Turbulent Flame Brush Thickness Research Articles

Revisiting the relation between premixed flame brush thickness and turbulent burning velocities from Ken Bray’s notes

Applying the Bray-Moss-Libby (BML) bi-modal asymptotic limit to a progress variable signal in a premixed turbulent flame, a relation is established between the variation rate of the mean turbulent flame brush thickness, the flame surface wrinkling and the turbulent burning velocity. This scaling suggests that the link between the amplification of the flame surface by turbulence and the increase of the turbulent burning velocity may need to be modulated by a corrective term proportional to the rate of variation of the turbulent flame brush thickness. This correction is expected to be driven by a short relaxation time scale, which is representative of the turbulent flame brush adjusting to its continuously varying turbulence environment. The analysis is grounded on the usual exact expressions for the various characteristic displacements and consumption speeds, widely used in turbulent combustion modeling. Prior to this analysis, the validity of the implication on these characteristic speeds of the thin flamelet framework, introduced to perform the derivation of the relation between the turbulent flame brush dynamics and the turbulent burning velocity, is evaluated from direct numerical simulation (DNS) of a turbulent premixed jet-flame.

Reynolds number scaling of burning rates in spherical turbulent premixed flames

Abstract

Flame speed characteristics of turbulent expanding flames in a rectangular channel

We present results from studies of freely expanding flames in a unique small-scale convective facility for different free-stream initial conditions, characterized by Taylor-Reynolds numbers in the range of Reλg=179−395 (using the streamwise RMS velocity component and the lateral Taylor-microscale) and an inertial subrange over two decades of wavenumbers. The isotropic, decaying turbulence is generated by an active vane grid. Adding natural gas far upstream, the premixed flow is ignited using Laser Induced Breakdown (LIB) ignition. The evolution of the resulting spherically expanding flames is investigated using qualitative OH-Planar Laser Induced Fluorescence (PLIF). It is shown that trends of flame speeds derived from mean flame radius growth agree well with results from different experimental setups, using a recently developed scaling based on a spectral closure of a thin flame model (Chaudhuri et al., Phys. Rev. E (2011)). Reliable computation of the flame surface density and turbulent flame brush thickness is enabled by the large number of ensembles that can be collected in this type of facility. Trends of these instantaneous statistical quantities are presented and used to further assess the results of time-dependent mean quantities.

Effects of strain rate, turbulence, reactant stoichiometry and heat losses on the interaction of turbulent premixed flames with stoichiometric counterflowing combustion products

Intense strain, turbulence, heat transfer, and mixing with combustion products can affect premixed flames in practical combustion devices. These effects are systematically studied in turbulent premixed CH4/N2/O2 flames using a reactant versus product counterflow system and independently varying bulk strain rate, turbulent Reynolds number, equivalence ratio of the reactant mixture, and temperature of the stoichiometric counterflowing combustion products. The flow field and the turbulent flames are investigated using particle image velocimetry (PIV) measurements and laser-induced fluorescence (LIF) imaging of OH. The OH-LIF images are used to identify the interface between the counterflowing streams, referred to here as the gas mixing layer interface (GMLI). The flame response for different flow conditions is compared in terms of the probability of localized extinction along the GMLI, the turbulent flame brush thickness, and flame position relative to the GMLI, by using an OH-LIF-based progress variable. The probability of localized extinction at the GMLI increases as the separation between the turbulent flame brush and the GMLI decreases. Flame fronts in the vicinity of the GMLI are more likely to extinguish as a result of heat losses, dilution of the reaction zone by the product stream, and large local strain rates. A higher probability of localized extinction at the GMLI is induced by either a larger bulk strain rate or a slower flame speed. As the turbulent Reynolds number increases, the corresponding increase in turbulent flame brush thickness enhances the interactions of the flame fronts with the GMLI. Heat losses are substantially less significant for cases in which the turbulent flame brush is sufficiently separated from the GMLI. For flames in close proximity to the GMLI, the effects of the product stream on the flame front differ for lean and rich reactant mixtures. These disparities are attributed in part to differences in the ignitibility of the reactant mixtures by the hot product stream.

Development and characterization of a variable turbulence generation system

Experimental turbulent combustion studies require systems that can simulate the turbulence intensities [u′/U0 ~ 20–30% (Koutmos and McGuirk in Exp Fluids 7(5):344–354, 1989)] and operating conditions of real systems. Furthermore, it is important to have systems where turbulence intensity can be varied independently of mean flow velocity, as quantities such as turbulent flame speed and turbulent flame brush thickness exhibit complex and not yet fully understood dependencies upon both U0 and u′. Finally, high pressure operation in a highly pre-heated environment requires systems that can be sealed, withstand high gas temperatures, and have remotely variable turbulence intensity that does not require system shut down and disassembly. This paper describes the development and characterization of a variable turbulence generation system for turbulent combustion studies. The system is capable of a wide range of turbulence intensities (10–30%) and turbulent Reynolds numbers (140–2,200) over a range of flow velocities. An important aspect of this system is the ability to vary the turbulence intensity remotely, without changing the mean flow velocity. This system is similar to the turbulence generators described by Videto and Santavicca (Combust Sci Technol 76(1):159–164, 1991) and Coppola and Gomez (Exp Therm Fluid Sci 33(7):1037–1048, 2009), where variable blockage ratio slots are located upstream of a contoured nozzle. Vortical structures from the slots impinge on the walls of the contoured nozzle to produce fine-scale turbulence. The flow field was characterized for two nozzle diameters using three-component Laser Doppler velocimetry (LDV) and hotwire anemometry for mean flow velocities from 4 to 50 m/s. This paper describes the key design features of the system, as well as the variation of mean and RMS velocity, integral length scales, and spectra with nozzle diameter, flow velocity, and turbulence generator blockage ratio.

Implementation and Validation of the G-equation Model Coupled with Flamelet Libraries for Simulating Premixed Combustion in I.C. Engines

The G-equation model was implemented in the commercial code ANSYS CFX and validated against experimental data in order to successfully simulate turbulent premixed combustion in internal combustion engines. The model is based on the level-set approach. Two transport equations are solved respectively for the G-scalar mean value, representing the local distance function from the time-averaged mean flame front, and its variance, correlated to the turbulent flame brush thickness. The model closure for tracking the flame front is based on an algebraic expression for the turbulent burning velocity. The composition of the reacted mixture is evaluated by coupling the code with flamelet libraries generated with the ANSYS CFX-RIF package by means of a reaction progress variable computed as a function of the G-related quantities. An innovative technique for periodically re-initializing the G-scalar field, in order to enforce geometrical consistency and avoid numerical instabilities, was developed, consisting of a least-square-based interface reconstruction and a minimization of the distance from the discretized flame front. In order to make the code suitable for spark-ignition engine applications the combustion model was coupled with a spark kernel model that simulates the early stages of the ignition process at sub-grid scales. The robustness and accuracy of the level-set approach with moving structured and unstructured meshes were assessed and the parallel performance of the combustion model was optimized in order to deal with large meshes in industrial applications. Validation was carried out by comparing simulations against experimental data for three different test-cases: a steady flame in a slot-burner, a transient spark-ignited premixed combustion in a cylinder with fixed walls and optical access and a spark-ignition research engine with flat head and flat piston. The results show good numerical properties and other attractive features in terms of geometrical description of the flame front and coupling with sub-models for detailed chemistry and spark-ignition. 2009 SAE International.

On unsteady premixed turbulent burning velocity prediction in internal combustion engines

In this work, it is shown how to extend the turbulent burning velocity approximation by Peters [N. Peters, Turbulent Combustion, Cambridge University Press, 2000.] for premixed flames in the flamelet regime in order to account for instationary turbulent flame development. Such instationary flame development occurs in spark ignition engines. The burning velocity approximation is embedded into the level set concept [F.A. Williams, in: J. Buckmaster (Ed.), The Mathematics of Combustion, SIAM, Philadelphia, 1985, pp. 97–131; N. Peters, J. Fluid Mech. 384 (1999) 107–132.] for premixed flames that distinguishes between large scale and small scale turbulence. Based on that formulation, a spark ignition criterion for successful ignition of premixed flames is presented. This criterion is based on the competition of premixed turbulent flame propagation and global curvature effects. The turbulent flame brush thickness is employed as a measure for the evolution of the flame. The combustion model is validated against homogeneous charge engine experiments. The results show that initial flame propagation is well predicted, which indicates that the unsteady evolution of the premixed flame is well captured.

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.

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.

Developing Premixed Turbulent Flames: Part I. A Self-Similar Regime of Flame Propagation

Contrary to numerous models addressing hypothetical, fully-developed premixed turbulent flames, the focus of this work is placed on the behavior of the developing flames, because they occur in most laboratory and industrial burners. By analyzing the available experimental data, the following trends are emphasized: (1) spatial profiles of the progress variable, presented in the dimensionless form by using the mean turbulent flame brush thickness, are collapsed to a universal curve well approximated by the complementary error function under a wide range of conditions; (2) the development of flame thickness, δ t (t), is well approximated by the turbulent diffusion theory in a range of 1/τ t ; and (3) the development of flame speed, St (t), and thickness are qualitatively different. Based on these trends, a self-similar regime of turbulent flame development is defined and its consequences for mean heat release models are considered. The ability of various models to describe this regime and, in particular, to yield the qualitatively different time-dependencies of the normalized St (t) and of δ t (t), indicated by experimental data, is assessed both analytically and numerically. It is shown that only time-dependent closures of the mean heat release rate can lead to the substantial difference between the development of the normalized flame speed and thickness. The numerical results indicate that the emphasized difference is a challenge for many current combustion models, but the so-called Flame Speed Closure model is well tailored to simulate it and other emphasized trends of turbulent flame development.

(2-10) Towards Evaluation of Turbulent Flame Speed((SI-4)S. I. Engine Combustion 4-Flame Propagation)

During the last decade, a new approach to multi-dimensional computations of premixed turbulent combustion has been developed. It consists of the use of an analytical expression for the local turbulent flame speed in order to close the averaged balance equations describing the combustion process. Several models have been suggested utilizing this approach and a number of successful applications to 3D computations of combustion in S. I. engines was reported at COMODIA 98. Although a submodel of turbulent flame speed, S_t, is at the core of this approach, a consensus has not been reached on this issue. The choice of the most reliable submodel is strongly impeded by the wide scatter of the published experimental data on S_t. Moreover, this scatter questions the physical correctness and practical usefulness of the concept of turbulent flame speed. The main goal of this work is to support the concept by discussing certain physical sources of the scatter and by outlining methods of reducing it. Three physical mechanisms are discussed in the paper. First, numerous experimental data indicate that typical premixed turbulent flames are developing flames, rather than fully developed ones, i. e., the mean turbulent flame brush thickness, δ_t, is not constant but grows permanently either with time in expanding flames or with the distance from the flame-holder in stationary flames. Due to the growth of δ_t, the speeds associated with different reference surfaces inside the flame brush can be substantially different, e. g., the difference can be as large as u'. A new method of unambigouosly defining the reference surface, the speed of which straightforwardly characterizes the mass burning rate, is developed by theoretically analyzing self-similar (i. e., spatial profiles of the mean progress variable, measured at different flame development times and presented in the dimensionless form by using δ_t(t), are collapsed to a universal curve) premixed turbulent flames in the statistically planar, one-dimensional case. This reference surface is characterized by the following reference value of the Favre-averaged progress variable [numerical formula] ; [numerical formula] ; [numerical formula], where ρ(ε)≡ρ^^-((x-x_f)/δ_t)/p_u is a universal dimensionless profile of the mean density (ρ(-∞)=1) and x_f(t) s the flame position. Numerical simulations indicate that the speed of this reference surface is equal to the mass burning rate divided by p_u and, thus, support the proposed method. Second, the mass burning rate in expanding spherical flames is well known to develop as the flame kernel grows, because, in particular, it experiences a wider range of the turbulence spectrum. Simple estimates discussed in the paper show that such transient effects can change the dependence of flame speed on turbulence characteristics not only quantitatively but even qualitatively. To suppress these effects, flame development time should be sufficiently large (e. g., larger than the turbulence time scale). Third, the speed of a statistically spherical flame differs from the speed of the planar one, other things being equal, due to (1) the mean flame curvature effects, and (2) the reduction in the maximum gas flow velocity induced by hot combustion product expansion, due to a wide flame thickness. In laminar flames, such effects are well known but weak. In turbulent flames, the effects can be substantial, because δ_t, is much larger than the laminar flame thickness. By analogy with the laminar combustion, the following equation [numerical formula], is proposed to be used in order to evaluate a fully developed turbulent flame speed, S^o_t, by processing the dependencies of the mean flame radius, r_f, on time, t, measured in expanding spherical flames. Here, Ma_t is a turbulent analog of the Markstein number used widely in laminar flame studies. This processing has been applied to the published experimental data. The

Measurements of the turbulent burning velocity and the structure of premixed flames on a low-swirl burner

A method has been developed to accurately determine the turbulent burning velocity in planar turbulent premixed flames stabilized by a low swirl. Six lean methane/air flames have been investigated covering the flamelet as well as the thin reaction zones regime. The probability of finding the instantaneous flame front is measured together with the velocity field by combining simultaneously OH–laser-induced predissociative fluorescence with either Rayleigh thermometry or particle image velocimetry (PIV). It is demonstrated that the turbulent flame brush thickness is independent of v� /sL and that the turbulent burning velocity agrees with predictions from a model equation for the flame surface area ratio using the level set approach. The measurements of the two-dimensional flowfield show a recirculation zone downstream of the flame stabilization area. This exhibits a comparable flow pattern to stagnation point flames. However, mean strain rates are much lower since the flames stabilize close to the burner exit, and the flame is not influenced by the recirculation zone. A comparison of the root-mean-square velocities obtained from Laser-Doppler Amemometry measurements to those determined by PIV show a good agreement. It can be shown that turbulence is attenuated in the flame zone and only moderately increased behind it.

Modification of the turbulent burning velocity by gas expansion

Premixed turbulent combustion in the corrugated flamelets regime has been addressed by modeling of a G-equation containing a gas-expansion term, the form of which was derived by generalizing results of Sivashinsky along lines initiated by Frankel. Previous analyses by the first author of the mean, variance, and two-point correlation spectrum of G, as well as their relation to the turbulent burning velocity, were extended to include the influences of gas expansion. It is shown that this effect has the same form as kinematic restoration but acts in the opposite direction. Because of this similarity in form, no new modeling approximations are required. On average, kinematic restoration dominates gas expansion. In physical terms, this means that the energy-containing eddies at the integral scale are strong enough to suppress gasdynamic instabilities at smaller scales. Gas expansion lessens the smoothing effect of kinematic restoration, thereby increasing the variance of G and the turbulent flame brush thickness. It also increases the turbulent burning velocity by a factor that increases with increasing ratio of unburned to burned gas density and with decreasing ratio of turbulence intensity to laminar burning velocity. The effect on the burning velocity, however, is not large, remaining less than 40% even as the turbulence intensity begins to decrease below the laminar burning velocity.

Modelling and Calculation of a Partially Premixed Turbulent Flame

A partially premixed turbulent flame has been modelled using the laminar flamelet concept, i.e. the assumption that laminar flames are embedded in the turbulent flow field. A combination of a premixed flamelet model and a diffusion flamelet model has been used for modelling this partially premixed flame. The premixed flamelet model uses a level set function G(x,t) and the diffusion flamelet model is based on the equation for the mixture fraction Z( x,t). To treat the turbulence closure problem use has been made of the standard κ-ϵ. model. Favre-aver-aged scalar quantities have been calculated from so-called flamelet libraries by making use of a presumed Probability Density Function (PDF) method. To evaluate the model, calculations for a partially premixed Hydrogen flame have been compared to measurement data of Wu el at. (1990). A good agreement has been found for the location of the premixed flame as well as for the turbulent flame brush thickness.

The turbulent burning velocity for large-scale and small-scale turbulence

The level-set approach is applied to a regime of premixed turbulent combustion where the Kolmogorov scale is smaller than the flame thickness. This regime is called the thin reaction zones regime. It is characterized by the condition that small eddies can penetrate into the preheat zone, but not into the reaction zone.By considering the iso-scalar surface of the deficient-species mass fraction Y immediately ahead of the reaction zone a field equation for the scalar quantity G(x, t) is derived, which describes the location of the thin reaction zone. It resembles the level-set equation used in the corrugated flamelet regime, but the resulting propagation velocity s*L normal to the front is a fluctuating quantity and the curvature term is multiplied by the diffusivity of the deficient species rather than the Markstein diffusivity. It is shown that in the thin reaction zones regime diffusive effects are dominant and the contribution of s*L to the solution of the level-set equation is small.In order to model turbulent premixed combustion an equation is used that contains only the leading-order terms of both regimes, the previously analysed corrugated flamelets regime and the thin reaction zones regime. That equation accounts for non-constant density but not for gas expansion effects within the flame front which are important in the corrugated flamelets regime. By splitting G into a mean and a fluctuation, equations for the Favre mean [Gtilde]and the variance [Gtilde]″2 are derived. These quantities describe the mean flame position and the turbulent flame brush thickness, respectively. The equation for [Gtilde]″2 is closed by considering two-point statistics. Scaling arguments are then used to derive a model equation for the flame surface area ratio [rhotilde]. The balance between production, kinematic restoration and dissipation in this equation leads to a quadratic equation for the turbulent burning velocity. Its solution shows the ‘bending’ behaviour of the turbulent to laminar burning velocity ratio sT/sL, plotted as a function of v′/sL. It is shown that the bending results from the transition from the corrugated amelets to the thin reaction zones regimes. This is equivalent to a transition from Damköhler's large-scale to his small-scale turbulence regime.