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.     

Large Eddy Simulation of a Propagating Turbulent Premixed Flame

A large eddy simulation of a turbulent premixed flame propagatingthrough a chamber containing a square obstruction is presented anddiscussed. The governing equations for compressible, reacting flowsare Favre filtered and turbulence closure is achieved using thedynamic Smagorinsky subgrid model. A simple flame surface densitymodel based on the flamelet concept is employed for the subgrid scalereaction rate. The simulation gives very good agreement with experimentalresults for the speed and the shape of the flame as it propagates throughthe chamber. The peak pressures, however, are underpredicted by20–30%. Reasons for this are discussed and it is concluded that amore sophisticated combustion model is required for complex flowssuch as this one, if a more accurate prediction of the pressureis to be achieved.     

Flame Surface Density in Turbulent Premixed V-Flame with Buoyancy

A fractional step numerical model is established for turbulent premixed combustion with buoyancy. The flame front propagation is described by the level-set method. Simulated results without buoyancy have been previously validated with available experimental data on a premixed V-flame. A new formula is presented to fit the flame surface density with respect to the reaction progress variable in a turbulent premixed V-flame. By numerical simulations, dynamical behaviour of the flame under the interaction of turbulence, exothermicity and buoyancy are investigated.     

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.     

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.

     

Modelling of a Premixed Swirl-stabilized Flame Using a Turbulent Flame Speed Closure Model in LES

This paper proposes a combustion model based on a turbulent flame speed closure (TFC) technique for large eddy simulation (LES) of premixed flames. The model was originally developed for the RANS (Reynolds Averaged Navier Stokes equations) approach and was extended here to LES. The turbulent quantities needed for calculation of the turbulent flame speed are obtained at the sub grid level. This model was at first experienced via an test case and then applied to a typical industrial combustor with a swirl stabilized flame. The paper shows that the model is easy to apply and that the results are promising. Even typical frequencies of arising combustion instabilities can be captured. But, the use of compressible LES may also lead to unphysical pressure waves which have their origin in the numerical treatment of the boundary conditions.     

Interactions Between Flame Topology and Turbulent Transport in High-Pressure Premixed Combustion

Flow, Turbulence and Combustion - Direct numerical simulations of a turbulent premixed stoichiometric methane-oxygen flame were conducted. The chosen combustion pressure was 20 bar, to...     

LES-CMC of a Partially Premixed,Turbulent Dimethyl Ether Jet Diffusion Flame

Large-eddy simulations have been coupled with a conservative formulation of the conditional moment closure (CMC) approach for the computation of a turbulent, partially-premixed dimethyl-ether jet flame. Two different numerical setups and 3 different detailed chemical mechanisms were investigated. The results are compared with measurements of velocity, temperature, and major and intermediate species. The general agreement between simulations and experiments is very good, and differences between the different mechanisms are limited to the predicted concentrations of intermediates only. Larger differences can be observed if the CMC grid size is reduced. This is due to reduced averaging effects on the conditionally averaged dissipation rates that allow to better capture high dissipation events that lead to larger deviations from a fully burning solution. A high CMC resolution provides excellent agreement with experiments throughout the flame and the results demonstrate CMC’s capability to accurately predict turbulence-chemistry interactions in partially-premixed flames involving complex chemistry.     

Combined Influence of Strain and Heat Loss on Turbulent Premixed Flame Stabilization

The present paper argues that the prediction of turbulent premixed flames under non-adiabatic conditions can be improved by considering the combined effects of strain and heat loss on reaction rates. The effect of strain in the presence of heat loss on the consumption speed of laminar premixed flames was quantified by calculations of asymmetric counterflow configurations (“fresh-to-burnt”) with detailed chemistry. Heat losses were introduced by setting the temperature of the incoming stream of products on the “burnt” side to values below those corresponding to adiabatic conditions. The consumption speed decreased in a roughly exponential manner with increasing strain rate, and this tendency became more pronounced in the presence of heat losses. An empirical relation in terms of Markstein number, Karlovitz Number and a non-dimensional heat loss parameter was proposed for the combined influence of strain and heat losses on the consumption speed. Combining this empirical relation with a presumed probability density function for strain in turbulent flows, an attenuation factor that accounts for the effect of strain and heat loss on the reaction rate in turbulent flows was deduced and implemented into a turbulent combustion model. URANS simulations of a premixed swirl burner were carried out and validated against flow field and OH chemiluminescence measurements. Introducing the effects of strain and heat loss into the combustion model, the flame topology observed experimentally was correctly reproduced, with good agreement between experiment and simulation for flow field and flame length.     

Self-Turbulent Flame Speeds

This paper reports an experimental investigation of premixed propane and methane-air flames propagating freely in tubes 1.5?m long and with diameters ranging from 26 to 141?mm. The thermo-acoustic instability was eliminated by means of a novel acoustic absorber placed at the closed end of the tube. We first remark that the flame can adopt different shapes either quasi-axisymmetric and normal to the mean direction of propagation, or inclined with a larger propagation speed because of the increase in flame surface area. The minima of the propagation speeds, corresponding to non-tilted flame propagation, are then analyzed using analytical models for the self-turbulent flame propagation. The concept of a cut-off wavelength appears to be relevant to explain the different behaviors observed on the rich side of methane-air and propane-air flames.     

Relations Between Statistics of Three-Dimensional Flame Curvature and its Two-Dimensional Counterpart in Turbulent Premixed Flames

The relations between the actual flame curvature probability density function (PDF) evaluated in three-dimensions and its two-dimensional counterpart based on planar measurements have been analytically derived subject to the assumptions of isotropy and statistical independence of various angles and two-dimensional curvature. These relations have been assessed based on Direct Numerical Simulation (DNS) databases of turbulent premixed (a) statistically planar and (b) statistically axisymmetric Bunsen flames. It has been found that the analytically derived relation interlinking the PDFs of actual three-dimensional curvature and its two-dimensional counterpart holds reasonably well for a range of curvatures around the mean value defined by the inverse of the thermal flame thickness for different turbulence intensities across different combustion regimes. The flame surface is shown to exhibit predominantly two-dimensional cylindrical curvature but there is a significant probability of finding saddle type flame topologies and this probability increases with increasing turbulence intensity. The presence of saddle type flame topologies affects the ratios of second and third moments of two-dimensional and three-dimensional curvatures. It has been demonstrated that the ratios of second and third moments of two-dimensional and three-dimensional curvatures cannot be accurately predicted based on two-dimensional measurements. The ratio of the third moments of two-dimensional and three-dimensional curvatures remains positive and thus the qualitative nature of curvature skewness can still be obtained based on two-dimensional curvature measurements. As the curvature skewness is often taken to be a marker of the Darrius-Landau instability, the conclusion regarding the presence of this instability can potentially be taken from the two-dimensional curvature measurements.

     

Towards the Development of an Evolution Equation for Flame Turbulence Interaction in Premixed Turbulent Combustion

Flame turbulence interaction is one of the leading order terms in the scalar dissipation \(\left (\widetilde {\varepsilon }_{c}\right )\) transport equation [35] and is thus an important phenomenon in premixed turbulent combustion. Swaminathan and Grout [36] and Chakraborty and Swaminathan [15, 16] have shown that the effect of strain rate on the transport of \(\widetilde {\varepsilon }_{c}\) is dominated by the interaction between the fluctuating scalar gradients and the fluctuating strain rate, denoted here by \(\overline {\rho }\widetilde {\Delta }_{c}= \overline {\rho {\alpha }\nabla c^{\prime \prime }S_{ij}^{\prime \prime }\nabla c^{\prime \prime }}\) ; this represents the flame turbulence interaction. In order to obtain an accurate representation of this phenomenon, a new evolution equation for \(\widetilde {\Delta }_{c}\) has been proposed. This equation gives a detailed insight into flame turbulence interaction and provides an alternative approach to model the important physics represented by \(\widetilde {\Delta }_{c}\) . The \(\widetilde {\Delta }_{c}\) evolution equation is derived in detail and an order of magnitude analysis is carried out to determine the leading order terms in the \(\widetilde {\Delta }_{c}\) evolution equation. The leading order terms are then studied using a Direct Numerical Simulation (DNS) of premixed turbulent flames in the corrugated flamelet regime. It is found that the behaviour of \(\widetilde {\Delta }_{c}\) is determined by the competition between the source terms (pressure gradient and the reaction rate), diffusion/dissipation processes, turbulent strain rate and the dilatation rate. Closures for the leading order terms in \(\widetilde {\Delta }_{c}\) evolution equation have been proposed and compared with the DNS data.     

Asymptotics for Turbulent Flame Speeds of the Viscous G-Equation Enhanced by Cellular and Shear Flows

G-equations are well-known front propagation models in turbulent combustion which describe the front motion law in the form of local normal velocity equal to a constant (laminar speed) plus the normal projection of fluid velocity. In level set formulation, G-equations are Hamilton–Jacobi equations with convex (L ¹ type) but non-coercive Hamiltonians. Viscous G-equations arise from either numerical approximations or regularizations by small diffusion. The nonlinear eigenvalue [`(H)]{\bar H} from the cell problem of the viscous G-equation can be viewed as an approximation of the inviscid turbulent flame speed s <sub>T</sub>. An important problem in turbulent combustion theory is to study properties of s <sub>T</sub>, in particular how s <sub>T</sub> depends on the flow amplitude A. In this paper, we study the behavior of [`(H)]=[`(H)](A,d){\bar H=\bar H(A,d)} as A → + ∞ at any fixed diffusion constant d > 0. For cellular flow, we show that

Geometrical Properties and Turbulent Flame Speed Measurements in Stationary Premixed V-flames Using Direct Numerical Simulation

Three dimensional, fully compressible direct numerical simulations (DNS) of premixed turbulent flames are carried out in a V-flame configuration. The governing equations and the numerical implementation are described in detail, including modifications made to the Navier?CStokes Characteristic Boundary Conditions (NSCBC) to accommodate the steep transverse velocity and composition gradients generated when the flame crosses the boundary. Three cases, at turbulence intensities, u??/s _L , of 1, 2, and 6 are considered. The influence of the flame holder on downstream flame properties is assessed through the distributions of the surface-conditioned displacement speed, curvature and tangential strain rates, and compared to data from similarly processed planar flames. The distributions are found to be indistinguishable from planar flames for distances greater than about 17?? _th downstream of the flame holder, where ?? _th is the laminar flame thermal thickness. Favre mean fields are constructed, and the growth of the mean flame brush is found to be well described by simple Taylor type diffusion. The turbulent flame speed, s _T is evaluated from an expression describing the propagation speed of an isosurface of the mean reaction progress variable $\tilde{c}$ in terms of the imbalance between the mean reactive, diffusive, and turbulent fluxes within the flame brush. The results are compared to the consumption speed, s _C , calculated from the integral of the mean reaction rate, and to the predictions of a recently developed flame speed model (Kolla et al., Combust Sci Technol 181(3):518?C535, 2009). The model predictions are improved in all cases by including the effects of mean molecular diffusion, and the overall agreement is good for the higher turbulence intensity cases once the tangential convective flux of $\tilde{c}$ is taken into account.     

Effects of the Local Flow Topologies Upon the Structure of a Premixed Methane-air Turbulent Jet Flame

Local flow topologies have been identified and their interactions with the iso-scalar surfaces geometries have been investigated using the results of a three-dimensional direct numerical simulation (DNS) of a turbulent premixed methane-air flame in a piloted Bunsen burner configuration with tabulated chemistry. The universal teardrop shape of the joint probability density function (jpdf) of the second and third invariants of the velocity-gradient tensor disappears in the different flame regions under study. A ‘canonical’ vortex, which affects the fine-scale structure of the turbulent premixed flame, has been identified and analyzed at three times, differing by increments of the order of the Kolmogorov time micro-scale.     

Analysis of the Combined Modelling of Sub-grid Transport and Filtered Flame Propagation for Premixed Turbulent Combustion

Flame surface density (FSD) based reaction rate closure is an important methodology of turbulent premixed flame modelling in the context of Large Eddy Simulations (LES). The transport equation for the Favre-filtered reaction progress variable needs closure of the filtered reaction diffusion imbalance (FRDI) term (i.e. filtered value of combined reaction rate and molecular diffusion rate) and the sub-grid scalar flux (SGSF). A-priori analysis of the FRDI and SGSF terms has in the past revealed advantages and disadvantages of the specific modelling attempts. However, it is important to understand the interaction of the FRDI and SGSF closures for a successful implementation of the FSD based closure. Furthermore, it is not known a-priori if the combination of the best SGSF model with the best FRDI model results in the most suitable overall modelling strategy. In order to address this question, a variety of SGSF models is analysed in this work together with one well established and one recent FRDI closure based on a-priori analysis. It is found that the success of the combined FRDI and SGSF closures depends on subtle details like the co-variances of the FRDI and SGSF terms. It is demonstrated that the gradient hypothesis model is not very successful in representing the SGSF term. However the gradient hypothesis provides satisfactory performance in combination of a recently proposed FRDI closure, whereas unsatisfactory results are obtained when used in combination with another existing closure, which was shown to predict the FRDI term satisfactorily in several previous analyses.     

Evaluations of SGS Combustion,Scalar Flux and Stress Models in a Turbulent Jet Premixed Flame

A newly developed fractal dynamic SGS (FDSGS) combustion model and a scale self-recognition mixed (SSRM) SGS stress model are evaluated along with other SGS combustion, scalar flux and stress models in a priori and a posteriori manners using DNS data of a hydrogen-air turbulent plane jet premixed flame. A posteriori tests reveal that the LES using the FDSGS combustion model can predict the combustion field well in terms of mean temperature distributions and peak positions in the transverse distributions of filtered reaction progress variable fluctuations. A priori and a posteriori tests of the scalar flux models show that a model proposed by Clark et al. accurately predicts the counter-gradient transport as well as the gradient diffusion, and introduction of the model of Clark et al. into the LES yields slightly better predictions of the filtered progress variable fluctuations than that of a gradient diffusion model. Evaluations of the stress models reveal that the LES with the SSRM model predicts the velocity fluctuations well compared to that with the Smagorinsky model.