A posteriori testing of the flame surface density transport equation for LES

Flame Surface Density (FSD) models for Large Eddy Simulation (LES) are implemented and tested for a canonical configuration and a practical bluff body stabilised burner, comparing common algebraic closures with a transport equation closure in the context of turbulent premixed combustion. The transported method is expected to yield advantages over algebraic closures, as the equilibrium of subgrid production and destruction of FSD is no longer enforced and resolved processes of strain, propagation and curvature are explicitly accounted for. These advantages might have the potential to improve the ability to capture large-scale unsteady flame propagation in situations with combustion instabilities or situations where the flame encounters progressive wrinkling with time. The initial study of a propagating turbulent flame in wind-tunnel turbulence shows that the Algebraic Flame Surface Density (FSDA) method can predict an excessively wrinkled flame under fine grid conditions, potentially increasing the consumption rate of reactants to artificially higher levels. In contrast, the Flame Surface Density Transport (FSDT) closure predicts a smooth flame front and avoids the formation of artificial flame cusps when the grid is refined. Five FSDA models and the FSDT approach are then applied to the LES of the Volvo Rig. The predicted mean velocities are found to be relatively insensitive to the use of the FSDT and FSDA approaches, whereas temperature predictions exhibit appreciable differences for different formulations. The FSDT approach yields very similar temperature predictions to two of the tested FSDA models, quantitatively capturing the mean temperature. Grid refinement is found to improve the FSDT predictions of the mean flame spread. Overall, the paper demonstrates that the apparently complicated FSD transport equation approach can be implemented and applied to realistic, strongly wrinkled flames with good success, and opens up the field for further work to improve the models and the overall FSDT approach.     

A LES/PDF simulator on block-structured meshes

A block-structured mesh large-eddy simulation (LES)/probability density function (PDF) simulator is developed within the OpenFOAM framework for computational modelling of complex turbulent reacting flows. The LES/PDF solver is a hybrid solution methodology consisting of (i) a finite-volume (FV) method for solving the filtered mass and momentum equations (LES solver), and (ii) a Lagrangian particle-based Monte Carlo algorithm (PDF solver) for solving the modelled transport equation of the filtered joint PDF of compositions. Both the LES and the PDF methods are developed and combined to form a hybrid LES/PDF simulator entirely within the OpenFOAM framework. The in situ adaptive tabulation method [S.B. Pope, Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation, Combust. Theory Model. 1 (1997), pp. 41–63; L. Lu, S.R. Lantz, Z. Ren, and B.S. Pope, Computationally efficient implementation of combustion chemistry in parallel PDF calculations, J. Comput. Phys. 228 (2009), pp. 5490–5525] is incorporated into the new LES/PDF solver for efficient computations of combustion chemistry with detailed reaction kinetics. The method is designed to utilise a block-structured mesh and can readily be extended to unstructured grids. The three-stage velocity interpolation method of Zhang and Haworth [A general mass consistency algorithm for hybrid particle/finite-volume PDF methods, J. Comput. Phys. 194 (2004), pp. 156–193] is adapted to interpolate the LES velocity field onto particle locations accurately and to enforce the consistency between LES and PDF fields at the numerical solution level. The hybrid algorithm is fully parallelised using the conventional domain decomposition approach. A detailed examination of the effects of each stage and the overall performance of the velocity interpolation algorithm is performed. Accurate coupling of the LES and PDF solvers is demonstrated using the one-way coupling methodology. Then the fully two-way coupled LES/PDF solver is successfully applied to simulate the Sandia Flame-D, and a turbulent non-swirling premixed flame and a turbulent swirling stratified flame from the Cambridge turbulent stratified flame series [M.S. Sweeney, S. Hochgreb, M.J. Dunn, and R.S. Barlow, The structure of turbulent stratified and premixed methane/air flames I: Non-swirling flows, Combust. Flame 159 (2012), pp. 2896–2911; M.S. Sweeney, S. Hochgreb, M.J. Dunn, and R.S. Barlow, The structure of turbulent stratified and premixed methane/air flames II: Swirling flows, Combust. Flame 159 (2012), pp. 2912–2929]. It is found that the LES/PDF method is very robust and the results are in good agreement with the experimental data for both flames.     

Assessment of dynamic closure for premixed combustion large eddy simulation

Turbulent piloted Bunsen flames of stoichiometric methane–air mixtures are computed using the large eddy simulation (LES) paradigm involving an algebraic closure for the filtered reaction rate. This closure involves the filtered scalar dissipation rate of a reaction progress variable. The model for this dissipation rate involves a parameter β_c representing the flame front curvature effects induced by turbulence, chemical reactions, molecular dissipation, and their interactions at the sub-grid level, suggesting that this parameter may vary with filter width or be a scale-dependent. Thus, it would be ideal to evaluate this parameter dynamically by LES. A procedure for this evaluation is discussed and assessed using direct numerical simulation (DNS) data and LES calculations. The probability density functions of β_c obtained from the DNS and LES calculations are very similar when the turbulent Reynolds number is sufficiently large and when the filter width normalised by the laminar flame thermal thickness is larger than unity. Results obtained using a constant (static) value for this parameter are also used for comparative evaluation. Detailed discussion presented in this paper suggests that the dynamic procedure works well and physical insights and reasonings are provided to explain the observed behaviour.     

Experimental and numerical study of a conical turbulent partially premixed flame

The structure and dynamics of a turbulent partially premixed methane/air flame in a conical burner were investigated using laser diagnostics and large-eddy simulations (LES). The flame structure inside the cone was characterized in detail using LES based on a two-scalar flamelet model, with the mixture fraction for the mixing field and level-set G-function for the partially premixed flame front propagation. In addition, planar laser induced florescence (PLIF) of CH and chemiluminescence imaging with high speed video were performed through a glass cone. CH and CH₂O PLIF were also used to examine the flame structures above the cone. It is shown that in the entire flame the CH layer remains very thin, whereas the CH₂O layer is rather thick. The flame is stabilized inside the cone a short distance above the nozzle. The stabilization of the flame can be simulated by the triple-flame model but not the flamelet-quenching model. The results show that flame stabilization in the cone is a result of premixed flame front propagation and flow reversal near the wall of the cone which is deemed to be dependent on the cone angle. Flamelet based LES is shown to capture the measured CH structures whereas the predicted CH₂O structure is somewhat thinner than the experiments.     

Large eddy simulations of turbulent flames using the filtered density function model

Large eddy simulations (LES) of the Sandia/Sydney swirl burners (SM1 and SMA1) and the Sandia/Darmstadt piloted jet diffusion flame (Flame D) are performed. These flames are part of the database of turbulent reacting flows widely considered as benchmark test cases for validating turbulent-combustion models. In the simulations presented in this paper, the subgrid scale (SGS) closure model adopted for turbulence-chemistry interactions is based on the transport filtered density function (FDF) model. In the FDF model, the transport equation for the joint probability density function (PDF) of scalars is solved. The main advantage of this model is that the filtered reaction rates can be exactly computed. However, the density field, computed directly from the FDF solver and needed in the hydrodynamic equations, is noisy and causes numerical instability. Two numerical approaches that yield a smooth density field are examined. The two methods are based on transport equations for specific sensible enthalpy (h_s) and RT, where R is the gas constant and T is the temperature. Consistency of the two methods is assessed in a bluff-body configuration using Reynolds averaged Navier-Stokes (RANS) methodology in conjunction with the transported PDF method. It is observed that the h_s method is superior to the RT method. Both methods are used in LES of the SM1 burner. In the near-field region, the h_s method produces better predictions of temperature. However, in the far-field region, both methods show deviation from data. Simulations of the SMA1 burner and Flame D are also presented using the h_s method. Some deficiencies are seen in the predictions of the SMA1 burner that may be related to the simple chemical kinetics model and mixing model used in the simulations. Simulations of Flame D show good agreement with data. These results indicate that, while further improvements to the methodology are needed, the LES/FDF method has the potential to accurately predict complex turbulent flames.     

Effects of combined dimension reduction and tabulation on the simulations of a turbulent premixed flame using a large-eddy simulation/probability density function method

A turbulent lean-premixed propane–air flame stabilised by a triangular cylinder as a flame-holder is simulated to assess the accuracy and computational efficiency of combined dimension reduction and tabulation of chemistry. The computational condition matches the Volvo rig experiments. For the reactive simulation, the Lagrangian Large-Eddy Simulation/Probability Density Function (LES/PDF) formulation is used. A novel two-way coupling approach between LES and PDF is applied to obtain resolved density to reduce its statistical fluctuations. Composition mixing is evaluated by the modified Interaction-by-Exchange with the Mean (IEM) model. A baseline case uses In Situ Adaptive Tabulation (ISAT) to calculate chemical reactions efficiently. Its results demonstrate good agreement with the experimental measurements in turbulence statistics, temperature, and minor species mass fractions. For dimension reduction, 11 and 16 represented species are chosen and a variant of Rate Controlled Constrained Equilibrium (RCCE) is applied in conjunction with ISAT to each case. All the quantities in the comparison are indistinguishable from the baseline results using ISAT only. The combined use of RCCE/ISAT reduces the computational time for chemical reaction by more than 50%. However, for the current turbulent premixed flame, chemical reaction takes only a minor portion of the overall computational cost, in contrast to non-premixed flame simulations using LES/PDF, presumably due to the restricted manifold of purely premixed flame in the composition space. Instead, composition mixing is the major contributor to cost reduction since the mean-drift term, which is computationally expensive, is computed for the reduced representation. Overall, a reduction of more than 15% in the computational cost is obtained.     

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

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

Conditional moment closure and transient flamelet modelling for detailed structure and NO x formation characteristics of turbulent nonpremixed jet and recirculating flames

This study has been mainly motivated to assess computationally and theoretically the conditional moment closure (CMC) model and the transient flamelet model for the simulation of turbulent nonpremixed flames. These two turbulent combustion models are implemented into the unstructured grid finite volume method that efficiently handles physically and geometrically complex turbulent reacting flows. Moreover, the parallel algorithm has been implemented to improve computational efficiency as well as to reduce the memory load of the CMC procedure. Example cases include two turbulent CO/H₂/N₂ jet flames having different flow timescales and the turbulent nonpremixed H₂/CO flame stabilized on an axisymmetric bluff-body burner. The Lagrangian flamelet model and the simplified CMC formulation are applied to the strongly parabolic jet flame calculation. On the other hand, the Eulerian particle flamelet model and full conservative CMC formulation are employed for the bluff-body flame with flow recirculation. Based on the numerical results, a detailed discussion is given for the comparative performances of the two combustion models in terms of the flame structure and NO _x formation characteristics.     

Flame propagation in a small-scale parallel flow

We consider the propagation of laminar premixed flames in the presence of a parallel flow whose scale is smaller than the laminar flame thickness. The study addresses fundamental aspects with relevance to flame propagation in narrow channels, to the emerging micro-combustion technology, and to the understanding of the effect of small scales in a (turbulent) flow on the flame structure. In part, the study extends the results of a previous analytical study carried out in the thick flame asymptotic limit which has in particular addressed the validity of Damköhler's second hypothesis in the context of laminar steady parallel flows. Several new contributions are made here.

Analytical contributions include the derivation of an explicit formula for the effective speed of a premixed flame U _T in the presence of an oscillatory parallel flow whose scale ? (measured with the laminar flame thickness δ _L ) is small and amplitude A (measured with the laminar flame speed U _L ) is (1). The formula shows a quadratic dependence on both the amplitude and the scale of the flow. The validity of the formula is established analytically in two distinguished limits corresponding to (1) frequencies of oscillations (measured with the natural frequency of the flame U _L /δ _L ), and to higher frequencies of (A/?) (the natural frequency of the flow). The analytical study yields partial support of Damköhler's second hypothesis in that it shows that the flame behaves as a planar flame (to leading order) with an increased propagation speed which depends on both the scale and amplitude of the velocity fluctuation. However our formula for U _T contradicts the formula given by Damköhler in his original paper where U _T has a square root dependence on the scale and amplitude.

Numerical contributions include a significant set of two-dimensional calculations which determine the range of validity of the asymptotic findings. In particular, these account for volumetric heat loss and differential diffusion effects. Good agreement between the numerics and asymptotics is found in all cases, both for steady and oscillatory flows, at least in the expected range of validity of the asymptotics. The effect of the frequency of oscillation is also discussed. Additional related aspects such as the difference in the response of thin and thick flames to the combined effect of heat loss and fluid flow are also addressed. It is found for example that the sensitivity of thick flames to volumetric heat loss is negligibly affected by the parallel flow intensity, in marked contrast to the sensitivity of thin flames. Interestingly, and somewhat surprisingly, thin flames are found to be more resistant to heat loss when a flow is present, even for unit Lewis number; this ceases to be the case, however, when the Lewis number is large enough.     

Large eddy simulation of piloting effects on turbulent swirling flames

Pilot flames, created by additional injectors of pure fuel, are often used in turbulent burners to enhance flame stabilization and reduce combustion instabilities. The exact mechanisms through which these additional rich zones modify the flame anchoring location and the combustion dynamics are often difficult to identify, especially when they include unsteady hydrodynamic motion. This study presents Large Eddy Simulations (LES) of the reacting flow within a large-scale gas turbine burner for two different cases of piloting, where either 2 or 6% of the total methane used in the burner is injected through additional pilot flame lines. For each case, LES shows how the pilot fuel injection affects both flame stabilization and flame stability. The 6% case leads to a stable flame and limited hydrodynamic perturbations in the initial flame zone. The 2% case is less stable, with a small-lift-off of the flame and a Precessing Vortex Core (PVC) in the cold stabilization zone. This PVC traps some of the lean cold gases issuing from the pilot passage stream, changes the flame stabilization point and induces instability.     

Identification of flame transfer functions in the presence of intrinsic thermoacoustic feedback and noise

The Large Eddy Simulation/System Identification (LES/SI) approach is a general and efficient numerical method for deducing a Flame Transfer Function (FTF) from the LES of turbulent reacting flow. The method may be summarised as follows: a simulated flame is forced with a broadband excitation signal. The resulting fluctuations of the reference velocity and of the global heat release rate are post-processed via SI techniques in order to estimate a low-order model of the flame dynamics. The FTF is readily deduced from the low-order model. The SI method most frequently applied in aero- and thermo-acoustics has been Wiener–Hopf Inversion (WHI). This method is known to yield biased estimates in situations with feedback, thus it was assumed that non-reflective boundary conditions are required to generate accurate results with the LES/SI approach. Recent research has shown that the FTF is part of the so-called Intrinsic ThermoAcoustic (ITA) feedback loop. Hence, identifying an FTF from a compressible LES is always a closed-loop problem, and consequently one should expect that the WHI would yield biased results. However, several studies proved that WHI results compare favourably with validation data. To resolve this apparent contradiction, a variety of identification methods are compared against each other, including models designed for closed-loop identification. In agreement with theory, we show that the estimate given by WHI does not converge to the actual FTF. Fortunately, the error made is small if excitation amplitudes can be set such that the signal-to-noise ratio is large, but not large enough to trigger nonlinear flame dynamics. Furthermore, we conclude that non-reflective boundary conditions are not essentially necessary to apply the LES/SI approach.     

Numerical analyses of deflagration initiation by a hot jet

Numerical simulations of axisymmetric reactive jets with one-step Arrhenius kinetics are used to investigate the problem of deflagration initiation in a premixed fuel–air mixture by the sudden discharge of a hot jet of its adiabatic reaction products. For the moderately large values of the jet Reynolds number considered in the computations, chemical reaction is seen to occur initially in the thin mixing layer that separates the hot products from the cold reactants. This mixing layer is wrapped around by the starting vortex, thereby enhancing mixing at the jet head, which is followed by an annular mixing layer that trails behind, connecting the leading vortex with the orifice rim. A successful deflagration is seen to develop for values of the orifice radius larger than a critical value a _c in the order of the flame thickness of the planar deflagration δ_L. Introduction of appropriate scales provides the dimensionless formulation of the problem, with flame initiation characterised in terms of a critical Damköhler number Δ_c=(a _c/δ_L)², whose parametric dependence is investigated. The numerical computations reveal that, while the jet Reynolds number exerts a limited influence on the criticality conditions, the effect of the reactant diffusivity on ignition is much more pronounced, with the value of Δ_c increasing significantly with increasing Lewis numbers . The reactant diffusivity affects also the way ignition takes place, so that for reactants with the flame develops as a result of ignition in the annular mixing layer surrounding the developing jet stem, whereas for highly diffusive reactants with Lewis numbers sufficiently smaller than unity combustion is initiated in the mixed core formed around the starting vortex. The analysis provides increased understanding of deflagration initiation processes, including the effects of differential diffusion, and points to the need for further investigations incorporating detailed chemistry models for specific fuel–air mixtures.