Numerical investigation of droplet evaporation modeling in
combustion environment
Citation for published version (APA):
Sacomano Filho, F. L., Krieger Filho, G. C., van Oijen, J. A., & Sadiki, A. (2018). Numerical investigation of droplet evaporation modeling in combustion environment. Paper presented at 14th International Conference on Liquid Atomization and Spray Systems (ICLASS 2018), Chicago, United States.
Document status and date: Published: 01/01/2018
Document Version:
Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)
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: openaccess@tue.nl
ICLASS 2018, 14 Triennial International Conference on Liquid Atomization and Spray Systems, Chicago, IL, USA, July 22-26, 2018
Numerical investigation of droplet evaporation modeling in combustion environment
F. L. Sacomano Filho
∗a, G. C. Krieger Filho
a, J. A. van Oijen
b, A. Sadiki
ca - Department of Mechanical Engineering, University of São Paulo, Brazil
b - Department of Mechanical Engineering, Technische Universiteit Eindhoven, Netherlands
c - Institut for Energy and Power Plant Technology, Technische Universität Darmstadt,
Germany
fernando.sacomano@usp.br, guenther@usp.br, J.A.v.Oijen@tue.nl and
sadiki@ekt.tu-darmstadt.de
Abstract
Two of the most employed droplet evaporation models in CFD (Computational Fluid Dynamics) applications and their subsequent impact on combustion processes are analyzed in a numerical context. The study comprehends a systematic investigation of both models and different procedures used to address thermo-chemical properties. Ini-tially, investigations are addressed in a single droplet framework. Herein, available experimental data give support to the corresponding discussions. In a second part, both selected models and the simplification of the surrounding gas mixture by air are investigated in the context of flames propagating in droplets mists. A detailed chemistry model is used to represent the combustion of ethanol in air. Results aim to help the choice of methods employed for droplet evaporation modeling in a general context. The methodology adopted in our analyses allows the assess-ment of each simplification and converges to an optimal combination of the studied methods.
Introduction
Droplet evaporation modeling is a common issue in CFD (Computational Fluid Dynamics) investigations of spray combustion processes [3, 6, 7, 13, 20]. The large disparity of scales involving heat and mass exchange on droplets and the others related to the flow dynamics makes the evaporation a sub grid phenomenon. Therefore, the computation of these exchange mechanisms is a matter of modeling. A great part of the available droplet evaporation models in the literature [1, 10, 19, 20] have been developed focusing on spray combustion processes. However, the validation of such models is typically performed in non-reacting or environments with strongly simplified thermo-chemical properties. It is the purpose of this work to investigate the influence of simplifications in the evaporation modeling and their subsequent impact on combustion processes. Therefore, a systematic study about different procedures used to address thermo-chemical properties in two of the most employed evaporation models in CFD (Computational Fluid Dynamics) applications is conducted in a numerical context.
The structure of this manuscript is divided in two parts. Initially, single droplet analyses are performed in a non-reacting atmospheres, in which experimental data is available. Various approaches used to compute the vapor liquid equilibrium (VLE) are investigated. In a second part, the different modeling strategies are compared in the framework of one-dimensional flames propagating in droplets mists of ethanol including a detailed description of the chemistry. Different methods used to derive thermo-chemical properties for the evaporation modeling are also tested. Namely, the actual representation of the gas mixture and its simplification as pure air at the same temperature and pressure.
Numerical Methods
An Eulerian-Lagrangian approach is applied to numerically describe flames propagating in droplets mists, whereas single droplet computations are conducted in an isolated scheme. In this last scenario, the surrounding gas properties are maintained constant at (when not explicitly specified in the text) experimentally defined conditions. Yet for the reactive cases, a full inter-phase two-way coupling is considered. In both cases, computations are performed with the CFD code CHEM1D [21], which has been extended with a Lagrangian module in [13] to include the effects of the liquid phase.
In order to isolate the diverse aspects of the spray combustion, the simulations presented in this manuscript mimic unstrained laminar flames propagating in mono-dispersed, homogeneous, and isotropic droplet mists. Sim-ilar to Neophytou and Mastorakos [11], the following simplifications and approximations are assumed: (a) the multi-dimensional aspects of the droplets dispersion does not modify the flame surface, (b) mists are diluted,
14thICLASS 2018 Numerical investigation of droplet evaporation modeling in combustion environment
thereby no droplets interaction are accounted for, (c) no micro-mixing model is included, so that all the mass evaporated from a drop fills instantaneously the host control volume∗. Furthermore, parcels are tracked instead of real drops. In this way, a parcel may represent more or even less than one real drop. The role played by them reduces to a dispersed source of fuel which follows the physical models described in the two following sections. By setting a high value of parcels, it is possible to guarantee that the distribution of droplets is uniform within the domain. In this sense, transitory effects (oscillations) caused by the discontinuous distribution of fuel can be avoided, attending the statistically steady and one-dimensional representation of isotropic mists.
Gas Phase
The description of the carrier phase follows a variable-density low Mach number formulation. According to the strategy presented by Somers [21], the set of equations used to compute steady freely propagating flat flames in CHEM1D is ∂ ˙m ∂s = S L vapor, (1) ∂( ˙mYi) ∂s − ∂ ∂s λ Leicp ∂Yi ∂s = ˙ωi+ δikSvaporL , and (2) ∂( ˙mh) ∂s − ∂ ∂s λ cp ∂h ∂s = ∂ ∂s λ cp Ns X i=1 1 Lei − 1 hi ∂Yi ∂s ! + ShL. (3)
Equation 1 ensures the mass conservation of the coupled system, where ˙m = ρu is the mixture mass flux, ρ the density, u the gas velocity, s the spatial coordinate, and SvaporL the source term of vapor. The conservation
of chemical species is described by Eq. 2. Herein, Yiis the mass fraction of the species i ∈ [1, Ns− 1], λ the
thermal conductivity, cpthe isobaric specific sensible heat, Lei the Lewis number for species i, ˙ωi the reaction
rate for species i, and δik the Kronecker delta. The subscript k in Eq. 2 refers to the vapor species. The last
equation of this set is associated to the conservation of energy, which is expressed in terms of the absolute enthalpy h. The absolute enthalpy of each transported species is represented by hi, while the coupling term between phases
is denoted by ShL. For details about the coupling source terms, the reader is referred to [13, 16].
To address the combustion reactions in a detailed chemistry context, the chemical mechanism proposed by Marinov [9] is employed. It represents the oxidation of ethanol in air by means of 57 species and 379 intermediate reactions.
Liquid Phase
In the one-dimensional Lagrangian framework, the tracking of a parcel is essentially described by two ordinary differential equations (ODE) (e.g. Sirignano [20])
dxp dt = up, and dup dt = 3 4 CD dp ρ ρp |u − up|(u − up) (4)
for the parcel position and acceleration, respectively. In the present context, drag is the unique force acting on a droplet. For both equations, quantities labeled with the subscript p are associated with droplet parcels. Specifically, xp corresponds to the droplet position, and dp is the diameter. To compute the drag coefficient CD the model
proposed by Yuen and Chen [23] is adopted.
Heat and mass exchanges are respectively described by dTp dt = f2Nu 3Pr θ1 τp (T − Tp) + LV cl m˙ p mp , (5) dmp dt = − Sh 3Sc mp τp HM, (6)
14 ICLASS 2018 Numerical investigation of droplet evaporation modeling in combustion environment
with T the temperature, Nu the Nusselt number, f2a correction factor due to evaporation (see Table 1), Pr the
Prandtl number, LV the heat of vaporization, θ1is a ratio of specific sensible heat (see Table 1), cl the specific
sensible heat of the liquid, τp = ρpd2p/18µ expresses the particle relaxation time and ˙mp= dmp/dt. In Eq. 6, Sh
is the Sherwood number, Sc the gas Schmidt number†, and HM represents the specific driving potential for mass
transfer (see Table 1). Observe that the heat transfer by radiation is not considered.
The structure of the heat and mass exchange equations proposed by Miller et al. [10] (i.e. Eqs. 5 and 6) is quite general and allows for the computation of the evaporation process with many modeling approaches. Two of them are selected for the present investigations. One is the infinite liquid conductivity version of the non-equilibrium evaporation model of Miller et al. [10], which is denoted hereafter as M7. The other is the Abramzon and Sirignano model (see [1]), which is identified by M2 throughout this manuscript. According to the structure of Eqs. 5 and 6 both models differ by the form which f2, HM, and θ1are computed. Table 1 specifies each one of these quantities
for both models. In Table 1, β is the non-dimensional evaporation parameter, cp the specific sensible heat at
Table 1. Specific variables of the selected models
Model f2 HM θ1 M2 − ˙mp mpBT0 3τpPr Nu ln1 + BM,eq cp,V cl M7 β eβ− 1 ln[1 + BM,neq] cp,G cl
Table 2. Used references for gas properties
Property Air N2
Binary diffusion coef. of vapor in gas - Dij [4] [4] Specific sensible heat - cp [8] [4]
Thermal conductivity - λ [22] [4]
Dynamic viscosity - µ [22] [4]
constant pressure, BT0 and BM denote the Spalding transfer numbers for energy and mass, respectively. Subscripts G andV correspond to surrounding gas properties and vapor properties, whileeq andneqto properties evaluated
with the assumption of phase equilibrium and considering effects of non-equilibrium, respectively. It is discussed in the next section that the surrounding gas is usually simplified as air. In this situation, air properties are obtained form the databases listed in Table 2. It is important to highlight that, gas density is obtained by the ideal gas law. A variable that receives more attention here is the vapor pressure at the droplet surface. With this quantity, the mass fraction of vapor on the droplet surface is computed, which is consequently used to estimate BM. Details of each
one of the variables presented in Table 1 can be found in [10].
Results and Discussion
Results are presented in two parts. In a first one, the relevance of different evaporation modeling features is assessed in a single droplet setup. Yet, the influence of evaporation models and the simplification of the surrounding mixture as pure air is evaluated in a second part.
Single droplet evaporation analyses
The decay of d2palong time presented in Fig. 1 illustrates the performance of both selected models for different
operating conditions. Herein, the experimental data obtained by Saharin et al. [18] are used as a benchmark. They correspond to diameter measurements sampled for suspended droplets in N2quiescent atmospheres at four
different operating conditions, which are summarized in Table 3. Both models can reasonably well describe the variations in initial droplet diameter and surrounding gas temperature. Invariably to all tested conditions, model M2 approaches better to the experimental data. Considering the last stage of the evaporation process, a variation on evaporation rates can be clearly identified in all experimental curves. Such a change is supposed to be originated by the multi-component liquid solution. The used anhydrous ethanol has a composition of 99.5% of ethanol and 0.5% water. It is important to highlight that such a mixture is an azeotrope, i.e. cannot be separated by distillation (see for instance [20]). Studies performed by Saharin [17] shows that by increasing the amount of water in the fuel the inflexion of d2pcurves becomes more evident.
†The non-dimensional numbers Pr and Sc are explicitly computed at each time integration of the evaporation equations based on material
14thICLASS 2018 Numerical investigation of droplet evaporation modeling in combustion environment 0 0.2 0.4 0.6 0.8 1 0 50 100 150 200 250 300 d 2/d p,0 2 [-] time [s] exp - case 1 exp - case 2 exp - case 3 exp - case 4 M2 - case 1 M2 - case 2 M2 - case 3 M2 - case 4 M7 - case 1 M7 - case 2 M7 - case 3 M7 - case 4
Figure 1. Performance of both selected models (M2 and M7) for ethanol droplets at different initial conditions
.
Table 3. Operating conditions for ethanol single droplet evaporation
Case T [K] dp,0[µm]
1 293 651
2 353 628
3 473 609
4 673 430
Simulations presented in Fig. 3 have been conducted with the vapor pressure model based on the Wagner equation (see [12]). As shown in Figs. 2 and 3 this models shows a better performance for a broad range of gas temperatures. During the development of this study, attention has been given to the relevance of the well prediction of the vapor pressure at the droplet surface. Typically, the vapor pressure at the droplet surface is used to estimate the mass transfer number (BM - see discussion in the description of liquid phase modeling) in various
evaporation models [10, 19, 20]. The different calculation methods for the vapor pressure are denoted here as VLE (vapor-liquid-equilibrium) models, which are listed in Table 4. Different procedures are found in the literature to compute this quantity. Herein, five of them (see Table 4) are chosen and evaluated. The simulations presented for this analysis have been performed with the model M2, since the Clausius-Clapeyron equation is intrinsically included in the model proposed by Miller et al. [10] (see [2]). Figures 2 and 3 show the behavior of different vapor
Table 4. Description of VLE labels.
Model Label
Clausius-Clapeyron as in [10] VLE1 Clausius-Clapeyron based on Pc(see [12]) VLE2 Wagner equation (see [12]) VLE3 Antoine equation (see [12]) VLE4 Antoine equation from NIST Web-book VLE5
pressure models for the two most extreme operating conditions listed in Table 3. Differences between models are evident for the low temperature scenario, while all of them behave similarly for the high temperature case. Specific to Fig. 2, Wagner and Antoine equation models behave quite similar since these are based on experimental data fitting. As mentioned by Poling et al. [12], Clausius-Clapeyron methods are suppose to introduce considerable errors on vapor pressure calculations for temperatures far from the one used as reference. Herein, the boiling point temperature of ethanol at 1.0 atm (351.5 K) is used for VLE 1 and VLE 2. Considering that the gas temperature is much higher than the boiling point temperature, it is not surprising that both Clausius-Clapeyron methods are not far from the other three VLE models in Fig. 3. Therefore, care must be taken when using this method to estimate the mass transfer number BM.
14 ICLASS 2018 Numerical investigation of droplet evaporation modeling in combustion environment 0 0.2 0.4 0.6 0.8 1 0 50 100 150 200 250 300 d 2 /d 0 2 [-] time [s] dp,0=651 µm | T=293 K exp VLE 1 VLE 2 VLE 3 VLE 4 VLE 5
Figure 2. VLE analysis at low temperature.
0 0.2 0.4 0.6 0.8 1 0 2 4 6 8 10 12 14 d 2 /d 0 2 [-] time [s] dp,0=430 µm | T=673 K exp VLE 1 VLE 2 VLE 3 VLE 4 VLE 5
Figure 3. VLE analysis at high temperature
The assumption that Sc = Pr which implies Le = 1 is investigated here. This is sometimes adopted to sim-plify properties calculations (see e.g. [10]) and modifies the relationship between heat and mass transfer numbers (BT and BM) and between Nu and Sh as well. Hereafter, analyses of ethanol evaporation are reserved to the case
4 of Table 3 since the higher gas temperature represents better the atmospheres found in reacting cases, which is our final object of study. Figure 4 shows that Le = 1 assumption does not strongly interfere with the evaporation modeling. This assumption slightly increase the evaporation rate for both models. Effects are more pronounced for forced convection cases extracted from [10]. Figures 5 and 6 respectively show for hexane at moderate gas tem-perature and high convection and decane at high temtem-perature and moderate convection‡ that, by assuming Le = 1 higher evaporation rates are obtained. This outcome indicates that influences are more evident for Nu and Sh than for the relationship between BT and BM. Regarding the performance of models M2 and M7 in forced convection
scenarios, model M2 better approaches the experimental data in both cases.
0 0.2 0.4 0.6 0.8 1 0 2 4 6 8 10 12 14 d 2 /d 0 2 [-] time [s] dp,0=430 µm | T=673 K exp M2 - Le≠1 M7 - Le≠1 M2 - Le=1 M7 - Le=1
Figure 4. Influence of Le for ethanol
0 1 2 3 0 2 4 6 8 10 12 d 2 [mm 2 ] time [s] dp,0=1.76 mm | T=437 K | Re0=110 exp M2 - Le≠1 M2 - Le=1 M7 - Le≠1 M7 - Le=1
Figure 5. Influence of Le for hexane The last part of this section is dedicated to the evaluation of a common simplification applied in simulations of turbulent spray flames. Commonly, surrounding gas properties are simplified as air properties at the same tem-perature of the mixture (e.g. [5–7, 14, 15]). This procedure is many times unavoidable since information about all participating species should be known to recover the actual mixture composition. Because of necessary simplifi-cations of the chemistry like in reduced mechanisms or due to storage reasons as in tabulated chemistry methods this information is usually not available during the computational time. In order to evaluate this simplification, properties listed in Table 2 are extracted from thermal and transport data provided in Marinov’s mechanism [9].
14thICLASS 2018 Numerical investigation of droplet evaporation modeling in combustion environment
Both property computation methods (i.e. from Table 2 and those using Marinov’s mechanism) are validated before advanced simulations. Hence, computations of d2pdecay assuming a mixture of pure air are also presented in Fig. 7. Results clearly demonstrate that the usage of properties listed in Table 2 (Fig. 7: M2 air data) and the ones based on data provided by Marinov’s mechanism (Fig. 7: M2 air code) match when assuming pure air as surrounding gas. Observe that a case computed with N2is included as reference (Fig. 7: M2 N2data) and simulations are
only conducted with model M2 to keep the analysis concise. Bearing in mind that a great part of air is N2, it is
not surprising that no significant changes occur when N2is substituted by air. These results demonstrate that the
computations base on data provided by Marinov’s mechanism are correctly performed, which allow the usage of this method for further investigations with other mixture compositions.
0 1 2 3 4 0 1 2 3 4 5 6 7 d 2 [mm 2 ] time [s] dp,0=2.0 mm | T=1000 K | Re0=17 exp M2 - Le≠1 M2 - Le=1 M7 - Le≠1 M7 - Le=1
Figure 6. Influence of Le for decane
0 0.2 0.4 0.6 0.8 1 0 2 4 6 8 10 12 14 d 2 /d 0 2 [-] time [s] dp,0=430 µm | T=673 K exp M2 N2 data M2 air data M2 air code M2 prod code
Figure 7. Analysis of gas composition To evaluate the influence of the detailed mixture composition in a single-droplet setup, N2is substituted by a
mixture of bunt products (quite close to the chemical equilibrium) obtained from an adiabatic freely propagating flame at stoichiometric conditions. The mixture temperature is the same as for case 4 of Table 3 to make both cases comparable. Results are included in Fig. 7 and show that the evaporation rate is increased by approximately 5%. This gives indication that assuming actual mixture properties to compute evaporation in combustion cases may influence the flame characteristics. To analyze it, simulations of freely propagating flames in droplets mists are addressed in the next part.
Influence of the evaporation modeling on flames propagating in droplets mists
The flame propagation speed is a simple and useful variable that can indicate the role played by the evapo-ration modeling and the simplification of the gas mixture in combustion processes. Since some turbulent spray combustion models do consider the laminar flame speed as an input [e.g. the Artificially Thickened Flame (ATF) model [14, 15]], the behavior of different models and simplifications investigated here are expected to scale at least in turbulent combustion of lean mixtures and those close to stoichiometry.
Figure 8 shows the behavior of the spray flame speed sl,s for mists with different droplet initial diameters
dp,0and a stoichiometric overall equivalence ratio φover§. For all flames simulated here, droplets are injected at
the same position (i.e. 3.0 cm upstream of the reaction zone). Both models M2 and M7 are compared together with the two different representations of the mixture, i.e. actual mixture composition and its simplification as air. This figure exhibits that the choice of evaporation modeling clearly interferes with the flame behavior. Model M7 delivers flames approximately 6% faster than those computed with model M2. Similar deviation is also observed for different values φoverwhen keeping dp,0constant as presented in Fig. 9. M7 flames are around 4.5% and 5.5%
faster than M2 flames at the leanest and the richest computed mixture compositions, respectively. Hence, the richer the overall mixture, the more pronounced is the impact of the evaporation modeling on the combustion process.
With respect to the simplification of the detailed mixture composition by air, differences do exist in both Figs. 8 and 9 but are not so pronounced as deviations observed between both evaporation models. Model M2 demonstrates to be more sensitive to this simplifications as M7. Deviations are also more pronounced for richer mixtures than leaner ones, as seen in Fig. 9. Their maximum values are respectively 2.4% and 1.3% for models M2 and M7
§φ
14 ICLASS 2018 Numerical investigation of droplet evaporation modeling in combustion environment 10 15 20 25 30 20 30 40 50 60 70 80 sl,s [cm/s] dp,0 [µm] φover=1.0 M2 air M2 mix M7 air M7 mix Figure 8. sl,sin function of dp,0 10 12 14 16 18 20 22 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 sl,s [cm/s] φover dp,0=50 [µm] M2 air M2 mix M7 air M7 mix
Figure 9. sl,sin function of φover
and are found for a mist of φover = 1.34 and dp,0 = 50µm. According to this evaluation, the simplification
does impact on the evaporation process but not significantly on lean cases. Influences increase in rich cases and are expected to be more evident beyond the calculated rich limits since droplets have higher exposure to different mixture compositions than air. Similar behavior is also expected if the injection distance to the flame is decreased.
Summary and Conclusions
Analyses of two droplet evaporation models have been conducted in single droplet environment and in flames propagating in homogeneous droplet mists. The study systematically evolves from non-reacting to reacting at-mospheres. Different procedures used to estimate the vapor pressure on droplet surface are evaluated in a single droplet context. Similarly, simplifications applied to the surrounding gas phase are assessed in the sequence. These include simplifications in the diffusion transport of the vapor (Le = 1), as well as in the detailed composition of the mixture by pure air. For the former simplification, tests are conducted for different fuels in quiescent and forced convection setups. The influence of the two selected evaporation models and the simplification of the detailed composition of the mixture by air are finally analyzed for flames propagating in droplets mists. The laminar flame speed is used to indicate the influence of the different models and procedures on combustion processes.
Along with the single droplet simulations the model denoted as M2 demonstrate to be more universal than the M7. It shows better performance for different operating conditions and liquid compositions as well. With respect to the different procedures used to address the vapor pressure, the Wagner equation (here labeled as VLE 3) and Antoine equations (VLE 4 and 5) agree quite well to each other. Considering that the Wagner equation covers a broad range of operating conditions (see Poling et al. [12]), this is therefore preferred here. The analysis of the unitary Lewis number assumption just confirm the expected (see for instance [20]). Namely, the non-unitary Le it is necessary to be considered otherwise wrong evaporation rates are computed. The last part of single droplet evaporation is dedicated to an artificial test about the influence of the detailed composition of the surrounding gas. Different evaporation rates could be identified, which motivates investigations in combustion processes. Numerical analyses of flames propagating in mists close the present study. It is noticed that the simplification of the detailed composition of the mixture by air does not influence the evolution of the flame speed for the investigated test cases as the evaporation model. Deviations between both models are clearly noticed for different overall mixture compositions and variations in initial droplets sizes. Together with the single-droplet investigations, these results show that care must be taken not only in the choice of a droplet evaporation model, but also in the simplifications and procedures adopted in their respective sub-models.
Acknowledgements
We acknowledge the financial support from São Paulo Research Foundation (FAPESP - grant # 2017/06815-7).
References
[1] B. Abramzon and W. A. Sirignano. Droplet vaporization model for spray combustion calculations. Int. J. Heat Mass Transf., 32(9):1605–1618, sep 1989.
14thICLASS 2018 Numerical investigation of droplet evaporation modeling in combustion environment
[2] J. Bellan and M. Summerfield. Theoretical examination of assumptions commonly used for the gas phase surrounding a burning droplet. Combust. Flame, 33:107–122, jan 1978.
[3] M. Chrigui, F. Sacomano, A. Sadiki, and A. R. Masri. Evaporation Modeling for Polydisperse Spray in Turbulent Flow. pages 55–77. 2014.
[4] I. V. Gnielinski. VDI-Wärmeatlas. VDI Buch. Springer Berlin Heidelberg, Berlin, Heidelberg, 2006. [5] Y. Hu, H. Olguin, and E. Gutheil. A spray flamelet/progress variable approach combined with a transported
joint PDF model for turbulent spray flames. Combust. Theory Model., 21(3):575–602, may 2017.
[6] P. Jenny, D. J. E. M. Roekaerts, and N. Beishuizen. Modeling of turbulent dilute spray combustion. Prog. Energy Combust. Sci., 38(6):846–887, dec 2012.
[7] E. Knudsen, Shashank, and H. Pitsch. Modeling partially premixed combustion behavior in multiphase LES. Combust. Flame, 162(1):159–180, jan 2015.
[8] E. W. Lemmon, R. T. Jacobsen, S. G. Penoncello, and D. G. Friend. Thermodynamic Properties of Air and Mixtures of Nitrogen, Argon, Oxygen from 60K to 2000K at Pressures to 2000MPa.pdf. J. Phys. Chem., 29(3):331, may 2000.
[9] N. Marinov. A detailed chemical kinetic model for high temperature ethanol oxidation. Int. J. Chem. Kinet., 31(3):183–220, 1999.
[10] R. S. Miller, K. Harstad, and J. Bellan. Evaluation of equlibrium and non-equlibrium evaporation models for many droplet gas liqud flow simulations. Int. J. Multiph. Flow, 24:1025–1055, 1998.
[11] A. Neophytou and E. Mastorakos. Simulations of laminar flame propagation in droplet mists. Combust. Flame, 156(8):1627–1640, aug 2009.
[12] B. Poling, J. M. Prausnitz, and J. P. O’Connell. The properties of gases and liquids. McGRAW-HILL, 5th edition, 2001.
[13] F. L. Sacomano Filho. Novel approach toward the consistent simulation of turbulent spray flames using tabulated chemistry. Phd thesis, Technische Universitaet Darmstadt, 2017.
[14] F. L. Sacomano Filho, J. Kadavelil, M. Staufer, A. Sadiki, and J. Janicka. Analysis of LES-based combustion models applied to an acetone turbulent spray flame. Combust. Sci. Technol., pages 1–14, apr 2018.
[15] F. L. Sacomano Filho, G. Kuenne, M. Chrigui, A. Sadiki, and J. Janicka. A consistent Artificially Thickened Flame approach for spray combustion using LES and the FGM chemistry reduction method: Validation in Lean Partially Pre-Vaporized flames. Combust. Flame, 184:68–89, 2017.
[16] F. L. Sacomano Filho, N. Speelman, J. A. van Oijen, L. P. H. de Goey, A. Sadiki, and J. Janicka. Numerical analyses of laminar flames propagating in droplets mists using detailed and tabulated chemistry (submitted). Combust. Theory Model., 2017.
[17] S. B. Saharin. Vaporization and Autoignition Characteristics of Ethanol and 1- propanol Droplets: Influence of Water. Phd thesis, University Burgundy, 2013.
[18] S. B. Saharin, B. Lefort, C. Morin, C. Chauveau, L. Le Moyne, and R. Kafafy. Vaporization characteristics of ethanol and 1-propanol droplets at high temperatures. At. Sprays, 22(3):207–226, 2012.
[19] S. S. Sazhin. Advanced models of fuel droplet heating and evaporation. Prog. Energy Combust. Sci., 32(2):162–214, 2006.
[20] W. A. Sirignano. Fluid Dynamics and Transport of Droplets and Sprays. Cambridge University Press, New York, NY, second edi edition, 2010.
[21] L. M. T. Somers. The simulation of flat flames with detailed and reduced chemical models. PhD thesis, Technische Universiteit Eindhoven, 1994.
[22] K. Stephan and A. Laesecke. The Thermal Conductivity of Fluid Air. J. Phys. Chem. Ref. Data, 14(1):227– 234, 1985.
[23] M. C. Yuen and L. W. Chen. On Drag of Evaporating Liquid Droplets. Combust. Sci. Technol., 14(4-6):147– 154, oct 1976.
