modeling diesel combustion with tabulated kinetics and
TRANSCRIPT
Modeling diesel combustion with tabulated kinetics and different
flame structure assumptions based on flamelet approachModeling
diesel combustion with tabulated kinetics and different flame
structure assumptions based on flamelet approach Citation for
published version (APA): Lucchini, T., Pontoni, D., D’Errico, G.,
& Somers, B. (2020). Modeling diesel combustion with tabulated
kinetics and different flame structure assumptions based on
flamelet approach. International Journal of Engine Research, 21(1),
89-100. https://doi.org/10.1177/1468087419862945
DOI: 10.1177/1468087419862945
Document Version: Accepted manuscript including changes made at the peer-review stage
Please check the document version of this publication:
• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication
General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.
• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.
If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement: www.tue.nl/taverne
Take down policy If you believe that this document breaches copyright please contact us at: [email protected] providing details and we will investigate your claim.
Download date: 01. Mar. 2022
Modeling diesel combustion with tabulated kinetics and different flame structure assumptions based on flamelet approach
Tommaso Lucchini1 , Daniel Pontoni1, Gianluca D’Errico1 and Bart Somers2
Abstract Computational fluid dynamics analysis represents a useful approach to design and develop new engine concepts and investigate advanced combustion modes. Large chemical mechanisms are required for a correct description of the com- bustion process, especially for the prediction of pollutant emissions. Tabulated chemistry models allow to reduce signifi- cantly the computational cost, maintaining a good accuracy. In the present work, an investigation of tabulated approaches, based on flamelet assumptions, is carried out to simulate turbulent Diesel combustion in the Spray A frame- work. The Approximated Diffusion Flamelet is tested under different ambient conditions and compared with Flamelet Generated Manifold, and both models are validated with Engine Combustion Network experimental data. Flame struc- ture, combustion process and soot formation were analyzed in this work. Computed results confirm the impact of the turbulent–chemistry interaction on the ignition event. Therefore, a new look-up table concept Five-Dimensional- Flamelet Generated Manifold, that accounts for an additional dimension (strain rate), has been developed and tested, giv- ing promising results.
Keywords Computational fluid dynamics, combustion modeling, diesel, Approximated Diffusion Flamelet, Flamelet Generated Manifold, Five-Dimensional-Flamelet Generated Manifold, Spray A
Date received: 8 March 2019; accepted: 20 June 2019
Introduction
The continuous development of the existing technology of compression ignition engines requires a deep knowl- edge of the complex thermal, chemical and fluid dynamics processes that govern the combustion process to further improve its efficiency and quality of exhaust gases.1–4 Novel advanced combustion systems as well as optimal chamber design and fuel injection strate- gies2,5,6 and more efficient after-treatment devices (SCR, LNT, DPF, DOC)7–10 are required to meet the more and more stringent regulations.11 Moreover, potentialities associated with the use alternative fuels, eventually mixed with the conventional ones, must be well assessed.12–15 To this end, it is necessary to per- form both fundamental and applied studies by means of advanced numerical and computational techniques. The Engine Combustion Network (ECN)16 has been built over the last decade supported by this motivation:
the creation and availability of large databases with high-quality experimental results generated at different international institutions to deep the fundamental understanding of the injection and combustion process and support the validation and development of compu- tational fluid dynamics (CFD) combustion models.17
Focusing on Diesel combustion, a large number of experiments were carried on not only by injecting n- dodecane sprays, chosen as Diesel fuel surrogate, in a
1Department of Energy, Politecnico di Milano, Milano, Italy 2Eindhoven University of Technology, Eindhoven, The Netherlands
Corresponding author:
Lambruschini 4, 20156 Milano, Italy.
Email: [email protected]
constant-volume vessel chamber, recording ignition delays (IDs) and pressure rise (and hence the rate of heat release rates), but also collecting quantitative information about the flame structure, such as lift-off lengths (LOLs) and soot distributions.
Open discussion in the ECN community evidenced the importance of a detailed chemical mechanism to be employed in the CFD approach to correctly estimate both global combustion parameters and details of tran- sient flame structure. However, the Direct integration of chemistry equations to compute reaction rates is computationally demanding since it involves a large number of species and the use of ordinary differential equation (ODE) stiff solvers. For this reason, the size of the chemical mechanism which can be used in practi- cal simulations is limited both in terms of species and reactions.18 An interesting alternative for the reduction of CPU time is the tabulated kinetic approach, in which the reaction rates are stored in a look-up table and retrieved during the simulation, as a function of the thermodynamic state of the system.18–21 The com- bustion models can then also include the effect of turbulence–chemistry interaction, for a better predic- tion of ignition and combustion of Diesel spray.22–24
To this aim, the flamelet approach is widely accepted where chemical reactions are assumed to take place in an ensemble of small laminar flames also called flame- lets.25 Objective of this work is to compare two approaches which are both based on the flamelet assumption and make us of tabulated kinetics. The first is called Approximated Diffusion Flamelet (ADF) while the second is the Flamelet Generated Manifold (FGM). Both the approaches are analyzed in terms of their capability to predict auto-ignition and flame stabi- lization process. ADF approach is based on approxi- mated flamelets, which are computed by employing the Homogeneous Reactor table.18,26 FGM model consists of storing and retrieving low-dimensional manifolds created using solutions of one-dimensional diffusive flames with direct integration of detailed kinetic chem- istry, by means of the CHEM1D application:27–29 the thermal state of a reacting spray is expressed as func- tion of four variables: pressure, ambient temperature, mixture fraction and progress variable. An extension of this approach, which was also tested in the current investigation, consists in a novel model, called Five- Dimensional-Flamelet Generated Manifold (5D- FGM): the additional dimension of the table is the applied strain rate. A better description of the whole combustion process was achieved, especially for the low reactivity cases, emphasizing the importance of turbulence–chemistry interaction for a correct predic- tion of ignition and flame stabilization.
Computational model
Diesel combustion is affected by the complex interplay between turbulence and chemistry which determines
the auto-ignition time, heat release rate during mixing controlled combustion and the distance from the nozzle at which the flame stabilizes (LOL).30 Different approaches to couple turbulence and chemistry were proposed in the past and they can be mainly classified in the way chemical kinetics and turbulence–chemistry interaction are handled. For what regards the computa- tion of the chemical species reaction rates, it is impor- tant to note that the two possible solutions are either to use direct integration or to generate an offline look-up table. Despite the fact that the first approach is surely more detailed and flexible, it is also computationally very demanding due to the necessity of employing stiff solvers with very small time-steps to estimate the chem- ical species reaction rates. This aspect introduces sev- eral limitations for the maximum number of species that can be used in practical simulations and the conse- quent accuracy of the adopted mechanism. Moreover, accounting for sub-grid mixing and turbulence– chemistry interaction introduces further computational overheads. This is related to the integration of the pre- sumed probability function, or the transport of many species and energy equations such as the number of simulated flow realizations or stochastic fields.31
Therefore, tabulated kinetics can offer a possible solu- tion to reduce the CPU time and to keep an acceptable accuracy. Reaction rates and chemical composition are stored in a look-up table which is generated from a chemical mechanism and the assumption of a certain flame structure like a well-stirred reactor or laminar diffusion flame.
Figure 1 illustrates how the CFD solvers based on tabulated kinetics work. Additional transport equations are solved with the Reynolds-averaged Navier–Stokes (RANS) method for mixture fraction ~Z, mixture frac- tion variance Z
002, progress variable ~C and unburned gas enthalpy ~hu which is then used to estimate the cor- responding unburned gas temperature Tu. In case diffusion-mixing effects are considered, the stoichio- metric scalar dissipation rate ~xst is also computed. The look-up table is accessed with local cell values of ~Z,
Figure 1. Operation of combustion models based on tabulated kinetics.
2 International J of Engine Research 00(0)
Z 002, ~C, p, Tu and ~xst, and it provides the chemical com-
position and the progress variable reaction rate to the solver.
Two different combustion models based on tabu- lated kinetics were employed in this work: their corre- sponding look-up tables are generated from laminar diffusion flame calculations. The models will be referred as ADF and FGM.
The main difference between ADF and FGM is related to the way reaction rates are estimated during the table generation process. In the ADF case, they are in turn taken from a look-up table based on homoge- neous auto-ignition calculations. Reaction rates are directly computed using detailed kinetics in the FGM table generation.
ADF table
Purpose of the ADF model is to provide a realistic description of the turbulent diffusion flamelet: it takes into account turbulence–chemistry interaction, sub-grid mixing and premixed propagation, thanks to the scalar dissipation rate x, which controls the diffusion rate of the species.19,21 Flamelet equations are solved in the mixture fraction space z in an approximate way, only for the progress variable and the enthalpy, assuming unity Lewis number22
r ∂C
∂t = r
∂t ð2Þ
where C is the progress variable, defined as the heat release by the combustion.19,22 The progress variable source term _C is taken from a look-up table which is generated from homogeneous reactor auto-ignition cal- culations.19 To avoid too anticipated ignitions related to progress variable diffusion, the progress variable reaction rate is set to zero in when the equivalence ratio f is higher than 3. ADF table is generated according to user-specified ranges of unburned temperature Tu, pres- sure p, equivalence ratio/mixture fraction Z, in addition to the stoichiometric scalar dissipation rate xst and the mixture fraction segregation factor SZ. Subsequently, the scalar dissipation rate x, for equations (1) and (2), is computed according to Peters’ model32
x = xst
exp( 2½erfc1(2z)2) exp( 2½erfc1(2Zst)2)
ð3Þ
To account for the sub-grid mixing, a b-distribution is assumed for both the chemical composition and the progress variable: the corresponding values at user- specified mixture fraction table points are
f t, ~Z,Z00 2
dz ð4Þ
where Z002 values are computed from the corresponding user-defined mixture fraction variance segregation factors
Z00 2 =SZ
~Z(1 ~Z) ð5Þ
to avoid numerical integration errors which might negatively affect the model consistency in terms of energy conservation; in case of very low variances, the b-distribution is approximated with a d-distribution.
A small time-step is necessary during the ADF table generation process to correctly account for the com- bined effects of mixing and reaction (Figure 2). ADF table should be generated with a large enough range of xst to include extinction, allowing a correct description of the diffusion flame stabilization process.
Solving the flamelet equations with tabulated kinetics introduces an approximation with respect to the case where detailed chemistry is used. To this end, authors have performed in Lucchini et al.18 constant- volume vessel spray combustion calculations with the representative interactive flamelet model using a single flamelet with both detailed and tabulated kinetics. Similar results were found for both the approaches, with the largest difference noticed for conditions of low ambient oxygen concentration.
FGM table
Unsteady counter-flow diffusion flame calculations with detailed kinetics are conveniently processed for the generation of the FGM look-up table (Figure 3). Computed results are parameterized as function of the mixture fraction Z and the progress variable c: a low- dimensional manifold is generated considering the solu- tion of unsteady one-dimensional flamelet equations in the physical space28,29,33
Figure 2. Generation of the ADF chemistry table.
Lucchini et al. 3
∂s
l
cp
∂h
∂s
ð8Þ
where s is the spatial coordinate perpendicular to the flame front, D is the diffusion coefficient and K is the flame stretch rate. This last variable has a large influ- ence on the mass burning rate: it is defined as the rela- tive rate change of mass contained in the infinitesimal volume33
K= 1
dt ð9Þ
The flamelet stretch field K is computed from the transverse momentum equation
∂ruK
∂x =
2rK2 + rua
2 ð10Þ
a denotes the applied strain rate at the oxidizer side and it is related to the velocity gradient. Equations (6)–(8) are solved by means of the CHEM1D tool. The user specifies the boundary conditions, namely Tu, Tfuel, p, a, air and fuel composition. Computed results are post- processed and stored in a look-up table by means of a MATLAB script.29
The progress variable source term and the chemical composition are determined as a function of c. Differently from the ADF model, the progress variable is defined as a linear combination of chemical species, which are assumed to be able to describe the whole combustion process, from ignition, low- and high- temperature heat release phases and eventually the fully established diffusion flame
C=2:70YHO2 +1:50YCH2O +0:9YCO +1:20YH2O
+1:20YCO2 ð11Þ
The FGM table is generated by post-processing the results provided by CHEM1D simulations. During such stage, the user specifies the table discretization in terms of mixture fraction Z and progress variable c. The FGM combustion model considers only one strain rate and it does not account for sub-grid mixing for the
estimation of the chemical composition in the computa- tional cells.
5D-FGM table
The 5D-FGM is a new concept developed in the con- text of this work with the main purpose to improve the prediction of the ID and flame stabilization process. The 5D-FGM table is generated by processing results of flamelet computations with multiple strain rates per- formed with CHEM1D. To be used in the CFD solver, the strain rate is converted into the stoichiometric sca- lar dissipation rate by means of Peters’ model32
xst = a
2
ð12Þ
The MATLAB script is employed for post- processing the flamelets. Accordingly, the table grows of one dimension, as reported in the variable hierarchy map, Figure 4.
Experimental validation
The Spray A experiment, which was widely studied in the context of the ECN,16 was used to validate the pro- posed combustion models. n-Dodecane fuel is delivered through a single-hole nozzle in a constant-volume ves- sel with a cubic shape where optical accessibility is ensured by sapphire windows. Different measurement techniques allow to gather information regarding the flame structure, heat release rate, LOL and soot distri- bution.6,34 Simulations were carried out in a two- dimensional computational mesh with the RANS tech- nique. The average mesh size was 0.5mm which was further reduced to 0.2mm in the nozzle region. In all the simulated operating conditions, the injection pres- sure and duration were set to 150MPa and 5.5ms, respectively. The injection profile of the 210370 nozzle was used in CFD simulation.35n-Dodecane oxidation chemistry is modeled using the mechanism proposed by Yao et al.,36 which includes 54 species and 269 reac- tions. Table 1 reports the main details of the simulated
Figure 3. Generation of the FGM chemistry table.
Figure 4. Hierarchical tree map of the five variables in 5D- FGM.
4 International J of Engine Research 00(0)
operating conditions: different ambient temperatures and oxygen concentrations were considered when keep- ing the vessel density to a constant value of 22.8 kg/m3.
A summary of the applied sub-models for Spray A simulation, turbulence and soot assessment is illustrated in Table 2.
Simulations were carried out using the standard ke turbulence model with the round jet correction (C1 =1:5). For assessment of spray and turbulence models, non-reacting conditions were first considered with the same ambient temperature of 900K used in the so-called baseline condition. Figure 5 shows that computed vapor penetration results are in rather good agreement with experimental data. Such result is a fun- damental pre-requisite for a successful simulation of the combustion process. Further validation under non- reacting conditions was reported in D’Errico et al.22
Four chemistry tables have been generated, one for each analyzed oxygen concentration, Table 3 reports the table discretizaion which represents a good tradeoff between accuracy, computational time and memory consumption. The stoichiometric scalar dissipation rate values follow a logarithmic curve and any further increase in xst resolution does not significantly improve the quality of the results.
For what regards the FGM combustion model setup, since the simulation of the flamelet is very time- consuming (direct integration of the chemistry), and to avoid computational memory issues, a lower number of discretization points in temperature and pressure have been selected, and the applied strain rate has been assumed to a fixed value equal to 700 s–1 (Table 4). In previous studies, such value was generally found close to the LOL.38,39
The baseline condition (O2 =15%, T=900K and ramb=22:8 kg=m3) was first considered to analyze
ADF and FGM results. In particular, Figure 6 com- pares the computed heat release rate (RoHR) with the apparent experimental value. Heat losses were not included in CFD simulations and this is the reason why the computed data overestimate the experimental ones. Figure 6 illustrates that both ADF and FGM models correctly describe the main features of the Diesel com- bustion process.
Three events can be clearly detected:
Ignition, corresponding to the RoHR peak; Mixing controlled combustion phase, where RoHR
reaches an almost stable value; Burnout, corresponding with the drop of RoHR.
The ADF model better predicts the ID time, heat release rate transition from auto-ignition to mixing
Table 1. Simulated conditions for ECN Spray A.
Case O2 (%) Temperature (K)
Baseline 15 900 Low-T 15 850 High-T 15 1000 O2-13 13 900 O2-21 21 900 Non-reacting 0 900
Table 2. Sub-models used on diesel spray simulations.
Phenomenon Model
Turbulence Standard ke Spray evolution Eulerian–Lagrangian Spray breakup Kelvin-Helmholtz &
Raileigh-Taylor Droplet heat transfer Ranz–Marshall Evaporation D2 law + Spalding mass number Scalar dissipation rate Peters Soot Leung et al.37
Figure 5. Non-reacting case: vapor penetration for ADF and experimental data; uncertainty is highlighted with green shadow.
Table 3. ADF table discretization.
Variable Number of points Range
Temperature (K) 21 750–1250 Pressure (bar) 3 40–80 Mixture fraction (–) 53 0–1 Normalized progress variable (-)
91 0–1
Mixture fraction segregation (–)
7 0–1
Table 4. FGM table discretization.
Variable Number of points
Range
Temperature (K) 5 800–1050 Pressure (bar) 3 50–70 Mixture fraction (–) 371 0–1 Normalized progress variable (–) 551 0–1
Lucchini et al. 5
controlled combustion and duration of the burnout phase. This aspect is probably related to the fact the ADF includes the effects of sub-grid mixing. Figure 7(a) and (b) compares the FGM and ADF models dur- ing the auto-ignition process in the temperature- mixture fraction plane. Time evolution of the most reactive mixture fraction conditions is illustrated with the black line while the red circles show temperature- mixture fraction scatter plot after auto-ignition. For both the models, the ignition is predicted at the side interface between spray and ambient air, and then the kernel moves burning the premixed fuel underneath. However, in FGM, the intermediate temperature reac- tions occur at richer mixture fraction location (as depicted in Figure 7(b)). To avoid a too anticipated ID, in all the ADF simulations, the reaction rate was set to zero for f . 3 and this is the reason why temperature clearly drops down at Zmax=0:124 in Figure 7(a).
FGM and ADF flame structures are compared in terms of scatter plots of OH, formaldehyde and acety- lene mass fraction as function of Z. The magnitude of YCH2O between the two combustion models is similar, but the location of the peak is different, more toward rich mixture (near the injector) in case of FGM as shown in Figure 8(a). The main reason is the limitation of progress variable source term in case of ADF. Both models predict a correct location of the OH peak close to the stoichiometric mixture fraction value. However, inclusion of sub-grid mixing via mixture fraction var- iance is probably the reason for a lower maximum OH value for ADF combined with a larger portion of the mixture fraction space where OH was found. A similar behavior can also be found for the C2H2 mass fraction as it can be seen from Figure 8(c).
Flame LOL and ID time were selected as combus- tion indicators for the validation of the proposed com- bustion models under the selected operating conditions reported in Table 1. Following ECN defini- tions,16 the LOL is computed as the axial distance between injector orifice and the first location where Favre-average OH mass fraction reaches 14% of its maximum in CFD domain; the ID time is identified by the instant where maximum temperature rise rate reaches the highest value. Effect of ambient tempera- ture on ID and LOL is presented in Figure 9. The ADF model is not fully capable to provide good rep- resentation of LOL, especially at low temperature. Shorter value computed with ADF seems to be related to the diffusion of the progress variable leading to a faster stabilization: a possible reason for such discrepancy might be related either to the use of approximate flamelet equations in the table genera- tion process or in the progress variable definition. Predicted LOL is very important for the computed soot distribution since it determines the
Figure 6. Baseline comparison of RoHR: ADF, FGM and experimental data.
(a) (b)
Figure 7. Red points: scatter plot of maximum temperature as function of mixture fraction; the black like illustrates the evolution of the maximum temperature during the intermediate and high temperature reactions: (a) ADF and (b) FGM.
6 International J of Engine Research 00(0)
amount of rich mixture which burns producing soot precursors.
Effects of oxygen concentration on combustion indi- cators are reported in Figure 10. Both the models
correctly predict an increase of LOL and ID time when reducing the O2 concentration at 900K ambient tem- perature. Computed ID times from the ADF combus- tion model are in better agreement with experimental data while the LOL is slightly underestimated.
Results from Figures 9 and 10 illustrate that the ADF model better estimates the ID compared to FGM probably because it accounts for mixing effects via xst. A correct prediction of ID is rather important, mainly in the case of engine operation under kinetically con- trolled combustion modes such as premixed charge compression ignition (PCCI) and reactivity controlled compression ignition (RCCI).
To investigate how stoichiometric scalar dissipation rate affects the auto-ignition process, in Figure 11, the state of mixing Z
002 and reaction progress c was reported as function of the stoichiometric scalar dissi- pation rate xst before auto-ignition for all the cells with f=2 which was identified as the most reactive equiva- lence ratio. Two different ambient temperatures, 850 and 1000K, were investigated. Ignition is possible only at low xst due to the lower mixture reactivity in the 850K ambient temperature condition: the maximum progress variable is found in the stoichiometric scalar
(a)
(c)
(b)
Figure 8. Comparison between FGM and ADF models using scatter plots of the most important chemical species used to describe the combustion process: (a) CH2O, (b) OH (b) and (c) C2H2. Results are reported at 4 ms after start of injection.
Figure 9. LOL and ID comparison between ADF, FGM and experimental data for different initial conditions of unburned gas temperature with 15% O2 concentration.
Lucchini et al. 7
dissipation rate range of 0–10 and then it decreases to zero. For this reason, ignition is expected to take place at the periphery of the jet. Reaction rate increases with ambient temperature and this is the reason why at the 1000K condition it is possible to find non-zero progress variable values also in the 10–100 range of xst
and the ignition spots are located closer to the nozzle. This investigation shows the importance of strain rate inclusion in the combustion model for a correct predic- tion of the ID.
5D-FGM
The 5D-FGM model was tested over the same condi- tions presented in Table 1. Inclusion of the strain rate effects is expected to improve the ID predictions. The
tabulated strain rate interval, following a logarithmic profile, is displayed in Table 5.
The inclusion of the strain rate effects improves the predictive capability of the 5D-FGM model. Figures 12 and 13 illustrate that IDs are better esti- mated for the low reactivity conditions (Tamb=850, 900K; O2=13%, 15%) where chemical reactions mainly take place in presence of low strain rates.
No significant improvements are reported for the prediction of the LOL, since it is mainly affected by high strain rate close to the nozzle and a reasonable value was already used for the generation of the FGM table. On the other hand, the high reactivity cases
Figure 10. LOL and ID comparison between ADF, FGM and experimental data at constant ambient temperature (900 K) and different O2 concentrations.
χ
Figure 11. Effects of mixing and turbulence for the most reactive cells right before ignition. Progress variable and mixture fraction variance are reported as function of the stoichiometric scalar dissipation rate. The most reactive equivalence ratio is assumed to be equal to 2.
Table 5. 5D-FGM table discretization.
Variable Number of points Range
Strain rate (s–1) 8 100–2000
Figure 12. ID and LOL comparison between FGM and 5D- FGM, for different ambient temperatures.
Figure 13. ID and LOL comparison between FGM and 5D- FGM, for different oxygen concentrations.
8 International J of Engine Research 00(0)
(1000K and 21%) are weakly affected, mainly because they sustain ignition and burning phases at higher xst, near the nozzle: the experimental LOL is small for the high reactivity case, indeed. The LOL is not strongly influenced, comparing FGM and 5D-FGM, and the trend remains close to the experimental curve.
Only the 13% oxygen case shows the highest differ- ence in terms of LOL. To investigate the reason for such variation, the combustion efficiency was analyzed in Figures 14 and 15. The experimental lower heating value (LHV) of n-dodecane was compared with the one resulting from the ratio between cumulative heat release and injected fuel mass in the FGM and 5D-FGM simu- lations. To respect the energy conservation, the esti- mated LHV must be as much close as possible to the experimental value. 5D-FGM better fulfills the energy conservation requirement with respect to the standard FGM model: the use of a single strain rate is the main reason for the underestimation of heat release during the end of combustion phase. The improvement is sig- nificant mainly for the O2=13% condition and this also explains the reason for a predicted shorter LOL. For the sake of completeness, the same efficiency analy- sis has been carried out for the ADF simulations: all the simulated points have a combustion efficiency higher than 99.50%.
Soot prediction of ADF model
The capability of the proposed combustion approach for soot prediction was investigated thanks to the avail- ability of soot volume fraction (fv) maps achieved by means of the diffused back illumination (DBI) tech- nique.40 The current FGM model implementation does not include the soot model and for this reason, only ADF results are shown in this section. Authors expect that they can also be representative of what could be predicted by the FGM model, since both the approaches estimate similar species distribution, ID
Figure 14. Cumulative RoHR comparison between FGM, 5D- FGM and LHV of n-dodecane, for different ambient temperatures.
Figure 15. Cumulative RoHR comparison between FGM, 5D- FGM and LHV of n-dodecane, for different oxygen concentrations.
(a) (b)
Figure 16. Soot assessment for the baseline condition (O2 = 15%, ramb = 22:8 kg=m3): (a) soot mass evolution in time and (b) soot fraction volume location and concentration at t = 4 ms.
Lucchini et al. 9
times and LOL values. Tuning of the Leung-Lindstedt and Jones (LLJ) model was carried out for the baseline condition including also the contribution of O and OH to soot oxidation.41,42Figure 16(a) shows the cumula- tive soot mass within the optical window for the base- line condition (O2=15%, ramb=22:8 kg=m3). The onset of soot production is well predicted, but the slope of the curve during the inception interval is lower in the CFD model. The soot mass peak is underestimated in magnitude, but the time when it occurs is fairly cap- tured. The steady-state value is correctly estimated, as the time and slope of the curve during the complete oxidation of soot particles. Figure 16(b) shows that the soot volume fraction distribution is rather well described by the ADF model. Such results are not only due to a correct selection of the LLJ model constants, but also due to a correct estimation of the flame LOL.
Figure 17 reports the evolution of the soot mass as function of time for the three different ambient tem- peratures Tamb at 15% ambient oxygen concentration. The model is capable to reproduce the increase in soot mass with the ambient temperature. However, com- puted steady-state mass values are underestimated for the 850K condition while they are overestimated when ambient Tamb is increased to 1100K. Such trend is not completely consistent with the prediction of the LOL which is illustrated in Figure 9.
A possible reason for such discrepancy can be mainly related to the temperature dependency of the model constants describing the soot formation. Such observa- tion is confirmed by the results illustrated in Figure 18, where the soot mass evolution is reported at 900K ambient temperature for three different tested oxygen concentrations. Computed results are in rather good agreement with experimental data. In particular, the highest amount of soot was formed for the 15% ambi- ent oxygen concentration: under such condition, the flame stabilizes at a relatively short distance from the nozzle and there is a reduced amount of O2 available
for soot oxidation. Similar amount of soot mass was found for the other two conditions. In the O2=21% condition, an increase in oxygen concentration enhances the soot oxidation rate. Reduction of O2 to 13% decreases the soot formation rate since the flame stabilizes at a higher distance from the nozzle compared to the other two conditions.
Conclusion
Two different Diesel combustion models which both use offline chemistry tabulation, namely the ADF and the FGM, were compared and assessed in terms of glo- bal heat release rate indicators and flame structure by simulating the ECN Spray A experiment in different conditions, including the variation of ambient tempera- ture and oxygen concentration. The main difference in the theoretical assumptions beyond these models is in the way reaction rates are estimated during the table generation process: in ADF they are based on homoge- neous auto-ignition calculations while in FGM unsteady counter-flow diffusion flames are solved. The latter is obviously much more demanding in terms of CPU time such that in the conventional model formu- lation a single strain rate is considered assuming that ID is not affected by it in a relatively large range of val- ues. In the ADF tabulation, instead the stoichiometric scalar dissipation rate xst and the variance mixture fraction Z002 are included to account for turbulence– chemistry interaction.
Models were tested considering n-dodecane sprays under constant-volume combustion conditions and considering variation of ambient temperature and oxy- gen concentration. It was observed how in general igni- tion occurs in rich region and then the reactions move toward stoichiometric zones. ADF results are clearly influenced by the turbulence–chemistry interaction: xst, Z002 and the reactivity play a fundamental role. The study of the main combustion tracers has given
Figure 17. Soot assessment as a function of ambient temperature (line = experimental data; squares = ADF).
Figure 18. Soot assessment as a function of oxygen concentration.
10 International J of Engine Research 00(0)
significant information about IDs, LOLs and flame structure. Agreement with experimental data was gen- erally good for both models, apart for the prediction of the LOL at low temperature given by the ADF model, probably due to an excessive diffusion of the progress variable, and for the prediction of the ID under the same condition for the FGM approach. To improve this aspect, a novel FGM implementation, 5D-FGM, which also include strain rate effects, was proposed: ID was better estimated since chemical reactions occur in presence of low strain rates for such low reactivity condition.
Finally, a preliminary assessment of the soot distri- bution given by the ADF model was proposed: qualita- tive trends agreed with the observed data, but further investigations are required to improve the quantitative estimations of soot mass, especially when varying the ambient temperature.
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publica- tion of this article.
Funding
The author(s) received no financial support for the research, authorship and/or publication of this article.
ORCID iD
References
1. Ho RJ, Yusoff MZ and Palanisamy K. Trend and future
of diesel engine: development of high efficiency and low
emission low temperature combustion diesel engine. IOP
C Ser Earth Env 2013; 16: 012112. 2. Johnson TV. Review of diesel emissions and control.
SAE Int J Fuel Lubr 2010; 3(1): 16–29. 3. Ali R. Effect of diesel emissions on human health: a
review. Int J Appl Eng Res 2011; 6(11): 1333–1342. 4. Karavalakis G, Poulopoulos S and Zervas E. Impact of
diesel fuels on the emissions of non-regulated pollutants.
Fuel 2012; 102: 85–91. 5. Angrill O, Geitlinger H, Streibel T, Suntz R and Bock-
horn H. Influence of exhaust gas recirculation on soot
formation in diffusion flames. P Combust Inst 2000;
28(2): 2643–2649. 6. Skeen S, Manin J and Pickett LM. Visualization of igni-
tion processes in high-pressure sprays with multiple injec-
tions of n-dodecane. SAE Int J Engine 2015; 8(2): 696–
715. 7. Yang L, Franco V, Campestrini A, German J and Mock
P. Nox control technologies for Euro 6 diesel passenger
cars (white paper). Berlin: International Council on
Clean Transportation (ICCT), 2015, pp.1–22. 8. Lapuerta M, Ramos A, Fernandez-Rodriguez D and
Gonzalez-Garca I. High-pressure versus low-pressure
exhaust gas recirculation in a Euro 6 diesel engine with
lean-NOx trap: effectiveness to reduce NOx emissions.
Int J Engine Res 2019; 20(1): 155–163. 9. Johnson TV. SAE 2009 world congress. Platin Met Rev
2010; 54(1): 37–43. 10. Guan B, Zhan R, Lin H and Huang Z. Review of state
of the art technologies of selective catalytic reduction of
NOx from diesel engine exhaust. Appl Therm Eng 2014;
66(1–2): 395–414. 11. Williams M and Minjares R. A technical summary of Euro
6/VI vehicle emission standards, vol. 10. Washington, DC:
International Council on Clean Transportation (ICCT),
2017. 12. Hosseini SM and Ahmadi R. Performance and emissions
characteristics in the combustion of co-fuel diesel-hydrogen
in a heavy duty engine. Appl Energ 2017; 205: 911–925. 13. Sinay J, Puskar M and Kopas M. Reduction of the NOx
emissions in vehicle diesel engine in order to fulfill future
rules concerning emissions released into air. Sci Total
Environ 2018; 624: 1421–1428. 14. Sanjid A, Masjuki HH, Kalam MA, Ashrafur Rahman
SM, Abedin MJ and Palash SM. Production of palm and
jatropha based biodiesel and investigation of palm-
jatropha combined blend properties, performance,
exhaust emission and noise in an unmodified diesel
engine. J Clean Prod 2014; 65: 295–303. 15. Rochussen J and Kirchen P. Characterization of reaction
zone growth in an optically accessible heavy-duty diesel/
methane dual-fuel engine. Int J Engine Res 2019; 20(5):
483–500. 16. Engine Combustion Network (ECN) website, https://
ecn.sandia.gov/ 17. Aubagnac-Karkar D, Michel J-B, Colin O and Darabiha
N. Combustion and soot modelling of a high-pressure
and high-temperature Dodecane spray. Int J Engine Res
2018; 19(4): 434–448. 18. Lucchini T, D’Errico G, Onorati A, Frassoldati A, Stagni
A and Hardy G. Modeling non-premixed combustion
using tabulated kinetics and different fame structure
assumptions. SAE Int J Engine 2017; 10(2): 593–607.
19. Lucchini T, D’Errico G, Cerri T, Onorati A and Hardy
G. Experimental validation of combustion models for
diesel engines based on tabulated kinetics in a wide range
of operating conditions. SAE technical paper 2017-24-
0029, 2017. 20. Desantes JM, Garca-Oliver JM, Novella R and Perez-
Sanchez EJ. Application of an unsteady flamelet model in
a RANS framework for spray A simulation. Appl Therm
Eng 2017; 117: 50–64. 21. Payri F, Novella R, Pastor JM and Perez-Sanchez EJ.
Evaluation of the approximated diffusion flamelet con-
cept using fuels with different chemical complexity. Appl
Math Model 2017; 49: 354–374. 22. D’Errico G, Lucchini T, Contino F, Jangi M and Bai X-
S. Comparison of well-mixed and multiple representative
interactive flamelet approaches for diesel spray combus-
tion modelling. Combust Theor Model 2014; 18(1): 65–88. 23. Pei Y, Hawkes ER and Kook S. Transported probability
density function modelling of the vapour phase of an n-
heptane jet at diesel engine conditions. P Combust Inst
2013; 34(2): 3039–3047. 24. Barths H, Hasse C and Peters N. Computational fluid
dynamics modelling of non-premixed combustion in
direct injection diesel engines. Int J Engine Res 2000;
1(3): 249–267.
combustion. Booval, QLD, Australia: R.T. Edwards, Inc., 2005.
26. Michel J-B, Colin O and Veynante D. Modeling ignition and chemical structure of partially premixed turbulent flames using tabulated chemistry. Combust Flame 2008; 152: 80–99.
27. Wehrfritz A, Kaario O, Vuorinen V and Somers B. Large Eddy Simulation of n-dodecane spray flames using Fla- melet Generated Manifolds. Combust Flame 2016; 167: 113–131.
28. Verhoeven LM, Ramaekers WJS, Van Oijen JA and de Goey LPH. Modeling non-premixed laminar co-flow flames using flamelet-generated manifolds. Combust
Flame 2012; 159(1): 230–241. 29. Maghbouli A, Akkurt B, Lucchini T, D’Errico G, Deen
NG and Somers B. Modelling compression ignition
engines by incorporation of the flamelet generated mani- folds combustion closure. Combust Theor Model. Epub ahead of print 24 October 2018. DOI: 10.1080/ 13647830.2018.1537522.
30. Dec JE. A conceptual model of DI diesel combustion based on laser-sheet imaging. SAE technical paper
970873, 1997. 31. Pickett LM and Siebers DL. Non-sooting, low flame tem-
perature mixing-controlled DI diesel combustion. SAE technical paper 2004-01-1399, 2004.
32. Peters N. Laminar diffusion flamelet models in non- premixed turbulent combustion. Prog Energ Combust
1984; 10(3): 319–339. 33. Van Oijen JA. Flamelet-generated manifolds: development
and application to premixed laminar flames. Eindhoven: Technische Universiteit Eindhoven, 2002.
34. Maes N, Dam N, Somers B, Lucchini T, D’Errico G and
Hardy G. Heavy-duty diesel engine spray combustion
processes: experiments and numerical simulations. SAE
technical paper 2018-01-1689, 2018. 35. CMT virtual injection rate generator, https://
www.cmt.upv.es/ECN03.aspx 36. Yao T, Pei Y, Zhong BJ, Som S and Lu T. A hybrid
mechanism for n-dodecane combustion with optimized
low-temperature chemistry. In: Proceedings of the 9th US
National combustion meeting, Cincinnati, OH, 17–20 May
2015, pp.1–10. 37. Leung KM, Lindstedt RP and Jones WP. A simplified
reaction mechanism for soot formation in nonpremixed
flames. Combust Flame 1991; 87(3–4): 289–305. 38. Bekdemir C, Somers LMT and de Goey LPH. Modeling
diesel engine combustion using pressure dependent Fla-
melet Generated Manifolds. P Combust Inst 2011; 33:
2887–2894. 39. Eguz U, Ayyapureddi S, Bekdemir C, Somers B and de
Goey LPH. Modeling fuel spray auto-ignition using the
FGM approach: effect of tabulation method. SAE tech-
nical paper 2012-01-0157, 2012. 40. Manin J, Pickett LM and Skeen SA. Two-color diffused
back-illumination imaging as a diagnostic for time-
resolved soot measurements in reacting sprays. SAE Int J
Engine 2013; 6(4): 1908–1921. 41. Brookes SJ and Moss JB. Predictions of soot and thermal
radiation properties in confined turbulent jet diffusion
flames. Combust Flame 1999; 116(4): 486–503. 42. Guo H, Liu F and Smallwood GJ. Soot and NO forma-
tion in counterflow ethylene/oxygen/nitrogen diffusion
flames. Combust Theor Model 2004; 8(3): 475–489.
12 International J of Engine Research 00(0)
DOI: 10.1177/1468087419862945
Document Version: Accepted manuscript including changes made at the peer-review stage
Please check the document version of this publication:
• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication
General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.
• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.
If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement: www.tue.nl/taverne
Take down policy If you believe that this document breaches copyright please contact us at: [email protected] providing details and we will investigate your claim.
Download date: 01. Mar. 2022
Modeling diesel combustion with tabulated kinetics and different flame structure assumptions based on flamelet approach
Tommaso Lucchini1 , Daniel Pontoni1, Gianluca D’Errico1 and Bart Somers2
Abstract Computational fluid dynamics analysis represents a useful approach to design and develop new engine concepts and investigate advanced combustion modes. Large chemical mechanisms are required for a correct description of the com- bustion process, especially for the prediction of pollutant emissions. Tabulated chemistry models allow to reduce signifi- cantly the computational cost, maintaining a good accuracy. In the present work, an investigation of tabulated approaches, based on flamelet assumptions, is carried out to simulate turbulent Diesel combustion in the Spray A frame- work. The Approximated Diffusion Flamelet is tested under different ambient conditions and compared with Flamelet Generated Manifold, and both models are validated with Engine Combustion Network experimental data. Flame struc- ture, combustion process and soot formation were analyzed in this work. Computed results confirm the impact of the turbulent–chemistry interaction on the ignition event. Therefore, a new look-up table concept Five-Dimensional- Flamelet Generated Manifold, that accounts for an additional dimension (strain rate), has been developed and tested, giv- ing promising results.
Keywords Computational fluid dynamics, combustion modeling, diesel, Approximated Diffusion Flamelet, Flamelet Generated Manifold, Five-Dimensional-Flamelet Generated Manifold, Spray A
Date received: 8 March 2019; accepted: 20 June 2019
Introduction
The continuous development of the existing technology of compression ignition engines requires a deep knowl- edge of the complex thermal, chemical and fluid dynamics processes that govern the combustion process to further improve its efficiency and quality of exhaust gases.1–4 Novel advanced combustion systems as well as optimal chamber design and fuel injection strate- gies2,5,6 and more efficient after-treatment devices (SCR, LNT, DPF, DOC)7–10 are required to meet the more and more stringent regulations.11 Moreover, potentialities associated with the use alternative fuels, eventually mixed with the conventional ones, must be well assessed.12–15 To this end, it is necessary to per- form both fundamental and applied studies by means of advanced numerical and computational techniques. The Engine Combustion Network (ECN)16 has been built over the last decade supported by this motivation:
the creation and availability of large databases with high-quality experimental results generated at different international institutions to deep the fundamental understanding of the injection and combustion process and support the validation and development of compu- tational fluid dynamics (CFD) combustion models.17
Focusing on Diesel combustion, a large number of experiments were carried on not only by injecting n- dodecane sprays, chosen as Diesel fuel surrogate, in a
1Department of Energy, Politecnico di Milano, Milano, Italy 2Eindhoven University of Technology, Eindhoven, The Netherlands
Corresponding author:
Lambruschini 4, 20156 Milano, Italy.
Email: [email protected]
constant-volume vessel chamber, recording ignition delays (IDs) and pressure rise (and hence the rate of heat release rates), but also collecting quantitative information about the flame structure, such as lift-off lengths (LOLs) and soot distributions.
Open discussion in the ECN community evidenced the importance of a detailed chemical mechanism to be employed in the CFD approach to correctly estimate both global combustion parameters and details of tran- sient flame structure. However, the Direct integration of chemistry equations to compute reaction rates is computationally demanding since it involves a large number of species and the use of ordinary differential equation (ODE) stiff solvers. For this reason, the size of the chemical mechanism which can be used in practi- cal simulations is limited both in terms of species and reactions.18 An interesting alternative for the reduction of CPU time is the tabulated kinetic approach, in which the reaction rates are stored in a look-up table and retrieved during the simulation, as a function of the thermodynamic state of the system.18–21 The com- bustion models can then also include the effect of turbulence–chemistry interaction, for a better predic- tion of ignition and combustion of Diesel spray.22–24
To this aim, the flamelet approach is widely accepted where chemical reactions are assumed to take place in an ensemble of small laminar flames also called flame- lets.25 Objective of this work is to compare two approaches which are both based on the flamelet assumption and make us of tabulated kinetics. The first is called Approximated Diffusion Flamelet (ADF) while the second is the Flamelet Generated Manifold (FGM). Both the approaches are analyzed in terms of their capability to predict auto-ignition and flame stabi- lization process. ADF approach is based on approxi- mated flamelets, which are computed by employing the Homogeneous Reactor table.18,26 FGM model consists of storing and retrieving low-dimensional manifolds created using solutions of one-dimensional diffusive flames with direct integration of detailed kinetic chem- istry, by means of the CHEM1D application:27–29 the thermal state of a reacting spray is expressed as func- tion of four variables: pressure, ambient temperature, mixture fraction and progress variable. An extension of this approach, which was also tested in the current investigation, consists in a novel model, called Five- Dimensional-Flamelet Generated Manifold (5D- FGM): the additional dimension of the table is the applied strain rate. A better description of the whole combustion process was achieved, especially for the low reactivity cases, emphasizing the importance of turbulence–chemistry interaction for a correct predic- tion of ignition and flame stabilization.
Computational model
Diesel combustion is affected by the complex interplay between turbulence and chemistry which determines
the auto-ignition time, heat release rate during mixing controlled combustion and the distance from the nozzle at which the flame stabilizes (LOL).30 Different approaches to couple turbulence and chemistry were proposed in the past and they can be mainly classified in the way chemical kinetics and turbulence–chemistry interaction are handled. For what regards the computa- tion of the chemical species reaction rates, it is impor- tant to note that the two possible solutions are either to use direct integration or to generate an offline look-up table. Despite the fact that the first approach is surely more detailed and flexible, it is also computationally very demanding due to the necessity of employing stiff solvers with very small time-steps to estimate the chem- ical species reaction rates. This aspect introduces sev- eral limitations for the maximum number of species that can be used in practical simulations and the conse- quent accuracy of the adopted mechanism. Moreover, accounting for sub-grid mixing and turbulence– chemistry interaction introduces further computational overheads. This is related to the integration of the pre- sumed probability function, or the transport of many species and energy equations such as the number of simulated flow realizations or stochastic fields.31
Therefore, tabulated kinetics can offer a possible solu- tion to reduce the CPU time and to keep an acceptable accuracy. Reaction rates and chemical composition are stored in a look-up table which is generated from a chemical mechanism and the assumption of a certain flame structure like a well-stirred reactor or laminar diffusion flame.
Figure 1 illustrates how the CFD solvers based on tabulated kinetics work. Additional transport equations are solved with the Reynolds-averaged Navier–Stokes (RANS) method for mixture fraction ~Z, mixture frac- tion variance Z
002, progress variable ~C and unburned gas enthalpy ~hu which is then used to estimate the cor- responding unburned gas temperature Tu. In case diffusion-mixing effects are considered, the stoichio- metric scalar dissipation rate ~xst is also computed. The look-up table is accessed with local cell values of ~Z,
Figure 1. Operation of combustion models based on tabulated kinetics.
2 International J of Engine Research 00(0)
Z 002, ~C, p, Tu and ~xst, and it provides the chemical com-
position and the progress variable reaction rate to the solver.
Two different combustion models based on tabu- lated kinetics were employed in this work: their corre- sponding look-up tables are generated from laminar diffusion flame calculations. The models will be referred as ADF and FGM.
The main difference between ADF and FGM is related to the way reaction rates are estimated during the table generation process. In the ADF case, they are in turn taken from a look-up table based on homoge- neous auto-ignition calculations. Reaction rates are directly computed using detailed kinetics in the FGM table generation.
ADF table
Purpose of the ADF model is to provide a realistic description of the turbulent diffusion flamelet: it takes into account turbulence–chemistry interaction, sub-grid mixing and premixed propagation, thanks to the scalar dissipation rate x, which controls the diffusion rate of the species.19,21 Flamelet equations are solved in the mixture fraction space z in an approximate way, only for the progress variable and the enthalpy, assuming unity Lewis number22
r ∂C
∂t = r
∂t ð2Þ
where C is the progress variable, defined as the heat release by the combustion.19,22 The progress variable source term _C is taken from a look-up table which is generated from homogeneous reactor auto-ignition cal- culations.19 To avoid too anticipated ignitions related to progress variable diffusion, the progress variable reaction rate is set to zero in when the equivalence ratio f is higher than 3. ADF table is generated according to user-specified ranges of unburned temperature Tu, pres- sure p, equivalence ratio/mixture fraction Z, in addition to the stoichiometric scalar dissipation rate xst and the mixture fraction segregation factor SZ. Subsequently, the scalar dissipation rate x, for equations (1) and (2), is computed according to Peters’ model32
x = xst
exp( 2½erfc1(2z)2) exp( 2½erfc1(2Zst)2)
ð3Þ
To account for the sub-grid mixing, a b-distribution is assumed for both the chemical composition and the progress variable: the corresponding values at user- specified mixture fraction table points are
f t, ~Z,Z00 2
dz ð4Þ
where Z002 values are computed from the corresponding user-defined mixture fraction variance segregation factors
Z00 2 =SZ
~Z(1 ~Z) ð5Þ
to avoid numerical integration errors which might negatively affect the model consistency in terms of energy conservation; in case of very low variances, the b-distribution is approximated with a d-distribution.
A small time-step is necessary during the ADF table generation process to correctly account for the com- bined effects of mixing and reaction (Figure 2). ADF table should be generated with a large enough range of xst to include extinction, allowing a correct description of the diffusion flame stabilization process.
Solving the flamelet equations with tabulated kinetics introduces an approximation with respect to the case where detailed chemistry is used. To this end, authors have performed in Lucchini et al.18 constant- volume vessel spray combustion calculations with the representative interactive flamelet model using a single flamelet with both detailed and tabulated kinetics. Similar results were found for both the approaches, with the largest difference noticed for conditions of low ambient oxygen concentration.
FGM table
Unsteady counter-flow diffusion flame calculations with detailed kinetics are conveniently processed for the generation of the FGM look-up table (Figure 3). Computed results are parameterized as function of the mixture fraction Z and the progress variable c: a low- dimensional manifold is generated considering the solu- tion of unsteady one-dimensional flamelet equations in the physical space28,29,33
Figure 2. Generation of the ADF chemistry table.
Lucchini et al. 3
∂s
l
cp
∂h
∂s
ð8Þ
where s is the spatial coordinate perpendicular to the flame front, D is the diffusion coefficient and K is the flame stretch rate. This last variable has a large influ- ence on the mass burning rate: it is defined as the rela- tive rate change of mass contained in the infinitesimal volume33
K= 1
dt ð9Þ
The flamelet stretch field K is computed from the transverse momentum equation
∂ruK
∂x =
2rK2 + rua
2 ð10Þ
a denotes the applied strain rate at the oxidizer side and it is related to the velocity gradient. Equations (6)–(8) are solved by means of the CHEM1D tool. The user specifies the boundary conditions, namely Tu, Tfuel, p, a, air and fuel composition. Computed results are post- processed and stored in a look-up table by means of a MATLAB script.29
The progress variable source term and the chemical composition are determined as a function of c. Differently from the ADF model, the progress variable is defined as a linear combination of chemical species, which are assumed to be able to describe the whole combustion process, from ignition, low- and high- temperature heat release phases and eventually the fully established diffusion flame
C=2:70YHO2 +1:50YCH2O +0:9YCO +1:20YH2O
+1:20YCO2 ð11Þ
The FGM table is generated by post-processing the results provided by CHEM1D simulations. During such stage, the user specifies the table discretization in terms of mixture fraction Z and progress variable c. The FGM combustion model considers only one strain rate and it does not account for sub-grid mixing for the
estimation of the chemical composition in the computa- tional cells.
5D-FGM table
The 5D-FGM is a new concept developed in the con- text of this work with the main purpose to improve the prediction of the ID and flame stabilization process. The 5D-FGM table is generated by processing results of flamelet computations with multiple strain rates per- formed with CHEM1D. To be used in the CFD solver, the strain rate is converted into the stoichiometric sca- lar dissipation rate by means of Peters’ model32
xst = a
2
ð12Þ
The MATLAB script is employed for post- processing the flamelets. Accordingly, the table grows of one dimension, as reported in the variable hierarchy map, Figure 4.
Experimental validation
The Spray A experiment, which was widely studied in the context of the ECN,16 was used to validate the pro- posed combustion models. n-Dodecane fuel is delivered through a single-hole nozzle in a constant-volume ves- sel with a cubic shape where optical accessibility is ensured by sapphire windows. Different measurement techniques allow to gather information regarding the flame structure, heat release rate, LOL and soot distri- bution.6,34 Simulations were carried out in a two- dimensional computational mesh with the RANS tech- nique. The average mesh size was 0.5mm which was further reduced to 0.2mm in the nozzle region. In all the simulated operating conditions, the injection pres- sure and duration were set to 150MPa and 5.5ms, respectively. The injection profile of the 210370 nozzle was used in CFD simulation.35n-Dodecane oxidation chemistry is modeled using the mechanism proposed by Yao et al.,36 which includes 54 species and 269 reac- tions. Table 1 reports the main details of the simulated
Figure 3. Generation of the FGM chemistry table.
Figure 4. Hierarchical tree map of the five variables in 5D- FGM.
4 International J of Engine Research 00(0)
operating conditions: different ambient temperatures and oxygen concentrations were considered when keep- ing the vessel density to a constant value of 22.8 kg/m3.
A summary of the applied sub-models for Spray A simulation, turbulence and soot assessment is illustrated in Table 2.
Simulations were carried out using the standard ke turbulence model with the round jet correction (C1 =1:5). For assessment of spray and turbulence models, non-reacting conditions were first considered with the same ambient temperature of 900K used in the so-called baseline condition. Figure 5 shows that computed vapor penetration results are in rather good agreement with experimental data. Such result is a fun- damental pre-requisite for a successful simulation of the combustion process. Further validation under non- reacting conditions was reported in D’Errico et al.22
Four chemistry tables have been generated, one for each analyzed oxygen concentration, Table 3 reports the table discretizaion which represents a good tradeoff between accuracy, computational time and memory consumption. The stoichiometric scalar dissipation rate values follow a logarithmic curve and any further increase in xst resolution does not significantly improve the quality of the results.
For what regards the FGM combustion model setup, since the simulation of the flamelet is very time- consuming (direct integration of the chemistry), and to avoid computational memory issues, a lower number of discretization points in temperature and pressure have been selected, and the applied strain rate has been assumed to a fixed value equal to 700 s–1 (Table 4). In previous studies, such value was generally found close to the LOL.38,39
The baseline condition (O2 =15%, T=900K and ramb=22:8 kg=m3) was first considered to analyze
ADF and FGM results. In particular, Figure 6 com- pares the computed heat release rate (RoHR) with the apparent experimental value. Heat losses were not included in CFD simulations and this is the reason why the computed data overestimate the experimental ones. Figure 6 illustrates that both ADF and FGM models correctly describe the main features of the Diesel com- bustion process.
Three events can be clearly detected:
Ignition, corresponding to the RoHR peak; Mixing controlled combustion phase, where RoHR
reaches an almost stable value; Burnout, corresponding with the drop of RoHR.
The ADF model better predicts the ID time, heat release rate transition from auto-ignition to mixing
Table 1. Simulated conditions for ECN Spray A.
Case O2 (%) Temperature (K)
Baseline 15 900 Low-T 15 850 High-T 15 1000 O2-13 13 900 O2-21 21 900 Non-reacting 0 900
Table 2. Sub-models used on diesel spray simulations.
Phenomenon Model
Turbulence Standard ke Spray evolution Eulerian–Lagrangian Spray breakup Kelvin-Helmholtz &
Raileigh-Taylor Droplet heat transfer Ranz–Marshall Evaporation D2 law + Spalding mass number Scalar dissipation rate Peters Soot Leung et al.37
Figure 5. Non-reacting case: vapor penetration for ADF and experimental data; uncertainty is highlighted with green shadow.
Table 3. ADF table discretization.
Variable Number of points Range
Temperature (K) 21 750–1250 Pressure (bar) 3 40–80 Mixture fraction (–) 53 0–1 Normalized progress variable (-)
91 0–1
Mixture fraction segregation (–)
7 0–1
Table 4. FGM table discretization.
Variable Number of points
Range
Temperature (K) 5 800–1050 Pressure (bar) 3 50–70 Mixture fraction (–) 371 0–1 Normalized progress variable (–) 551 0–1
Lucchini et al. 5
controlled combustion and duration of the burnout phase. This aspect is probably related to the fact the ADF includes the effects of sub-grid mixing. Figure 7(a) and (b) compares the FGM and ADF models dur- ing the auto-ignition process in the temperature- mixture fraction plane. Time evolution of the most reactive mixture fraction conditions is illustrated with the black line while the red circles show temperature- mixture fraction scatter plot after auto-ignition. For both the models, the ignition is predicted at the side interface between spray and ambient air, and then the kernel moves burning the premixed fuel underneath. However, in FGM, the intermediate temperature reac- tions occur at richer mixture fraction location (as depicted in Figure 7(b)). To avoid a too anticipated ID, in all the ADF simulations, the reaction rate was set to zero for f . 3 and this is the reason why temperature clearly drops down at Zmax=0:124 in Figure 7(a).
FGM and ADF flame structures are compared in terms of scatter plots of OH, formaldehyde and acety- lene mass fraction as function of Z. The magnitude of YCH2O between the two combustion models is similar, but the location of the peak is different, more toward rich mixture (near the injector) in case of FGM as shown in Figure 8(a). The main reason is the limitation of progress variable source term in case of ADF. Both models predict a correct location of the OH peak close to the stoichiometric mixture fraction value. However, inclusion of sub-grid mixing via mixture fraction var- iance is probably the reason for a lower maximum OH value for ADF combined with a larger portion of the mixture fraction space where OH was found. A similar behavior can also be found for the C2H2 mass fraction as it can be seen from Figure 8(c).
Flame LOL and ID time were selected as combus- tion indicators for the validation of the proposed com- bustion models under the selected operating conditions reported in Table 1. Following ECN defini- tions,16 the LOL is computed as the axial distance between injector orifice and the first location where Favre-average OH mass fraction reaches 14% of its maximum in CFD domain; the ID time is identified by the instant where maximum temperature rise rate reaches the highest value. Effect of ambient tempera- ture on ID and LOL is presented in Figure 9. The ADF model is not fully capable to provide good rep- resentation of LOL, especially at low temperature. Shorter value computed with ADF seems to be related to the diffusion of the progress variable leading to a faster stabilization: a possible reason for such discrepancy might be related either to the use of approximate flamelet equations in the table genera- tion process or in the progress variable definition. Predicted LOL is very important for the computed soot distribution since it determines the
Figure 6. Baseline comparison of RoHR: ADF, FGM and experimental data.
(a) (b)
Figure 7. Red points: scatter plot of maximum temperature as function of mixture fraction; the black like illustrates the evolution of the maximum temperature during the intermediate and high temperature reactions: (a) ADF and (b) FGM.
6 International J of Engine Research 00(0)
amount of rich mixture which burns producing soot precursors.
Effects of oxygen concentration on combustion indi- cators are reported in Figure 10. Both the models
correctly predict an increase of LOL and ID time when reducing the O2 concentration at 900K ambient tem- perature. Computed ID times from the ADF combus- tion model are in better agreement with experimental data while the LOL is slightly underestimated.
Results from Figures 9 and 10 illustrate that the ADF model better estimates the ID compared to FGM probably because it accounts for mixing effects via xst. A correct prediction of ID is rather important, mainly in the case of engine operation under kinetically con- trolled combustion modes such as premixed charge compression ignition (PCCI) and reactivity controlled compression ignition (RCCI).
To investigate how stoichiometric scalar dissipation rate affects the auto-ignition process, in Figure 11, the state of mixing Z
002 and reaction progress c was reported as function of the stoichiometric scalar dissi- pation rate xst before auto-ignition for all the cells with f=2 which was identified as the most reactive equiva- lence ratio. Two different ambient temperatures, 850 and 1000K, were investigated. Ignition is possible only at low xst due to the lower mixture reactivity in the 850K ambient temperature condition: the maximum progress variable is found in the stoichiometric scalar
(a)
(c)
(b)
Figure 8. Comparison between FGM and ADF models using scatter plots of the most important chemical species used to describe the combustion process: (a) CH2O, (b) OH (b) and (c) C2H2. Results are reported at 4 ms after start of injection.
Figure 9. LOL and ID comparison between ADF, FGM and experimental data for different initial conditions of unburned gas temperature with 15% O2 concentration.
Lucchini et al. 7
dissipation rate range of 0–10 and then it decreases to zero. For this reason, ignition is expected to take place at the periphery of the jet. Reaction rate increases with ambient temperature and this is the reason why at the 1000K condition it is possible to find non-zero progress variable values also in the 10–100 range of xst
and the ignition spots are located closer to the nozzle. This investigation shows the importance of strain rate inclusion in the combustion model for a correct predic- tion of the ID.
5D-FGM
The 5D-FGM model was tested over the same condi- tions presented in Table 1. Inclusion of the strain rate effects is expected to improve the ID predictions. The
tabulated strain rate interval, following a logarithmic profile, is displayed in Table 5.
The inclusion of the strain rate effects improves the predictive capability of the 5D-FGM model. Figures 12 and 13 illustrate that IDs are better esti- mated for the low reactivity conditions (Tamb=850, 900K; O2=13%, 15%) where chemical reactions mainly take place in presence of low strain rates.
No significant improvements are reported for the prediction of the LOL, since it is mainly affected by high strain rate close to the nozzle and a reasonable value was already used for the generation of the FGM table. On the other hand, the high reactivity cases
Figure 10. LOL and ID comparison between ADF, FGM and experimental data at constant ambient temperature (900 K) and different O2 concentrations.
χ
Figure 11. Effects of mixing and turbulence for the most reactive cells right before ignition. Progress variable and mixture fraction variance are reported as function of the stoichiometric scalar dissipation rate. The most reactive equivalence ratio is assumed to be equal to 2.
Table 5. 5D-FGM table discretization.
Variable Number of points Range
Strain rate (s–1) 8 100–2000
Figure 12. ID and LOL comparison between FGM and 5D- FGM, for different ambient temperatures.
Figure 13. ID and LOL comparison between FGM and 5D- FGM, for different oxygen concentrations.
8 International J of Engine Research 00(0)
(1000K and 21%) are weakly affected, mainly because they sustain ignition and burning phases at higher xst, near the nozzle: the experimental LOL is small for the high reactivity case, indeed. The LOL is not strongly influenced, comparing FGM and 5D-FGM, and the trend remains close to the experimental curve.
Only the 13% oxygen case shows the highest differ- ence in terms of LOL. To investigate the reason for such variation, the combustion efficiency was analyzed in Figures 14 and 15. The experimental lower heating value (LHV) of n-dodecane was compared with the one resulting from the ratio between cumulative heat release and injected fuel mass in the FGM and 5D-FGM simu- lations. To respect the energy conservation, the esti- mated LHV must be as much close as possible to the experimental value. 5D-FGM better fulfills the energy conservation requirement with respect to the standard FGM model: the use of a single strain rate is the main reason for the underestimation of heat release during the end of combustion phase. The improvement is sig- nificant mainly for the O2=13% condition and this also explains the reason for a predicted shorter LOL. For the sake of completeness, the same efficiency analy- sis has been carried out for the ADF simulations: all the simulated points have a combustion efficiency higher than 99.50%.
Soot prediction of ADF model
The capability of the proposed combustion approach for soot prediction was investigated thanks to the avail- ability of soot volume fraction (fv) maps achieved by means of the diffused back illumination (DBI) tech- nique.40 The current FGM model implementation does not include the soot model and for this reason, only ADF results are shown in this section. Authors expect that they can also be representative of what could be predicted by the FGM model, since both the approaches estimate similar species distribution, ID
Figure 14. Cumulative RoHR comparison between FGM, 5D- FGM and LHV of n-dodecane, for different ambient temperatures.
Figure 15. Cumulative RoHR comparison between FGM, 5D- FGM and LHV of n-dodecane, for different oxygen concentrations.
(a) (b)
Figure 16. Soot assessment for the baseline condition (O2 = 15%, ramb = 22:8 kg=m3): (a) soot mass evolution in time and (b) soot fraction volume location and concentration at t = 4 ms.
Lucchini et al. 9
times and LOL values. Tuning of the Leung-Lindstedt and Jones (LLJ) model was carried out for the baseline condition including also the contribution of O and OH to soot oxidation.41,42Figure 16(a) shows the cumula- tive soot mass within the optical window for the base- line condition (O2=15%, ramb=22:8 kg=m3). The onset of soot production is well predicted, but the slope of the curve during the inception interval is lower in the CFD model. The soot mass peak is underestimated in magnitude, but the time when it occurs is fairly cap- tured. The steady-state value is correctly estimated, as the time and slope of the curve during the complete oxidation of soot particles. Figure 16(b) shows that the soot volume fraction distribution is rather well described by the ADF model. Such results are not only due to a correct selection of the LLJ model constants, but also due to a correct estimation of the flame LOL.
Figure 17 reports the evolution of the soot mass as function of time for the three different ambient tem- peratures Tamb at 15% ambient oxygen concentration. The model is capable to reproduce the increase in soot mass with the ambient temperature. However, com- puted steady-state mass values are underestimated for the 850K condition while they are overestimated when ambient Tamb is increased to 1100K. Such trend is not completely consistent with the prediction of the LOL which is illustrated in Figure 9.
A possible reason for such discrepancy can be mainly related to the temperature dependency of the model constants describing the soot formation. Such observa- tion is confirmed by the results illustrated in Figure 18, where the soot mass evolution is reported at 900K ambient temperature for three different tested oxygen concentrations. Computed results are in rather good agreement with experimental data. In particular, the highest amount of soot was formed for the 15% ambi- ent oxygen concentration: under such condition, the flame stabilizes at a relatively short distance from the nozzle and there is a reduced amount of O2 available
for soot oxidation. Similar amount of soot mass was found for the other two conditions. In the O2=21% condition, an increase in oxygen concentration enhances the soot oxidation rate. Reduction of O2 to 13% decreases the soot formation rate since the flame stabilizes at a higher distance from the nozzle compared to the other two conditions.
Conclusion
Two different Diesel combustion models which both use offline chemistry tabulation, namely the ADF and the FGM, were compared and assessed in terms of glo- bal heat release rate indicators and flame structure by simulating the ECN Spray A experiment in different conditions, including the variation of ambient tempera- ture and oxygen concentration. The main difference in the theoretical assumptions beyond these models is in the way reaction rates are estimated during the table generation process: in ADF they are based on homoge- neous auto-ignition calculations while in FGM unsteady counter-flow diffusion flames are solved. The latter is obviously much more demanding in terms of CPU time such that in the conventional model formu- lation a single strain rate is considered assuming that ID is not affected by it in a relatively large range of val- ues. In the ADF tabulation, instead the stoichiometric scalar dissipation rate xst and the variance mixture fraction Z002 are included to account for turbulence– chemistry interaction.
Models were tested considering n-dodecane sprays under constant-volume combustion conditions and considering variation of ambient temperature and oxy- gen concentration. It was observed how in general igni- tion occurs in rich region and then the reactions move toward stoichiometric zones. ADF results are clearly influenced by the turbulence–chemistry interaction: xst, Z002 and the reactivity play a fundamental role. The study of the main combustion tracers has given
Figure 17. Soot assessment as a function of ambient temperature (line = experimental data; squares = ADF).
Figure 18. Soot assessment as a function of oxygen concentration.
10 International J of Engine Research 00(0)
significant information about IDs, LOLs and flame structure. Agreement with experimental data was gen- erally good for both models, apart for the prediction of the LOL at low temperature given by the ADF model, probably due to an excessive diffusion of the progress variable, and for the prediction of the ID under the same condition for the FGM approach. To improve this aspect, a novel FGM implementation, 5D-FGM, which also include strain rate effects, was proposed: ID was better estimated since chemical reactions occur in presence of low strain rates for such low reactivity condition.
Finally, a preliminary assessment of the soot distri- bution given by the ADF model was proposed: qualita- tive trends agreed with the observed data, but further investigations are required to improve the quantitative estimations of soot mass, especially when varying the ambient temperature.
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publica- tion of this article.
Funding
The author(s) received no financial support for the research, authorship and/or publication of this article.
ORCID iD
References
1. Ho RJ, Yusoff MZ and Palanisamy K. Trend and future
of diesel engine: development of high efficiency and low
emission low temperature combustion diesel engine. IOP
C Ser Earth Env 2013; 16: 012112. 2. Johnson TV. Review of diesel emissions and control.
SAE Int J Fuel Lubr 2010; 3(1): 16–29. 3. Ali R. Effect of diesel emissions on human health: a
review. Int J Appl Eng Res 2011; 6(11): 1333–1342. 4. Karavalakis G, Poulopoulos S and Zervas E. Impact of
diesel fuels on the emissions of non-regulated pollutants.
Fuel 2012; 102: 85–91. 5. Angrill O, Geitlinger H, Streibel T, Suntz R and Bock-
horn H. Influence of exhaust gas recirculation on soot
formation in diffusion flames. P Combust Inst 2000;
28(2): 2643–2649. 6. Skeen S, Manin J and Pickett LM. Visualization of igni-
tion processes in high-pressure sprays with multiple injec-
tions of n-dodecane. SAE Int J Engine 2015; 8(2): 696–
715. 7. Yang L, Franco V, Campestrini A, German J and Mock
P. Nox control technologies for Euro 6 diesel passenger
cars (white paper). Berlin: International Council on
Clean Transportation (ICCT), 2015, pp.1–22. 8. Lapuerta M, Ramos A, Fernandez-Rodriguez D and
Gonzalez-Garca I. High-pressure versus low-pressure
exhaust gas recirculation in a Euro 6 diesel engine with
lean-NOx trap: effectiveness to reduce NOx emissions.
Int J Engine Res 2019; 20(1): 155–163. 9. Johnson TV. SAE 2009 world congress. Platin Met Rev
2010; 54(1): 37–43. 10. Guan B, Zhan R, Lin H and Huang Z. Review of state
of the art technologies of selective catalytic reduction of
NOx from diesel engine exhaust. Appl Therm Eng 2014;
66(1–2): 395–414. 11. Williams M and Minjares R. A technical summary of Euro
6/VI vehicle emission standards, vol. 10. Washington, DC:
International Council on Clean Transportation (ICCT),
2017. 12. Hosseini SM and Ahmadi R. Performance and emissions
characteristics in the combustion of co-fuel diesel-hydrogen
in a heavy duty engine. Appl Energ 2017; 205: 911–925. 13. Sinay J, Puskar M and Kopas M. Reduction of the NOx
emissions in vehicle diesel engine in order to fulfill future
rules concerning emissions released into air. Sci Total
Environ 2018; 624: 1421–1428. 14. Sanjid A, Masjuki HH, Kalam MA, Ashrafur Rahman
SM, Abedin MJ and Palash SM. Production of palm and
jatropha based biodiesel and investigation of palm-
jatropha combined blend properties, performance,
exhaust emission and noise in an unmodified diesel
engine. J Clean Prod 2014; 65: 295–303. 15. Rochussen J and Kirchen P. Characterization of reaction
zone growth in an optically accessible heavy-duty diesel/
methane dual-fuel engine. Int J Engine Res 2019; 20(5):
483–500. 16. Engine Combustion Network (ECN) website, https://
ecn.sandia.gov/ 17. Aubagnac-Karkar D, Michel J-B, Colin O and Darabiha
N. Combustion and soot modelling of a high-pressure
and high-temperature Dodecane spray. Int J Engine Res
2018; 19(4): 434–448. 18. Lucchini T, D’Errico G, Onorati A, Frassoldati A, Stagni
A and Hardy G. Modeling non-premixed combustion
using tabulated kinetics and different fame structure
assumptions. SAE Int J Engine 2017; 10(2): 593–607.
19. Lucchini T, D’Errico G, Cerri T, Onorati A and Hardy
G. Experimental validation of combustion models for
diesel engines based on tabulated kinetics in a wide range
of operating conditions. SAE technical paper 2017-24-
0029, 2017. 20. Desantes JM, Garca-Oliver JM, Novella R and Perez-
Sanchez EJ. Application of an unsteady flamelet model in
a RANS framework for spray A simulation. Appl Therm
Eng 2017; 117: 50–64. 21. Payri F, Novella R, Pastor JM and Perez-Sanchez EJ.
Evaluation of the approximated diffusion flamelet con-
cept using fuels with different chemical complexity. Appl
Math Model 2017; 49: 354–374. 22. D’Errico G, Lucchini T, Contino F, Jangi M and Bai X-
S. Comparison of well-mixed and multiple representative
interactive flamelet approaches for diesel spray combus-
tion modelling. Combust Theor Model 2014; 18(1): 65–88. 23. Pei Y, Hawkes ER and Kook S. Transported probability
density function modelling of the vapour phase of an n-
heptane jet at diesel engine conditions. P Combust Inst
2013; 34(2): 3039–3047. 24. Barths H, Hasse C and Peters N. Computational fluid
dynamics modelling of non-premixed combustion in
direct injection diesel engines. Int J Engine Res 2000;
1(3): 249–267.
combustion. Booval, QLD, Australia: R.T. Edwards, Inc., 2005.
26. Michel J-B, Colin O and Veynante D. Modeling ignition and chemical structure of partially premixed turbulent flames using tabulated chemistry. Combust Flame 2008; 152: 80–99.
27. Wehrfritz A, Kaario O, Vuorinen V and Somers B. Large Eddy Simulation of n-dodecane spray flames using Fla- melet Generated Manifolds. Combust Flame 2016; 167: 113–131.
28. Verhoeven LM, Ramaekers WJS, Van Oijen JA and de Goey LPH. Modeling non-premixed laminar co-flow flames using flamelet-generated manifolds. Combust
Flame 2012; 159(1): 230–241. 29. Maghbouli A, Akkurt B, Lucchini T, D’Errico G, Deen
NG and Somers B. Modelling compression ignition
engines by incorporation of the flamelet generated mani- folds combustion closure. Combust Theor Model. Epub ahead of print 24 October 2018. DOI: 10.1080/ 13647830.2018.1537522.
30. Dec JE. A conceptual model of DI diesel combustion based on laser-sheet imaging. SAE technical paper
970873, 1997. 31. Pickett LM and Siebers DL. Non-sooting, low flame tem-
perature mixing-controlled DI diesel combustion. SAE technical paper 2004-01-1399, 2004.
32. Peters N. Laminar diffusion flamelet models in non- premixed turbulent combustion. Prog Energ Combust
1984; 10(3): 319–339. 33. Van Oijen JA. Flamelet-generated manifolds: development
and application to premixed laminar flames. Eindhoven: Technische Universiteit Eindhoven, 2002.
34. Maes N, Dam N, Somers B, Lucchini T, D’Errico G and
Hardy G. Heavy-duty diesel engine spray combustion
processes: experiments and numerical simulations. SAE
technical paper 2018-01-1689, 2018. 35. CMT virtual injection rate generator, https://
www.cmt.upv.es/ECN03.aspx 36. Yao T, Pei Y, Zhong BJ, Som S and Lu T. A hybrid
mechanism for n-dodecane combustion with optimized
low-temperature chemistry. In: Proceedings of the 9th US
National combustion meeting, Cincinnati, OH, 17–20 May
2015, pp.1–10. 37. Leung KM, Lindstedt RP and Jones WP. A simplified
reaction mechanism for soot formation in nonpremixed
flames. Combust Flame 1991; 87(3–4): 289–305. 38. Bekdemir C, Somers LMT and de Goey LPH. Modeling
diesel engine combustion using pressure dependent Fla-
melet Generated Manifolds. P Combust Inst 2011; 33:
2887–2894. 39. Eguz U, Ayyapureddi S, Bekdemir C, Somers B and de
Goey LPH. Modeling fuel spray auto-ignition using the
FGM approach: effect of tabulation method. SAE tech-
nical paper 2012-01-0157, 2012. 40. Manin J, Pickett LM and Skeen SA. Two-color diffused
back-illumination imaging as a diagnostic for time-
resolved soot measurements in reacting sprays. SAE Int J
Engine 2013; 6(4): 1908–1921. 41. Brookes SJ and Moss JB. Predictions of soot and thermal
radiation properties in confined turbulent jet diffusion
flames. Combust Flame 1999; 116(4): 486–503. 42. Guo H, Liu F and Smallwood GJ. Soot and NO forma-
tion in counterflow ethylene/oxygen/nitrogen diffusion
flames. Combust Theor Model 2004; 8(3): 475–489.
12 International J of Engine Research 00(0)