Large eddy simulation of soot evolution in turbulent nonpremixed bluff body flames

Large Eddy Simulation (LES) is utilized to investigate soot evolution in a series of turbulent nonpremixed bluff body flames featuring different bluff body diameters. The modeling framework relies on recent development in the soot subfilter Probability Density Function (PDF) model that can correctly account for the distribution of soot with respect to mixture fraction, correcting errors in previous soot subfilter PDF models that significantly overpredict soot oxidation. With the previous soot subfilter PDF model, no soot was observed outside of the recirculation zone in past studies on similar bluff body flames. Results obtained with the current LES modeling approach compare favorably with the experimental measurements of the flow field and the soot volume fraction. Notably, the current LES modeling approach correctly predicts large soot volume fractions in the recirculation zone, a decrease in the soot volume fraction through the high-strain neck region, and then an increase again in the downstream jet-like region. Consistent with the experimental measurements, the larger bluff body diameter, with its larger recirculation zone with longer residence times, generates more soot in the recirculation zone and also more soot in the high-strain neck region. Analysis of the soot volume fraction source terms lead to mechanistic understanding of soot evolution in the entirety of the bluff body flames. Most of the soot generated in the recirculation zone is oxidized but some escapes unoxidized and is passively transported through the neck region. Virtually no new soot forms in the downstream jet-like region, and the increase in the soot volume fraction in the jet-like region is due to acetylene-based surface growth of the soot transported through the neck region. This mechanism could not be predicted with the previous soot subfilter PDF model, with the recent soot subfilter PDF model being critical in the understanding of this basic mechanism.     

Stratified turbulent Bunsen flames: flame surface analysis and flame surface density modelling

In this paper it is investigated whether the Flame Surface Density (FSD) model, developed for turbulent premixed combustion, is also applicable to stratified flames. Direct Numerical Simulations (DNS) of turbulent stratified Bunsen flames have been carried out, using the Flamelet Generated Manifold (FGM) reduction method for reaction kinetics. Before examining the suitability of the FSD model, flame surfaces are characterized in terms of thickness, curvature and stratification.

All flames are in the Thin Reaction Zones regime, and the maximum equivalence ratio range covers 0.1?φ?1.3. For all flames, local flame thicknesses correspond very well to those observed in stretchless, steady premixed flamelets. Extracted curvature radii and mixing length scales are significantly larger than the flame thickness, implying that the stratified flames all burn in a premixed mode. The remaining challenge is accounting for the large variation in (subfilter) mass burning rate.

In this contribution, the FSD model is proven to be applicable for Large Eddy Simulations (LES) of stratified flames for the equivalence ratio range 0.1?φ?1.3. Subfilter mass burning rate variations are taken into account by a subfilter Probability Density Function (PDF) for the mixture fraction, on which the mass burning rate directly depends. A priori analysis point out that for small stratifications (0.4?φ?1.0), the replacement of the subfilter PDF (obtained from DNS data) by the corresponding Dirac function is appropriate. Integration of the Dirac function with the mass burning rate m=m(φ), can then adequately model the filtered mass burning rate obtained from filtered DNS data. For a larger stratification (0.1?φ?1.3), and filter widths up to ten flame thicknesses, a β-function for the subfilter PDF yields substantially better predictions than a Dirac function. Finally, inclusion of a simple algebraic model for the FSD resulted only in small additional deviations from DNS data, thereby rendering this approach promising for application in LES.     

Large Eddy Simulation composition equations for single-phase and two-phase fully multicomponent flows

The Large Eddy Simulation (LES) equations for multicomponent (MC) fuel single-phase (SP) flow and two-phase (TP) flow with phase change are derived from the Direct Numerical Simulation (DNS) equations by filtering the DNS equations using a top-hat filter. Additional to the equations solved for single-component (SC) fuels, composition equations enter the formulation. The species composition is represented through a Probability Distribution Function (PDF), and DNS equations for the PDF moments are solved to find the composition. The TP filtered equations contain three categories of subgrid-scale (SGS) terms: (1) SGS–flux terms, (2) filtered source terms (FSTs) and (3) terms representing the ‘LES assumptions’. For SP flows no FSTs exist. The SGS terms in the LES equations must be either shown negligible or modeled. It is shown that for the composition equations, two equivalent forms of the DNS equations lead to two non-equivalent forms of the LES equations. Criteria are proposed to select the form best suited for LES. These criteria are used in conjunction with evaluations based on a DNS database portraying mixing and phase change, and lead to choosing one of the LES forms which satisfies all criteria. It is shown that the LES assumptions lead to additional SGS terms which require modeling. Further considerations are made for reactive flows.     

Multi-scale properties of large eddy simulations: correlations between resolved-scale velocity-field increments and subgrid-scale quantities

We provide analytical and numerical results concerning multi-scale correlations between the resolved velocity field and the subgrid-scale (SGS) stress-tensor in large eddy simulations (LES). Following previous studies for Navier–Stokes equations, we derive the exact hierarchy of LES equations governing the spatio-temporal evolution of velocity structure functions of any order. The aim is to assess the influence of the subgrid model on the inertial range intermittency. We provide a series of predictions, within the multifractal theory, for the scaling of correlation involving the SGS stress and we compare them against numerical results from high-resolution Smagorinsky LES and from a-priori filtered data generated from direct numerical simulations (DNS). We find that LES data generally agree very well with filtered DNS results and with the multifractal prediction for all leading terms in the balance equations. Discrepancies are measured for some of the sub-leading terms involving cross-correlation between resolved velocity increments and the SGS tensor or the SGS energy transfer, suggesting that there must be room to improve the SGS modelisation to further extend the inertial range properties for any fixed LES resolution.     

Relevance of the subgrid-scales for large eddy simulations of turbulence-radiation interactions in a turbulent plane jet

An a priori study based on direct numerical simulation (DNS) of a non-isothermal turbulent plane jet has been carried out in order to analyse the role of the small-scales of turbulence on thermal radiation. Filtered DNS and large eddy simulation (LES) without subgrid-scale (SGS) model have been estimated for the radiative heat transfer. The comparison of the results highlights the subgrid-scale influence over the filtered radiation quantities, such as the radiative intensity and the radiative emission. The influence of the optical thickness is also studied. It is shown that the subgrid-scales are not significant near the centerline of the jet, where the radiative heat transfer is more important, and therefore that the SGS can be neglected in this configuration. However, when the optical thickness increases, the SGS become relevant and SGS modeling may be needed.     

Statistics of reaction progress variable and mixture fraction gradients of a pulverised coal jet flame using Direct Numerical Simulation data

The statistical behaviour of the variances, covariance and gradients of the reaction progress variable (c), and the mixture fraction (ξ) have been analysed in a pulverised coal jet flame using a three-dimensional carrier phase direct numerical simulation (DNS) dataset. It has been observed that the Favre-probability density functions (PDFs) of c and ξ can be parametrised by the standard β function. Furthermore, the log-normal distribution has been found to accurately represent |?c| and |?ξ|. It is also found that ?c and ?ξ remain aligned throughout the flame brush. Finally the joint PDF of |?c| and |?ξ| has been compared with the product of the PDF of |?c| and PDF of |?ξ| extracted from carrier phase DNS, and it has been found that |?c| and |?ξ| are not statistically independent in the case investigated.The bivariate log-normal distributions with and without correlation have also been considered, and the former is found to be in better agreement with the carrier phase DNS data.     

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.     

Evaluation of assumed-PDF methods in two-phase flows using direct numerical simulation

The hypothesis of uncorrelated temperature (T) and vapor-fuel mass fraction (Y_v), frequently made when modeling reaction rates using assumed-PDF models, is examined utilizing transitional databases from direct numerical simulation (DNS) of three-dimensional mixing-layers two-phase (TP) flows with evaporation. Because the databases do not contain chemical reaction, which would further correlate variables, finding here a correlation between T and Y_v is sufficient for invalidating reaction rate modeling of the joint (T, Y_v) probability distribution function (PDF) as a product of the marginal PDFs. The databases comprise four multicomponent fuels, two mass loadings and two free-stream gas temperatures. For comparison, databases for single-phase (SP) flows are also analyzed at two initial Reynolds numbers. The examination is conducted in the mixing layer excluding the free streams and in a more restricted part of the mixing layer constituting its core. The analysis is performed at the DNS and large eddy simulation (LES) scales, and subgrid scale (SGS). To obtain the LES database, the DNS database is filtered, and an evaluation of the examined correlation at the LES and SGS scales is made at two filter sizes. At the DNS scale, T and Y_v are practically uncorrelated for SP flows, showing the weak influence of the perfect-gas equation of state, whereas for TP flows the correlation is strong and increases with mass loading indicating the powerful effect of the phase change. At the LES scale, the findings emulate those at the DNS scale. The fluctuations of the SGS scale are uncorrelated for SP flows, but the product of the marginal PDFs is different from the joint PDF. For TP flows, the fluctuations are correlated and the correlation increases with temperature, casting doubt on current assumed PDFs used to model chemistry in reacting sprays. These results are independent of filter size. The joint PDFs for TP and SP fluctuations are successfully modeled.     

A multivariate quadrature based moment method for LES based modeling of supersonic combustion

The transported probability density function (PDF) approach is a powerful technique for large eddy simulation (LES) based modeling of scramjet combustors. In this approach, a high-dimensional transport equation for the joint composition-enthalpy PDF needs to be solved. Quadrature based approaches provide deterministic Eulerian methods for solving the joint-PDF transport equation. In this work, it is first demonstrated that the numerical errors associated with LES require special care in the development of PDF solution algorithms. The direct quadrature method of moments (DQMOM) is one quadrature-based approach developed for supersonic combustion modeling. This approach is shown to generate inconsistent evolution of the scalar moments. Further, gradient-based source terms that appear in the DQMOM transport equations are severely underpredicted in LES leading to artificial mixing of fuel and oxidizer. To overcome these numerical issues, a semi-discrete quadrature method of moments (SeQMOM) is formulated. The performance of the new technique is compared with the DQMOM approach in canonical flow configurations as well as a three-dimensional supersonic cavity stabilized flame configuration. The SeQMOM approach is shown to predict subfilter statistics accurately compared to the DQMOM approach.     

Prediction of soot formation characteristics in a pulverized-coal combustion field by large eddy simulations with the TDP model

In this study, the soot formation characteristics in a pulverized-coal combustion field formed by a 4 kW Central Research Institute of Electric Power Industry (CRIEPI) jet burner were predicted by large eddy simulation (LES) employing a tabulated-devolatilization-process model (TDP model) [N. Hashimoto et al., Combust. Flame 159 (2012) 353–366]. This model enables to take into account the effect of coal particle heating rate on coal pyrolysis. The coal-derived soot formation model proposed by Brown and Fletcher [A. L. Brown and T. H. Fletcher, Energy Fuels 12 (1998) 745–757] was employed in the LES. A comparison between the data predicted by LES and the soot volume fraction distribution data measured by laser induced incandescence confirmed that the soot formation characteristics in the coal combustion field of the CRIEPI burner can be accurately predicted by LES. A detailed analysis of the data predicted by LES showed that the soot particle distribution in this burner is narrow because the net soot formation rate is negative on both sides of the base of the soot volume fraction. At these positions, soot particles diffused from the peak position of soot volume fraction are oxidized due to a relatively high oxygen concentration. Finally, the effect of soot radiation on the predicted gas temperature distribution was examined by comparing the simulation results obtained with and without soot radiation. This comparison showed that the maximum gas temperature predicted by the simulation performed with soot radiation was over 100 K lower than that predicted by the simulation performed without soot radiation. From result strongly suggests the importance of considering a soot formation model for performing numerical simulations of a pulverized-coal combustion filed.     

Assessment of LES of intermittent soot production in an aero-engine model combustor using high-speed measurements

Soot production in turbulent flames is an extremely intermittent phenomenon since it is the result of specific thermochemical conditions occasionally occurring in space and time. In realistic configurations such as the swirling flames used in gas-turbines, the presence of large-scale flow motions can additionally affect soot formation processes, leading to even more pronounced intermittency. Classically, the validation of numerical simulations is performed by comparing time-averaged results with experimental data of the phenomenon under investigation. This comparison can be considered as rigorous only if a statistically converged numerical representation is obtained. In case of sporadic events such as intermittent soot formation in turbulent flames, this means to perform the simulation over thousands of milliseconds of physical time, which can have extremely high CPU demands when performing Large Eddy Simulation (LES). In this work, a possible strategy to overcome this issue is proposed based on the use of high-speed measurements and numerically synthesized signals from LES. To illustrate the approach, numerical and experimental soot light scattering signals are considered here by looking at the model aero-engine combustor developed at DLR for the study of pressurized swirled sooting flames. The light scattering signal is numerically synthesized from an LES. Experimental high-speed measurements are used to statistically account for the high temporal and spatial variability of soot when considering time intervals similar to what is today achievable with LES. The feasibility of this approach is finally demonstrated by comparing numerical results to the ensemble of possible soot production states observed experimentally in the DLR burner allowing to eventually validate the present LES results.     

Effect of fuel/air ratio and aromaticity on the molecular weight distribution of soot in premixed n-heptane flames

Soot growth from inception to mass-loading is studied in a wide range of molecular weights (MW) from 10⁵ to 10¹⁰u by means of size exclusion chromatography (SEC) coupled with on-line UV-visible spectroscopy. The evolution of MW distributions of soot is also numerically predicted by using a detailed kinetic model coupled with a discrete-sectional approach for the modeling of the gas-to-particle process. Two premixed flames burning n-heptane in slightly sooting and heavily sooting conditions are studied. The effect of aromatic addition to the fuel is studied by adding n-propylbenzene (10% by volume) to n-heptane in the heavily sooting condition. A progressive reduction of the MW distribution from multimodal to unimodal is observed along the flames testifying the occurrence of particle growth and agglomeration. These processes occur earlier in the aromatic-doped n-heptane flame due to the overriding role of benzene on soot formation which results in bigger young soot particles. Modeled MW distributions are in reasonable agreement with experimental data although the model predicts a slower coagulation process particularly in the slightly sooting n-heptane flame. Given the good agreement between model predictions and experiments, the model is used to explore the role of fuel chemistry on MW distributions. Two flames of n-heptane and n-heptane/n-propylbenzene in heavily sooting conditions with the same temperature profile and inert dilution are modeled. The formation of larger soot particles is still evident in the n-heptane/n-propylbenzene flame with respect to the n-heptane flame in the same operating conditions of temperature and dilution. In addition the model predicts a larger formation of molecular particles in the flame containing n-propylbenzene and shows that soot inception occurs in correspondence of their maximum formation thus indicating the importance of molecular growth in soot inception.     

Laser-induced incandescence for soot-particle sizing at elevated pressure

This paper describes the applicability of laser-induced incandescence (LII) as a measurement technique for primary soot particle sizes at elevated pressure. A high-pressure burner was constructed that provides stable, laminar, sooting, premixed ethylene/air flames at 1–10 bar. An LII model was set up that includes different heat-conduction sub-models and used an accommodation coefficient of 0.25 for all pressures studied. Based on this model experimental time-resolved LII signals recorded at different positions in the flame were evaluated with respect to the mean particle diameter of a log-normal particle-size distribution. The resulting primary particle sizes were compared to results from TEM images of soot samples that were collected thermophoretically from the high-pressure flame. The LII results are in good agreement with the mean primary particle sizes of a log-normal particle-size distribution obtained from the TEM-data for all pressures, if the LII signals are evaluated with the heat-conduction model of Fuchs combined with an aggregate sub-model that describes the reduced heat conduction of aggregated primary soot particles. The model, called LIISim, is available online via a web interface. PACS 65.80.+n; 78.20.Nv; 42.62.-b; 47.70.Pq     

In-Situ Adaptive Manifolds: Enabling computationally efficient simulations of complex turbulent reacting flows

Reduced-order manifold approaches to turbulent combustion modeling traditionally involve precomputation of manifold solutions and pretabulation of the thermochemical database versus a small number of manifold variables. However, additional manifold variables are required as the complexity of turbulent combustion processes increases through consideration of, for example, multi-modal, non-adiabatic, or non-isobaric combustion, or combustion featuring multiple and/or inhomogeneous inlets. This increase in the number of manifold variables comes with an increase in the computational cost of precomputing a greater number of manifold solutions, most of which are never actually utilized in a CFD calculation. The memory required to store the pretabulated high-dimensional thermochemical database also increases, practically limiting the complexity of manifold-based combustion models. In this work, a new In-Situ Adaptive Manifolds (ISAM) approach is developed that overcomes this limitation by combining ‘on-the-fly’ calculation of manifold solutions with In-Situ Adaptive Tabulation (ISAT), enabling the use of more complex manifold-based turbulent combustion models. The performance of ISAM is evaluated via LES of turbulent nonpremixed jet flames with both hydrogen and hydrocarbon fuels. A performance assessment indicates that the computational overhead associated with ISAM compared to pretabulation ranges from negligible up to a factor of two, with most of this overhead associated with convolution of the thermochemical state against a presumed subfilter PDF. In addition, the memory requirements of ISAM are more than two orders of magnitude less than conventional tabulation. These results demonstrate the potential for ISAM to accommodate significantly more complex manifold-based combustion models.     

Unstrained and strained flamelets for LES of premixed combustion

The unstrained and strained flamelet closures for filtered reaction rate in large eddy simulation (LES) of premixed flames are studied. The required sub-grid scale (SGS) PDF in these closures is presumed using the Beta function. The relative performances of these closures are assessed by comparing numerical results from large eddy simulations of piloted Bunsen flames of stoichiometric methane–air mixture with experimental measurements. The strained flamelets closure is observed to underestimate the burn rate and thus the reactive scalars mass fractions are under-predicted with an over-prediction of fuel mass fraction compared with the unstrained flamelet closure. The physical reasons for this relative behaviour are discussed. The results of unstrained flamelet closure compare well with experimental data. The SGS variance of the progress variable required for the presumed PDF is obtained by solving its transport equation. An order of magnitude analysis of this equation suggests that the commonly used algebraic model obtained by balancing source and sink in this transport equation does not hold. This algebraic model is shown to underestimate the SGS variance substantially and the implications of this variance model for the filtered reaction rate closures are highlighted.     

Employing Taylor and Heisenberg subfilter viscosities to simulate turbulent statistics in LES models

A turbulent subfilter viscosity for Large Eddy Simulation (LES) based on the Taylor statistical diffusion theory is proposed. This viscosity is described in terms of a velocity variance and a time scale, both associated to the inertial subrange. This new subfilter viscosity contains a cutoff wavenumber k_c, presenting an identical form (differing by a constant) to the Heisenberg subfilter viscosity. Therefore, both subfilter viscosities are described in terms of a sharp division between large and small wavenumbers of a turbulent flow and, henceforth, Taylor and Heisenberg subfilter viscosities are in agreement with the sharp Fourier filtering operation, frequently employed in LES models. Turbulent statistics of different orders, generated from atmospheric boundary layer simulations employing both Taylor and Heisenberg subfilter viscosities have been compared with observations and results provided by other simulations. The comparison shows that the LES model utilizing the approaches of Taylor and Heisenberg reproduces these turbulent statistics correctly in different vertical regions of a planetary convective boundary layer (CBL).     

Simulations of sooting turbulent jet flames using a hybrid flamelet/stochastic Eulerian field method

The stochastic Eulerian field method is applied to simulate 12 turbulent C₁?C₃ hydrocarbon jet diffusion flames covering a wide range of Reynolds numbers and fuel sooting propensities. The joint scalar probability density function (PDF) is a function of the mixture fraction, enthalpy defect, scalar dissipation rate and representative soot properties. Soot production is modelled by a semi-empirical acetylene/benzene-based soot model. Spectral gas and soot radiation is modelled using a wide-band correlated-k model. Emission turbulent radiation interactions (TRIs) are taken into account by means of the PDF method, whereas absorption TRIs are modelled using the optically thin fluctuation approximation. Model predictions are found to be in reasonable agreement with experimental data in terms of flame structure, soot quantities and radiative loss. Mean soot volume fractions are predicted within a factor of two of the experiments whereas radiant fractions and peaks of wall radiative fluxes are within 20%. The study also aims to assess approximate radiative models, namely the optically thin approximation (OTA) and grey medium approximation. These approximations affect significantly the radiative loss and should be avoided if accurate predictions of the radiative flux are desired. At atmospheric pressure, the relative errors that they produced on the peaks of temperature and soot volume fraction are within both experimental and model uncertainties. However, these discrepancies are found to increase with pressure, suggesting that spectral models describing properly the self-absorption should be considered at over-atmospheric pressure.     

Jittering wave-packet models for subsonic jet noise

Three simplified wave-packet models of the coherent structures in subsonic jets are presented. The models comprise convected wave-packets with time-dependent amplitudes and spatial extents. The dependence of the radiated sound on the temporal variations of the amplitude and spatial extent of the modulations are studied separately in the first two model problems, being considered together in the third. Analytical expressions for the radiated sound pressure are obtained for the first and third models.Results show that temporally localised changes in the wave-packet can lead to radiation patterns which are directional and which comprise high-amplitude bursts; such intermittency is observed in subsonic jets at the end of the potential core, and so the models may help explain the higher noise levels and intermittent character of the sound radiated to low emission angles for subsonic jets. By means of an efficiency metric, relating the radiated acoustic power to the fluctuation energy of the source, we show that the source becomes more powerful as its temporal localisation is increased. This result extends that of Sandham et al. (Journal of Sound and Vibration 294(1) (2006) 355–361) who found similar behaviour for an infinitely extended wavy-wall.The pertinence of the model is assessed using two sets of data for a Mach 0.9 jet. One corresponds to a direct numerical simulation (DNS) of a Reynolds number 3600 turbulent jet and the other to a large eddy simulation (LES) of a Reynolds number 4×10⁵ jet. Both time-averaged and time-dependent amplitudes and spatial extents are extracted from the velocity field of the numerical data. Computing the sound field generated by the wave-packet models we find for both simulations that while the wave-packet with a time-averaged envelope shows discrepancies of more than an order of magnitude with the sound field, when the wave-packet ‘jitters’ in a way similar to the intermittency displayed by the simulations, we obtain agreement to within 1.5 dB at low axial angles. This shows that the ‘jitter’ of the wave-packet is a salient source feature, and one which should be modelled explicitly.