Large eddy simulation of autoignition with a subgrid probability density function method

ABSTRACTA gas turbine model combustor is studied using Large Eddy Simulation with a transported Probability Density Function approach solved by the Eulerian stochastic field method. The chemistry is represented by a reduced methane mechanism containing 15 steps and 19 species while the subgrid scale stresses and scalar fluxes are modelled, respectively, via a dynamic Smagorinsky model and a gradient diffusion approximation. The test case comprises a partially premixed swirl flame in a complex geometry. Four stochastic fields are utilised in the simulations, which are performed for two different combustor operating conditions involving a stable and an unstable flame. Good agreement between the simulation and measurement data is shown in a comparison of mean velocity, temperature and species mass fraction profiles, as well as scatter plots of the instantaneous thermochemical properties. In conclusion, the predictive capabilities of the employed Large Eddy Simulation method are successfully demonstrated in this work.

A flamelet-based Eulerian transported PDF method for the modeling and simulation of supersonic combustion

An accurate prediction of the probability density function (PDF) of the mixture fraction is crucial to the prediction of combustion since mixing plays an important role in turbulent non-premixed and partially premixed flames. This work provides an assessment of the large-eddy simulation (LES)/filtered density function (FDF) method for the prediction of the PDF of the mixture fraction. The advantage of the LES/FDF method is that it provides the full predictions of the statistical distribution of scalars including the mixture fraction. The predictive accuracy of the method for the PDF is yet to be fully validated. Assessing the prediction of the PDF of the mixture fraction, a conserved scalar, is an important starting point. The Sydney/Sandia inhomogeneous inlet jet flame is used as a test case. A quick comparison shows that the LES/FDF predicted PDF shapes of the mixture fraction deviate significantly from the commonly presumed Beta-PDF as well as from the experimental data in the flame. To examine the source of the discrepancy, we clarify the different PDF definitions used in the comparison among the predictions, measurements, and presumed shape PDFs. The discrepancy observed from the comparison is largely reconciled by clarifying the difference between the PDFs that are examined. The PDF of the resolved mixture fraction is shown to be close to the Beta-PDF in both the measurements and predictions, while the PDF directly deduced from the LES/FDF particles deviates significantly from the Beta-PDF. A multimodal PDF analysis and a pseudo convergence analysis are conducted to provide plausible evidence to support the predicted multimodal PDF shapes. The sub-filter scale FDF is shown to be close to the Beta-PDF too through the construction of a synthesised PDF, which supports the common presumed Beta-PDF assumption used in the presumed PDF methods when combined with LES.

Reactive flow simulations using large-eddy simulations (LES) require modelling of sub-filter fluctuations. Although conserved scalars like mixture fraction can be represented using a beta-function, the reactive scalar probability density function (PDF) does not follow an universal shape. A one-point one-time joint composition PDF transport equation can be used to describe the evolution of the scalar PDF. The high-dimensional nature of this PDF transport equation requires the use of a statistical ensemble of notional particles and is directly coupled to the LES flow solver. However, the large grid sizes used in LES simulations will make such Lagrangian simulations computationally intractable. Here we propose the use of a Eulerian version of the transported-PDF scheme for simulating turbulent reactive flows. The direct quadrature method of moments (DQMOM) uses scalar-type equations with appropriate source terms to evolve the sub-filter PDF in terms of a finite number of delta-functions. Each delta-peak is characterized by a location and weight that are obtained from individual transport equations. To illustrate the feasibility of the scheme, we compare the model against a particle-based Lagrangian scheme and a presumed PDF model for the evolution of the mixture fraction PDF. All these models are applied to an experimental bluff-body flame and the simulated scalar and flow fields are compared with experimental data. The DQMOM model results show good agreement with the experimental data as well as the other sub-filter models used.

An investigation of a turbulent spray flame using Large Eddy Simulation with a stochastic breakup model

Modeling of turbulent dilute spray combustion

Probability density function (PDF) methods provide an elegant and effective resolution to the closure problems that arise from averaging or filtering chemical source terms and other nonlinear terms in the equations that govern chemically reacting turbulent flows. PDF methods traditionally have been associated with studies of turbulence-chemistry interactions in laboratory-scale, atmospheric pressure, nonluminous, statistically-stationary nonpremixed turbulent flames; and Lagrangian particle-based Monte Carlo numerical algorithms have become the predominant method for solving modeled PDF transport equations. The emphasis in this chapter is on recent advances, new trends and perspectives in PDF methods. These include advances in particle-based algorithms, alternatives to particle-based algorithms (e.g., Eulerian field methods), treatment of combustion regimes beyond low-to-moderate-Damkohler-number nonpremixed systems (e.g., premixed flamelets), extensions to include radiation heat transfer and multiphase systems (e.g., soot and fuel sprays), and the use of PDF-based methods as the basis for modeling in large-eddy simulation.

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.

This work focuses on the impact of the devolatilization and char combustion mode modelling on the structure of a large-scale, biomass and coal co-fired flame using large eddy simulations. The coal modelling framework previously developed for the simulation of combustion in large-scale facilities is extended for biomass capabilities. An iterative procedure is used to obtain devolatilization kinetics of coal and biomass for the test-case specific fuels and heating conditions. This is achieved by calibrating the model constants of two empirical models: the single first-order model and the distributed activation energy model. The reference data for calibration are devolatilization yields obtained with predictive coal and biomass multistep kinetic mechanisms. The variation of both particle density and diameter during char combustion is governed by the conversion mode, which is modelled using two approaches: the power law using a constant parameter that assumes a constant mode during char combustion and a constant-free model that considers a variable mode during combustion. Three numerical cases are considered: single first-order reaction with constant char combustion mode, distributed activation energy with constant char combustion mode, and single first-order reaction with variable char combustion mode. The numerical predictions from the large eddy simulations are compared with experimental results of a high co-firing rate large-scale laboratory flame of coal and biomass. Furthermore, results from single particle conversion under idealised conditions, isolating the effects of turbulence, are presented to assist the interpretation of the predictions obtained with large eddy simulations. The effects of the devolatilization and conversion mode modelling on the flame lift-off, flame length, and spatial distribution and radial profiles of O2 and CO2 are presented and discussed. Both the devolatilization and conversion mode modelling have a significant effect on the conversion of particles under idealised conditions. The large eddy simulations results show that the devolatilization model has a strong impact on the flame structure, but not on the flame lift-off. On the other hand, for the tested numerical conditions, the char combustion mode model has a marginal impact on the predicted results.

An investigation of turbulent premixed counterflow flames using large-eddy simulations and probability density function methods

LES/PDF modeling of swirl-stabilized non-premixed methane/air flames with local extinction and re-ignition

The mapping closure of Chen et al. [Phys. Rev. Lett., 63, 1989] is a transported probability density function (PDF) method that has proven very efficient for modelling of turbulent mixing in homogeneous turbulence. By utilizing a Gaussian reference field, the solution to the mapping function (in homogeneous turbulence) can be found analytically for a range of initial conditions common for turbulent combustion applications, e.g. for binary or trinary mixing. The purpose of this paper is to investigate the possibility of making this solution a presumed mapping function (PMF) for inhomogeneous flows. The PMF in turn will imply a presumed mixture fraction PDF that can be used for a wide range of models in turbulent combustion, e.g. flamelet models, the conditional moment closure (CMC) or large eddy simulations. The true novelty of the paper, though, is in the derivation of highly efficient, closed algebraic expressions for several existing models of conditional statistics, e.g. for the conditional scalar dissipation/diffusion rate or the conditional mean velocity. The closed form expressions nearly eliminates the overhead computational cost that usually is associated with nonlinear models for conditional statistics. In this respect it is argued that the PMF is particularly well suited for CMC that relies heavily on manipulations of the PDF for consistency. The accuracy of the PMF approach is shown with comparison to DNS of a single scalar mixing layer to be better than for the β-PDF. Not only in the shape of the PDF itself, but also for all conditional statistics models computed from the PDF.

The tabulated premixed conditional moment closure (T-PCMC) method has been shown to provide the capability to model turbulent, premixed methane flames with detailed chemistry and reasonable runtimes in Reynolds-averaged Navier–Stokes (RANS) environment by Martin et al. (2013, “Modeling an Enclosed, Turbulent Reacting Methane Jet With the Premixed Conditional Moment Closure Method,” ASME Paper No. GT2013-95092). Here, the premixed conditional moment closure (PCMC) method is extended to large eddy simulation (LES). The new model is validated with the turbulent, enclosed reacting methane backward facing step data from El Banhawy et al. (1983, “Premixed, Turbulent Combustion of a Sudden-Expansion Flow,” Combust. Flame, 50, pp. 153–165). The experimental data have a rectangular test section at atmospheric pressure and temperature with an inlet velocity of 10.5 m/s and an equivalence ratio of 0.9 for two different step heights. Contours of major species, velocity, and temperature are provided. The T-PCMC model falls into the class of table lookup turbulent combustion models in which the combustion model is solved offline over a range of conditions and stored in a table that is accessed by the computational fluid dynamic (CFD) code using three controlling variables: the reaction progress variable (RPV), variance, and local scalar dissipation rate. The local scalar dissipation rate is used to account for the affects of the small-scale mixing on the reaction rates. A presumed shape beta function probability density function (PDF) is used to account for the effects of subgrid scale (SGS) turbulence on the reactions. SGS models are incorporated for the scalar dissipation and variance. The open source CFD code OpenFOAM is used with the compressible Smagorinsky LES model. Velocity, temperature, and major species are compared to the experimental data. Once validated, this low “runtime” CFD turbulent combustion model will have great utility for designing the next generation of lean premixed (LPM) gas turbine combustors.

LES-based Eulerian PDF approach for the simulation of scramjet combustors

A database of transitional direct numerical simulation (DNS) realizations of a supercritical mixing layer is analysed for understanding small-scale behaviour and examining subgrid-scale (SGS) models duplicating that behaviour. Initially, the mixing layer contains a single chemical species in each of the two streams, and a perturbation promotes roll-up and a double pairing of the four spanwise vortices initially present. The database encompasses three combinations of chemical species, several perturbation wavelengths and amplitudes, and several initial Reynolds numbers specifically chosen for the sole purpose of achieving transition. The DNS equations are the Navier-Stokes, total energy and species equations coupled to a real-gas equation of state; the fluxes of species and heat include the Soret and Dufour effects. The large-eddy simulation (LES) equations are derived from the DNS ones through filtering. Compared to the DNS equations, two types of additional terms are identified in the LES equations: SGS fluxes and other terms for which either assumptions or models are necessary. The magnitude of all terms in the LES conservation equations is analysed on the DNS database, with special attention to terms that could possibly be neglected. It is shown that in contrast to atmospheric-pressure gaseous flows, there are two new terms that must be modelled: one in each of the momentum and the energy equations. These new terms can be thought to result from the filtering of the nonlinear equation of state, and are associated with regions of high density-gradient magnitude both found in DNS and observed experimentally in fully turbulent high-pressure flows. A model is derived for the momentum-equation additional term that performs well at small filter size but deteriorates as the filter size increases, highlighting the necessity of ensuring appropriate grid resolution in LES. Modelling approaches for the energy-equation additional term are proposed, all of which may be too computationally intensive in LES. Several SGS flux models are tested on an a priori basis. The Smagorinsky (SM) model has a poor correlation with the data, while the gradient (GR) and scale-similarity (SS) models have high correlations. Calibrated model coefficients for the GR and SS models yield good agreement with the SGS fluxes, although statistically, the coefficients are not valid over all realizations. The GR model is also tested for the variances entering the calculation of the new terms in the momentum and energy equations; high correlations are obtained, although the calibrated coefficients are not statistically significant over the entire database at fixed filter size. As a manifestation of the small-scale supercritical mixing peculiarities, both scalar-dissipation visualizations and the scalar-dissipation probability density functions (PDF) are examined. The PDF is shown to exhibit minor peaks, with particular significance for those at larger scalar dissipation values than the mean, thus significantly departing from the Gaussian behaviour.