Flame Brush Thickness Research Articles

Simulations of Scalar Transport in Developing Turbulent Flames Solving a Conditioned Balance Equation

A balance equation for the difference in the conditioned velocities and , derived and validated recently (Lipatnikov, 2008a, 2008b), is numerically solved in a statistically planar, one-dimensional case in order to (a) highlight the influence of premixed turbulent flame development on the direction of the mean scalar flux and (b) assess the equation by comparing computed trends with available experimental and DNS data. Numerical results show that (a) the flux is gradient during an early stage of flame development followed by a transition to countergradient scalar transport (i.e., ) at certain instant t tr ; (b) the transition time t tr is increased by the rms turbulent velocity and decreases when the density ratio or the laminar flame speed increases; and (c) even after the transition from gradient to countergradient scalar transport, the mean flame brush thickness grows because the mean rate of product creation overwhelms the transport term in the combustion progress variable balance equation and serves to not only control the turbulent burning rate, but also cause the growth of the thickness.

Multi-scale energy injection: a new tool to generate intense homogeneous and isotropic turbulence for premixed combustion

Nearly homogeneous and isotropic, highly turbulent flow, generated by an original multi-scale injector is experimentally studied. This multi-scale injector is made of three perforated plates shifted in space such that the diameter of their holes and their blockage ratio increase with the downstream distance. The Multi-Scale Turbulence Injector (hereafter, MuSTI) is compared with a Mono-Scale Turbulence Injector (MoSTI), the latter being constituted by only the last plate of MuSTI. This comparison is done for both cold and reactive flows. For the cold flow, it is shown that, in comparison with the classical mono-scale injector, for the MuSTI injector: (i) the turbulent kinetic energy is roughly twice larger, and the kinetic energy supply is distributed over the whole range of scales. This is emphasized by second and third order structure functions. (ii) the transverse fluxes of momentum and energy are enhanced, (iii) the homogeneity and isotropy are reached earlier ($\approx 50$%), (iv) the jet merging distance is the relevant scaling length-scale of the turbulent flow, (v) high turbulence intensity ($\approx 15$%) is achieved in the homogeneous and isotropic region, although the Reynolds number based on the Taylor microscale remains moderate ($Re_\lambda \approx 80$). In a second part, the interaction between the multi-scale generated turbulence and the premixed flame front is investigated by laser tomography. A lean V-shaped methane/air flame is stabilised on a heated rod in the homogeneous and isotropic region of the turbulent flow. The main observation is that the flame wrinkling is hugely amplified with the multi-scale generated injector, as testified by the increase of the flame brush thickness.

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.

Testing Premixed Turbulent Combustion Models by Studying Flame Dynamics

First, the following universal feature of premixed turbulent flame dynamics is highlighted: During an early stage of flame development, the burning velocity grows much faster than the mean flame brush thickness, because the two processes are controlled by the small-scale and large-scale turbulent eddies, respectively. Second, this feature of developing flames is exploited in order to test a number of different models of premixed turbulent combustion by theoretically and numerically studying an interaction of an initially laminar, planar, one-dimensional flame with a statistically stationary, planar, one-dimensional, and spatially uniform turbulent flow not affected by combustion. To test as many models as possible in a simple and unified manner, various combustion models are divided into three generalized groups: (i) algebraic models, which invoke an algebraic expression for the mean rate of product creation, (ii) gradient models, which involve a gradient-type source term in a balance equation for the mean combustion progress variable, and (iii) two-equation models, which deal not only with a balance equation for the mean combustion progress variable but also with either a balance equation for the flame surface density or a balance equation for the mean scalar dissipation rate. Analytical and numerical results reported in the paper indicate that solely the gradient models are able to yield substantially different growth rates of the turbulent burning velocity and the mean flame brush thickness.

Dynamic behavior of a freely-propagating turbulent premixed flame under global stretch rate oscillations

Dynamic features of a freely propagating turbulent premixed flame under global stretch rate oscillations were investigated by utilizing a jet-type low-swirl burner equipped with a high-speed valve on the swirl jet line. The bulk flow velocity, equivalence ratio and the nominal mean swirl number were 5 m/s, 0.80 and 1.23, respectively. Seven velocity forcing amplitudes, from 0.09 to 0.55, were examined with a single forcing frequency of 50 Hz. Three kinds of optical measurements, OH-PLIF, OH ∗ chemiluminescence and PIV, were conducted. All the data were measured or post-processed in a phase-locked manner to obtain phase-resolved information. The global transverse stretch rate showed in-phase oscillations centering around 60 (1/s). The oscillation amplitude of the stretch rate grew with the increment of the forcing amplitude. The turbulent flame structure in the core flow region varied largely in axial direction in response to the flowfield oscillations. The flame brush thickness and the flame surface area oscillated with a phase shift to the stretch rate oscillations. These two properties showed a maximum and minimum values in the increasing and decreasing stretch periods, respectively, for all the forcing amplitudes. Despite large variations in flame brush thickness at different phase angles, the normalized profiles collapse onto a consistent curve. This suggests that the self-similarity sustains in this dynamic flame. The global OH ∗ fluctuation response (i.e. response of global heat-release rate fluctuation) showed a linear dependency to the forcing velocity oscillation amplitudes. The flame surface area fluctuation response showed a linear tendency as well with a slope similar to that of the global OH ∗ fluctuation. This indicated that the flame surface area variations play a critical role in the global flame response.

Bidimensional simulation of premixed turbulent flame characteristics in an adiabatic vessel using Monte Carlo method

The main objective of this work is to simulate premixed turbulent flame in an adiabatic closed vessel using Monte Carlo scalar PDF transport method in two-dimensional geometry. We try principally to define turbulent flame characteristics during flame front propagation as: flame mean radius, flame turbulent radius, flame-wrinkling rate, flame-brush thickness and turbulent flame velocity. It is worth noting that the flame Kernel in the two-dimensional configuration grows having a wrinkled circular shape. Furthermore, the flame mean radius and the flame turbulent radius enhance more rapidly when increasing turbulence intensity or equivalence ratio.

FL1-3: A Two-Zone Thermodynamic Model for Hydrogen-Fueled S.I. Engines(FL: Fuels and Lubricants,General Session Papers)

Because of significantly different physical and chemical properties of hydrogen, compared to hydrocarbons, running an engine on hydrogen or modeling the combustion of hydrogen in engines is not straightforward. This paper focuses on modeling the power cycle of a hydrogen-fueled spark-ignition engine. The authors have investigated the laminar burning velocity u_1 of hydrogen/air mixtures, with allowance for residuals, as this is a fundamental parameter in turbulent burning velocity models. The correlation for u_1 was evaluated in a quasi-dimensional engine code by a comparison to experimental data on a single cylinder hydrogen engine. A two-equation combustion model was used to allow for flame brush thickness effects. Several models for the turbulent burning velocity were used to provide values for the turbulent 'entrainment' velocity. All models were able to correctly predict the effects of varying compression ratio and ignition timing. The ability to recover the effects of changes in equivalence ratio, one of the features in which a hydrogen engine differs clearly from hydrocarbon-fueled engines, is shown to be the benchmark to distinguish between models.

Simulation of flame surface density and burning rate of a premixed turbulent flame using contour advection

In this paper, a 2-dimensional rod-stabilized V-shaped flame is simulated using contour advection with surgery as well as the random vortex method. Effects of turbulence on various quantities, such as flame brush thickness and flame surface density, are investigated. The flame surface density Σ is estimated using the Bray–Moss–Libby formulation, which involves the use of a mean orientation factor σ c . As a comparison, values of Σ are also obtained using Shepherd's model, which employs the values of mean flame surface area and mean flame length. Local flame structure is characterized in terms of turbulent flame brush, orientation factor, and flame surface density. Profiles of Σ obtained using the two different models are compared and show that discrepancy is more evident with increasing turbulence intensity.

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.

Effects of flame development on stationary premixed turbulent combustion

A typical stationary premixed turbulent flame is a developing flame, as indicated by the growth of mean flame brush thickness with distance from the flame-stabilization point. The goal of this work is to assess the importance of modeling flame development for RANS of confined stationary premixed turbulent flames. For this purpose, computations of lean propane–air flames stabilized behind a bluff body in a channel under the conditions of the Validation Rig I experiments have been performed using eight different combustion models, all other things being equal. The models step-by-step address various phenomena associated with premixed turbulent flame development, in particular, (i) the growth of mean flame brush thickness, (ii) the development of turbulent diffusivity D t, and (iii) the development of turbulent burning velocity U t. Numerical results show that all these phenomena affect transverse profiles of the normalized Reynolds-averaged temperature in the studied flames. The effect of the development of U t on the computed profiles is well-pronounced even at large distances from the bluff body. The effect of the development of D t on the profiles decreases with distance. The flame speed closure model of premixed turbulent combustion, which addresses all the above phenomena, predicts the measured profiles reasonably well.

Global stretch effects in premixed turbulent combustion

Effects of large-scale stretching of a premixed turbulent flame by a spatially non-uniform mean flow on the burning velocity are studied in the simple case of an expanding spherical flame. Assuming that the mean flame structure is self-similar during flame kernel growth, an analytical expression is obtained for the difference in the burning velocities of statistically one-dimensional, planar and spherical flames, all other things being equal. In the limit case of a weakly curved flame, the expression is simplified to characterize the linear response of turbulent burning velocity to the curvature of the mean flame brush by introducing a “turbulent” Markstein number via analogy with the laminar case. The two aforementioned expressions (non-linear for highly curved flames and linear for weakly curved ones) are tested against the experimental data recently obtained in the Leeds fan-stirred bomb. When the ratio of the mean flame brush thickness to the flame radius is markedly less than unity, the linear expression and the turbulent Markstein number work well. When this ratio is comparable with unity, non-linear effects play a substantial role and the non-linear expression should be used to predict the experimental data. The analysis shows that the global stretching and development of the expanding spherical turbulent flame substantially affect turbulent burning velocity. In particular, the linear growth of the observed flame speed with time, well documented in the Leeds bomb, is explained. A method of processing the dependencies of flame radius on time is proposed to evaluate the fully developed unperturbed turbulent burning velocity.

Flame characteristics of turbulent lean premixed methane/air flames at high pressure: Turbulent flame speed and flame brush thickness

The effects of operating conditions and turbulence on flame front position, turbulent flame speed and flame brush thickness of lean premixed methane/air flames at high pressure are investigated experimentally. A comparison of the measured turbulent flame speeds with existing correlations is presented and discussed. The measurements were performed in an axis-symmetric, generic combustor at pressures up to p = 1.44 MPa, equivalence ratios in the range Φ = 0.43–0.56, preheating temperatures T = 673–773 K and for an inlet bulk velocity range of u BULK = 30–60 m/s. The turbulence intensity and the integral length scale at the combustor inlet were varied by means of turbulence grids with different geometry and by changing the grid position in the inlet channel. The isothermal flow field was characterized by two-dimensional particle image velocimetry (PIV). The characterization of the flame front was based on the statistical analysis of two-dimensional instantaneous images of the laser induced fluorescence of the OH radical (OH-PLIF). The analyses revealed that pressure has no effect on the flame front position, the turbulent flame speed, or on the flame front fluctuation (flame brush thickness). Decreasing the fuel concentration from Φ = 0.43 to Φ = 0.56 results in a flame elongation by a factor of 2 and a corresponding decrease of the turbulent flame speed by a factor of 3. For the same variation of the fuel concentration the flame brush thickness increases by a factor of 2. Additionally, the flame brush thickness was consistently observed to vary proportionally to the square root of the flame front position. The experimental values of the turbulent flame speed are in satisfactory agreement with the existing correlations.

Scaling of premixed turbulent flames in the corrugated regime

A novel apparatus for studying premixed combustion, involving the flow through a wide-angled diffuser, is described. Flames in pure methane/air mixtures and in methane/hydrogen/air have been stabilised at various heights in the diffuser, with various types of turbulence generators at inlet. The stabilisation conditions thus embraced a range of turbulence levels and integral length scales in the corrugated flamelet regime. Particle image velocimetry and planar laser-induced fluorescence were deployed to obtain the instantaneous velocity field in the unburnt mixture and the location of the flame front. Ensemble averages over 200 images allowed the statistics for 2-D flamelet surface density and the thickness of the flame brush to be measured in flames that were nearly planar in the mean. The flamelet surface density Σ was shown to be related to the length scale and the turbulence level, albeit in a nonlinear manner. However, there was no clear correlation for the flame brush thickness δ T , two different perforated plates generating turbulence at the same level and of the same length scale but giving very different thicknesses. Integrating Σ across the flame and combining with information from elsewhere on the effect of stretch on the laminar burning velocity, the consumption speed was estimated. As in all determinations of this parameter in the literature, this was found to be very much less than the turbulent displacement speed. Residual mean flame curvature is not thought to be sufficient to account for this, and explanations are being sought in a more complex response of the flamelets to the turbulence than just pure corrugation.

A Numerical Study Promoting Algebraic Models for the Lewis Number Effect in Atmospheric Turbulent Premixed Bunsen Flames

This numerical investigation carried out on turbulent lean premixed flames accounts for two algebraic – the Lindstedt–Vaos (LV) and the classic Bray–Moss–Libby (BML) – reaction rate models. Computed data from these two models is compared with the experimental data of Kobayashi et al. on 40 different methane, ethylene and propane Bunsen flames at 1 bar, where the mean flame cone angle is used for comparison. Both models gave reasonable qualitative trend for the whole set of data, in overall. In order to characterize quantitatively, firstly, corrections are made by tuning the model parameters fitting to the experimental methane–air (of Le = 1.0) flame data. In case of the LV model, results obtained by adjusting the pre-constant, i.e., reaction rate parameter, CR, from its original value 2.6 to 4.0, has proven to be in good agreement with the experiments. Similarly, for the BML model, with the tuning of the exponent n, in the wrinkling length scale, Ly = Cl⋅ lx(sL/u′)n from value unity to 1.2, the outcome is in accordance with the measured data. The deviation between the measured and calculated data sharply rises from methane to propane, i.e., with increasing Lewis number. It is deduced from the trends that the effect of Lewis number (for ethylene–air mixtures of Le = 1.2 and propane–air mixtures of Le = 1.62) is missing in both the models. The Lewis number of the fuel–air mixture is related to the laminar flame instabilities. Second, in order to quantify for its influence, the Lewis number effect is induced into both the models. It is found that by setting global reaction rate inversely proportional to the Lewis number in both the cases leads to a much better numerical prediction to this set of experimental flame data. Thus, by imparting an important phenomenon (the Lewis number effect) into the reaction rates, the generality of the two models is enhanced. However, functionality of the two models differs in predicting flame brush thickness, giving scope for further analysis.

Spatial Coherence of the Heat Release Fluctuations in Turbulent Jet and Swirl Flames

The noise generation of turbulent flames is governed by temporal changes of the total flame volume due to local heat release fluctuations. On the basis of the wave equation an expression for the relationship between the acoustic power and the heat release fluctuations is derived and a correlation function is obtained which reveals that the sound pressure level of flames is governed by the spatial coherence. Noise models rely on precise coherence information in terms of characteristic length scales, which are the measure of the acoustic efficiency of the flame. Since the published length scale information is scarce and inconsistent, length scales were measured for a number of laboratory flames using two measurement techniques developed for this purpose: A planar LIF-system with a repetition rate of 1 kHz acquires the instantaneous flame front position and heat release, whereas two chemiluminescence probes with an optics confining the measurement volume to a line of sight provide further spatial correlation data. For all flames investigated the length scales are smaller than the height of the burner exit annulus and they are of the order of the local flame brush thickness. Using the measured length scales, the coherent volume and the efficiency of the noise generation are calculated, which are three orders of magnitude higher than measured. However, the proper order of magnitude is obtained, if only the measured fluctuating part of the thermal power is used in the model and if the periodic formation of local zones with heat release overshoot and deficit are properly incorporated.

Modeling and 3D-Simulation of the Kinetic Effects in the Post-Flame Region of Turbulent Premixed Flames Based on the G-Equation Approach

In order to simulate the premixed turbulent flame and to study the thermodynamical and chemical state in the post flame region we integrate a number of appropriate submodels in a complete model. The flame front position is described as an iso-surface of a field variable G, and chemistry and turbulence-chemistry interaction models are conditioned on the flame front position following the conditioned progress variable approach (CPVA). Three special features of the model have been addressed to clarify following questions: (1) Is it really necessary to apply the conditioned progress variable approach, or is the ILDM based on the multivariate presumed PDF alone able to predict the flame behavior with reasonable accuracy? (2) Is the CPVA based on ILDM notedly advantageous compared to that based on the chemistry equilibrium? (3) How noticeable is the influence of some model parameters for the description of the flame brush thickness on the prediction of species concentration in the postflame region? For this purpose, some simulation results are presented and compared with experimental data of a turbulent premixed flame, the so-called “F2” case experimentally investigated by Chen et al. [Combust. Flame 107 (1996) 223–224]. Comparison results with different model combinations along with equilibrium chemistry consideration reveal that the CPVA based on ILDM achieved better agreement with experimental data provided suitable value for the model parameter is used.

High-order upwind compact scheme and simulation of turbulent premixed V-flame

A high-order accurate upwind compact difference scheme with an optimal control coefficient is developed to track the flame front of a premixed V-flame. In multi-dimensional problems, dispersion effect appears in the form of anisotropy. By means of Fourier analysis of the operators, anisotropic effects of the upwind compact difference schemes are analysed. Based on a level set algorithm with the effect of exothermicity and baroclinicity, the flame front is tracked. The high-order accurate upwind compact scheme is employed to approximate the level set equation. In order to suppress numerical oscillations, the group velocity control technique is used and the upwind compact difference scheme is combined with the random vortex method to simulate the turbulent premixed V-flame. Distributions of velocities and flame brush thickness are obtained by this technique and found to be comparable with experimental measurement. Copyright © 2005 John Wiley & Sons, Ltd.

A simple model of the World Trade Center fireball dynamics

An analytical model of the initial expansion of a fireball is presented. The model is based on an exact solution of the low Mach number combustion equations in the form initially proposed by the authors. The equations consist of the conservation of mass, momentum, and energy with an isobaric equation of state. The heat release rate is a prescribed spherically symmetric function characterized by a flame expansion velocity, a flame brush thickness that increases with time, and a heat release rate per unit surface area. The introduction of a prescribed heat release rate obviates the need for an explicit turbulence model. Thus, the inviscid forms of the conservation equations can be used in the analysis. The velocity field is decomposed into a spherically symmetric expansion field and a solenoidal component determined by the buoyancy induced vorticity field. The expansion field together with the induced pressure rise and temperature fields are spherically symmetric. However, the buoyancy forces induce vorticity where the temperature changes rapidly and break the spherical symmetry of the velocity field. The solution is used to study the initial expansion of the fireballs generated in the attack on the World Trade Center south tower. Video images are used to estimate the expansion rate of the fireball. This information, when combined with the analysis, leads to an estimate of the fuel consumed in the fireball that is independent of any assumptions about either the initial fuel distribution or the state of the building following the crash.

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.

A theoretical study of premixed turbulent flame development

Flame development in a statistically stationary and uniform, planar, one-dimensional turbulent flow is theoretically studied. A generalized balance equation for the mean combustion progress variable, which includes turbulent diffusion and pressure-driven transport terms, as well as the mean rate of product creation, is introduced and analyzed by invoking the sole assumption of a self-similar flame structure, well-supported by numerous experiments. The assumption offers the opportunity to simplify the problem by splitting the aforementioned partial differential equation into two ordinary differential equations, which separately model spatial variations of the progress variable and time variations of flame speed and thickness. The self-similar profile of the progress variable, obtained in numerous experiments, is theoretically predicted. Closures of the normalized pressure-driven transport term and mean rate of product creation are obtained. The closed balance equation shows that turbulent diffusion dominates during the initial stage of flame development, followed by the transition to counter-gradient transport in a sufficiently developed flame. A criterion of the transition is derived. The transition is promoted by the heat release and pressure-driven transport. Fully developed mean flame brush thickness and speed are shown to decrease when either density ratio or pressure-driven transport increases. Solutions for the development of the thickness are obtained. The development is accelerated by the pressure-driven transport and heat release.