Turbulent propagation of premixed flames in the presence of Darrieus–Landau instability

We investigate the role played by hydrodynamic instability in the wrinkled flamelet regime of turbulent combustion, where the intensity of turbulence is small compared to the laminar flame speed and the scale large compared to the flame thickness. To this end the Michelson–Sivashinsky (MS) equation for flame front propagation in one and two spatial dimensions is studied in the presence of uncorrelated and correlated noise representing a turbulent flow field. The combined effect of turbulence intensity, integral scale, and an instability parameter related to the Markstein length are examined and turbulent propagation speed monitored for both stable planar flames and corrugated flames for which the planar conformation is unstable. For planar flames a particularly simple scaling law emerges, involving quadratic dependence on intensity and a linear dependence on the degree of instability. For corrugated flames we find the dependence on intensity to be substantially weaker than quadratic, revealing that corrugated flames are more resilient to turbulence than planar flames. The existence of a threshold turbulence intensity is also observed, below which the corrugated flame in the presence of turbulence behaves like a laminar flame. We also analyze the conformation of the flame surface in the presence of turbulence, revealing primary, large-scale wrinkles of a size comparable to the main corrugation. When the integral scale is much smaller than the characteristic corrugation length we observe, in addition to primary wrinkles, secondary small-scale wrinkles contaminating the surface. The flame then acquires a multi-scale, self-similar conformation, with a fractal dimension, for one-dimensional flames, plateauing at 1.23 for large intensities. The existence of an intermediate integral scale is also found at which the turbulent speed is maximized. When two-dimensional flames are subject to turbulence, the primary wrinkling patterns give rise to polyhedral-cellular structures which bear a very close resemblance to those observed in experiments on hydrodynamically unstable expanding spherical flames.     

Strain rates,flow patterns and flame surface densities in hydrodynamically unstable,weakly turbulent premixed flames

Recent numerical and experimental studies have unveiled a potentially marked difference between the laminar as well as turbulent propagation of premixed flames exhibiting Darrieus–Landau (DL) (or hydrodynamic) instabilities from flames for which instabilities are inhibited. In this study we utilize two-dimensional numerical simulations of slot burner flames as well as experimental Propane–Air Bunsen flames to analyse differences in turbulent propagation, strain rate and induced flow patterns of hydrodynamically stable and unstable flames. We also investigate the effects of hydrodynamic instability on quantities which are directly related to reaction rate closure models, such as flame surface density and stretch factor. A clear enhancement of turbulent flame speed can be observed for unstable flames, generally mitigated at higher turbulence intensity, which is attributed to a flame area increase induced by the characteristic cusp-like DL-induced corrugation, absent in stable flames, which occurs concurrently and in synergy with turbulent wrinkling. Unstable flames also exhibit, both numerically and experimentally, a different correlation between strain rate and flame curvature and are observed to give rise to a channeling of the induced flow in the fresh mixture. Conditionally averaged flame surface density is also observed to attain smaller values in unstable flames, as a result of the thicker turbulent flame brush, indicating that closure models should incorporate instability-related parameters in addition to turbulence-related parameters.     

Propagation of Darrieus–Landau unstable laminar and turbulent expanding flames

The propagation of laminar and turbulent expanding flames subjected to Darrieus–Landau (DL), hydrodynamic instability was experimentally studied by employing stoichiometric H₂/O₂/N₂ flames under quiescent and turbulent conditions performed in a newly developed medium-scale, fan-stirred combustion chamber. In quiescent environment, DL unstable laminar flame exhibits three-stage propagation, i.e. smooth expansion, transition acceleration, and self-similar acceleration. The self-similar acceleration is characterized by a power-law growth of acceleration exponent, α, with normalized Peclet number, which is different from the usually suggested self-similar propagation with a constant α. The imposed turbulence advances the onset of both transition acceleration and self-similar acceleration stages and promotes the strength of flame acceleration as additional wrinkles are invoked by turbulence eddies. A DL–turbulent interaction regime is confirmed to be the classical corrugated flamelets regime. Furthermore, the DL instability significantly facilitates the propagation of expanding flames in medium and even intense turbulence. The development of DL cells is not suppressed by turbulence eddies, and it needs to be considered in turbulent combustion.     

Effects of Lewis number,density ratio and gravity on burning velocity and conditional statistics in stagnating turbulent premixed flames

DNS is performed to analyse the effects of Lewis number (Le), density ratio and gravity in stagnating turbulent premixed flames. The results show good agreement with those of Lee and Huh (Combustion and Flame, Vol. 159, 2012, pp. 1576–1591) with respect to the turbulent burning velocity, S_T, in terms of turbulent diffusivity, flamelet thickness, mean curvature and displacement speed at the leading edge. In all four stagnating flames studied, a mean tangential strain rate resulting in a mean flamelet thickness smaller than the unstretched laminar flame thickness leads to an increase in S_T. A flame cusp of positive curvature involves a superadiabatic burned gas temperature due to diffusive–thermal instability for an Le less than unity. Wrinkling tends to be suppressed at a larger density ratio, not enhanced by hydrodynamic instability, in the stagnating flow configuration. Turbulence is produced, resulting in highly anisotropic turbulence with heavier unburned gas accelerating through a flame brush by Rayleigh–Taylor instability. Results are also provided on brush thickness, flame surface density and conditional velocities in burned and unburned gas and on flame surfaces to represent the internal brush structures for all four test flames.     

Turbulent flame and the darrieus–landau instability in a three-dimensional flow

The velocity of a weakly turbulent flame influenced by the Darrieus–Landau (DL) instability in a three-dimensional geometry is investigated on the basis of a model nonlinear equation. The equation takes into account realistically large thermal expansion of burning matter, external turbulence and thermal conduction related to small, but finite flame thickness. An external turbulent flow is imitated by a model obeying the Kolmogorov law. The effects of the DL instability and external turbulence are studied, first separately and then as they influence the flame dynamics together for different values of the turbulent intensity, different thermal expansion of the burning matter and different length scales of the hydrodynamic motion controlled by the width of a hypothetic tube with ideally adiabatic walls. The velocity increase obtained is in a good agreement with experimental results in the case of relatively weak turbulent intensity.     

Analytical Interaction of the Acoustic Wave and Turbulent Flame

A modified resonance model of a weakly turbulent flame in a high-frequency acoustic wave is derived analytically. Under the mechanism of Darrieus-Landau instability, the amplitude of flame wrinkles, which is as functions of the expansion coefficient and the perturbation wave number, increases greatly independent of the stationary＇ turbulence. The high perturbation wave number makes the resonance easier to be triggered but weakened with respect to the extra acoustic wave. In a closed burning chamber with the acoustic wave induced by the flame itself, the high perturbation wave number is to restrain the resonance for a realistic flame.     

稀甲烷/氢气预混湍流传播火焰实验研究

本文采用定容湍流燃烧弹获取了稀甲烷/氢气/空气在强湍流条件下的火焰发展历程,研究了湍流火焰在负马克斯坦数条件下的传播特性.结果表明,湍流火焰呈现自相似传播特性,即使在强湍流条件下,湍流传播火焰仍然会受到不稳定性的影响.并且随着马克斯坦数的减小,不稳定性对湍流传播火焰的影响增强。同时,本文获得一种新的湍流燃烧速度拟合公式,包含了负马克斯坦数条件下不稳定性对湍流燃烧速度的影响。     

Large scale effects in weakly turbulent premixed flames

In this study we numerically investigate large scale premixed flames in weakly turbulent flow fields. A large scale flame is classified as such based on a reference hydrodynamic lengthscale being larger than a neutral (cutoff) lengthscale for which the hydrodynamic or Darrieus–Landau (DL) instability is balanced by stabilizing diffusive effects. As a result, DL instability can develop for large scale flames and is inhibited otherwise. Direct numerical simulations of both large scale and small scale three-dimensional, weakly turbulent flames are performed at constant Karlovitz and turbulent Reynolds number, using two paradigmatic configurations, namely a statistically planar flame and a slot Bunsen flame. As expected from linear stability analysis, DL instability induces its characteristic cusp-like corrugation only on large scale flames. We therefore observe significant morphological and topological differences as well as DL-enhanced turbulent flame speeds in large scale flames. Furthermore, we investigate issues related to reaction rate modeling in the context of flame surface density closure. Thicker flame brushes are observed for large scale flames resulting in smaller flame surface densities and overall larger wrinkling factors.     

湍流预混火焰中的浮力效应

本文利用数值模拟研究了浮力对湍流预混V形火焰平均速度场的影响,发现浮力效应主要体现在远场区域,而在火焰刷附近非常有限;利用落塔和 OH-PLIF 方法在正常重力和微重力下观测了火焰皱褶,发现浮力压制火焰皱褶的程度与湍流强度密切相关。分析表明斜压机理是浮力影响火焰皱褶的重要原因。     

Characteristic regimes of premixed gas combustion in high-porosity micro-fibrous porous media

Dynamical behaviour of the premixed flame propagating in the inert high-porosity micro-fibrous porous media has been studied numerically. Effects of mixture filtration velocity, equivalence ratio and burner transverse size on the flame structure have been investigated and the regions of existence of different combustion regimes have been determined. It was found that the influence of the hydrodynamic instability on the flame dynamics is significant in the case of the moderate and high filtration velocities and this effect is negligible at the low velocities. At the moderate filtration velocities the effect of hydrodynamic instability manifests in the flame front deformation and in particular in the flame inclination. It was found that the flame can be stabilized within the whole interval of the filtration gas velocity, whereas in the ordinary porous media the standing wave is settled only at fixed value of gas filtration velocity. This finding is in line with recent experimental results on combustion in micro-fibrous porous media (Yang et al., Combust. Sci. Tech. 181 (2009), 1–16). Possible physical interpretation of the flame anchoring effect may be given on the base of present numerical analysis. At the high filtration velocities the hydrodynamic instability manifests itself in periodical appearance of the moving wrinkles on the flame front surface which forms non stationary high temperature trailing spots behind the leading part of the flame front. Such dynamics may be associated with splitting wave structures which were revealed in previous experiments (Yang et al., Combust. Sci. Tech. 181 (2009), 1–16).     

Analysis of turbulent premixed flame structure using simultaneous PIV-OH PLIF

In the present study, we used a simultaneous PIV-OH PLIF measurement to acquire the strain rate and the chemical intensity and suggested a new combustion phase diagram. This simultaneous measurement was used to analyze the flame structure and to classify the combustion regimes of the opposed impinging jet combustor according to the change of the orifice diameters at the pre-chambers. The shear strain rates were obtained from the velocity measurement by PIV to represent flow characteristics and the OH radical intensities were obtained from OH PUF to indicate the flame characteristics. When the strain rate and OH intensity at each point of the measurement zones are plotted at the strain rate-chemical intensity diagram, the distribution of each case showed the characteristics of each flame regime. The change of combustor condition made different distribution in the combustion phase diagram. As the orifice diameter of the pre-chamber decreases, well-mixed turbulent flames are produced and the combustion phase is moved from the moderated turbulence regime to the thickened reaction regime.     

Compressible turbulent flame speeds of highly turbulent standing flames

In this paper we present the first measurement of turbulent burning velocities of a highly turbulent compressible standing flame induced by shock-driven turbulence in a Turbulent Shock Tube. High-speed schlieren, chemiluminescence, PIV, and dynamic pressure measurements are made to quantify flame–turbulence interaction for high levels of turbulence at elevated temperatures and pressure. Distributions of turbulent velocities, vorticity and turbulent strain are provided for regions ahead and behind the standing flame. The turbulent flame speed is directly measured for the high-Mach standing turbulent flame. From measurements of the flame turbulent speed and turbulent Mach number, transition into a non-linear compressibility regime at turbulent Mach numbers above 0.4 is confirmed, and a possible mechanism for flame generated turbulence and deflagration-to-detonation transition is established.     

Transport and Turbulence Experiments in Three Regimes of a Magnetized Plasma

The occurrence of turbulence and its influence on plasma viscosity have been investigated. A simple model of turbulence has been obtained by the balance of the growth of the combined Rayleigh-Taylor and Kelvin-Helmholtz instability with the damping by friction against the neutrals, by kinetic viscosity and by turbulent viscosity itself. In the experiment, a hollow cathode arc, three regimes can be distinguished: a kinetic, a frictional and a turbulent regime. By variations of the discharge parameters around a suitably chosen operating point, transitions between the three regimes are caused. It appears that the longitudinal drift velocity is also influenced by the turbulence. A dispersion relation for the large scale oscillation of the whole arc has been derived and checked experimentally.     

Stimulated Brillouin scattering in a plasma with ion-acoustic turbulence

A theory of stimulated Brillouin scattering (STBS) in a plasma with ion-acoustic turbulence is developed using concepts of parametric instability under conditions when equations of two-temperature hydrodynamics can be used to describe ion-acoustic perturbations of the electron density. The temporal growth rate of the absolute instability and the spatial gain of the scattered wave are determined. The dependence of the threshold density of the radiation flux on the angle between the scattering wave vector and the direction of anisotropy of the turbulent noise is described. A new effect of STBS forbiddenness caused by anomalous turbulent heating of the ions is predicted for a plasma with a high level of turbulent noise.     

Impact of turbulence on flame brush development of acoustically excited rod-stabilized flames

Coherent structures, such as those arising from hydrodynamic instabilities or excited by thermoacoustic oscillations, can significantly impact flame structure and, consequently, the nature of heat release. The focus of this work is to study how coherent oscillations of varying amplitudes can impact the growth of the flame brush in a bluff-body stabilized flame and how this impact is influenced by the free stream turbulence intensity of the flow approaching the bluff body. We do this by providing external acoustic excitation at the natural frequency of vortex shedding to simulate a highly-coupled thermoacoustic instability, and we vary the in-flow turbulence intensity using perforated plates upstream of the flame. We use high-speed stereoscopic particle image velocimetry to obtain the three-component velocity field and we use the Mie-scattering images to quantify the behavior of the flame edge. Our results show that in the low-turbulence conditions, presence of high-amplitude acoustic excitation can cause the flame brush to exhibit a step-function growth, indicating that the presence of strong vortical structures close to the flame can suppress flame brush growth. This impact is strongly dependent on the in-flow turbulence intensity and the flame brush development in conditions with higher levels of in-flow turbulence are minimally impacted by increasing amplitudes of acoustic excitation. These findings suggest that the sensitivity of the flow and flame to high-amplitude coherent oscillations is a strong function of the in-flow turbulence intensity.     

Subgrid modeling of intrinsic instabilities in premixed flame propagation

This work is devoted to the investigation and subgrid-scale modeling of intrinsic flame instabilities occurring in the propagation of a deflagration wave. Such instabilities, of hydrodynamic and thermodiffusive origin, are expected to be of particular relevance in recent technological trends such as in the use of hydrogen as a clean energy carrier or as a secondary fuel in hydrogen enriched combustion. A dedicated set of direct numerical simulations is presented and used, in conjunction with coherent literature results, in order to develop scaling arguments for the propagation speed of self-wrinkled flames which are also supported by the outcomes of a weakly non-linear model, namely the Sivashinsky equation. The observed scaling is based on the definition of the number of unstable wavelengths in a reference hydrodynamic lengthscale, in other words the ratio between the neutral or cutoff lengthscale of intrinsic instabilities and the lateral domain of a planar flame. The scalings are then employed to develop an algebraic model for the wrinkling factor in the context of a flame surface density closure approach. An a-priori analysis shows that the model correctly captures the flame wrinkling caused by intrinsic instability at sub grid level. A strategy to include the developed self-wrinkling model in the context of a turbulent combustion model is finally discussed on the basis of the turbulence induced cut-off concept.     

Detailed measurements of local scalar front structures in stagnation-type turbulent premixed flames

Local scalar front structures of OH mole fraction, reaction progress variable, and its three-dimensional gradient have been measured in stagnation-type turbulent premixed flames. The reaction progress variable front is observed to change with increasing turbulence from parallel iso-scalar contours but reduced progress variable gradients, called the lamella-like front, to disrupted non-parallel iso-contours that deviate substantially from those of wrinkled laminar flamelets, called the non-flamelet front. This transition is attributed to the different scales of interaction between the flame internal structure and a spectrum of turbulence extending from the integral scale to the Kolmogorov scale. The lamella-like front pattern occurs when the length scales of interaction are smaller than the laminar flame thickness but the time scales are greater than the flame residence time. The non-flamelet front pattern occurs when the length scales of interaction are greater than the laminar flame thickness but the time scales are smaller than the flame residence time. This difference corresponds to the change of combustion regime from complex-strain flame front to turbulent flame front on a revised regime diagram. A correlation is also proposed for the turbulent flame brush thickness as a function of turbulent Reynolds number and heat release parameter. The heat release parameter is considered to arise from the non-passive effects of flame-surface wrinkling.     

Experimental analysis of local flame extinction in a turbulent jet diffusion flame by high repetition 2-D laser techniques and multi-scalar measurements

In this paper, we present a detailed experimental study of turbulence chemistry interactions in the “DLR_B” turbulent jet diffusion flame. The flame operates on mixtures of CH₄, H₂, and N₂ in the fuel stream at Re = 22,800 and is a target flame within the TNF workshop. Extinction and re-ignition events can be tracked in real time and related to the underlying flow field phenomena and temperature fields. Time resolved measurements of OH radical concentration fields are performed in combination with temperature and velocity field measurements. For this purpose, we combined high repetition rate (33 kHz) PLIF imaging with stereoscopic PIV and double pulse Rayleigh imaging techniques. Comparisons are made with results from multi-scalar Raman/Rayleigh/LIF point measurements that reveal the thermochemical state of the flame. The large deviations from equilibrium observed on resulting OH/temperature joint pdfs could be related to strain rate and Damköhler number variations caused by turbulent flow structures leading to frequent extinctions. The 2D measurement series uniquely reveal the underlying mechanism that can lead to such events. Finally, comparisons are made to strained laminar flame calculations, which are generally found to be in good agreement with the measured data.     

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

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