Klimov-Williams Criterion Research Articles

Premixed flames subjected to extreme levels of turbulence part I: Flame structure and a new measured regime diagram

This paper presents high-fidelity flame structure measurements of premixed methane–air Bunsen flames subjected to extreme levels of turbulence. Specifically, 28 cases were studied with longitudinal integral length scales (Lx) as large as 43 mm, turbulence levels (u′/SL) as high as 246, and turbulent Reynolds (ReT,0) and Karlovitz (KaT) numbers up to 99,000 and 533, respectively. Two techniques were employed to measure the preheat and reaction layer thicknesses of these flames. One consisted of planar laser-induced fluorescence (PLIF) imaging of CH radicals, while the other involved taking the product of simultaneously acquired PLIF images of formaldehyde (CH2O) and hydroxyl (OH) to produce “overlap-layers.” The average preheat layer thicknesses are found to increase with increasing u′/SL and with axial distance from the burner (x/D). In contrast, average reaction layer (i.e. CH- and overlap-layer) thicknesses did not increase appreciably even as u′/SL increased by a factor of ∼ 60. Furthermore, the reaction layer thicknesses (based on the CH images only) did not increase with increasing x/D. The reaction layers are also observed to remain continuous; that is, local extinction events are rarely observed. Although based on a sequence of combined CH–OH PLIF images acquired at a rate of 10 kHz, it is apparent that when instances of local extinction do occur they are the result of cool gas entrainment. The results presented here, as well as those from 12 prior experimental and 9 numerical investigations, do not agree with the predicted Klimov–Williams boundary on the theoretical Borghi Diagram. Thus, a new Measured Regime Diagram is proposed wherein the Klimov–Williams criterion is replaced by a metric that relates the turbulent diffusivity (DT=u′Lx) to the molecular diffusivity within the preheat layer (D*=SLδF,L). Justification for this replacement is based on physical reasoning and the fact that the line defined by DT/D* ≈ 180 accurately separates cases with thin flamelets from those with broadened preheat yet thin reaction layers (i.e. BP-TR flames). Additionally, the results suggest that the BP-TR regime extends well beyond what was previously theorized since neither broken nor broadened reaction layers were observed under conditions with Karlovitz numbers as high as 533, which is five times higher than the theoretical boundary.

Validation of turbulent flame speed models for methane–air-mixtures at high pressure gas engine conditions

To describe the premixed combustion of natural gas in internal combustion engines, the flamelet approach is often assumed to be appropriate. It postulates a thin flame front which is wrinkled by turbulence but locally spreads like a laminar flame. Numerous correlations for the macroscopic turbulent flame speed to the local laminar flame speed exist. In this study seven correlations are validated at engine conditions, i.e., at high pressure (up to 7.0MPa) and high turbulence (turbulent Reynolds number up to 4.4·104), with the help of measurements from a single cylinder research gas engine. The stoichiometry, the exhaust gas recirculation rate, and the engine speed are varied. Simulations of the detailed reaction kinetics with the diffusive species and energy transport are performed to calculate the laminar flame speed. The flame propagation is described by a zonal cylinder model on the basis of the measured in-cylinder pressure traces, to determine the turbulent flame speed with respect to the thermal expansion of the reacting gas. Additionally, Computational Fluid Dynamics (CFD) simulations of the in-cylinder charge motion are performed to describe the turbulent flow field. It is found that four flame speed correlations including a pressure-dependent term predict flame speed ratios in quantitative accordance to the measurements. This is noteworthy, as these correlations are mostly developed for lower turbulence and at considerable lower pressure. It supports the hypothesis that flamelet-like combustion is still found above the Klimov–Williams criterion.

A transition on minimum ignition energy for lean turbulent methane combustion in flamelet and distributed regimes

Minimum ignition energy (MIE) of lean methane–air mixtures is quantitatively measured using a high-power pulse generator which can vary ignition energies of a spark-electrode in the central position of a large fan-stirred cruciform burner. The burner equipped with a pair of counter-rotating fans and perforated plates can be used to generate isotropic turbulence having a very wide range of turbulent intensities ( u′) up to 8 m/s with negligible mean velocities. Observations of ignition, flame kernel development, and subsequent flame propagation in the central uniform region of the burner are recorded by a CMOS high-speed camera (5000 frames/s), showing distributed-like flames of very dispersive and fragmental structures with filiform edges for the first time. A complete MIE data set of lean methane–air mixtures at the equivalence ratio ϕ = 0.6 as a function of u′/ S L is obtained, where S L is the laminar burning velocity. It is found that there is a transition on values of MIE due to different modes of combustion. Before the transition, MIE only increases gradually with u′/ S L. Across the transition when u′/ S L > 24 corresponding to the commonly defined turbulent Karlovitz number Ka = ( u′/ S L) 2( Re T) −0.5 > 8, MIE increases abruptly, where Re T is the turbulent Reynolds number based on the integral length scale of turbulence. This transitional value of Ka is much greater than the Klimov–Williams criterion ( Ka = 1). Since values of MIE under different levels of turbulence should be relevant to the size of the reaction zone at least in the beginning of turbulent combustion, MIE ∼ δ 3 based on an order-of-magnitude criterion where δ is the reaction zone thickness. It is thus concluded that this new experimental finding proves the existence of both thin and broken reaction zones regimes proposed by Peters for a new regime diagram of premixed turbulent combustion.

The burning rate of premixed flames in moderate and intense turbulence

Burning rate measurements have been performed in lean (φ = 0.7) premixed methane/air flames stabilized on a low-swirl burner in moderate and intense turbulence, ( Re t = 460–1400). The purpose of this paper is to reconcile the burning rate determined by two widely used experimental methods: flow-velocity measurements and scalar measurements of the flame-surface density, Σ. The two sets of measurements, of conditional mass fluxes by Laser Doppler Velocimetry (LDV) and flame-surface density, were determined from the instantaneous flame-front positions obtained from OH Planar Laser Induced Fluorescence (OH-PLIF) images. It is important when making these comparisons to distinguish two measures of the turbulent burning velocity: the displacement, S D, and consumption speed, S C. Measurement of the consumption speed by the conditional flux method using laser Doppler velocimetry can account for the multidimensional affects of burner/flow geometry. In this burner geometry S C was found to be 30% of the cold-boundary flow velocity, S D. Both the turbulent displacement and consumption velocities were found to have linear dependencies on u′/ S L for values up to u′/ S L ∼7.3. The consumption speed is the more fundamental measure of the burning rate and is directly comparable to that derived from integration of flame-surface-density measurements. The similarity of the scalar and mass flux burning rates indicates that measurements of Σ, which are usually much simpler to perform than the flux measurements, can be used to test theoretical models and investigate the affect of upstream turbulence parameters on global flame-burning characteristics. Furthermore, comparison of the flux and scalar measurements has shown that even at flow/flame conditions above the Klimov-Williams criterion the affect of the turbulence on the local laminar burning rate, as expected from the Markstein number for this mixture, is small in the mean. Preliminary comparisons with models have been performed.

An experimental correlation of turbulent burning velocities for premixed turbulent methane-air combustion

This paper is devoted to the general correlation of turbulent burning velocities in terms of straining rates for premixed flames propagating in intense turbulence. This problem was investigated by the Leeds group led by Professor Bradley and many other researchers. We present here a new methodology based upon a downward propagating premixed CH4–air flame through a nearly isotropic turbulent flow field with a pair of specially designed ion probes for quantitative measurements of turbulent burning velocities. The improvements are that the flame propagation is not influenced by the ignition source and the unwanted turbulence from walls, effects of buoyancy and pressure rise due to burning are minimized, and a greater parameter range than hitherto is covered. The results show that both the turbulent burning velocity bending and the vitality of turbulent premixed flames are certain and surprising. Logarithmic plots of turbulent burning velocities S T/ S L – 1 against the turbulent intensities u '/ S L reveal a transition, where S L is the laminar burning velocity. Across the transition, the slope n changes from positive to negative when values of u '/ S L and/or Karlovitz number are greater than some critical values. This transition seems to correspond to the Klimov–Williams criterion that separates corrugated flamelets from distributed reaction zones. Interestingly, no global quenching of premixed turbulent flames is observed, even at u ' S L ≊ 40, a value significantly higher than in most previous measurements. At a fixed u '/ S L, values of the S T/ S L data vary with the equivalence ratio ϕ. This indicates that the common expression of the form S T/ S L = 1 + C ( u '/ S L) n cannot be applicable generally, because values of the constant C are different for different mixture compositions. It is found that all of the present data with different values of ϕ can be approximated by a simple expression, ( S T – S L)/ u ' ≊ 0.06 Da 0.59, where Da is the Damkohler number. Hence a better correlation of turbulent burning velocities in terms of straining rates for premixed turbulent (methane–air) combustion is proposed.

Measurement of the instantaneous detailed flame structure in turbulent premixed combustion

Simultaneous two-dimensional UV-Rayleigh thermometry and 2D laser-induced fluorescence of OH radicals were used to analyze highly turbulent, premixed natural gas/air flames with up to 130-kW heat release, where the turbulence conditions are approximately homogeneous in the measurement area. The turbulent Reynolds number has been varied between 60 and 2500, and the turbulent Karlovitz numbers ( Ka ), between 0.03 and 14. The simultaneously recorded single-shot images resolve the instantaneous structure of turbulent premixed flames to a spatial resolution of about 0.1 mm. For flames with Ka <1, the local flame-front structure (temperature and OH concentration profiles normal to the flame front) is similar to calculations Δ of laminar premixed flames. For flames with 1< Ka <14, the mean thermal flame-front thickness is significantly decreased compared with laminar unstrained calculations of flames with the same stoichiometry. This is contrary to the expectation of thickened flames (Klimov-Williams criterion). The mean flame thickness based on the OH concentration ascend is found to be independent of Ka . Obvious strongly localized deviations from a laminar-like flamelet structure were found for flames with Ka >5. In a few regions, temperatures above 1400 K, but no OH radicals, were observed, indicating regions with local extinction. A comparison of the size of small-scale eddies with the laminar eldovich flame-front thickness and the thermal thickness indicates that these eddies do have much smaller influence than has been expected by the Klimov-Williams criterion.

Experimental study of premixed flames in intense isotropic turbulence

A methodology for investigating premixed turbulent flames propagating in intense isotropic turbulence has been developed. The burner uses a turbulence generator developed by Videto and Santavicca and the flame is stabilized by weak-swirl generated by air injectors. This setup produces stable premixed turbulent flames under a wide range of mixture conditions and turbulence intensities. The experiments are designed to investigate systematically the changes in flame structures for conditions which can be classified as wrinkled laminar flames, corrugated flames, and flames with distributed reaction zones. Laser Doppler anemometry and Rayleigh scattering techniques are used to determine the turbulence and scalar statistics. In the intense turbulence, the flames are found to produce very little changes in the mean and rms velocities. Their flame speed increase linearly with turbulence intensity as for wrinkled laminar flames. The Rayleigh scattering probability density functions (pdfs) for flames within the distributed reaction zone regime are distinctly bimodal. The probabilities of the reacting states (i.e. contributions from within the reaction zone) is not higher than those of wrinkled laminar flame. These results show that there is no drastic changes in flame structures at Karlovitz number close to unity. This suggest that the Klimov Williams criterion underpredicts the resilience of wrinkled flamelets to intense turbulence.

Images of the quenching of a flame by a vortex—To quantify regimes of turbulent combustion

A laminar toroidal vortex is interacted with a laminar premixed flame in order to isolate and to visualize some of the fundamental physics of turbulent combustion. Localized quenching of the flame was observed using planar laser-induced fluorescence imaging of superequilibrium OH molecules in the counterflow flamefront region near the vortex leading edge. A quenching limit curve was measured as a function of vortex size and strength. In the second part of the study, the measurements are combined with concepts proposed by Poinsot, Veynante, and Candel in order to infer the thin flame limit, namely, the onset of distributed reactions, on a classical premixed turbulent combustion regime diagram. The measured thin flame limit indicates when laminar flamelet theories become invalid, since quenching allows hot products and reactants to coexist. Results are compared with the Klimov-Williams criterion. Vortex core diameters were as small as the flame thickness in some cases. The main conclusion is that small vortices are less effective at quenching a flame than was previously believed; therefore the inferred regime within which thin flame theories are valid extends to a turbulence intensity that is more than an order of magnitude larger than that which was previously predicted. Results also indicate that micromixing models, which assume that the smallest eddies exert the largest strain on a flame, are not realistic. Measured trends are in agreement with direct numerical simulations of Poinsot et al., but absolute values differ. The measured vortex Karlovitz number that is required to quench a flame is not constant but decreases by a factor of four as vortex size increases from one to five flame thicknesses. Thin-film pyrometry was used to quantify the radiative heat losses; quenching occurs when the products cool to approximately 1300 K, which is in agreement with stretched laminar flame calculations that include detailed chemistry. The quenching Karlovitz number for propane-air flames differs from that of methane-air flames, indicating the importance of detailed chemistry and transport properties. Flame curvature was observed to cause enhancement (or reduction) of the local reaction rate, depending on the Lewis number, in a manner that is consistent with stretched flame theory.

Quenching processes and premixed turbulent combustion diagrams

The structure of premixed turbulent flames is a problem of fundamental interest in combustion theory. Possible flame geometries have been imagined and diagrams indicating the corresponding regimes of combustion have been constructed on the basis of essentially intuitive and dimensional considerations. A new approach to this problem is described in the present paper. An extended definition of flamelet regimes based on the existence of a continuous active (not quenched) flame front separating fresh gases and burnt products is first introduced. Direct numerical simulations of flame/vortex interactions using the full Navier–Stokes equations and a simplified chemistry model are then performed to predict flame quenching by isolated vortices. The formulation includes non-unity Lewis number, non-constant viscosity and heat losses so that the effect of stretch, curvature, transient dynamics and viscous dissipation can be accounted for. As a result, flame quenching by vortices (which is one of the key processes in premixed turbulent combustion) may be computed accurately. The effects of curvature and viscous dissipation on flame/vortex interactions may also be characterized by the same simulations. The influence of non-unity Lewis number and of thermo-diffusive processes in turbulent premixed combustion is discussed by comparing flame responses for two values of the Lewis number (Le = 0.8 and 1.2). An elementary (‘spectral’) diagram giving the response of one flame to a vortex pair is constructed. This spectral diagram is then used, along with certain assumptions, to establish a turbulent combustion diagram similar to those proposed by Borghi (1985) or Williams (1985). Results show that flame fronts are much more resistant to quenching by vortices than expected from the classical theories. A cut-off scale and a quenching scale are also obtained and compared with the characteristic scales proposed by Peters (1986). Results show that strain is not the only important parameters determining flame/vortex interaction. Heat losses, curvature, viscous dissipation and transient dynamics have significant effects, especially for small scales and they strongly influence the boundaries of the combustion regimes. It is found, for example, that the Klimov–Williams criterion which is generally advocated to limit the flamelet region, underestimates the size of this region by more than an order of magnitude.

Local reaction zone thickness of a high intensity turbulent premixed flame

The present study has been performed to explore the detailed aspects of the reaction zone of a high intensity turbulent premixed flame, classified as a distributed reaction zone flame based on the Klimov-Williams criterion. A co-axial burner, and a micro-electrostatic probe were used to examine the local reaction intensity profiles across the flame. The measured ion current records imply that unburned mixtures and burned gases exist separately in the flame zone and local reaction zones of thicknesses much thinner than the flame zone can be defined. Assuming that the half value period of an ion curent fluctuation is a measure of the local reaction zone thickness in the direction passing the probe, the probability density function of it was examined to explore the aspects of local reaction zones in the flame zone. In order to interpret the probability density function distrubution of half value period, the ion current fluctuations to be recorded were predicted on the basis of the knowledge of ion current characteristics at premixed flame measurements. Considering the fluctuations of the inclined angle and velocity of the local reaction zones passing the probe, the probability density functions of the half value period were predicted for various thicknesses of the local reaction zones. Comparing the predicted probability density functions with the experimentally obtained ones, it was concluded that even in the extremely intense turbulence which satisfies the distributed reaction zone condition based on the Klimov-Williams criterion, the local reaction zone thickness is close to that of the laminar flame. This implies necessity to discuss the structure of the distributed reaction or to establish a novel criterion for existence of the distributed reaction zone not based on the characteristics of unbruned mixture turbulence.

Diagrams of premixed turbulent combustion based on direct simulation

The structure and morphology of premixed turbulent flames is a problem of fundamental interest in combustion theory. Diagrams indicating the typical structure of a flame submitted to a given turbulent flow have been constructed on the basis of essentially intuitive and dimensional considerations. Knowing the turbulence integral scale and the turbulent kinetic energy, these diagrams indicate if the flow will feature flamelets, pockets or distributed reaction zones. A new approach to this problem is described in the present paper. The method is based on direct numerical simulations of flame/vortex interactions. The interaction of a laminar flame front with a vortex pair is computed using the full Navier-Stokes equations. The formulation includes non-unity Lewis number, non-constant viscosity and heat losses so that the effects of stretch, curvature, transient dynamics and viscous dissipation can be accounted for. As a result, flame quenching by vortices (which is one of the key-processes in premixed turbulent combustion) may be computed accurately. An elementary (‘spectral’) diagram giving the response of one flame to a vortex pair is constructed. This spectral diagram is then used along with certain assumptions to establish a turbulent combustion diagram similar to those proposed by Borghi 2 or Williams 5 . Results show that flame fronts are more resistant to quenching by vortices than expected from the classical theories. A cut-off scale and a quenching scale are also obtained and compared to the characteristic scales proposed by Peters. 3 Stretch is not the only important parameter determining flame/vortex interaction. Curvature, viscous dissipation and transient dynamics have large effects, especially for small scales and they strongly influence the boundaries of the combustion regimes. For example, the Klimov-Williams criterion which has been advocated to limit the flamelet region, underestimates the size of this region by more than an order of magnitude.

An evaluation of the Klimov-Williams criterion

Different expressions of the Klimov-Williams criterion are explored and the relations between them are established. Five different calculation methods of the K-W criterion are proposed. The sensitivity of the criterion to its quantitative evaluation based on cold flow or flame turbulence parameters and to the use of various definitions of the laminar flame front thickness is assessed by using experimental data coming from V-shaped turbulent premixed flames. It is shown that when the Zeldovich characteristic length is adopted, the values of the K-W criterion are scattered around 0.2 either when the cold flow or the flame turbulence parameters are used. Its values range around unity when the total visible flame front thickness is used. Other implications for the interpretation of the structure of turbulent premixed flames of these various calculation methods are discussed.

Comment on the paper “Flame quenching by turbulence,” J. Chomiak and J. Jarosiński, Combust. Flame, 48:241–249 (1982)

Different expressions of the Klimov-Williams criterion are explored and the relations between them are established. Five different calculation methods of the K-W criterion are proposed. The sensitivity of the criterion to its quantitative evaluation based on cold flow or flame turbulence parameters and to the use of various definitions of the laminar flame front thickness is assessed by using experimental data coming from V-shaped turbulent premixed flames. It is shown that when the Zeldovich characteristic length is adopted, the values of the K-W criterion are scattered around 0.2 either when the cold flow or the flame turbulence parameters are used. Its values range around unity when the total visible flame front thickness is used. Other implications for the interpretation of the structure of turbulent premixed flames of these various calculation methods are discussed.