Premixed turbulent combustion modeling using tabulated detailed chemistry and PDF

Tabulated chemistry and presumed probability density function (PDF) approaches are combined to perform RANS modeling of premixed turbulent combustion. The chemistry is tabulated from premixed flamelets with three independent parameters: the equivalence ratio of the mixture, the progress of reaction, and the specific enthalpy, to account for heat losses at walls. Mean quantities are estimated from presumed PDFs. This approach is used to numerically predict a turbulent premixed flame diluted by hot burnt products at an equivalence ratio that differs from the main stream of reactants. The investigated flame, subjected to high velocity fluctuations, has a thickened-wrinkled structure. A recently proposed closure for scalar dissipation rate that includes an estimation of the coupling between flame wrinkling and micromixing is retained. Comparisons of simulations with experimental measurements of mean velocity, temperature, and reactants are performed.     

Modelling alkali metal emissions in large-eddy simulation of a preheated pulverised-coal turbulent jet flame using tabulated chemistry

The numerical modelling of alkali metal reacting dynamics in turbulent pulverised-coal combustion is discussed using tabulated sodium chemistry in large eddy simulation (LES). A lookup table is constructed from a detailed sodium chemistry mechanism including five sodium species, i.e. Na, NaO, NaO₂, NaOH and Na₂O₂H₂, and 24 elementary reactions. This sodium chemistry table contains four coordinates, i.e. the equivalence ratio, the mass fraction of the sodium element, the gas-phase temperature, and a progress variable. The table is first validated against the detailed sodium chemistry mechanism by zero-dimensional simulations. Then, LES of a turbulent pulverised-coal jet flame is performed and major coal-flame parameters compared against experiments. The chemical percolation devolatilisation (CPD) model and the partially stirred reactor (PaSR) model are employed to predict coal pyrolysis and gas-phase combustion, respectively. The response of the five sodium species in the pulverised-coal jet flame is subsequently examined. Finally, a systematic global sensitivity analysis of the sodium lookup table is performed and the accuracy of the proposed tabulated sodium chemistry approach has been calibrated.     

Effects of subgrid scale and combustion modelling on flame structure of a turbulent premixed flame within LES and tabulated chemistry framework

The effects of combustion and SubGrid Scale (SGS) modelling on the overall flame characteristics of a turbulent premixed flame are investigated. This is achieved in terms of mean flow statistics, variances and flame surfaces. In particular, the chemical flame structure is analysed and compared. The Artificially Thickened Flame (ATF) approach coupled with the Flamelet Generated Manifolds (FGMs) and Filtered TAbulated Chemistry for LES (F-TACLES) approaches are used for this investigation. A Germano like procedure for dynamical calculation of SGS wrinkling is used which ensures the conservation of the total flame surface for both models. It turns out that using the dynamic SGS wrinkling model improves the results. Although the results of both combustion models in terms of statistics, mean and variances show very good agreement, the resolved flame surfaces hide different dynamic behaviour.     

Using self-similar properties of turbulent premixed flames to downsize chemical tables in high-performance numerical simulations

Detailed chemical mechanisms have to be incorporated in turbulent combustion modelling to predict flame propagation, ignition, extinction or pollutant formation. Unfortunately, hundreds of species and thousands of elementary reactions are involved in hydrocarbon chemical schemes and cannot be handled in practical simulations, because of the related computational costs and the need to model the complexity of their interaction with turbulent motions. Detailed chemistry may be handled using look-up tables, where chemical parameters such as reaction rates and/or species mass fractions are determined from a reduced set of coordinates, progress variables or mixture fractions, as proposed in ILDM, FPI or FGM methods. Nevertheless, these tables may require large computer memory spaces and non-negligible access times. This issue becomes of crucial importance when running on massively parallel computers: to implement these databases in shared memories would induce a large number of data exchanges, reducing the overall code performance; on the other hand duplicating databases in every local processor memory may become impossible either for large databases or small local memories. This work proposes to take advantage of the self-similar behaviour of turbulent premixed flames to reduce the size of these chemical databases, specifically when running on massively parallel machines, under the FPI (Flame Prolongation of ILDM) framework. Several approaches to reduce the database are investigated and discussed both in terms of memory requirements and access times. A very good compromise is obtained for methane–air turbulent premixed flames, where the size of the database is decreased by a factor of 1000, while the access time is reduced by about 60%.     

The performance of in situ adaptive tabulation in computations of turbulent flames

This paper presents a detailed characterization of the local and global errors associated with the in situ adaptive tabulation (ISAT) algorithm, which is used in conjunction with a transported PDF method. Calculations of a non-premixed turbulent methane/air piloted jet flame (Sandia flame D) using a skeletal chemical mechanism were performed using ISAT coupled with the computational fluid dynamics (CFD) code FLUENT. The three strategies implemented in ISAT for the growing of the ellipsoids of accuracy (EOAs) are discussed, and the cumulative distribution function (CDF) of the local error is presented for each of the three growing strategies. Computations are also performed to characterize the global error in the ISAT/PDF calculation. The computations used to characterize the global error were performed in parallel to achieve substantial savings in computational time.

In general the local error is well controlled, but there is a small probability of relatively large errors. Results from the investigation suggest that large retrieve errors are due to the region of accuracy (ROA) being non-convex, where the ROA is the connected region for which the error does not exceed the error tolerance, ?_tol. The global error in ISAT is found to be small compared to statistical error for ?_tol ≤ 10^?4, and is found to vary linearly with ?_tol.     

Large Eddy Simulations of a piloted lean premix jet flame using finite-rate chemistry

A Large Eddy Simulation (LES) model capable of accurately representing finite-rate chemistry effects in turbulent premixed combustion is presented. The LES computations use finite-rate chemistry and implicit LES combustion modelling to simulate an experimentally well-documented lean-premixed jet flame stabilized by a stoichiometric pilot. The validity of the implicit LES assumption is discussed and criteria are expressed in terms of subgrid scale Damköhler and Karlovitz numbers. Simulation results are compared to experimental data for velocity, temperature and species mass fractions of CH₄, CO and OH. The simulation results highlight the validity and capability of the present approach for the flame and in general the combustion regime examined. A sensitivity analysis to the choice of the finite-rate chemistry mechanism is reported, this analysis indicates that the one and two-step global reaction mechanisms evaluated fail to capture the reaction layer with sufficient accuracy, while a 20-species skeletal mechanism reproduces the experimental observations accurately including the key finite-rate chemistry indicators CO and OH. The LES results are shown to be grid insensitive and that the grid resolution within the bounds examined is far less important compared to the sensitivity of the finite-rate chemistry representation. The results are analyzed in terms of the flame dynamics and it is shown that intense small scale mixing (high Karlovitz number) between the pilot and the jet is an important mechanism for the stabilization of the flame.     

Transported probability density function modeling of a bluff body stabilized turbulent flame

A transported probability density function (PDF) approach closed at the joint scalar level is used to model the bluff body stabilized turbulent diffusion flame (HM1) investigated experimentally by Masri and co-workers (Re = 15,800). The current effort extends previous work through the introduction of comprehensive thermochemistry computed via a systematically reduced C/H/N/O mechanism featuring 300 reactions, 20 solved, and 28 steady-state species. Molecular mixing is modelled using the modified Curl’s model. The current computations have been performed via a hybrid Monte Carlo/Finite Volume algorithm. The joint scalar PDF equations are solved using moving particles in a Lagrangian framework, and the velocity field is closed at the second moment level. The redistribution terms are modelled using the Generalized Langevin Model of Haworth and Pope. The principal aim was to investigate the thermochemical effects, and thus a steady-state calculation procedure is adopted. The computations are shown to reproduce experimental mean and rms values of velocities, temperature, mixture, and species mass fractions. In particular, mass fractions of CO and NO are well predicted. Conditional PDFs are also well reproduced although uncertainties in boundary conditions influence results close to the bluff body.     

Large eddy simulation of turbulent premixed combustion using tabulated detailed chemistry and presumed probability density function

A method of chemistry tabulation combined with presumed probability density function (PDF) is applied to simulate piloted premixed jet burner flames with high Karlovitz number using large eddy simulation. Thermo-chemistry states are tabulated by the combination of auto-ignition and extended auto-ignition model. To evaluate the predictive capability of the proposed tabulation method to represent the thermo-chemistry states under the condition of different fresh gases temperature, a-priori study is conducted by performing idealised transient one-dimensional premixed flame simulations. Presumed PDF is used to involve the interaction of turbulence and flame with beta PDF to model the reaction progress variable distribution. Two presumed PDF models, Dirichlet distribution and independent beta distribution, respectively, are applied for representing the interaction between two mixture fractions that are associated with three inlet streams. Comparisons of statistical results show that two presumed PDF models for the two mixture fractions are both capable of predicting temperature and major species profiles, however, they are shown to have a significant effect on the predictions for intermediate species. An analysis of the thermo-chemical state-space representation of the sub-grid scale (SGS) combustion model is performed by comparing correlations between the carbon monoxide mass fraction and temperature. The SGS combustion model based on the proposed chemistry tabulation can reasonably capture the peak value and change trend of intermediate species. Aspects regarding model extensions to adequately predict the peak location of intermediate species are discussed.     

Prediction of local extinction and re-ignition effects in non-premixed turbulent combustion using a flamelet/progress variable approach

The flamelet/progress variable approach (FPVA) has been proposed by Pierce and Moin as a model for turbulent non-premixed combustion in large-eddy simulation. The filtered chemical source term in this model appears in unclosed form, and is modeled by a presumed probability density function (PDF) for the joint PDF of the mixture fraction Z and a flamelet parameter λ. While the marginal PDF of Z can be reasonably approximated by a beta distribution, a model for the conditional PDF of the flamelet parameter needs to be developed. Further, the ability of FPVA to predict extinction and re-ignition has also not been assessed. In this paper, we address these aspects of the model using the DNS database of Sripakagorn et al. It is first shown that the steady flamelet assumption in the context of FPVA leads to good predictions even for high levels of local extinction. Three different models for the conditional PDF of the flamelet parameter are tested in an a priori sense. Results obtained using a delta function to model the conditional PDF of λ lead to an overprediction of the mean temperature, even with only moderate extinction levels. It is shown that if the conditional PDF of λ is modeled by a beta distribution conditioned on Z, then FPVA can predict extinction and re-ignition effects, and good agreement between the model and DNS data for the mean temperature is observed.     

Large eddy simulation of a turbulent nonpremixed piloted methane jet flame (Sandia Flame D)

Large eddy simulation (LES) is conducted of the Sandia Flame D [Proc. Combust. Inst. 27 (1998) 1087, Sandia National Laboratories (2004)], which is a turbulent piloted nonpremixed methane jet flame. The subgrid scale (SGS) closure is based on the scalar filtered mass density function (SFMDF) methodology [J. Fluid Mech. 401 (1999) 85]. The SFMDF is basically the mass weighted probability density function (PDF) of the SGS scalar quantities [Turbulent Flows (2000)]. For this flame (which exhibits little local extinction), a simple flamelet model is used to relate the instantaneous composition to the mixture fraction. The modelled SFMDF transport equation is solved by a hybrid finite-difference/Monte Carlo scheme. This is the first LES of a realistic turbulent flame using the transported PDF method as the SGS closure. The results via this method capture important features of the flame as observed experimentally.     

Effects of confinement on premixed turbulent swirling flame using large Eddy simulation

This paper utilises large eddy simulation (LES) to study swirling reacting flows by comparison with experimental observations. The purpose is to provide further insights in engineering designs, as well as to improve modelling. A reduced-scale swirl burner has been developed for the experiments. Comparison of particle image velocimetry (PIV) measurements with LES results using finite rate chemistry shows that LES captures all the salient features of an unconfined flame including velocity and temperature distributions. However, when the flame is confined within a cylindrical combustor, the simulated flame shape is initially not consistent with experimental observation. Investigations show that the discrepancy is caused by the often practised assumption of adiabatic wall temperature. With the use of an assumed wall temperature distribution guided by laboratory observation, results of LES are consistent with experiments. Although the latter LES approach requires more computational resources, the improvement is found to be justified.     

An abstraction layer for efficient memory management of tabulated chemistry and flamelet solutions

A large number of methods for simulating reactive flows exist, some of them, for example, directly use detailed chemical kinetics or use precomputed and tabulated flame solutions. Both approaches couple the research fields computational fluid dynamics and chemistry tightly together using either an online or offline approach to solve the chemistry domain. The offline approach usually involves a method of generating databases or so-called Lookup-Tables (LUTs). As these LUTs are extended to not only contain material properties but interactions between chemistry and turbulent flow, the number of parameters and thus dimensions increases. Given a reasonable discretisation, file sizes can increase drastically. The main goal of this work is to provide methods that handle large database files efficiently. A Memory Abstraction Layer (MAL) has been developed that handles requested LUT entries efficiently by splitting the database file into several smaller blocks. It keeps the total memory usage at a minimum using thin allocation methods and compression to minimise filesystem operations. The MAL has been evaluated using three different test cases. The first rather generic one is a sequential reading operation on an LUT to evaluate the runtime behaviour as well as the memory consumption of the MAL. The second test case is a simulation of a non-premixed turbulent flame, the so-called HM1 flame, which is a well-known test case in the turbulent combustion community. The third test case is a simulation of a non-premixed laminar flame as described by McEnally in 1996 and Bennett in 2000. Using the previously developed solver ‘flameletFoam’ in conjunction with the MAL, memory consumption and the performance penalty introduced were studied. The total memory used while running a parallel simulation was reduced significantly while the CPU time overhead associated with the MAL remained low.     

LES modelling of turbulent non-premixed jet flames with correlated dynamic adaptive chemistry

Large eddy simulations (LES) for turbulent flames with detailed kinetic mechanisms have received growing interest. However, a direct implementation of detailed kinetic mechanisms in LES modelling of turbulent combustion remains a challenge due to the requirement of huge computational resources. An on-the-fly mechanism reduction method named correlated dynamic adaptive chemistry (CoDAC) is proposed to overcome this issue. A LES was conducted for Sandia Flame-D, with the reaction mechanism of GRI-Mech 3.0 consisting of 53 species and 325 reactions. The reduction threshold used in LES was obtained a priori by using auto-ignition model and partially stirred reactor (PaSR) with pairwise mixing model. LES results with CoDAC are in good agreement with experimental data and those without reduction. The conditional mean of the number of selected species indicates that a large size of locally reduced mechanism is required in the reaction zone where CH₄ is destructed. A computational time analysis shows that the PaSR model predicts better than the auto-ignition model on the wall time reduction with CoDAC in LES.     

The impact of reduced chemistry on auto-ignition of H2 in turbulent flows

The auto-ignition behaviour of hydrogen in a turbulent flow field has been studied through a combination of detailed and systematically reduced chemistry with a transported PDF approach closed at the joint-scalar level. Radiation is accounted for through the RADCAL method and the inclusion of enthalpy into the joint-scalar PDF. Molecular mixing is closed using the modified Curl's model with the mixing frequency accounted for via two algebraic closures. The main aim of the work is to compare the impact of alternative chemical mechanisms on auto-ignition and to explore the accuracy that can be expected when reactive scalars are sequentially removed through the application of quasi-steady-state approximations (QSSAs). Two different detailed mechanisms were tested to establish the effects of intrinsic uncertainties in the detailed chemistry and to provide reference points to past work. The mechanisms feature nine solved species and 19 or 20 reversible chemical reactions. The chemical mechanisms were subsequently systematically reduced to five, four and three independent scalars through the successive introduction of QSSAs for H₂O₂, HO₂ and O. Resulting inaccuracies were quantified following each simplification step with reference to experimental data obtained in shock tubes and under turbulent flow conditions in the Cabra burner configuration. A sensitivity analysis was also performed to identify the relative impact of uncertainties in key reactions as compared to systematic simplification process. It was found that alternative recommended rates for the O + H₂ = OH + H reaction have an impact on the point of flame stabilization that is similar to that observed as a consequence of the simplification process. The work also shows that realistic results can be obtained with simplified chemistry. However, it is also concluded that the temporal evolution of the radical pool and the point of stabilization is affected by the introduction of a QSSA for the O radical. Furthermore, it is shown by comparisons with time resolved OH radical data obtained in shock tubes that the progressive elimination of species via QSSA leads to a shortening of ignition delay times and that the same effects are present, but less severe, in turbulent flow fields.     

Alkali metal emissions in an early-stage pulverized-coal flame: DNS analysis of reacting layers and chemistry tabulation

The intricate coupling between coal pyrolysis, gas phase combustion and the emissions of alkali metal, such as sodium, is studied in the early stage of a temporally evolving three-dimensional planar turbulent jet carrying pulverized-coal particles. Complex chemistry is used to account for both the combustion of volatile hydrocarbons and the sodium containing species. The response of the sodium chemistry is analyzed in the mixture fraction space, along with the topology of the reactions zones. Combustion is found to start preferentially in partially premixed flames, which then evolve toward diffusion-like reactive layers and reach chemical equilibrium. From the direct numerical simulation (DNS) database, the possibility of modeling the dynamics of sodium species using one-dimensional premixed flamelet generated manifolds (FGM) is investigated. A chemical lookup table is constructed for the combustion of the partially premixed volatiles and an additional three-dimensional simulation is performed to compare the tabulated sodium species against their reference counterparts with complex chemistry. Quantitative analysis of the performance of the developed chemistry tabulation confirms the validity of the approach. Perspectives for the modeling of sodium emissions in pulverized-coal furnaces and boilers are finally drawn.     

Fluctuating characteristics of radiative source term in hydrogen turbulent jet diffusion flame

The laminar flamelet model in combination with joint probability density function transport equation of mixture fraction and turbulence frequency is used to simulate turbulent jet diffusion flames of hydrogen. The frequency distributions of radiative source terms are calculated for four important infrared bands of water vapor. The results show that, for the given ensemble, about 95% samples of radiative source term for each band locate within the region of ±3.0 standard deviation of the mean radiative source term. Due to the different relation between band intensity parameters and temperature for every band, the symmetrization of frequency distributions for each band is different.