Large Eddy Simulation of a Bluff Body Stabilised Premixed Flame Using Flamelets

Large Eddy Simulations of an unconfined turbulent lean premixed flame, which is stabilised behind a bluff body, are conducted using unstrained flamelets as the sub-grid scale combustion closure. The statistics from the simulations are compared with the corresponding data obtained from the experiment and it is demonstrated that the experimental observations are well captured. The relative positioning of the shear layers and the flame brush are analysed to understand the radial variations of the turbulent kinetic energy at various streamwise locations. These results are also compared to confined bluff body stabilised flames, to shed light on the relative role of incoming and shear driven turbulence on the behaviour of the flame brush and the turbulent kinetic energy variation across it.     

Assessment of the performances of sub-grid scalar flux models for premixed flames with different global Lewis numbers: A Direct Numerical Simulation analysis

The statistical behaviours of sub-grid flux of reaction progress variable has been assessed for premixed turbulent flames with global Lewis number Le (=thermal diffusivity/mass diffusivity) ranging from 0.34 to 1.2 using a Direct Numerical Simulation (DNS) database of freely propagating statistically planar flames. It is known that the sub-grid scalar flux shows counter-gradient transport when the velocity jump across the flame due to heat release overcomes the effects of turbulent velocity fluctuation. The results show that the sub-grid scalar flux components exhibit counter-gradient transport for all cases considered here. The extent of counter-gradient transport increases with increasing filter width Δ and decreasing value of Le. This is due to the fact that flames with Le ≪ 1 (e.g. Le = 0.34) exhibit thermo-diffusive instabilities, which in turn increases the extent of counter-gradient transport. The effects of heat release and flame normal acceleration weaken with increasing Le. Several established algebraic models have been assessed in comparison to the sub-grid scalar flux components extracted from explicitly filtered DNS data in terms of their correlation coefficients at the vector level and their mean variation conditional on the Favre-filtered progress variable. The gradient transport closure does neither capture the quantitative nor the qualitative behaviour of the different sub-grid scalar flux components for all filter widths in all cases considered here. Models which account for local flame normal acceleration perform better, especially when the flame remains completely unresolved. In particular those models that account for the alignment of local resolved velocity and scalar gradients by using a tensor diffusivity, perform relatively better than the other alternative models irrespective of Le.     

Scale similarity based models and their application to subgrid scale scalar flux modelling in the context of turbulent premixed flames

The performance of a variety of scale similarity (SS) type models for closure of sub-grid scalar flux in the context of Large Eddy Simulations (LES) of premixed turbulent combustion has been assessed. In addition to the well-known SS models, a more recent development by Anderson and Domaradzki (2012) is included in the analysis and also further model extensions and improvements are discussed. The work is based on a priori analysis of two Direct Numerical Simulation (DNS) databases of freely propagating turbulent premixed flames with a range of different Lewis and turbulent Reynolds numbers. Depending on the balance between the effects of flame normal acceleration due to heat release and the effects of turbulent velocity fluctuations, as well as the filter size, the subgrid-scalar flux exhibits both local gradient and counter-gradient transport which presents a considerable modelling challenge. The assessment is based on a correlation analysis and on the magnitude of the model expressions conditional on the Favre averaged reaction progress variable in comparison to the value obtained from DNS. Despite the fact that most of the models have been developed in the context of momentum transport in non-reactive flows they show either comparable or better performance in comparison to more conventional models used for reactive scalar flux closure. It is found that some models are sensitive to the test filter width and recommendations are provided in this regard. Further it is observed that the use of a Favre test filter substantially increases the correlation strength in direction of mean flame propagation where effects of heat release are most pronounced.     

A DNS Study of Closure Relations for Convection Flux Term in Transport Equation for Mean Reaction Rate in Turbulent Flow

The present work aims at modeling the entire convection flux \(\overline {\rho \mathbf {u}W}\) in the transport equation for a mean reaction rate \(\overline {\rho W}\) in a turbulent flow, which (equation) was recently put forward by the present authors. In order to model the flux, several simple closure relations are developed by introducing flow velocity conditioned to reaction zone and interpolating this velocity between two limit expressions suggested for the leading and trailing edges of the mean flame brush. Subsequently, the proposed simple closure relations for \(\overline {\rho \mathbf {u}W}\) are assessed by processing two sets of data obtained in earlier 3D Direct Numerical Simulation (DNS) studies of adiabatic, statistically planar, turbulent, premixed, single-step-chemistry flames characterized by unity Lewis number. One dataset consists of three cases characterized by different density ratios and is associated with the flamelet regime of premixed turbulent combustion. Another dataset consists of four cases characterized by different low Damköhler and large Karlovitz numbers. Accordingly, this dataset is associated with the thin reaction zone regime of premixed turbulent combustion. Under conditions of the former DNS, difference in the entire, \(\overline {\rho {u}W}\), and mean, \(\tilde {u}\overline {\rho W}\), convection fluxes is well pronounced, with the turbulent flux, \(\overline {\rho u^{\prime \prime }W^{\prime \prime }}\), showing countergradient behavior in a large part of the mean flame brush. Accordingly, the gradient diffusion closure of the turbulent flux is not valid under such conditions, but some proposed simple closure relations allow us to predict the entire flux \(\overline {\rho \mathbf {u}W}\) reasonably well. Under conditions of the latter DNS, the difference in the entire and mean convection fluxes is less pronounced, with the aforementioned simple closure relations still resulting in sufficiently good agreement with the DNS data.     

Transition from Countergradient to Gradient Scalar Transport in Developing Premixed Turbulent Flames

A simple model of turbulent scalar flux developed recently by the present authors is applied to determine the direction of the flux in a statistically planar one-dimensional premixed flame that does not affect turbulence and has self-similar mean structure. Results obtained in the case of statistically stationary turbulence indicate that transition from countergradient to gradient turbulent scalar transport may occur during flame development, as the peak mean rate of product creation moves to the trailing edge of the flame brush. In the case of decaying turbulence, the opposite transition (from gradient to countergradient transport) was simulated in line with available DNS data. In both cases, transition instant depends strongly on turbulence and mixture characteristics. In particular, countergradient transport is suppressed by an increase in the rms turbulent velocity and by a decrease in the laminar flame speed or density ratio, in line with available experimental and DNS data. The obtained results lend qualitative support to the model of turbulent scalar flux addressed in the present work.     

Statistical Analysis of Scalar Dissipation Rate Transport in Turbulent Partially Premixed Flames: A Direct Numerical Simulation Study

Statistically planar turbulent premixed and partially premixed flames for different initial turbulence intensities are simulated for global equivalence ratios ??>?=?0.7 and ??>?=?1.0 using three-dimensional Direct Numerical Simulations (DNS) with simplified chemistry. For the simulations of partially premixed flames, a random distribution of equivalence ratio following a bimodal distribution of equivalence ratio is introduced in the unburned reactants ahead of the flame. The simulation parameters in all of the cases were chosen such that the combustion situation belongs to the thin reaction zones regime. The DNS data has been used to analyse the behaviour of the dissipation rate transports of both active and passive scalars (i.e. the fuel mass fraction Y _F and the mixture fraction ξ) in the context of Reynolds Averaged Navier–Stokes (RANS) simulations. The behaviours of the unclosed terms of the Favre averaged scalar dissipation rates of fuel mass fraction and mixture fraction (i.e. \(\widetilde {\varepsilon }_Y =\overline {\rho D\nabla Y_F^{\prime \prime } \cdot \nabla Y_F^{\prime \prime } } /\overline{\rho }\) and \(\widetilde {\varepsilon }_\xi =\overline {\rho D\nabla \xi ^{\prime \prime }\cdot \nabla \xi ^{\prime \prime }} /\overline {\rho })\) transport equations have been analysed in detail. In the case of the \(\widetilde {\varepsilon }_Y \) transport, it has been observed that the turbulent transport term of scalar dissipation rate remains small throughout the flame brush whereas the terms due to density variation, scalar–turbulence interaction, reaction rate and molecular dissipation remain the leading order contributors. The term arising due to density variation remains positive throughout the flame brush and the combined contribution of the reaction and molecular dissipation to the \(\widetilde {\varepsilon }_Y \) transport remains negative throughout the flame brush in all cases. However, the behaviour of scalar–turbulence interaction term of the \(\widetilde {\varepsilon }_Y \) transport equation is significantly affected by the relative strengths of turbulent straining and the straining due to chemical heat release. In the case of the \(\widetilde {\varepsilon }_\xi \) transport, the turbulent transport term remains small throughout the flame brush and the density variation term is found to be negligible in all cases, whilst the reaction rate term is exactly zero. The scalar–turbulence interaction term and molecular dissipation term remain the leading order contributors to the \(\widetilde {\varepsilon }_\xi \) transport throughout the flame brush in all cases that have been analysed in the present study. Performances of existing models for the unclosed terms of the transport equations of \(\widetilde {\varepsilon }_Y \) and \(\widetilde {\varepsilon }_\xi \) are assessed with respect to the corresponding quantities obtained from DNS data. Based on this exercise either suitable models have been identified or new models have been proposed for the accurate closure of the unclosed terms of both \(\widetilde {\varepsilon }_Y \) and \(\widetilde {\varepsilon }_\xi \) transport equations in the context of Reynolds Averaged Navier–Stokes (RANS) simulations.     

Effects of Lewis Number on Scalar Variance Transport in Premixed Flames

The influences of differential diffusion rates of heat and mass on the transport of the variances of Favre fluctuations of reaction progress variable and non-dimensional temperature have been studied using three-dimensional simplified chemistry based Direct Numerical Simulation (DNS) data of statistically planar turbulent premixed flames with global Lewis number ranging from Le?= 0.34 to 1.2. The Lewis number effects on the statistical behaviours of the various terms of the transport equations of variances of Favre fluctuations of reaction progress variable and non-dimensional temperature have been analysed in the context of Reynolds Averaged Navier Stokes (RANS) simulations. It has been found that the turbulent fluxes of the progress variable and temperature variances exhibit counter-gradient transport for the flames with Lewis number significantly smaller than unity whereas the extent of this counter-gradient transport is found to decrease with increasing Lewis number. The Lewis number is also shown to have significant influences on the magnitudes of the chemical reaction and scalar dissipation rate contributions to the scalar variance transport. The modelling of the unclosed terms in the scalar variance equations for the non-unity Lewis number flames have been discussed in detail. The performances of the existing models for the unclosed terms are assessed based on a-priori analysis of DNS data. Based on the present analysis, new models for the unclosed terms of the active scalar variance transport equations are proposed, whenever necessary, which are shown to satisfactorily capture the behaviours of unclosed terms for all the flames considered in this study.     

Joint PDF Closure of Turbulent Premixed Flames

In this paper, a novel model for turbulent premixed combustion in the corrugated flamelet regime is presented, which is based on transporting a joint probability density function (PDF) of velocity, turbulence frequency and a scalar vector. Due to the high dimensionality of the corresponding sample space, the PDF equation is solved with a Monte-Carlo method, where individual fluid elements are represented by computational particles. Unlike in most other PDF methods, the source term not only describes reaction rates, but accounts for “ignition” of reactive unburnt fluid elements due to propagating embedded quasi laminar flames within a turbulent flame brush. Unperturbed embedded flame structures and a constant laminar flame speed (as expected in the corrugated flamelet regime) are assumed. The probability for an individual particle to “ignite” during a time step is calculated based on an estimate of the mean flame surface density (FSD), latter gets transported by the PDF method. Whereas this model concept has recently been published [21], here, a new model to account for local production and dissipation of the FSD is proposed. The following particle properties are introduced: a flag indicating whether a particle represents the unburnt mixture; a flame residence time, which allows to resolve the embedded quasi laminar flame structure; and a flag indicating whether the flame residence time lies within a specified range. Latter is used to transport the FSD, but to account for flame stretching, curvature effects, collapse and cusp formation, a mixing model for the residence time is employed. The same mixing model also accounts for molecular mixing of the products with a co-flow. To validate the proposed PDF model, simulation results of three piloted methane-air Bunsen flames are compared with experimental data and very good agreement is observed.     

Subgrid Modeling of Turbulent Premixed Flames in the Flamelet Regime

Large eddy simulation (LES) models for flamelet combustion are analyzed by simulating premixed flames in turbulent stagnation zones. ALES approach based on subgrid implementation of the linear eddy model(LEM) is compared with a more conventional approach based on the estimation of the turbulent burning rate. The effects of subgrid turbulence are modeled within the subgrid domain in the LEM-LES approach and the advection (transport between LES cells) of scalars is modeled using a volume-of-fluid (VOF) Lagrangian front tracking scheme. The ability of the VOF scheme to track the flame as a thin front on the LES grid is demonstrated. The combined LEM-LES methodology is shown to be well suited for modeling premixed flamelet combustion. The geometric characteristics of the flame surfaces, their effects on resolved fluid motion and flame-turbulence interactions are well predicted by the LEM-LES approach. It is established here that local laminar propagation of the flamelets needs to be resolved in addition to the accurate estimation of the turbulent reaction rate. Some key differences between LEM-LES and the conventional approach(es) are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Scalar Gradient Alignment Statistics of Flame Kernels and its Modelling Implications for Turbulent Premixed Combustion

The effects of mean flame curvature on reaction progress variable gradient, $\nabla c$ , alignment with local turbulent strain rate are studied based on three-dimensional Direct Numerical Simulation (DNS) data of turbulent premixed flame kernels with different initial radii under decaying turbulence. A statistically planar flame is also considered in order to compare the results obtained from the kernels with a flame of zero mean curvature. It is found that the dilatation rate effects diminish with decreasing kernel radius due to defocusing of heat in the positively curved regions. This gives rise to a decrease in the extent of reaction progress variable gradient alignment with most extensive principal strain rate with decreasing kernel radius. The modelling implications of the statistics of the alignment of $\nabla c$ with local strain rate have been studied in terms of scalar dissipation rate transport. A new modelling methodology for the contribution of the scalar-turbulence interaction term in the transport equation for the mean scalar dissipation is suggested addressing the reduced effects of dilatation rate for flame kernels and the diminished value of turbulent straining at the small length scales at which turbulence interacts with small flame kernels. The performance of the new models is found to be satisfactory while comparing to DNS results. The existing models for the dilatation contribution and the combined chemical reaction and molecular dissipation contributions to the transport of mean scalar dissipation, which were originally proposed for statistically planar flames, are found to satisfactorily predict the corresponding quantities for turbulent flame kernels.     

Near-Equidiffusion Disturbed Premixed Flames with Wider Reaction Zones

Most of the asymptotic considerations of the interaction of premixed flames with a general flow, i.e. curved and stretched flames subjected to time dependent flow, are dedicated to high activation energy asymptotes. Therefore, in these considerations the reaction zone is thin and the temperature within the reaction zone is constant to the leading order of approximation. Here we consider an order unity activation energy for near-equidiffusion flames and show that the flame speed relations obtained are distinct from those obtained by high activation energy asymptotes. The flame is assumed to be thin in comparison with the flow scales but the reaction zone is no longer thin in comparison with the flame width. Although obtaining analytical solutions is problematic even for undisturbed flames with wide reaction zones, we found that the propagation speed of disturbed premixed flames with wide reaction zones is determined by analytical integrals involving the temperature profile of the undisturbed flame. We also found independent effects of curvature and stretch for the flames with wider reaction zones. This revised version was published online in July 2006 with corrections to the Cover Date.     

Turbulence Intensity and Length Scale Effects on Premixed Turbulent Flame Propagation

The effects of varying turbulence intensity and turbulence length scale on premixed turbulent flame propagation are investigated using Direct Numerical Simulation (DNS). The DNS dataset contains the results of a set of turbulent flame simulations based on separate and systematic changes in either turbulence intensity or turbulence integral length scale while keeping all other parameters constant. All flames considered are in the thin reaction zones regime. Several aspects of flame behaviour are analysed and compared, either by varying the turbulence intensity at constant integral length scale, or by varying the integral length scale at constant turbulence intensity. The turbulent flame speed is found to increase with increasing turbulence intensity and also with increasing integral length scale. Changes in the turbulent flame speed are generally accounted for by changes in the flame surface area, but some deviation is observed at high values of turbulence intensity. The probability density functions (pdfs) of tangential strain rate and mean flame curvature are found to broaden with increasing turbulence intensity and also with decreasing integral length scale. The response of the correlation between tangential strain rate and mean flame curvature is also investigated. The statistics of displacement speed and its components are analysed, and the findings indicate that changes in response to decreasing integral length scale are broadly similar to those observed for increasing turbulence intensity, although there are some interesting differences. These findings serve to improve current understanding of the role of turbulence length scales in flame propagation.

     

One-Dimensional Modeling of Turbulent Premixed Jet Flames - Comparison to DNS

The one-dimensional turbulence (ODT) model, formulated in an Eulerian reference frame, is applied to a temporally-evolving premixed turbulent hydrogen plane-jet flame and results are compared with direct numerical simulation (DNS) data. This is the first published study to perform direct comparisons of ODT to DNS for premixed flames. The ODT model solves the full set of conservation equations for mass, momentum, energy, and species on a one-dimensional domain corresponding to the transverse jet direction. The effects of turbulent mixing are modeled via a stochastic process, while the full range of diffusive-reactive length and time scales are resolved directly on the one-dimensional domain. A detailed chemical mechanism for hydrogen combustion consisting of 9 species and 21 reactions and a mixture-averaged transport model are used (consistent with the DNS). Cases with two different Damköhler numbers are considered and comparisons between the ODT and DNS data are shown with respect to flow dynamics and thermochemistry. The ODT compared favorably with the DNS in terms of the overall entrainment as judged by the streamwise velocity profile and in terms of local flamelet structure as judged by progress-variable conditional reaction and scalar dissipation rates. While the ODT agreed qualitatively with the overall flame evolution, the net fuel consumption rate was somewhat over-predicted for a brief early period and under-predicted later on, leading to an overly long flame burnout time. It was demonstrated that adjusting a parameter controlling the selection of large eddies improved the prediction of the peak fuel consumption rate and overall reaction progress but worsened the prediction of jet entrainment. An analysis of the 1D nature of ODT is presented that suggests the FSD in ODT needs to be much higher than the FSD in the DNS in order to achieve the same overall burning rate, suggesting that the FSD is under-predicted by a significant fraction. While the success of the ODT in reproducing many of the salient features of nonpremixed flames has been demonstrated, the current study suggests that improvements are needed when applied to premixed flames. It is also important to note that the DNS required approximately 40×10⁶ CPU hours while the ODT required approximately 10³ CPU hours.     

Assessment of FSD and SDR Closures for Turbulent Flames of Alternative Fuels

Detailed-chemistry DNS studies are becoming more common due to the advent of more powerful modern computer architectures, and as a result more realistic flames can be simulated. Such flames involve many alternative fuels such as syngas and blast furnace gas, which are usually composed of many species and of varying proportions. In this study, we evaluate whether some of the commonly used models for the scalar dissipation rate and flame surface density can be used to model such flames in the LES context. A priori assessments are conducted using DNS data of multi-component fuel turbulent premixed flames. These flames offer unique challenges because of their complex structure having many distinct consumption layers for the different fuel components unlike in a single-component fuel. Some of the models tested showed good agreement with the DNS data and thus they can be used for the multi-component fuel combustion.     

Flame Induced Flow Features in the Presence of Darrieus-Landau Instability

The onset of hydrodynamic or Darrieus-Landau (DL) instability can largely impact on premixed flame morphology, turbulent flame speed and induced flow field. In this work, we focus on the latter induced flow by means of two dimensional direct numerical simulations (DNS) of slot burner flames performed in a parametric fashion. Results from linear stability analysis are used to select the adequate parameter range to be investigated. The presence of DL instability is initially assessed using a recently proposed statistical marker related to flame morphology. The differences between stable and unstable flames are then statistically investigated, utilizing a single, laminar, DL-induced corrugation as a reference state. Such DL-induced effects are investigated at various turbulence intensities, in terms of local propagation, induced strain rate patterns and flow field as well as vorticity production and transformation. Using displacement speed as a measure of local propagation, no noticeable statistical difference is observed between stable and unstable flames while strain rate and vorticity patterns are shown to be largely influenced by the DL induced morphology. From the modeling point view, an enhancement of counter gradient type transport for turbulent scalar fluxes is observed for hydrodynamically unstable flames.     

Turbulence Statistics and Scalar Transport in Highly-Sheared Premixed Flames

This paper describes recent progress in the analysis of the nature of turbulent premixed flames stabilised behind an axisymmetric baffle which are of fundamental interest in the development of new and cleaner combustion systems. The work includes the use of laser-based diagnostics for velocity and temperature measurements, which are extended to the analysis of turbulence statistics, including the energy spectrum and typical length scales in a reacting shear layer. The results provided experimental evidence of the extension of the flamelet regime beyond the Klimov--Williams criterion. Arguments based on the shape of the weighted-joint-probability distributions of axial velocity and temperature fluctuations show that the counter-gradient nature of heat flux is associated with the preferential deceleration of products of combustion in relation to the cold reactants.     

Study of a Filtered Flamelet Formulation for Large Eddy Simulation of Premixed Turbulent Flames

Despite significant advances in the understanding and modelling of turbulent combustion, no general model has been proposed for simulating flames in industrial combustion devices. Recently, the increase in computational possibilities has raised the hope of directly solving the large turbulent scales using large eddy simulation (LES) and capturing the important time-dependant phenomena. However, the chemical reactions involved in combustion occur at very small scales and the modelling of turbulent combustion processes is still required within the LES framework. In the present paper, a recently presented model for the LES of turbulent premixed flames is presented, analysed and discussed. The flamelet hypothesis is used to derive a filtered source term for the filtered progress variable equation. The model ensures proper flame propagation. The effect of subgrid scale (SGS) turbulence on the flame is modelled through the flame-wrinkling factor. The present modelling of the source term is successfully tested against filtered direct numerical simulation (DNS) data of a V-shape flame. Further, a premixed turbulent flame, stabilised behind an expansion, is simulated. The predictions agree well with the available experimental data, showing the capabilities of the model for performing accurate simulations of unsteady premixed flames.     

Thermal-field structure of a non-premixed turbulent flame formed in a strong pressure-gradient flow

Statistical characteristics of a non-premixed turbulent flame formed in a curved-rectangular duct and spatio-temporal structures of the thermal field were investigated experimentally. The flame was much affected by a strong pressure gradient in the radial direction of the duct curvature, which caused strong gradient diffusion in turbulent heat transfer on the inner-wall side of the flame and, in contrast, counter-gradient heat transfer on the outer-wall side. Two-point correlation measurement of temperature fields revealed that, in the strong gradient diffusion region, a spatial thermal pattern generated by turbulent mixing of high- and low-temperature fluid parcels was advected downstream with little diffusion. In contrast, the pattern was attenuated and diffused rapidly in the counter-gradient diffusion region. These results accurately correspond to the generation mechanism of the counter-gradient heat transport so far observed in stably stratified turbulent flows.     

Flame Curvature Distribution in High Pressure Turbulent Bunsen Premixed Flames

The flame curvature statistics of turbulent premixed Bunsen flames have been analysed in this paper using a Direct Numerical Simulation (DNS) database of turbulent Bunsen flames at ambient and elevated pressures. In order to be able to perform a large parametric study in terms of pressure, heat release parameter, turbulence conditions and nozzle diameter, a single step Arrhenius type irreversible chemistry has been used for the purpose of computational economy, where thermo-chemical parameters are adjusted to match the behavior of stoichiometric methane-air flames. This analysis focuses on the characterization of the local flame geometry in response to turbulence and hydro-dynamic instability. The shape of the flame front is found to be consistent with existing experimental data. Although the Darrieus Landau instability promotes cusp formation, a qualitatively similar flame morphology can be observed for hydro-dynamically stable flames. A criterion has been suggested for the curvature PDF to become negatively skewed.     

Towards an Extension of TFC Model of Premixed Turbulent Combustion

In order to determine the mean rate of product creation within the framework of the Turbulent Flame Closure (TFC) model of premixed combustion, the model is combined with a simple closure of turbulent scalar flux developed recently by the present authors based on the flamelet concept of turbulent burning. The model combination is assessed by numerically simulating statistically planar, one-dimensional, developing premixed flames that propagate in frozen turbulence. The mean rate of product creation yielded by the combined model decreases too slowly at the trailing edges of the studied flames, with the effect being more pronounced at longer flame-development times and larger ratios of rms turbulent velocity u′ to laminar flame speed S _L . To resolve the problem, the above closure of turbulent scalar flux is modified and the combination of the modified closure and TFC model yields reasonable behaviour of the studied rate. In particular, simulations indicate an increase in the mean combustion progress variable associated with the maximum rate by u′/S _L , in line with available DNS data. Finally, the modified closure of turbulent scalar flux is validated by computing conditioned velocities and turbulent scalar fluxes in six impinging-jet flames. The use of the TFC model for simulating such flames is advocated.