Wrinkled Flame Front Research Articles

Dynamic flame surface density modelling of flame deflagration in vented explosion

The propagation of transient, turbulent premixed flames in a vented explosion chamber in the presence of a series of obstacles is numerically investigated by a dynamic formulation for the Flame Surface Density (FSD) with the Large Eddy Simulations (LES) technique. The chemistry is modelled by a one-step overall reaction, which simulates the reaction of a stoichiometric propane-air mixture. The FSD modelling in the reaction rate model is numerically employed with two different sub-grid scale (SGS) models. The first one is based on an empirical correlation of the SGS velocity fluctuations and the second one is based on similarity ideas involved in solving the wrinkled flame front considered as a fractal surface. The numerical predictions are analyzed and compared against an algebraic, simple FSD model together with experimental data. The calculations show that the dynamic FSD models provide superior results as compared with the algebraic FSD model. The comparisons demonstrate the importance of the contributions from the unresolved FSD and provide good agreement with experimental data for the flame structure, overpressure, and burning velocities.

On third order density contrast expansion of the evolution equation for wrinkled unsteady premixed flames

The dynamics of flat-on-average wrinkled flame front propagating through gaseous premixtures is considered. Leading the asymptotic expansions in powers of the burnt to unburned fractional density contrast (0<γ<1) to third order, an evolution equation (called S3) is obtained for the instantaneous front shapes. It reduces to Sivashinsky's original equation (called S1) as γ⟶0. It also modifies a previous attempt by Sivashinsky and Clavin (called S2) to improve it. Numerical integrations of the S3 equation reveals that the new quadratic and cubic non-linearities featured at 3rd order happen to mutually compensate partially one another for realistic γ's, and are negligible at γ⪡1. As a result, the flame shape and speed solutions to S3 nearly coincide with those of a S1/S2 type of equation, even for a 10-fold density variation (γ=0.9) and for unsteady situations, provided a singleO(1) coefficient a(γ) be adjusted therein, once for all for each γ. The O(γ2) (and small) correction to it mainly originates from a quartic non-linearity of geometrical origin. The agreement carries over to comparisons with some DNS of 2D steady wrinkled fronts. A phenomenological (yet asymptotically correct at γ⪡1 and exact in the linear limit) interpolating model equation is finally proposed to try and account for inertia effects associated with fast transients (e.g. acoustics related) while reproducing the above results on steady patterns.

Modelling and simulation of lean premixed turbulent methane/hydrogen/air flames with an effective Lewis number approach

Recent work on reaction modelling of turbulent lean premixed combustion has shown a significant influence of the Lewis number even at high turbulence intensities, if different fuels and varied pressure is regarded. This was unexpected, as the Lewis number is based on molecular transport quantities (ratio of molecular thermal diffusivity to mass diffusivity), while highly turbulent flames are thought to be dominated from turbulent mixing and not from molecular transport. A simple physical picture allows an explanation, assuming that essentially the leading part of the wrinkled flame front determines the flame propagation and the average reaction rate, while the rear part of the flame is of reduced importance here (determining possibly the burnout process and the flame brush thickness but not the flame propagation). Following this argumentation, mostly positively curved flame elements determine the flame propagation and the average reaction rate, where the influence of the preferential molecular diffusion and the Lewis number can easily seen to be important. Additionally, an extension of this picture allows a simple derivation of an effective Lewis number relation for lean hydrogen/methane mixtures. The applicability and the limit of this concept is investigated for two sets of flames: turbulent pressurized Bunsen flames, where hydrogen content and pressure is varied (from CNRS Orléans), and highly turbulent pressurized dump combustor flames where the hydrogen content is varied (from PSI Baden). For RANS simulations, comparison of flame length data between experiment and an effective Lewis number model shows a very good agreement for all these flames with hydrogen content of the fuel up to 20 vol.%, and even rather good agreement for 30% and 40% hydrogen.

Dynamics of a Longitudinally Forced, Bluff Body Stabilized Flame

This paper describes an investigation of the response of bluff body stabilized flames to harmonic oscillations. This problem involves two key elements – the excitation of hydrodynamic flow instabilities by acoustic waves, and the response of the flame to these harmonic flow instabilities. In the present work, data were obtained with inlet temperatures from 311 K to 866 K and flow velocities from 38 m/s to 170 m/s. These data show that the flame front response at the acoustic forcing frequency first increases linearly with downstream distance, then peaks and decays. The corresponding phase decreases linearly with axial distance, showing that wrinkles on the flame propagate with a nearly constant convection velocity. These results are compared to those obtained from a theoretical solution of the G-equation excited by a harmonically oscillating, convecting disturbance. This kinematic model shows that the key processes controlling the response are 1) the anchoring of the flame at the bluff body, 2) the excitation of flame-front wrinkles by the oscillating velocity, and 3) flame propagation normal to itself at the local flame speed. The first two process control the growth of the flame response and the last process controls the decay. These predictions are shown to describe the key features of the measured flame response characteristics.

Flame structure and radiation characteristics of CO/H2/CO2/air turbulent premixed flames at high pressure

Experimental study on turbulent premixed flames for a CO/H2/CO2/air mixture as a model of coal gasification syngas in a high pressure environment was performed up to 1.0MPa. CH4/air flames with laminar burning velocity and adiabatic flame temperature identical to those of CO/H2/CO2/air mixture were also employed, and then the flame structure and turbulent burning velocity analyzed using OH-PLIF as well as flame radiation characteristics were compared. Results showed that in the case of the CO/H2/CO2/air flame, very fine cusps were seen, these small cusps being generated on a large scale wrinkled flame front even for low u′/SL. Flame surface density of the CO/H2/CO2/air flame was higher than that of the CH4/air flame, and the mean volume of the turbulent flame region of CO/H2/CO2/air flame was smaller than that of the CH4/air flames at high pressure. Bending of ST/SL with u′/SL for the CO/H2/CO2/air flame was not observed in this experiment, while such bending was clearly seen for the CH4/air flame. The difference in the bending characteristics can be explained based on the scale relation between the smallest scale of flame wrinkles represented by the fractal inner cutoff and characteristic flame instability scale. The spectrum of flame radiation for the CO/H2/CO2/air flame at 0.5MPa showed continuous emission in the visible range of the wavelength, while that for CH4/air flames for the equivalence ratio of unity showed very intense H2O emission in the IR range. When the flames with identical adiabatic flame temperature for the CO/H2/CO2/air flame and the CH4/air flame were compared, the total radiation intensity of the former mixture was observed to be strong. The intense emission from the CO/H2/CO2/air flame is thought to be one of the mechanisms which generate very fine flame cusps as enhanced cellar instability for smaller Lewis number.

Estimation of three-dimensional flame surface densities from planar images in turbulent premixed combustion

Turbulence motions are, by nature, three-dimensional while planar imaging techniques, widely used in turbulent combustion, give only access to two-dimensional information. For example, to extract flame surface densities, a key ingredient of some turbulent combustion models, from planar images implicitly assumes an instantaneously two-dimensional flow, neglecting the unresolved flame front wrinkling. The objective here is to estimate flame surface densities from two-dimensional measurements assuming that (1) the flow is statistically two dimensional; (2) the measuring plane is a plane of symmetry of the mean flow, either by translation (homogeneous third direction as in slot burners for example) or by rotation (axi-symmetrical flows such as jets) and (3) flame movements in transverse directions are similar. The unknown flame front wrinkling is then modelled from known quantities. An excellent agreement is achieved against direct numerical simulation (DNS) data where all three-dimensional quantities are known, but validations in other conditions (larger DNS, experiments) are required.

E112 高圧環境におけるCO/H_2/CO_2/air乱流予混合火炎の構造に関する研究(OS-12:次世代の燃焼技術(I))

Experimental study of turbulent premixed flames for CO/H_2/CO_2/air mixture as a model of coal gasification syngas in a high pressure environment was performed up to 1.0 MPa. Flame structure and turbulent burning velocity were analyzed using OH-PLIF images. Results showed that very fine cusps were seen for CO/H_2/CO_2/air flames, these small cusps being generated on a large scale wrinkled flame front even for low u'/SL. Flame surface density of CO/H_2/CO_2/air flames was higher than that of CH_4/air flames, while the mean volume of the turbulent flame region was smaller.

Renormalization group and instantons in stochastic nonlinear dynamics

Stochastic counterparts of nonlinear dynamics are studied by means of nonperturbative functional methods developed in the framework of quantum field theory (QFT). In particular, we discuss fully developed turbulence, including leading corrections on possible compressibility of fluids, transport through porous media, theory of waterspouts and tsunami waves, stochastic magneto-hydrodynamics, turbulent transport in crossed fields, self-organized criticality, and dynamics of accelerated wrinkled flame fronts advancing in a wide canal. This report would be of interest to the broad auditorium of physicists and applied mathematicians, with a background in nonperturbative QFT methods or nonlinear dynamical systems, having an interest in both methodological developments and interdisciplinary applications.

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.

Linear response of stretch-affected premixed flames to flow oscillations

The linear response of 2D wedge-shaped premixed flames to harmonic velocity disturbances was studied, allowing for the influence of flame stretch manifested as variations in the local flame speed along the wrinkled flame front. Results obtained from analyzing the G-equation show that the flame response is mainly characterized by a Markstein number σ ˆ C , which measures the curvature effect of the wrinkles, and a Strouhal number, St f , defined as the angular frequency of the disturbance normalized by the time taken for the disturbance to propagate the flame length. Flame stretch is found to become important when the disturbance frequency satisfies σ ˆ C St f 2 ∼ O ( 1 ) , i.e. St f ∼ O ( σ ˆ C − 1 / 2 ) . Specifically, for disturbance frequencies below this order, stretch effects are small and the flame responds as an unstretched one. When the disturbance frequencies are of this order, the transfer function, defined as the ratio of the normalized fluctuation of the heat release rate to that of the velocity, is contributed mostly from fluctuations of the flame surface area, which is now affected by stretch. Finally, as the disturbance frequency increases to St f ∼ O ( σ ˆ C − 1 ) , i.e. σ ˆ C St f ∼ O ( 1 ) , the direct contribution from the stretch-affected flame speed fluctuation to the transfer function becomes comparable to that of the flame surface area. The present study phenomenologically explains the experimentally observed filtering effect in which the flame wrinkles developed at the flame base decay along the flame surface for large frequency disturbances as well as for thermal-diffusively stable and weakly unstable mixtures.

Spatiotemporal measurements of flame stretch and propagation rates for lean and rich CH 4/air premixed flames interacting with a turbulent-wake

A 1.5 m long turbulent-wake combustion vessel with a 0.15 m × 0.15 m cross-sectional area is proposed for spatiotemporal measurements of curvature, strain, dilatation and burning rates along a freely downward-propagating premixed flame interacting with a parallel row of staggered vortex pairs having both compression (negative) and extension (positive) strains simultaneously. The wanted wake is generated by rapidly withdrawing an electrically-controlled, horizontally-oriented sliding plate of 5 mm thickness for flame–wake interactions. Both rich and lean CH 4/air flames at the equivalence ratios ϕ = 1.4 and ϕ = 0.7 with nearly the same laminar burning velocity are studied, where flame–wake interactions and their time-dependent velocity fields are obtained by high-speed, high-resolution DPIV and laser-tomography. Correlations among curvature, strain, stretch, and dilatation rates along wrinkled flame fronts at different times are measured and thus their influences on front propagation rates can be analyzed. It is found that strain-related effects have significant influence on front propagation rates of rich CH 4/air (diffusionally stable) flames even when the curvature weights more in the total stretch than the strain rate does. The local propagation rates along the wrinkled flame front are more intense at negative strain rates corresponding to positive peak dilatation rates but the global propagation rate averaged along the rich flame front remains constant during all period of flame–wake interaction. For lean CH 4/air (diffusionally unstable) flames, the curvature becomes a dominant parameter influencing the structure and propagation of the wrinkled flame front, where both local and global propagation rates increase significantly with time, showing unsteady flame propagation. These experimental results suggest that the theory of laminar flame stretch can be applicable to a more complex flame–wake interaction involving unsteadiness and multitudinous interactions between vortices.

COMPARISON BETWEEN RNG AND FRACTAL COMBUSTION MODELS FOR LES OF UNCONFINED EXPLOSIONS

The largest hydrogen-air explosion in the open atmosphere is analysed using large eddy simulation (LES) with two combustion models. The first model is based on the analysis of flame front self-induced turbulence by Karlovitz with a maximum augmentation of the stoichiometric hydrogen-air burning velocity of 3.6. Flame front wrinkling due to flow turbulence is modelled using a combustion model based on the renormalization group theory. The second approach uses fractal theory and increases the burning rate with radius as R1/3. The first model provided a nearly constant flame velocity after initial acceleration, contradictory to theory and experiments. The second model provided better agreement with experiment on flame radius and acceleration, but overestimated the pressure wave peak in the positive phase. Analysis of the results demonstrates that the theoretical value of the fractal dimension D = 2.33 in the simulations could be reduced, particularly due to partial resolution of flame front wrinkling by LES.

Rethinking the Physics of a Large-Scale Vented Explosion and its Mitigation

The issue of large-scale vented deflagration modelling and mitigation is overviewed briefly. The physics of the phenomenon of coherent deflagrations, i.e., coupled internal and external explosions, in a system vented enclosure-atmosphere is studied further. Results of large eddy simulations (LES) of coherent deflagrations for the empty 547-m3 SOLVEX enclosure are presented. Numerical simulations of initial stages of wrinkled flame front propagation inside the enclosure and pressure generation up to the well-known first pressure peak demonstrate an excellent agreement with experimental observations without introduction of any adjustable parameter. The anisotropic component of turbulent combustion in an external vortical structure after the flame touches the vent edge is thought to be responsible for the significant increase of the flame surface density during deflagration outside the enclosure. The University of Ulster's LES model, based on the renormalization group (RNG) analysis of subgrid-scale modelling of isotropic turbulence and premixed combustion, is developed further to account for the anisotropic component in turbulent combustion in external vortex. The simple modification of the existent LES model allowed reproducing the experimental pressure dynamics inside and outside the enclosure at distances up to 54 m as well as the shape of the external deflagration. The numerical simulations confirmed results of former analysis that there is no extra intensification of combustion inside the enclosure. The increased second pressure peak inside the enclosure is mainly due to the pressure rise during highly turbulent external combustion and the decrease of outflow from the enclosure resulting from the pressure rise. It is concluded that in many practical cases physically sound simulations of coherent deflagrations are impossible without proper modelling of external combustion. It is suggested that in such cases the mitigation strategy should aim primarily at the suppression of combustion outside the enclosure.

A consistent level set formulation for large-eddy simulation of premixed turbulent combustion

A consistent formulation of the G-equation approach for LES is developed. The unfiltered G equation is valid only at the instantaneous flame front location. Hence, in a filtering procedure applied to derive the appropriate LES equation, only the instantaneous unfiltered flame surface can be considered. A new filter kernel is provided, which averages along the flame surface. The filter kernel is used to derive the G equation for the filtered flame front location. This equation has two unclosed terms, involving a flame front conditional averaged flow velocity, and a filtered propagation term. A model for the conditional velocity is derived, expressing this quantity in terms of the Favre-filtered flow velocity, which is typically known from a flow solver. This model leads to the appearance of a density ratio in the propagation term of the G equation. LES of combustion in the thin reaction zones regime is discussed in the LES regime diagram. A new line is identified separating the thin reaction zones regime into two parts, where the broadened flame thickness is larger and smaller than the filter size, respectively. A model for the propagation term is provided. This leads to a term including the subfilter turbulent burning velocity and an additional term proportional to the resolved flame front curvature. For the former, an algebraic model is provided from an equation for the subfilter flame front wrinkling. The latter term depends on the inverse of the subfilter Damköhler number and disappears in the corrugated flamelets regime.

Electric-field-induced flame speed modification

The effects of pulsed and continuous DC electric fields on the reaction zones of premixed propane–air flames have been investigated using several types of experimental measurements. All observed effects on the flame are dependent on the applied voltage polarity, indicating that negatively charged flame species do not play a role in the perturbation of the reaction zone. Experiments designed to characterize the electric-field-induced modifications of the shape and size of the inner cone, and the concomitant changes in the temperature profiles of flames with equivalence ratios between 0.8 and 1.7, are also reported. High-speed two-dimensional imaging of the flame response to a pulsed DC voltage shows that the unperturbed conical flame front (laminar flow) is driven into a wrinkled laminar flamelet (cellular) geometry on a time scale of the order of 5 ms. Temperature distributions derived from thin filament pyrometry (TFP) measurements in flames perturbed by continuous DC fields show similar large changes in the reaction zone geometry, with no change in maximum flame temperature. All measurements are consistent with the observed flame perturbations being a fluid mechanical response to the applied field brought about by forcing positive flame ions counter to the flow. The resulting electric pressure decreases Lewis numbers of the ionic species and drives the effective flame Lewis number below unity. The observed increases in flame speed and the flame fronts trend toward turbulence can be described in terms of the flame front wrinkling and concomitant increase in reaction sheet area. This effect is a potentially attractive means of controlling flame fluid mechanical characteristics. The observed effects require minimal input electrical power (<1 W for a 1 kW burner) due to the much better electric field coupling achieved in the present experiments compared to the previous studies.

CELLULAR STRUCTURE OF EXPLOSION FLAMES: MODELING AND LARGE-EDDY SIMULATION

Simulations of deflagration propagation through initially quiescent stoichiometric hydrogen/air mixture inside a large-scale 2.3-m-diameter spherical vessel are performed. A large-eddy simulation (LES) model of premixed combustion is suggested, which is based on a subgrid-scale turbulence model of renormalization group theory, a gradient method for combustion modeling and the dependence of burning velocity on transient pressure and temperature. An unstructured grid with one level of refinement/de-refinement around the flame front area is used. Wrinkled by hydrodynamic instability, the flame front structure has been resolved for the first time in LES of large-scale explosions. The growth of cell sizes with flame radius is reproduced numerically in agreement with theoretical and experimental results. The minimum resolved size of the flame cells is of the order of the simulated flame front thickness, which is about three control volume edges. The fractal dimension of the wrinkled flame front surface grows and reaches a value of 2.15, close to observed in experiments.

The Temporal Rate of Fractal Dimension Growth in Flame Front Wrinkles during the Early Phase of Flame Propagation in an SI Engine.

Turbulent premixed flame fronts during the early phase of flame propagation were visualized by a laser-light sheet technique in an optically accessible spark ignition engine. Time-resolved continuous images of wrinkling flame fronts were captured by a high-speed video camera. The test engine was operated at various engine speeds and compression ratios. The image data were processed to measure the fractal dimension in a time series for each cycle and to investigate the nature of fractal dimension growth in the early phase of flame development. The results show that the temporal rate of fractal dimension growth increases as the engine speed and the compression ratio increase. The empirical correlation was derived for the temporal rate of fractal dimension growth as a function of turbulence intensity and pressure.

Effects of buoyancy on open turbulent lean premixed methane-air V-flames

The behavior of lean premixed methane-air open V-flames of wrinkled flame fronts was studied both numerically and experimentally. In the numerical simulation, the mean flow fields of the flames were investigated when gravity was switched on and off to see the buoyancy influence on velocity and flame stretch. The results show that buoyancy accelerates the upward motion of the hot product plumes and hence changes the flow field. However, the changes are mainly concentrated in the far field area and not apparent in the area near flame brushes. The mean stretch of the flame brushes does change under the influence of gravity, but it seems that this does not influence the flame brushes strongly since the stretch rate is rather low. The experiments were done in the Bremen drop tower and the flame wrinkles were observed under both 1g0 and µg by using OH-PLIF. It can be clearly seen that the flame wrinkles were augmented under µg especially in the cases of weak turbulence. Thickness of the flame brushes was calculated according to the iso-lines of mean progress variable ē in order to see the buoyancy influence on the flame wrinkles. It was found that the impact of buoyancy is inversely related to the intensity of turbulence. The two possible mechanisms of the buoyancy influence on flame wrinkles, baroclinic mechanism and the impact of mean stretch, are discussed according to the numerical and experimental results. It seems that baroclinic mechanism is the controlling factor.

Visualization study of natural gas direct injection combustion

A visualization study of natural gas direct injection combustion was carried out by using a high speed video camera. The results show that the distribution of the stratified mixture di ers with the injection mode, with parallel and single injection tending to form a higher degree of mixture stratification than opposed injection. Flame propagates toward the downstream direction in the cases of parallel and single-injection combustion, and flame propagates outward from the centre of the combustion chamber in the case of opposed injection combustion. A characteristic of turbulent combustion with a wrinkled flame front is presented in natural gas direct injection combustion. Super-lean combustion can be realized owing to the formation of an ignitable stratified mixture with the optimum setting of the fuel injection timing.

Geometric interpretation of fractal parameters measured in turbulent premixed Bunsen flames

Fractal analyses have been conducted to investigate flame-front wrinkling of turbulent premixed Bunsen flames. Emphasis is placed on the geometric interpretation of measured fractal parameters and their relationship with parameters used in current combustion models. The outer cutoff scale is found to be four times the integral length scale of flame-front wrinkling defined in the Bray–Moss–Libby model. A revised Gibson length scale is derived by taking into account the curvature effect. Dependency of the revised Gibson scale on the Karlovitz number agrees better with the bulk of available data for the inner cutoff scale than the original definition. The term “self-similarity dimension” is proposed for the fractal dimension measured at finite spatial resolution to highlight the self-similarity feature of local flame fronts. The self-similarity dimension is found to increase linearly with time, and correlates well with the turbulent flame brush thickness.