise levels agree well with recently reported measurements and show a sensitivity to K values.

A PrioriAssessment of Algebraic Flame Surface Density Models in the Context of Large Eddy Simulation for Nonunity Lewis Number Flames in the Thin Reaction Zones Regime

The performance of algebraic flame surface density (FSD) models has been assessed for flames with nonunity Lewis number (Le) in the thin reaction zones regime, using a direct numerical simulation (DNS) database of freely propagating turbulent premixed flames with Le ranging from 0.34 to 1.2. The focus is on algebraic FSD models based on a power-law approach, and the effects of Lewis number on the fractal dimensionDand inner cut-off scaleηihave been studied in detail. It has been found thatDis strongly affected by Lewis number and increases significantly with decreasing Le. By contrast,ηiremains close to the laminar flame thermal thickness for all values of Le considered here. A parameterisation ofDis proposed such that the effects of Lewis number are explicitly accounted for. The new parameterisation is used to propose a new algebraic model for FSD. The performance of the new model is assessed with respect to results for the generalised FSD obtained from explicitly LES-filtered DNS data. It has been found that the performance of the most existing models deteriorates with decreasing Lewis number, while the newly proposed model is found to perform as well or better than the most existing algebraic models for FSD.

Heat release rate correlation and combustion noise in premixed flames

The sound emission from open turbulent flames is dictated by the two-point spatial correlation of the rate of change of the fluctuating heat release rate. This correlation in premixed flames can be represented well using Gaussian-type functions and unstrained laminar flame thermal thickness can be used to scale the correlation length scale, which is about a quarter of the planar laminar flame thermal thickness. This correlation and its length scale are observed to be less influenced by the fuel type or stoichiometry or turbulence Reynolds and Damkohler numbers. The time scale for fluctuating heat release rate is deduced to be about τc/34 on an average, where τc is the planar laminar flame time scale, using direct numerical simulation (DNS) data. These results and the spatial distribution of mean reaction rate obtained from Reynolds-averaged Navier–Stokes (RANS) calculations of open turbulent premixed flames employing the standard model and an algebraic reaction rate closure, involving a recently developed scalar dissipation rate model, are used to obtain the far-field sound pressure level from open flames. The calculated values agree well with measured values for flames of different stoichiometry and fuel types, having a range of turbulence intensities and heat output. Detailed analyses of RANS results clearly suggest that the noise level from turbulent premixed flames having an extensive and uniform spatial distribution of heat release rate is low.

Erratum to: Geometrical Properties and Turbulent Flame Speed Measurements in Stationary Premixed V-flames Using Direct Numerical Simulation

Three dimensional, fully compressible direct numerical simulations (DNS) of premixed turbulent flames are carried out in a V-flame configuration. The governing equations and the numerical implementation are described in detail, including modifications made to the Navier–Stokes Characteristic Boundary Conditions (NSCBC) to accommodate the steep transverse velocity and composition gradients generated when the flame crosses the boundary. Three cases, at turbulence intensities, u′/sL, of 1, 2, and 6 are considered. The influence of the flame holder on downstream flame properties is assessed through the distributions of the surface-conditioned displacement speed, curvature and tangential strain rates, and compared to data from similarly processed planar flames. The distributions are found to be indistinguishable from planar flames for distances greater than about 17δth downstream of the flame holder, where δth is the laminar flame thermal thickness. Favre mean fields are constructed, and the growth of the mean flame brush is found to be well described by simple Taylor type diffusion. The turbulent flame speed, sT is evaluated from an expression describing the propagation speed of an isosurface of the mean reaction progress variable \(\tilde{c}\) in terms of the imbalance between the mean reactive, diffusive, and turbulent fluxes within the flame brush. The results are compared to the consumption speed, sC, calculated from the integral of the mean reaction rate, and to the predictions of a recently developed flame speed model (Kolla et al., Combust Sci Technol 181(3):518–535, 2009). The model predictions are improved in all cases by including the effects of mean molecular diffusion, and the overall agreement is good for the higher turbulence intensity cases once the tangential convective flux of \(\tilde{c}\) is taken into account.

On the correlation of heat release rate in turbulent premixed flames

Two-point spatial correlation of rate of change of fluctuating heat release rate dictates the sound emission from open turbulent flames and this correlation is not directly addressed in past studies. The results from Direct Numerical Simulation and laser diagnostics of turbulent premixed flames are analyzed to study this correlation function and the two-point spatial correlation of the fluctuating heat release rate. The analyses showed that these correlation functions can be represented very well using Gaussian functions. The integral length scale, ℓ, for the fluctuating heat release rate is about one to two planar laminar flame thermal thickness, δLo, and this is not influenced by turbulence Reynolds number and swirl. The length scale for the rate of change of fluctuating heat release rate is about δLo/4. The far field sound pressure levels of open turbulent premixed flames calculated by post processing RANS simulation results along with the above length scales compare very well with measured values.

Experimental annular stratified flames characterisation stabilised by weak swirl

A burner for the investigation of lean stratified premixed flames propagating in intense isotropic turbulence has been developed. Lean pre-mixtures of methane at different equivalence ratios were divided between two concentric co-flows to obtain annular stratification. Turbulence generators were used to control the level of turbulence intensity in the oncoming flow. A third annular weakly swirling airflow provided the flame stabilisation mechanism. A fundamental characteristic was that flame stabilisation did not rely on flow recirculation. The flames were maintained at a position where the local mass flux balanced the burning rate, resulting in a freely propagating turbulent flame front. The absence of physical surfaces in the vicinity of the flame provided free access for laser diagnostics. Stereoscopic Planar Image Velocimetry (SPIV) was applied to obtain the three components of the instantaneous velocity vectors on a vertical plane above the burner at the point of flame stabilisation. The instantaneous temperature fields were determined through Laser Induced Rayleigh (LIRay) scattering. Planar Laser Induced Fluorescence (PLIF) of acetone was used to calculate the average equivalence ratio distributions. Instantaneous turbulent burning velocities were extracted from SPIV results, while flame curvature and flame thermal thickness were calculated using the instantaneous temperature fields. The PDFs of these quantities were analysed to consider the separate influence of equivalence ratio stratification and turbulence. Increased levels of turbulence resulted in the expected higher turbulent burning velocities and flame front wrinkling. Flames characterised by higher fuel gradients showed higher turbulent burning velocities. Increased fuel concentration gradients gave rise to increased flame wrinkling, particularly when associated with positive small radius of curvature.

Numerical modeling of H 2–O 2 flames involving electronically-excited species [formula omitted], [formula omitted] and [formula omitted

The promoting action of electrical discharges on combustion processes results in reduction of the ignition delay, improvement of flame stability as well as extension of the flammability limits. These features are key technical issues for combustion improvement. One particularly promising approach consists of plasma-enhanced activation of the oxidizing substance, such as when transforming molecular oxygen into its electronically excited singlet delta O 2 ( a 1 Δ g ) and singlet sigma O 2 ( b 1 Σ g + ) states. In contrast with non-excited reactants, singlet oxygen molecules display a higher chemical activity and can affect reaction kinetics due to a decrease of the energy barrier associated with endoenergetic reactions. Previous publications have presented results of recent feasibility experiments on singlet oxygen generation in non-equilibrium electric discharges, from reduced pressures up to atmospheric pressure and for different discharge powers, using a high voltage pulse generator. It was possible to produce O 2 ( b 1 Σ g + ) and O 2 ( a 1 Δ g ) molecules and to detect them by optical emission spectroscopy. As a complement, the present study is devoted to the numerical study of ignition and combustion in subsonic flows of diluted hydrogen–air mixtures including electronically-excited O 2 molecules, as they appear in the experiments. All computations rely on a detailed reaction scheme implemented within the package CHEMKIN. The reaction mechanism involves the excited species O 2 ∗ ( = O 2 ( a 1 Δ g ) ) , O ∗ ( = O ( 1 D ) ) and OH ∗ ( = OH ( 2 Σ + ) ) . Results show that in the presence of excited oxygen in the initial mixture, a reduction of the ignition delay and of the minimum temperature for inflammation is observed, together with an increase of the laminar flame speed, the thermal flame thickness and of the maximum concentration of all main radicals. The extinction strain rate increases with oxygen excitation.

Scalar gradient and related quantities in turbulent premixed flames

Three-dimensional gradient measurements of a progress variable, c, in laminar and turbulent premixed flames are presented as rates of scalar dissipation, N, and scalar diffusion, D. A two-plane laser imaging technique is employed to obtain spatially resolved images of Rayleigh scattering in two planes instantaneously. Conditionally averaged quantities 〈 α∇ c · ∇ c| c = ζ〉 and 〈∇ · α∇ c| c = ζ〉 are measured in turbulent flames, and they show departure from the values in laminar flames. Local thickening of the thermal flame thickness is evident, and the broadening effect is more severe at higher turbulence Reynolds numbers. Joint pdfs of N and ζ indicate a global increase of broadened flame fronts as turbulence level increases. Pdfs of ζ show obvious bimodality with spikes at ζ = 0 and 1. The value of P(ζ) at ζ = 0.5 is about 0.1 for all cases studied. The ratio between the conditional and unconditional means of N seems to be similar for the turbulent flames studied. Scalar diffusion shows a more dominant peak in the reaction zone than in the preheat zone. The trend of the magnitude of D qualitatively follows that of N with respect to the turbulence level.

A numerical study of laminar flame wall quenching

Laminar flame quenching at the cold wall of a combustion chamber has been studied, using a numerical model to describe the reactive flow. The model combines an unsteady treatment of the fluid mechanics and a detailed chemical kinetic reaction mechanism. Fuels considered included both methane and methanol. Catalytic reactions at the wall surface are not included in the kinetic model. The one-dimensional case of flame propagation perpendicular to the wall was studied. Two reference cases are described in detail for flame quenching at 10 atm pressure and a wall temperature of 300°K with stoichiometric mixtures of methane-air and methanol-air. In each case a conventional laminar flame propagates toward the wall, approaching to within a distance determined by the thermal flame thickness. Chemical kinetic factors, particularly differences between the temperature dependence of radical recombination reactions and conventional chain branching and chain propagation reactions, are shown to be responsible for quenching the flame near the wall. The flame stagnates, but fuel remaining near the wall diffuses out of the boundary region and is rapidly oxidized away from the wall. Subsequent model calculations demonstrate the effects of variations in pressure, fuel-air equivalence ratio, wall temperature, and type of fuel. Computer results from these methane and methanol flame quenching models indicate that the total unburned hydrocarbon content is considerably smaller than is commonly believed and that thermal wall quenching may not be the major source for hydrocarbon emissions from internal combustion engines at near-stoichiometric conditions.

On the fundamentals of the boundary layer theory

The conditions that lead to the extinction of a premixed flame propagating along a channel of height 2h1 ∼ δT are studied using the thermo-diffusive approximation, with δT = DT/SL, DT and SL representing, respectively, the thermal flame thickness, the thermal conductivity and the planar flame speed.It is found that flame propagation is greatly affected by conductive heat losses to the wall ∂T/∂n=b˜(T-T0), where n denotes the transverse distance to the wall, T and T0 are, respectively, the fluid’s and wall’s temperature and b˜ is the heat transfer parameter. The sensitivity of the flame to heat losses grows as the channel narrows, leading to complete flame extinction at extremely small values of b˜=b˜c.As a way to overcome flame quenching at the walls, Lloyd and Weinberg [1] proposed the recirculation of part of the heat stored in the exhaust gases to preheat the cold combustible mixture. In order to understand the flame dynamics in the presence of heat recirculation, we analyze the problem of two parallel channels with a combustible mixture and an inert fluid moving in opposite directions, with maximum velocities m1 and m2 respectively, and where heat exchange is permitted through the common wall separating both channels. It is shown that flame extinction occurs if the velocity ratio m2/m1 is outside the range m2/m1 ∈ [m21,min m21.max], where the limiting values m21,min and m21.max are obtained numerically for a given set of parameters. The amplitude of this range depends, mainly, on the Damkhöler number d = [h1/(DT/SL)]2, quantity that represents the ratio between the channel’s height h1 and the thermal flame thickness DT/SL. It is shown that heat recirculation is capable of extending combustion to very small h1, but there is still a minimum value of the Damkhöler number dmin below which combustion is not possible. The evolution of dmin is computed numerically to give values as small as d = 0.0025 for a given combination of the geometric parameters of the problem. The maximum flame temperature computed in the parallel channel configuration rises above the adiabatic flame temperature Te due to the effect of the heat recirculation. This effect becomes more significant as d is reduced, leading to maximum temperatures close to T ≃ 1.4Te in very narrow channels.