Eulerian Stochastic Field Research Articles

A Comparative Study of the Hydrogen Auto-Ignition Process in Oxygen–Nitrogen and Oxygen–Water Vapor Oxidizer: Numerical Investigations in Mixture Fraction Space and 3D Forced Homogeneous Isotropic Turbulent Flow Field

In this paper, we analyze the auto-ignition process of hydrogen in a hot oxidizer stream composed of oxygen–nitrogen and oxygen–water vapor with nitrogen/water vapor mass fractions in a range of 0.1–0.9. The temperature of the oxidizer varies from 1100 K to 1500 K and the temperature of hydrogen is assumed to be 300 K. The research is performed in 1D mixture fraction space and in a forced homogeneous isotropic turbulent (HIT) flow field. In the latter case, the Large Eddy Simulation (LES) method combined with the Eulerian Stochastic Field (ESF) combustion model is applied. The results obtained in mixture fraction space aim to determine the most reactive mixture fraction, maximum flame temperature, and dependence on the scalar dissipation rate. Among others, we found that the ignition in H2-O2-H2O mixtures occurs later than in H2-O2-N2 mixtures, especially at low oxidizer temperatures. On the other hand, for a high oxidizer temperature, the ignitability of H2-O2-H2O mixtures is extended, i.e., the ignition occurs for a larger content of H2O and takes place faster. The 3D LES-ESF results show that the ignition time is virtually independent of initial conditions, e.g., randomness of an initial flow field and turbulence intensity. The latter parameter, however, strongly affects the flame evolution. It is shown that the presence of water vapor decreases ignitability and makes flames more prone to extinction.

LES of autoignition process in a turbulent droplet-laden mixing layer – impact of an evaporation model and discretisation method

This paper focuses on the numerical modelling of the autoignition process in an ethanol-air mixture within a turbulent droplet-laden temporally evolving mixing layer, utilising the Large Eddy Simulation (LES) method. We compare results obtained by implementing two notably distinct discretisation methods (second-order Total Variation Diminishing – TVD, and fifth-order Weighted Essentially Non-Oscillatory – WENO) in the species and energy transport equations. Additionally, we examine three widely recognised evaporation models (the ‘ D 2 ’ model, the Abramzon–Sirignano model, and a non-equilibrium model based on the Langmuir-Knudsen law). For modelling the combustion process, we employ the Eulerian Stochastic Field method and a laminar chemistry model. The simulations encompass two droplet diameter distributions, one with low and the other with significant diameter non-uniformity. Furthermore, nine distinct initial conditions are considered. Our findings indicate that adjusting the discretisation scheme or the evaporation model can yield simulation outcomes differing to a substantial degree, similar to the impact of modifying the actual properties of the spray droplets or their initial distribution. This is particularly pronounced in the case of sprays featuring a narrowed droplet diameter distribution. We found that the Abramzon–Sirignano model results in the most rapid autoignition. The TVD scheme contributes to a more even spatial distribution of the evaporated fuel, consequently facilitating quicker evaporation and faster autoignition. Using the WENO scheme generates higher fuel vapor gradients near the droplets, leading to less intense evaporation and slower fuel transport in space.

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.

Hydrogen Jet Flame Control by Global Mode

In this study, we employ the potential of the global instability phenomenon to qualitatively alter the dynamics of a turbulent flame. We adopt the large eddy simulation method and an in-house numerical code. For the combustion process we do not include explicit sub-filter modeling. The accuracy of this ‘no combustion model’ approach is verified by comparison against the Eulerian Stochastic Fields method. We include several test cases representing different flow regimes, including convective and absolutely unstable conditions. The focus is on a counter-current configuration, which includes a central jet nozzle supplying hydrogen fuel surrounded by a somewhat larger co-axial nozzle sucking fluid from the surroundings of the central nozzle. The suction generates a counterflow where global instability is found to be triggered if sufficiently strong suction is applied. The critical suction value IGI\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$I_{GI}$$\\end{document} is larger if the level of the inlet turbulence intensity Ti\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_i$$\\end{document} is increased. Depending on the suction strength, the flame quickly stabilizes, either as being attached to the nozzle or as a lifted flame hovering at a height of a few fuel nozzle diameters. Additionally, it is shown that increasing Ti\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_i$$\\end{document} can assist an initially lifted flame to attach to the nozzle. Flame lifting is the result of self-induced strong toroidal vortices that lead to leaner combustion conditions of the mixture upstream of the flame base. The toroidal vortices prevent upstream flame propagation and lead to a very intense mixing process that gives rise to the lifted reaction zone. This ensures almost complete fuel combustion at a short distance from the inlet. On the contrary, when the suction strength is below IGI\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$I_{GI}$$\\end{document}, the flames are attached and a high temperature near the fuel inlet causes an increase in molecular viscosity. This tends to laminarize the mixing layer between the fuel and oxidizer. The flames appear as if they were laminar and non-premixed over a long distance from the inlet. In such a situation, a significant amount of fuel remains unburned.

Numerical investigation of AdBlue film formation and NH3 conversion in generic SCR system using Eulerian stochastic fields method

In this paper, the Eulerian stochastic fields (ESF) method in a LES framework is applied to a generic selective catalytic reduction (SCR) configuration in order to retrieve seamlessly the effect of turbulence–chemistry interaction on the NH3-conversion and AdBlue film formation. The ESF method is based on the transport equation of a joint scalar filtered density function. The injection of AdBlue and relevant spray dynamics are modeled by the Lagrange-particle description where a computational parcel represents a cluster of real AdBlue droplets. Owing to the low injection pressure, weak atomization of AdBlue leads to intense droplet wall-impingement and film formation on the SCR duct wall and/or on the mixer elements, if present. A 2-D thin film approach is adopted to model the film formation and dynamics in combination with multi-regimes droplet–wall interaction model. After verification tasks against the reference data for simple gas phase reactive cases, the verified ESF method is coupled with a one-equation based LES turbulence model together with the Lagrange particle-tracking which is combined with the 2-D thin film approach to simulate the AdBlue injection and the film formation in the generic SCR configuration. At first, the assessment of the adopted LES mesh is carried out in terms of the so-called LES quality of index to determine the optimal mesh resolution. Next, to ensure the convergence with respect to the number of required ESF and mesh resolution, SCR simulations are performed by using various (2, 4, 6, 8, 12 and 16) stochastic fields and also with refined mesh. Thereby, the sensitivity of the predictive capability of the numerical tool is evaluated for the production of NH3 and HNCO with and without ESFs. This clearly indicates the importance of an accurate description of the turbulence–chemistry interaction to retrieve reliably the conversion of NH3. Finally, the film dynamics especially the evolution of the film thickness described with six required ESF and without ESF is compared with experimental data from the generic SCR configurations. To further demonstrate the potential of suggested numerical approach, a detailed numerical analysis is provided in terms of spray-impingement dynamics, scalar uniformity index, droplet life time and characteristics of the droplets prone to form solid deposits in the monolith channel.

An extended FGM model with transported PDF for LES of spray combustion

An enhanced flamelet generated manifold (FGM) model for large eddy simulation (LES) of turbulent spray combustion is presented. In the enhanced FGM model, a transported probability density function (TPDF) description of the FGM variables is employed. The TPDF is represented using the Eulerian stochastic fields (ESF) approach, and the method is applied to LES of spray combustion under conditions relevant to internal combustion engines. The new ESF/FGM method achieves an improved accuracy of predictions due to the ESF modelling of the subgrid-scale turbulence-chemistry interaction. It also achieves high computational efficiency due to the FGM tabulation of the chemical kinetic mechanism. The performance of the new ESF/FGM model is assessed by simulation of the Spray-A flames from Engine Combustion Network (ECN) and comparison of the results, firstly, with experimental measurements, and secondly, with conventional FGM model simulation results. It is shown that the ESF/FGM method is capable of predicting both global and local combustion characteristics, i.e., pressure rise, ignition delay time, flame lift-off length and the thermo-chemical structure of the spray flames with improved accuracy compared to the conventional FGM model that is based on the presumed PDF description of FGM variables. The sensitivity of the predictions using ESF/FGM to the number of stochastic fields is examined by varying the number of these fields in the range of 4–128. Furthermore, the influence of different FGM reaction progress variables on the simulations is investigated, and a new reaction progress variable based on the local consumption of oxygen is proposed. The results show that the new progress variable improves predictions of spray combustion, including the prediction of the start of injection, the quasi-steady state liftoff length, the post-injection oxidation, and the pressure evolution.

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.

The Exergy Losses Analysis in Adiabatic Combustion Systems including the Exhaust Gas Exergy.

The entropy generation analysis of adiabatic combustion systems was performed to quantify the exergy losses which are mainly the exergy destroyed during combustion inside the chamber and in the exhaust gases. The purpose of the present work was therefore: (a) to extend the exergy destruction analysis by including the exhaust gas exergy while applying the hybrid filtered Eulerian stochastic field (ESF) method coupled with the FGM chemistry tabulation strategy; (b) to introduce a novel method for evaluating the exergy content of exhaust gases; and (c) to highlight a link between exhaust gas exergy and combustion emissions. In this work, the adiabatic Sandia flames E and F were chosen as application combustion systems. First, the numerical results of the flow and scalar fields were validated by comparison with the experimental data. The under-utilization of eight stochastic fields (SFs), the flow field results and the associated scalar fields for the flame E show excellent agreement contrary to flame F. Then, the different exergy losses were calculated and analyzed. The heat transfer and chemical reaction are the main factors responsible for the exergy destruction during combustion. The chemical exergy of the exhaust gases shows a strong relation between the exergy losses and combustion emission as well as the gas exhaust temperature.

Effects of pre-injection on ignition, combustion and emissions of spray under engine-like conditions

Large-eddy simulation (LES) of multiple-injection spray combustion under engine-like conditions is performed using a coupled model of an Eulerian stochastic field transported probability density function (ESF T-PDF) and a flamelet generated manifold (FGM). This coupled model allows the use of the T-PDF methods in modeling the interaction of turbulence and chemistry at affordable computational costs for engine applications. Simulation results are compared with the available experimental data for spray flames with multiple-injection and at a high level of exhaust gas recirculation (EGR) under conditions relevant to internal combustion engines. It is shown that the T-PDF/FGM LES model is capable of reproducing not only global combustion characteristics, such as the pressure rise and ignition delay time but also replicating the evolution of liftoff length and the spray flame structure.The effects of pre-injection strategies are then investigated, by systematically varying the pre-injection duration and the dwell time between two injections, while keeping the total injected fuel mass constant. The LES results reveal different mechanisms by which a pre-injection can change the ignition delay time, the combustion mode and the emissions in spray flames, depending on the injection timing. It is shown that even an extremely short non-igniting pre-injection can substantially change the ignition and emissions characteristics of the main-injection. It is shown that the combustion mode of a single-injection can be altered by splitting the injection to pre- and main-injections. The current study also demonstrates that decreasing the dwell time, within the range that is examined here, at a given pre-injection, will potentially increase the soot oxidation rates while it does not significantly change the rate of soot formation.

A numerical study of a lifted hbox {H}_2/hbox {N}_2 flame excited by an axial and flapping forcing

The large eddy simulation method combined with the Eulerian stochastic field approach has been used to study excited lifted hydrogen flames in a stream of hot co-flow in a configuration closely corresponding to the so-called Cabra flame. The excitation is obtained by adding to an inlet velocity profile three types of forcing [(1) axial; (2) flapping; (3) combination of both] with the amplitude of 15% of the fuel jet velocity and the frequency corresponding to the Strouhal numbers St=0.30,, 0.45,, 0.60, ,text {and}, ,0.75. It is shown that such a type of forcing significantly changes the lift-off height (L_h) of the flame and its global shape, resulting in the flame occupying a large volume or the flame, which transforms from the circular one into a quasi-planar one. Both the L_h and size of the flames were found to be a function of the type of forcing and its frequency. The minimum value of L_h has been found for the case when the axial and flapping forcing were combined and acted at the forcing frequency close to the preferred one in the non-excited configuration. The impact of the flapping forcing manifested through a widening of the flame in the flapping direction. It was shown that the excitation increases the level of temperature fluctuations caused by an intensified mixing process. The computational results are validated based on the solutions obtained for the non-excited flame for which experimental data are available.

Reaction-Diffusion Manifolds including differential diffusion applied to methane/air combustion in strong extinction regimes

Detailed chemistry simulations of turbulent reacting flows involving combustion of hydrocarbons can easily exceed the available computational resources, depending on the dimensions of the chemical system. Previous work of the authors showed how the combination of the Eulerian Stochastic Fields (ESF) model with tabulated chemistry based on 2-dimensional Reaction-Diffusion Manifolds (REDIM) provided a significant computational speed-up, compared to the finite rate ESF solver. In this work, the behaviour for flame F, featuring a strong degree of extinction, is further investigated. A comparison is performed for 2D and 3D databases, both using simplified and detailed transport, where the scalar dissipation rate is included as the third table parameter. The results show that the upstream sections are well captured by the REDIM built for detailed transport, while the downstream sections are better captured by the simplified transport database. While a 3D-REDIM based on simplified transport seems to be necessary to capture the extinction events, a 2D-REDIM with differential diffusion already provides satisfactory results. Overall, the use of a 3D-REDIM with differential diffusion better describes the global behaviour of flame F.

Analysis of Local Exergy Losses in Combustion Systems Using a Hybrid Filtered Eulerian Stochastic Field Coupled with Detailed Chemistry Tabulation: Cases of Flames D and E

A second law analysis in combustion systems is performed along with an exergy loss study by quantifying the entropy generation sources using, for the first time, three different approaches: a classical-thermodynamics-based approach, a novel turbulence-based method and a look-up-table-based approach, respectively. The numerical computation is based on a hybrid filtered Eulerian stochastic field (ESF) method coupled with tabulated detailed chemistry according to a Famelet-Generated Manifold (FGM)-based combustion model. In this work, the capability of the three approaches to capture the effect of the Re number on local exergy losses is especially appraised. For this purpose, Sandia flames D and E are selected as application cases. First, the validation of the computed flow and scalar fields is achieved by comparison to available experimental data. For both flames, the flow field results for eight stochastic fields and the associated scalar fields show an excellent agreement. The ESF method reproduces all major features of the flames at a lower numerical cost. Next, the second law analysis carried out with the different approaches for the entropy generation computation provides comparable quantitative results. Using flame D as a reference, for which some results with the thermodynamic-based approach exist in the literature, it turns out that, among the sources of exergy loss, the heat transfer and the chemical reaction emerge notably as the main culprits for entropy production, causing 50% and 35% of it, respectively. This fact-finding increases in Sandia flame E, which features a high Re number compared to Sandia flame D. The computational cost is less once the entropy generation analysis is carried out by using the Large Eddy Simulation (LES) hybrid ESF/FGM approach together with the look-up-table-based or turbulence-based approach.

Implementation of a probabilistic surface density volume of fluid approach for spray atomisation

Eulerian Stochastic methods in Large Eddy Simulation context have been successfully used in reactive flows. They have been recently applied to spray atomisation, using surface and liquid volume as independent variables. These methods involve the solutions of Stochastic Partial Differential Equations, which are continuous in space and discontinuous in time. The implementation of these equations into a conventional finite volume solver can be challenging due to both the numerical diffusion of the scalar fields and the numerical integration of the stochastic source terms. This work presents the implementation and validation of the Eulerian Stochastic Fields surface/liquid volume atomisation method within the OpenFOAM framework. The paper discusses how algebraic compression methods can be used for the stochastic fields to minimise the numerical diffusion and the effects of the stochastic source term implementation. The model targets a-priori spray atomisation at large Weber numbers, although the implementation recovers the correct solution at low Weber model and captures correctly the capillary effects on liquid–gas interfaces. A turbulent liquid jet is used for validation and discussion of the accuracy and relative cost of the model implementation. The approach is then applied to a multi-hole gasoline direct injector where the agreement with experimental data showcases the capabilities of the solver for realistic injectors and atomisation regimes.

Coupling the Multiple Mapping Conditioning Mixing Model with Reaction-diffusion Databases in LES of Methane/air Flames

ABSTRACT The Multiple Mapping Conditioning (MMC) model for sparse Lagrangian Large-Eddy Simulations (LES) is coupled with tabulated chemistry based on reaction-diffusion manifolds (REDIM). In addition to assessing the reduction in computational cost compared to direct integration on the fly, a comparison with the previously implemented REDIM solver based on the Eulerian Stochastic Fields (ESF) is performed. The methane/air Sandia flames D and E are selected as a benchmark, which are amenable to a 2D REDIM database having a passive scalar and one progress variable as dimensions. A comparison between direct integration ESF and MMC shows that the latter gives better predictions of the conditional means and fluctuations, offering at the same time a significantly reduced computational cost. When coupled with REDIM, MMC and ESF models provide similar results, indicating the significant sensitivity of the predictions to the thermochemical states which are restricted to the same REDIM manifold. When the states are projected back onto the REDIM surface in the direction where the progress variables remain almost constant, accuracy is lost in the cold fuel-lean region with MMC. Furthermore, the computational performance gain in MMC compared to ESF is reduced when the REDIM tabulation is used, pointing to non-chemistry related computational bottlenecks in the MMC algorithms.

On element mass conservation in Eulerian stochastic fields modeling of turbulent combustion

Eulerian stochastic fields (ESF) based transported PDF method has evolved as one of the general purpose methods for the numerical simulation of complex chemically reactive turbulent flows in which the effect of turbulence on the chemical reaction rates can be computed directly without the need of modeling. It is found that ESF method may suffer from violation of the element mass conservation law due to the stochastic Wiener process and the highly non-linear dependence of the chemical reaction rates on the stochastic fields. This paper presents a modified ESF method to remove the error in the element mass conservation. The method is evaluated in numerical simulation of two turbulent flames, (i) Reynolds averaged Navier-Stokes (RANS) simulation of a turbulent non-premixed methane/air counterflow flame under stationary burning and transient flame extinction conditions, (ii) large eddy simulation of swirling turbulent methane/air non-premixed flames under local extinction and re-ignition conditions. The original ESF method violates the element mass conservation in both flames, and the element mass error would not disappear even if a large number of stochastic fields were used. The new method yields a satisfactory prediction of the element mass conservation even with a small number of stochastic fields. The new and original methods predict similar stationary flame structures but the results under flame extinction and re-ignition conditions are rather different.

Numerical Study of the Influence of Turbulence–Chemistry Interaction on URANS Simulations of Diesel Spray Flame Structures under Marine Engine-like Conditions

The present work performs unsteady Reynolds-averaged Navier-Stokes simulations to study the effect of turbulence-chemistry interaction (TCI) on diesel spray flames. Three nozzle diameters (d0) of 100, 180, and 363 μm are considered in the present study. The Eulerian stochastic fields (ESF) method (with the TCI effect) and well-stirred reactor (WSR) model (without the TCI effect) are considered in the present work. The model evaluation is carried out for ambient gas densities (ρam) of 30.0 and 58.5 kg/m3. The ESF method is demonstrated to be able to reproduce the ignition delay time (IDT) and lift-off length (LOL) with an improved accuracy than that from the WSR method. Furthermore, TCI has relatively more influence on LOL than on IDT. A normalized LOL (LOL*) is introduced, which considers the effect of d0, and its subsequent effect on the fuel-richness in the rich premixed core region is analyzed. The RO2 distribution is less influenced by the TCI effect as ambient density increases. The ESF model generally predicts a longer and wider CH2O distribution. The difference in the spatial distribution of CH2O between the ESF and WSR model diminishes as d0 increases. At ρam = 30.0 kg/m3, the ESF method results in a broader region of OH with lower peak OH values than in the WSR case. However, at ρam = 58.5 kg/m3, the variation of the peak OH value is less susceptible to the increase in d0 and the presence of the TCI model. Furthermore, the influence of TCI on the total OH mass decreases as d0 increases. The total NOx mass qualitatively follows the same trend as the total OH mass. This present work clearly shows that the influence of TCI on the global spray and combustion characteristics becomes less prominent when d0 increases. (Less)

Large Eddy Simulation of an Ethanol Spray Flame with Secondary Droplet Breakup

A computational investigation of three configurations of the Delft Spray in Hot-diluted Co-flow (DSHC) is presented. The selected burner comprises a hollow cone pressure swirl atomiser, injecting an ethanol spray, located in the centre of a hot co-flow generator, with the conditions studied corresponding to Moderate or Intense Low-oxygen Dilution (MILD) combustion. The simulations are performed in the context of Large Eddy Simulation (LES) in combination with a transport equation for the joint probability density function (pdf) of the scalars, solved using the Eulerian stochastic field method. The liquid phase is simulated by the use of a Lagrangian point particle approach, where the sub-grid-scale interactions are modelled with a stochastic approach. Droplet breakup is represented by a simple primary breakup model in combination with a stochastic secondary breakup formulation. The approach requires only a minimal knowledge of the fuel injector and avoids the need to specify droplet size and velocity distributions at the injection point. The method produces satisfactory agreement with the experimental data and the velocity fields of the gas and liquid phase both averaged and ‘size-class by size-class’ are well depicted. Two widely accepted evaporation models, utilising a phase equilibrium assumption, are used to investigate the influence of evaporation on the evolution of the liquid phase and the effects on the flame. An analysis on the dynamics of stabilisation sheds light on the importance of droplet size in the three spray flames; different size droplets play different roles in the stabilisation of the flames.

Numerical Prediction of Turbulent Spray Flame Characteristics Using the Filtered Eulerian Stochastic Field Approach Coupled to Tabulated Chemistry

The Eulerian stochastic fields (ESF) method, which is based on the transport equation of the joint subgrid scalar probability density function, is applied to Large Eddy Simulation of a turbulent dilute spray flame. The approach is coupled with a tabulated chemistry approach to represent the subgrid turbulence–chemistry interaction. Following a two-way coupled Eulerian–Lagrangian procedure, the spray is treated as a multitude of computational parcels described in a Lagrangian manner, each representing a heap of real spray droplets. The present contribution has two objectives: First, the predictive capabilities of the modeling framework are evaluated by comparing simulation results using 8, 16, and 32 stochastic fields with available experimental data. At the same time, the results are compared to previous studies, where the artificially thickened flame (ATF) model was applied to the investigated configuration. The results suggest that the ESF method can reproduce the experimental measurements reasonably well. Comparisons with the ATF approach indicate that the ESF results better describe the flame entrainment into the cold spray core of the flame. Secondly, the dynamics of the subgrid scalar contributions are investigated and the reconstructed probability density distributions are compared to common presumed shapes qualitatively and quantitatively in the context of spray combustion. It is demonstrated that the ESF method can be a valuable tool to evaluate approaches relying on a pre-integration of the thermochemical lookup-table.

Validation of an Eulerian Stochastic Fields Solver Coupled with Reaction\u2013Diffusion Manifolds on LES of Methane/Air Non-premixed Flames

The Eulerian stochastic fields (ESF) combustion model can be used in LES in order to evaluate the filtered density function to describe the process of turbulence–chemistry interaction. The method is typically computationally expensive, especially if detailed chemistry mechanisms involving hydrocarbons are used. In this work, expensive computations are avoided by coupling the ESF solver with a reduced chemistry model. The reaction–diffusion manifold (REDIM) is chosen for this purpose, consisting of a passive scalar and a suitable reaction progress variable. The latter allows the use of a constant parametrization matrix when projecting the ESF equations onto the manifold. The piloted flames Sandia D–E were selected for validation using a 2D-REDIM. The results show that the combined solver is able to correctly capture the flame behavior in the investigated sections, although local extinction is underestimated by the ESF close to the injection plate. Hydrogen concentrations are strongly influenced by the transport model selected within the REDIM tabulation. A total solver performance increase by a factor of 81% is observed, compared to a full chemistry ESF simulation with 19 species. An accurate prediction of flame F instead required the extension of the REDIM table to a third variable, the scalar dissipation rate.