Transported Probability Density Function Approach Research Articles

Longitudinal and azimuthal thermo-acoustic instabilities in an industrial gas turbine combustor operating at elevated pressure

This work numerically investigates longitudinal and azimuthal thermo-acoustic instabilities in the swirl-stabilised can-type industrial SGT-100 gas turbine combustor operated at elevated pressures of 3 and 6 bar. Previous experiments have shown that the combustor is susceptible to self-excited flame oscillations sustained by a thermo-acoustic feedback loop at specific operating conditions. In order to gain a better understanding of this feedback loop, a fully compressible large eddy simulation method is applied. The unknown sub-grid scale turbulence-chemistry interactions are modelled via a transported probability density function approach solved by the Eulerian stochastic fields method. First, the reaction zones and global flame topology at both operating pressures are analysed and compared to experimental images providing good qualitative agreement. Radial profiles of time-averaged and root-mean-square quantities furthermore demonstrate good quantitative agreement with the available measurement data. The applied simulation approach is capable of successfully reproducing self-excited thermo-acoustic instabilities in the longitudinal direction. The fundamental frequency of the predicted limit-cycle oscillation matches the experimentally measured frequency with high accuracy. Similar to the experimental observations, the fluctuation amplitudes of the pressure and global heat release rate increase significantly upon increasing the mean operating pressure from 3 to 6 bar. In addition to the dominant longitudinal mode, a high-frequency, low-amplitude azimuthal mode is also identified at both pressures. This azimuthal mode is periodically amplified and attenuated by the superposed longitudinal mode and induces small asymmetric (around the burner circumference) fluctuations of the local fuel and total mixture mass flow rates entering the flame region.

Large Eddy Simulation of a Reacting Kerosene Spray in Hot Vitiated Cross-Flow

The evaporation and combustion characteristics of a kerosene spray injected perpendicularly into a cross-flow of high-temperature vitiated air is investigated. This fundamental flow configuration has wider implications for the future development of ultra-low emission aeronautical combustors, particularly with respect to technologies involving MILD combustion. Large eddy simulations with a Eulerian–Lagrangian framework are performed to investigate the spray evolution and the characteristics of the reaction zone for a range of conditions. For the closure of turbulence-chemistry interactions at the sub-grid scales, a transported probability density function approach solved by the Eulerian stochastic fields method is applied. A configuration based on the use of airblast atomisation is assessed first and compared with experimental observations. The effect of the atomiser air-to-liquid mass flow ratio is studied in greater detail, both in terms of the resulting gas-phase properties and the droplet evaporation process. Then, the effect of ambient pressure on the global spray flame behaviour is examined. For this part of the study, no atomising air is included in the simulation to separate the effects of ambient pressure on the spray from the interaction with the air jet. Analysis of the flame and spray properties at cross-flow operating pressures of 1 atm, 2 bar and 4 bar highlights the strong coupling between the reacting flow and droplet evaporation characteristics, which are highly affected by the penetration of the spray into a flow field characterised by relatively large gradients of temperature. The results reported in this work provide fundamental understanding for the development of novel low-emission combustion technologies and demonstrate the feasibility of applying large eddy simulation with detailed chemistry for the investigation of reacting aviation fuel sprays in hot vitiated cross-flow.

Computation of Entropy Production in Stratified Flames Based on Chemistry Tabulation and an Eulerian Transported Probability Density Function Approach

This contribution presents a straightforward strategy to investigate the entropy production in stratified premixed flames. The modeling approach is grounded on a chemistry tabulation strategy, large eddy simulation, and the Eulerian stochastic field method. This enables a combination of a detailed representation of the chemistry with an advanced model for the turbulence chemistry interaction, which is crucial to compute the various sources of exergy losses in combustion systems. First, using detailed reaction kinetic reference simulations in a simplified laminar stratified premixed flame, it is demonstrated that the tabulated chemistry is a suitable approach to compute the various sources of irreversibilities. Thereafter, the effects of the operating conditions on the entropy production are investigated. For this purpose, two operating conditions of the Darmstadt stratified burner with varying levels of shear have been considered. The investigations reveal that the contribution to the entropy production through mixing emerging from the chemical reaction is much larger than the one caused by the stratification. Moreover, it is shown that a stronger shear, realized through a larger Reynolds number, yields higher entropy production through heat, mixing and viscous dissipation and reduces the share by chemical reaction to the total entropy generated.

Modeling of turbulent flames with the large eddy simulation–probability density function (LES–PDF) approach, stochastic fields, and artificial neural networks

This work proposes a chemical mechanism tabulation method using artificial neural networks (ANNs) for turbulent combustion simulations. The method is employed here in the context of the Large-Eddy Simulation (LES)–Probability Density Function (PDF) approach and the method of stochastic fields for numerical solution, but can also be employed in other methods featuring real-time integration of chemical kinetics. The focus of the paper is on exploring an ANN architecture aiming at improved generalization, which uses a single multilayer perceptron (MLP) for each species over the entire training dataset. This method is shown to outperform previous approaches which take advantage of specialization by clustering the composition space using the Self-Organizing Map (SOM). The ANN training data are generated using the canonical combustion problem of igniting/extinguishing one-dimensional laminar flamelets with a detailed methane combustion mechanism, before being augmented with randomly generated data to produce a hybrid random/flamelet dataset with improved composition space coverage. The ANNs generated in this study are applied to the LES of a turbulent non-premixed CH4/air flame, Sydney flame L. The transported PDF approach is used for reaction source term closure, while numerical solution is obtained using the method of stochastic fields. Very good agreement is observed between direct integration (DI) and the ANNs, meaning that the ANNs can successfully replace the integration of chemical kinetics. The time taken for the reaction source computation is reduced 18-fold, which means that LES–PDF simulations with comprehensive mechanisms can be performed on modest computing resources.

Transported probability density function based modelling of soot particle size distributions in non-premixed turbulent jet flames

The need to establish actual particle size distributions (PSDs) of soot emissions from the nanoscale upwards, along with the current global indicators based on soot mass, stems from increasingly strict regulatory demands. In the current work, a mass and number density preserving sectional model is coupled with a transported probability density function (PDF) method to study the evolution of soot PSDs in two non-premixed turbulent jet flames at Reynolds numbers of 10,000 and 20,000. The transported PDF approach is closed at joint-scalar level and includes mass fractions of gas phase species, soot sections, as well as enthalpy, leading to a fully coupled 78-dimensional joint-scalar space, treating interactions between turbulence and gas phase/soot chemistry as well as radiation without further approximation. The gas phase chemistry features 144 reactions, 15 solved and 14 steady-state species and an acetylene-based soot inception model is calibrated using comprehensive detailed chemistry up to pyrene and applied to a well-stirred/plug flow reactor configuration. The derived nucleation rate is subsequently applied in the turbulent flame calculations. Soot surface growth is treated via a PAH analogy and oxidation via O, OH and O2 is accounted for. The sectional model features 62 sections covering particle sizes in the range 0.38 nm ≤ dp ≤ 4.4 µm and includes a model for the collision efficiency of small particles ( ≤ 10 nm) based on the Lennard–Jones potential. The computed results reproduce the evolution of the PSDs with encouraging accuracy. It is also shown that the distribution of soot in mixture fraction space is affected by local extinction events.

Application of the Eulerian subgrid Probability Density Function method in the Large Eddy Simulation of a partially premixed swirl flame

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.

Simulation of MILD combustion using Perfectly Stirred Reactor model

A simple model based on a Perfectly Stirred Reactor (PSR) is proposed for moderate or intense low-oxygen dilution (MILD) combustion. The PSR calculation is performed covering the entire flammability range and the tabulated chemistry approach is used with a presumed joint probability density function (PDF). The jet, in hot and diluted coflow experimental set-up under MILD conditions, is simulated using this reactor model for two oxygen dilution levels. The computed results for mean temperature, major and minor species mass fractions are compared with the experimental data and simulation results obtained recently using a multi-environment transported PDF approach. Overall, a good agreement is observed at three different axial locations for these comparisons despite the over-predicted peak value of CO formation. This suggests that MILD combustion can be effectively modelled by the proposed PSR model with lower computational cost.

Prediction of external intermittency using RANS-based turbulence modelling and a transported PDF approach

This paper investigates the modelling of external intermittency in turbulent round jets using a RANS approach coupled to solutions of the transported probability density function (PDF) equation for scalar variables. Solutions to the descriptive equations are obtained using a finite-volume method, combined with an adaptive mesh refinement algorithm, applied in both physical and compositional space. The effects of intermittency on the flow field are accommodated using intermittency-modified eddy viscosity and second-moment turbulence closures, as well as through modifications to the mixing model embodied within the transported PDF equation. Predictions of the model are validated against data on the velocity and scalar fields in jets, as well as against measurements of scalar PDFs and intermittency profiles, with reasonable agreement obtained. From the cases examined, predictions of the second-moment closure are superior, although both approaches provide realistic predictions of the bimodal features to the measured PDFs.

Joint-scalar transported PDF modeling of soot formation and oxidation

The ability of the transported probability density function (PDF) approach to reproduce the evolution of mean, rms fluctuations, and conditional PDFs of soot is explored in the context of two turbulent ethylene diffusion flames at Reynolds numbers of 11,800 and 15,600. The chemical similarity between surface reactions and PAH formation is explored on the basis of a second ring PAH analogy, and soot oxidation is accounted for through reactions with O, OH, and O 2. The method of moments is used to account for coagulation and agglomeration in the coalescent and fractal aggregate limits. The soot model is coupled with a transported PDF approach closed at the joint-scalar level to directly account for interactions between turbulence, and the solid and gas phase chemistry. The latter is represented by a systematically reduced reaction mechanism for ethylene featuring 144 reactions, 15 solved and 14 steady-state species. Radiation from soot and gas phase species is accounted for through the RADCAL method and the inclusion of enthalpy into the joint-scalar PDF. Predicted temperature and soot statistics compare well with experimental data indicating the practical potential of the approach and the importance of turbulence-chemistry interactions in the context of soot formation and burnout.

A model for the mixing time scale of a turbulent reacting scalar

Current micromixing models in transported PDF (probability density function equation) modeling of initially nonpremixed, turbulent reacting flows ignore the direct influence of chemistry on the dissipation rate of reacting scalar fluctuations. Following mapping closure, a model for the time scale of reactive scalar mixing in the flamelet regime is developed and comparisons made with direct numerical simulations of a turbulent reacting jet. The modeling results show a significant improvement over the generally used estimate of substituting the time scale of the reacting scalar by that of a conserved scalar in traditional transported PDF approaches. The model can readily be applied to many existing mixing submodels used in transported PDF modeling when the time scales of the reacting scalars appear explicitly in the formulation. The submodels allow the transported PDF approach to now encompass the fast as well as slow chemistry regimes.