Sandia Flame Research Articles

Sparse-Lagrangian FDF simulations of Sandia Flame E with density coupling

Sparse-Lagrangian filtered density function (FDF) simulations are performed for Sandia flame E. A generalised multiple mapping conditioning (MMC) mixing model for the Lagrangian field enforces mixing localisation in the Eulerian large eddy simulation (LES) mixture fraction space. The modelled level of local extinction is determined by the appropriate pairing of mixing particles and the timescale of their mixing interaction. A major development presented in this paper is the inclusion of density coupling between the Eulerian LES and Lagrangian particle fields achieved through use of the equivalent enthalpy method adapted for sparse conditions. Results for two sparse simulation cases, one with one Lagrangian particle per eight Eulerian LES grid cells and the other with one particle per 32 Eulerian LES grid cells, show that accurate FDF predictions of passive and reactive scalars can be achieved for a relatively modest computational cost.

Stochastic multiple mapping conditioning for a piloted, turbulent jet diffusion flame

A stochastic implementation of the multiple mapping conditioning (MMC) approach has been applied to a turbulent jet diffusion flame (Sandia Flame D). This implementation combines the advantages of the basic concepts of a mapping closure methodology with a probability density approach. A single reference variable has been chosen. Its evolution is described by a Markov process and then mapped to the mixture fraction space. Scalar micro-mixing is modelled by a modified “interaction by exchange with the mean” (IEM) mixing model where the particles mix with their -in reference space- conditionally averaged means. The formulation of the closure leads to localness of mixing in mixture fraction space and consequently improved localness in composition space. Results for mixture fraction and reactive species are in good agreement with the experimental data. The MMC methodology allows for the introduction of an additional “minor dissipation time scale” that controls the fluctuations around the conditional mean. A sensitivity analysis based on the conditional temperature fluctuations as a function of this time scale does not endorse earlier estimates for its modelling, but only relatively large dissipation time scales of the order of the integral turbulence time scale yield acceptable levels of conditional fluctuations that agree with experiments. With the choice of a suitable dissipation time scale, MMC-IEM thus provides a simple mixing model that is capable of capturing extinction phenomena, and it gives improved predictions over conventional PDF predictions using simple IEM mixing models.

Conditionally filtered diffusion of mixture fraction and temperature in turbulent partially premixed flames

Recent studies have shown that the subgrid-scale (SGS) mixture fraction has different structures and probability distributions for different SGS scalar variances. We study the effects of these structures on the scalar diffusion and temperature diffusion in the context of large-eddy simulation (LES) of turbulent combustion. Line images obtained in turbulent partially premixed (Sandia) flames are used to analyze the scalar and temperature diffusion filtered conditionally on the scalar and temperature, which must be correctly modeled in LES. The results show that for small SGS variance the scalar and temperature diffusion have a relatively simple structure. For large SGS variance the diffusion is much more complex, with the flamelet structure and local extinction playing important roles. The results show that it is important that mixing models for filtered density function methods be able to account for the different SGS mixture fraction and temperature structures for small and large SGS variance.

Capturing localised extinction in Sandia Flame F with LES–CMC

A Large Eddy Simulation (LES) using the Conditional Moment Closure (CMC) as a sub-grid turbulence-chemistry model has been applied to piloted jet diffusion flames (Sandia D&F). A 3D CMC grid was used which allowed different CMC boundary conditions to be applied in the jet and pilot streams. The code was found to give very good agreement with experiment in the low extinction case of Flame D. For Flame F transient extinction and re-ignition events were observed with LES–CMC which lead to reductions in averaged unconditional and conditional temperature consistent with experimental observations. Further analysis revealed that the CMC extinction/ignition events were the result of a combination of high conditional scalar dissipation rate and transport in the CMC grid.

Noise Correction and Length Scale Estimation for Scalar Dissipation Rate Measurements in Turbulent Partially Premixed Flames

A recently developed conditional sampling-based method for correcting noise effects in scalar dissipation rate measurements and for estimating the extent of resolution of the dissipation rate is employed to analyze the data obtained in turbulent partially premixed (Sandia) flames. The method uses conditional sampling to select instantaneous fully resolved local scalar fields, which are analyzed to determine the measurement noise and to correct the Favre mean, conditional, and conditionally filtered dissipation rates. The potentially under-resolved local scalar fields, also selected using conditional sampling, are corrected for noise and are analyzed to examine the extent of resolution. The error function is used as a model for the potentially under-resolved local scalar to evaluate the scalar dissipation length scales and the percentage of the dissipation resolved. The results show that the Favre mean dissipation rate, the mean dissipation rate conditional on the mixture fraction, and dissipation rate filtered conditionally on the mixture fraction generally are well resolved in the flames. Analyses of the dissipation rates filtered conditionally on the mixture fraction and temperature show that the length scale increases with temperature, due to lower dissipation rate and higher diffusivity. The dissipation rate is well resolved for temperatures above 1,300 K but is less resolved at lower temperatures, although the probability of very low temperature events is low. To fully resolve these rare events the sample spacing needs to be reduced by approximately one half. The present study further demonstrates the effectiveness of the new noise correction and length scale estimation method.

Large Eddy Simulation of the Sandia Flame Series (D–F) using the Eulerian stochastic field method

Three turbulent piloted methane jet flames with increasing levels of local extinction (Sandia Flames D–F) have been computed using Large Eddy Simulation. The smallest unresolved scales of the flow, in which combustion occurs, are represented using the filtered probability density function method where the corresponding evolution equation is solved directly. A dynamic model for the sub-grid stresses together with a simple gradient diffusion approximation for the scalar fluxes is applied in conjunction with the linear mean square estimation closure for sub-filter scale mixing. An augmented reduced mechanism (ARM) derived from the full GRI 3.0 mechanism is incorporated to describe the chemical reaction. The results demonstrate the ability of the method in capturing quantitatively finite rate effects such as extinction and re-ignition in turbulent flames.

A simple model for the filtered density function for passive scalar combustion LES

LES models for turbulent non-premixed combustion usually require knowledge of the filtered density function of the conserved scalar, and we propose to use a simple top-hat function. Such top-hat distributions were developed as probability density functions for RANS applications in the 1970s but were soon surpassed by the β function. We find that in the context of LES, the top-hat distribution provides an excellent alternative to the now much more common β function. The top-hat function is assessed through a phenomenological analysis of Direct Numerical Simulation (DNS) data from a planar jet and of experimental data from a turbulent opposed jet. The approach is then tested a posteriori for a piloted diffusion flame (Sandia Flame D). Advantages of the top-hat function are the ease of implementation and the reduced dimensionality of look-up tables. The present paper also discusses inconsistencies of sub-grid β-FDFs, the FDFs sensitivity on implicit filtering, and the regime in which a β assumption can be a valid filtered density function for LES.

A Priori Testing of Flamelet Generated Manifolds for Turbulent Partially Premixed Methane/Air Flames

To reduce high computational cost associated with simulations of reacting flows chemistry tabulation methods like the Flamelet Generated Manifold (FGM) method are commonly used. However, H2, CO and OH predictions in RANS and LES simulations using the FGM (or a similar) method usually show a substantial deviation from measurements. The goal of this study is to assess the accuracy of low-dimensional FGM databases for the prediction of these species in turbulent, partially-premixed reacting flows. It will be examined to what extent turbulent, partially-premixed jet flames can be described by FGM databases based on premixed or counterflow diffusion flamelets and to what extent the chosen molecular transport model for the flamelet influences the accuracy of species mass fraction predictions in CFD-simulations. For LES and RANS applications a model that accounts for subgrid fluctuations has to be added introducing additional errors in numerical results. A priori analysis of FGM databases enables the exclusion of numerical errors (scheme accuracy, convergence) that occur in CFD simulations as well as the exclusion of errors originating from subgrid modeling assumptions in LES and RANS. Four different FGM databases are compared for H2O, H2, CO, CO2 and OH predictions in Sandia Flames C to F. Species mass fractions will be compared to measurements directly and conditioned on mixture fraction. Special attention is paid to the representation of experimentally observed differential diffusion effects by FGM databases.

Modeling of scalar mixing in turbulent jet flames by multiple mapping conditioning

Multiple mapping conditioning (MMC) combines the probability density function (PDF) and the conditional moment closure (CMC) methods via the application of a generalized mapping function to a prescribed reference space. Stochastic and deterministic formulations of MMC exist, and the deterministic implementation has been applied here to a piloted jet diffusion flame (Sandia Flame D). This paper focuses on the feasibility of MMC and its closures for real (laboratory) flames and a relatively simple one-dimensional reference space that represents mixture fraction has been used. The remaining chemically reactive species are implicitly conditioned on mixture fraction and their fluctuations around the conditional mean are neglected. This work primarily evaluates the ability of the deterministic form of MMC to provide accurate and consistent closures for the mixture fraction PDF and the conditional scalar dissipation which do not rely on presumed shape functions for the PDF such as the commonly used β-PDF. Computed probability distributions agree well with measurements, and a detailed comparison of the modeled conditional and mean scalar dissipation with experimental data and conventional closures demonstrate MMC’s potential. Predictions of reactive species and temperature are in good agreement with experimental data and similar in quality to singly conditioned, first-order CMC predictions. MMC therefore provides an attractive-since consistent-alternative approach for the modeling of scalar mixing in turbulent reacting flows.

Application of reduced state spaces to laser-based measurements in combustion

A systematic exploitation of state variable correlations for increasing the accuracy and significance of laser-based measurements in combustion is proposed, formally developed and applied to an example. Correlations between state variables (species concentrations and temperature) lead to the phenomenon that the realizable states in a combustion system are on or close to low-dimensional manifolds in state space, allowing an approximate description of the system state in terms of a few variables. This makes it feasible to approximately determine the full state of a combustion system by means of just a few simultaneous laser-based measurements. As an example application of the method, a simple system with a low-dimensional manifold is constructed by steady and unsteady flamelets. The fuel and oxidizer correspond to a series of well-documented, turbulent, non-premixed methane/air jet flames (Sandia Flames A–F). This low-dimensional manifold is then used to determine state variables via polarized/depolarized Rayleigh-signals. The results show that even in very complex, turbulent flames, many quantities can be determined by means of just two signals. Some quantities are more prone to errors than others. The errors originate in the sensitivities of species with respect to signal noise and with respect to deviations of the actual states from the assumed, steady/unsteady-flamelet-based low-dimensional manifold.

A sparse-Lagrangian multiple mapping conditioning model for turbulent diffusion flames

A sparse-Lagrangian multiple mapping conditioning (MMC) model for turbulent diffusion flames is presented and tested against experimental data for a piloted methane/air jet diffusion flame (Sandia Flame D). The model incorporates a large eddy simulation for the flow field and a stochastic multiple mapping conditioning (MMC) approach for the reactive scalars. The stochastic MMC models the filtered density function of the scalar composition field. The numerical implementation involves a sparse-Lagrangian particle scheme in which there are fewer particles than there are LES grid cells. Predictions of similar accuracy to previously published Flame D simulations are achieved using only 35,000 particles (of these only 10,000 are chemically active). Sub-filter conditional dissipation is modelled by interactions between pairs of particles which are closely located in a reference mixture fraction space interpolated from the underlying Eulerian filtered field. A model is developed for the mixing time-scale which is proportional to the distance between mixing particles. It is shown that the time-scale can be adjusted to achieve good predictions for time-averaged mean and fluctuating statistics of passive and reactive scalars.

LES of the Sandia Flame D Using Laminar Flamelet Decomposition for Conditional Source-Term Estimation

A variation of the Laminar Flamelet Decomposition (LFD) method for the Conditional Source Term (CSE) model developed by Bushe and Steiner (Phys Fluids 15:1564–1575, 2003) is implemented into an existing LES code. In this approach, the set of basis functions, on which the decomposition is based, is reduced using the mixture fraction dissipation rate as external parameter for the selection. It was found that reducing the basis improves and stabilises the inversion, resulting in reasonably accurate approximation for the average conditional quantities. Some modifications have been introduced to improve the inversion process by reducing the number of flamelets. This modification is found to help stabilize the inversion and keep the dimension of the linear system small. The model is used to simulate the turbulent non-premixed piloted SANDIA Flame D. Reasonably good predictions for conditional and unconditional average variables were found for different planes and at centreline of the flow field. However, an over prediction of the consumption rate in the near field of the flame is found, which may be partially attributed to the use of the Steady Laminar Flamelets (SLF) as functions for the decomposition and the use of a constant boundary condition for the species mass fractions in solving the flamelets. The present simulation of a turbulent reacting jet is the first test of the LFD approach in a realistic scenario using only the temperature field to calculate the inversion. The model is found to be computationally inexpensive.

A Generalised Multiple Mapping Conditioning Approach for Turbulent Combustion

This paper follows the evolution in understanding of the multiple mapping conditioning (MMC) approach for turbulent combustion and reviews different implementations of MMC models. As the MMC name suggests, the original version represents a consistent combination of CMC-type conditional equations (conditional moment closure) and generalised mapping closure. It seems that the strength of the MMC model, and especially that of its stochastic version, lies in a more general (and much more transparent) interpretation. In this new generalised interpretation, we can replace complicated derivations by physical reasoning and the model appears to be a natural extension of modelling approaches developed in recent decades. MMC can be seen as a methodology for enforcing certain known characteristics of turbulence on a conventional mixing model. This is achieved by localising the mixing operation in a reference space. The reference space variables are selected to emulate the properties of a turbulent flow which have a strong effect on reactive quantities. The best and simplest example is an MMC model which has a single reference variable emulating the mixture fraction. In diffusion flames turbulent fluctuations of reacting quantities are strongly correlated with fluctuations of the mixture fraction. By making mixing local in the reference mixture fraction space a CMC-type mixing closure is enforced. In the original interpretation of MMC the reference variables are modelled as Markov processes. Since the reference variables should emulate properties of turbulent flows as realistically as possible the next step, and the basis of generalised MMC, is to remove the Markovian restriction and set reference variables equal to traced Lagrangian quantities within DNS or LES flow fields. Indeed, no Markov value can emulate the mixture fraction better than the mixture fraction itself. (Using a Markov vector process of dimension higher than the number of conditioning variables represents a more economical alternative for producing reference variables in generalised MMC.) The generalised MMC approach effectively incorporates the mixture fraction-based models, the PDF methods and LES/DNS techniques into a single methodology with possibility of blending useful features developed previously for conventional models. The generalised approach to MMC stimulates a more flexible understanding of simulations using sparsely placed Lagrangian particles as tools that may provide accurate joint distributions of reactive scalars at relatively low computational cost. The physical reasoning behind the new interpretation of MMC is supported by example computations for a partially premixed methane/air diffusion flame (Sandia Flame D). The scheme utilises LES for the dynamic field and a sparse-Lagrangian filtered density function method with MMC mixing for the scalar field. Two different particle mixing schemes are tested. Simulations are performed using only 35,000 Lagrangian particles (of these only 10,000 are chemically active) on a single workstation. The relatively low computational cost allows the use of realistic chemical kinetics containing 34 reactive species and 219 reactions.

Subgrid Scale Modeling in Large-Eddy Simulation of Turbulent Combustion Using Premixed Flamelet Chemistry

Large-eddy simulation (LES) of turbulent combustion with premixed flamelets is investigated in this paper. The approach solves the filtered Navier-Stokes equations supplemented with two transport equations, one for the mixture fraction and another for a progress variable. The LES premixed flamelet approach is tested for two flows: a premixed preheated Bunsen flame and a partially premixed diffusion flame (Sandia Flame D). In the first case, we compare the LES with a direct numerical simulation (DNS). Four non-trivial models for the chemical source term are considered for the Bunsen flame: the standard presumed beta-pdf model, and three new propositions (simpler than the beta-pdf model): the filtered flamelet model, the shift-filter model and the shift-inversion model. A priori and a posteriori tests are performed for these subgrid reaction models. In the present preheated Bunsen flame, the filtered flamelet model gives the best results in a priori tests. The LES tests for the Bunsen flame are limited to a case in which the filter width is only slightly larger than the flame thickness. According to the a posteriori tests the three models (beta-pdf, filtered flamelet and shift-inversion) show more or less the same results as the trivial model, in which subgrid reaction effects are ignored, while the shift-filter model leads to worse results. Since LES needs to resolve the large turbulent eddies, the LES filter width is bounded by a maximum. For the present Bunsen flame this means that the filter width should be of the order of the flame thickness or smaller. In this regime, the effects of subgrid reaction and subgrid flame wrinkling turn out to be quite modest. The LES-results of the second case (Sandia Flame D) are compared to experimental data. Satisfactory agreement is obtained for the main species. Comparison is made between different eddy-viscosity models for the subgrid turbulence, and the Smagorinsky eddy-viscosity is found to give worse results than eddy-viscosities that are not dominated by the mean shear.

One-dimensional turbulence-based closure with extinction and reignition

Scalar statistics from stand-alone one-dimensional turbulence (ODT) simulations are constructed to develop a doubly conditioned table based on the mixture fraction and temperature for the prediction of extinction and reignition in piloted methane–air jet diffusion flames. The ODT-based closure approach is formulated to predict scalar statistics coupled with the Reynolds-averaged Navier–Stokes (RANS) approach. Comparison with experimental correlations of reactive scalars with the two conditioning variables show that double conditioning may be adequate to prescribe scalar statistics in the jet diffusion flames. The results also show that the ODT model may be used to construct these statistics. The 2D conditioning table is coupled with RANS to compute Sandia flames D, E, and F, which exhibit increasing rates of extinction followed by reignition as the Reynolds numbers are increased. The coupling also requires the transport of the means and variances of the mixture fraction and temperature. Closure terms in the temperature mean and variance equations are obtained by using the 2D table for reaction source terms and by assuming a presumed PDF shape for the temperature PDF. Comparisons show adequate predictions of axial and radial profiles of the mixture fraction, the streamwise velocity, and the reactive scalars for flames D and E and mixed results for flame F. Nonetheless, qualitative trends of increasing the jet Reynolds numbers resulting in more pronounced extinctions are obtained with the RANS-ODT approach. The discrepancy between computation and experiment may be attributed primarily to the closure for the temperature and its variance and to the presumed PDF shape for the temperature.

Prediction of extinction and reignition in nonpremixed turbulent flames using a flamelet/progress variable model: 1. A priori study and presumed PDF closure

Previously conducted studies of the flamelet/progress variable model for the prediction of nonpremixed turbulent combustion processes identified two areas for model improvements: the modeling of the presumed probability density function (PDF) for the reaction progress parameter and the consideration of unsteady effects [Ihme et al., Proc. Combust. Inst. 30 (2005) 793]. These effects are of particular importance during local flame extinction and subsequent reignition. Here, the models for the presumed PDFs for conserved and reactive scalars are re-examined and a statistically most likely distribution (SMLD) is employed and tested in a priori studies using direct numerical simulation (DNS) data and experimental results from the Sandia flame series. In the first part of the paper, the SMLD model is employed for a reactive scalar distribution. Modeling aspects of the a priori PDF, accounting for the bias in composition space, are discussed. The convergence of the SMLD with increasing number of enforced moments is demonstrated. It is concluded that information about more than two moments is beneficial to accurately represent the reactive scalar distribution in turbulent flames with strong extinction and reignition. In addition to the reactive scalar analysis, the potential of the SMLD for the representation of conserved scalar distributions is also analyzed. In the a priori study using DNS data it is found that the conventionally employed beta distribution provides a better representation for the scalar distribution. This is attributed to the fact that the beta-PDF implicitly enforces higher moment information that is in excellent agreement with the DNS data. However, the SMLD outperforms the beta distribution in free shear flow applications, which are typically characterized by strongly skewed scalar distributions, in the case where higher moment information can be enforced.

A Premixed Flamelet−PDF Model for Biomass Combustion in a Grate Furnace

In this paper, a new modeling approach for biomass furnaces is presented. A flamelet model is applied for the prediction of combustion and NO x emissions in a pilot-scale low-NO x biomass grate furnace. The model describes the combustion chemistry using premixed flamelets. The chemical system is mapped on three control variables—the mixture fraction, enthalpy, and a reaction progress variable—by means of the flamelet-generated manifold chemical reduction technique (FGM). The density and source terms are tabulated as functions of the control variables in a preprocessing step to speed up the numerical calculations. The turbulence—chemistry interaction is described by an assumed shape probability density function (PDF) approach. Generally, transport equations are solved for mean and variance of mixture fraction, mean progress variable, and the mean enthalpy. The FGM-PDF model is first validated for a diffusion flame: Sandia Flame D. Good agreement of predictions with measurements is found. The model is then applied to a 2D cross section of a biomass combustion grate furnace. FGM-PDF is compared with the standard eddy dissipation concept model (EDC). The predictions of the two models are similar. The FGM-PDF model reduces the calculation time with GRI-Mech2.11 reaction mechanism from weeks to hours, when compared to EDC. Furthermore, in FGM-PDF more physics can be taken into account thanks to the integration of flamelets in the turbulence—chemistry interaction.

Spatial resolution effects on the measurement of scalar variance and scalar gradient in turbulent nonpremixed jet flames

The effect of spatial averaging is important for scalar gradient measurements in turbulent nonpremixed flames, especially when the local dissipation length scale is small. Line imaging of Raman, Rayleigh and CO-LIF is used to investigate the effects of experimental resolution on the scalar variance and radial gradient in the near field of turbulent nonpremixed CH4/H2/N2 jet flames at Reynolds numbers of 15,200 and 22,800 (DLR-A and B) and in piloted CH4/air jet flames at Reynolds numbers of 13,400, 22,400 and 33,600 (Sandia flames C/D/E). The finite spatial resolution effects are studied by applying the Box filter with varying filter widths. The resulting resolution curves for both scalar variance and mean squared-gradient follow nearly the same trends as theoretical curves calculated from the model turbulence kinetic energy spectrum of Pope. The observed collapse of resolution curves of mean squared-gradient for nearly all studied cases implies the shape of the dissipation spectrum is approximately universal. Fluid transport properties are shown to have no effect on the dissipation resolution curve, which implies that the dissipation length scale inferred from the square gradient is equivalent to the length scale for the scalar dissipation rate, which includes the diffusion coefficient. With the Box filter, the required spatial resolution to resolve 98% of the mean dissipation rate is about one−two times of the dissipation cutoff length scale (analogous to the Batchelor scale in turbulent isothermal flows). The effects of resolution on the variances of mixture fraction, temperature, and the inverted Rayleigh signal are also compared. The ratio of the filtered variance to the true variance is shown to depend nearly linearly on the probe resolution. The inverted Rayleigh scattering signal can be used to study the resolution effect on temperature variance even when the Rayleigh scattering cross section is not constant. The experimental results also indicate that these laboratory scale turbulent jet flames have small effective Reynolds numbers, such that there is some direct interaction of the large (energy containing) and small (dissipative) scalar length scales, especially for the near field case at x/d = 7.5 of the piloted Sandia flames C/D/E.

Comparison of submodels for conditional velocity and scalar dissipation in CMC simulation of piloted jet and bluff-body flames

No meaningful difference is observed between the predictions with the conditional velocity modeled by linear scaling and gradient diffusion assumption for the test flames under consideration. The AMC and Girimaji's model for CSDR show similar results, while the pdf integration method results in an asymmetric profile with some deviation from the other two. The difference tends to decrease as mixing proceeds, to result in a lower level of scalar dissipation at downstream locations. Reasonable agreement is achieved with measured scalar dissipation rates at different axial locations for the Sandia Flame D, while direct comparison is difficult due to radially averaged pdfs and no measured scalar dissipation rates being available for the Sydney bluff-body flame.

Monte Carlo simulation of radiative heat transfer and turbulence interactions in methane/air jet flames

A Photon Monte Carlo method combined with a composition PDF method is employed to model radiative heat transfer in combustion applications. Turbulence–radiation interactions (TRIs) can be fully taken into account using the proposed method. Sandia's Flame D and artificial flames derived from it are simulated and good agreement with experimental data is found. The effects of different TRI components are investigated. It is shown that, to predict the radiation field accurately, emission TRI must be taken into account, while, as expected, absorption TRI is negligible in the considered nonsooting methane/air jet flames if the total radiation quantities are concerned, but non-negligible for evaluation of local quantities. The influence of radiation on the turbulent flow field is also discussed.