Gasoline-ethanol blend formulation to mimic laminar flame speed and auto-ignition quality in automotive engines

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Gasoline-ethanol blend formulation to mimic laminar flame speed and autoignition quality in automotive engines M. Del Pecchia⁎, V. Pessina⁎, F. Berni⁎, A. d'Adamo, S. Fontanesi⁎ Department of Engineering “Enzo Ferrari”, University of Modena and Reggio Emilia, Modena, Italy

ARTICLE INFO

ABSTRACT

Keywords: Laminar flame speed correlation Gasoline-ethanol blend ETRF surrogate 1D chemical kinetics simulation Engine-like conditions Internal combustion engine

Several environment agencies worldwide have identified biofuels as a viable solution to meet the stringent targets imposed by future regulations in terms of on-road transport emissions. In the last decades, petroleumbased gasoline has been increasingly blended with oxygenated fuels, mostly ethanol. Blending ethanol with gasoline has two major effects: an increase of the octane number, thus promoting new scenarios for engine efficiency optimization, and a potential reduction of soot emissions. 3D-CFD simulations represent a powerful tool to optimize the use of ethanol-gasoline blends in internal combustion engines. Since most of the combustion models implemented in 3D-CFD codes are based on the “flamelet assumption”, they require laminar flame speed as an input. Therefore, a thorough understanding of the gasoline-ethanol blend chemical behavior at engine-relevant conditions is crucial. While several laminar flame speed correlations are available in literature for both gasoline and pure ethanol at ambient conditions, none is available, to the extent of authors’ knowledge, to describe laminar flame speed of gasoline-ethanol blends (for different ethanol volume contents) at engine relevant conditions. For this reason, in the present work, laminar flame speed correlations based on 1D detailed chemical kinetics calculations are derived targeting typical fullload engine-like conditions, for different ethanol-gasoline blends. A methodology providing a surrogate able to match crucial properties of a fuel is presented at first and validated against available experimental data. Then, laminar flame speed correlations obtained from 1D chemical kinetics simulations are proposed for each fuel blend surrogate.

1. Introduction 1.1. Background As reported in the Official Journal of the European Union (EU) [1], threats related to climate change and global warming pushed the EU to impose very challenging targets in order to firmly decrease the anthropogenic greenhouse gas (GHG) emissions. The binding target of a minimum reduction equal to 40% by 2030 compared to 1990 was formally approved, while the long-term objective of zero net GHG emissions was set. According to the European parliament and council [2], the road transport was responsible for 22% of the EU GHG emissions in 2015. For this reason, a Renewable Energy Directive (REDII) [3] imposed that at least 10% of the energy used in transportation must be bio-based by 2020. The same directive forced fuel suppliers to a minimum market share equal to 6.8% of low-emissions and renewable fuels, including advanced biofuels, by 2030. In the light of this scenario, biofuels have increasingly gained the

⁎

attention of researchers in the automotive industry as a feasible solution to move towards cleaner powertrains, in compliance with the EU regulations. Ethanol is a renewable source of energy with lower production costs compared to other alcohols, such as n-butanol or methanol. Consequently, it is the main biofuel used in current production engines [4,5]. Several experimental studies investigated the effect of pure bioalcohols fuels on combustion characteristics in modern direct-injection spark-ignition engines (DISI). Irimescu et al. [6] compared stoichiometric butanol and ethanol mixtures in terms of combustion indicators and emissions in an optically accessible DISI research engine operated at full load. In order to analyze the impact of the injection strategy, three different start of injections (SOIs) were investigated. Despite ethanol exhibited advantages in terms of HC and CO emissions, a nonnegligible decrease of performance was found for deviations from the optimal injection phasing. Different studies [7–9] discouraged the use of pure ethanol with a standard engine hardware, as highly corrosive, thus detrimental for the injection system components. Conversely, other studies [10] reported that minor modifications to both hardware

Corresponding authors. E-mail addresses: [email protected] (M. Del Pecchia), [email protected] (V. Pessina).

https://doi.org/10.1016/j.fuel.2019.116741 Received 26 August 2019; Received in revised form 12 November 2019; Accepted 23 November 2019 0016-2361/ © 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: M. Del Pecchia, et al., Fuel, https://doi.org/10.1016/j.fuel.2019.116741

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Nomenclature GHG SOI ETRF DISI ECU OPs UHC LHV LFS ECFM-3Z CFD FFV AFR RON MON TFR ETRF PRF ULG95 H C O CO HC NOx s

Eth H/C

O/C Oxygen-to-Carbon Atomic Ratio ACA Average Carbon Atoms Number AHA Average Hydrogen Atoms Number AOA Average Oxygen Atoms Number RON MON AKI Anti-knock Index defined asAKI = 2 Sensitivity Sensitivity = RON-MON Φ Equivalence Ratio EGR Exhaust Gas Recirculation PIONA n-Paraffins, iso-Paraffins, Olefins, Naphthenes, Aromatics Tb Boiling Temperature Laminar Flame Speed of the Mixture sL xi Mole Fraction of species “i” RONi RON number of species “i” Hi Hydrogen atom number of species “i” Carbon atom number of species “i” Ci f f f f x = |x iso , x nhept , x tol | The Final TRF Composition Array Expressed in Molar Fractions ECs Engine Conditions E0-E5-E10-E20-E85 Gasoline-Ethanol surrogates with 0%, 5%, 10%, 20% and 85% of Ethanol respectively ICE Internal Combustion Engine WOT Wide Open Throttle p0 Reference Pressure (near-stoichiometric fitting) T0 Reference Temperature (near-stoichiometric fitting) Yres Diluent mass fraction Yres fres EGR scaling factor sLn,lean Normalized Laminar Flame Speed-Lean Branch sLn,rich Normalized Laminar Flame Speed-Rich Branch TPS Temperature Pressure Scaling Factor

Greenhouse Gas Start of Injection Ethanol Toluene Reference Fuel Direct Injection Spark Ignition Electronic Control Unit Operating Points Unburnt Hydrocarbons Lower Heating Value Laminar Flame Speed 3-Zone Extended Coherent Flame Model Computational Fluid Dynamics Flex-Fuel Vehicles Air-to-Fuel Stoichiometric Ratio Research Octane Number Motor Octane Number Toluene Reference Fuel Ethanol Toluene Reference Fuels Primary Reference Fuel Un-Leaded Gasoline-RON95 Hydrogen Atom Number Carbon Atom Number Oxygen Atom Number Carbon Monoxide Hydrocarbons Nitrogen Oxides Stoichiometric Air to Fuel Ratio Ethanol Content Hydrogen-to-Carbon Atomic Ratio

and electronic control unit (ECU) are needed for ethanol contents up to 30% by volume. Therefore, many researchers focused the attention on gasoline-ethanol blends as a feasible compromise to meet the upcoming regulations retaining the overall architecture of modern DISI units. Several experimental studies were carried out on standard SI engines, with various architectures and injection systems, at different operating points (OPs). Different gasoline-ethanol blends in terms of ethanol content were investigated. As a general trend, each experimental dataset confirmed the benefits in terms of CO and unburned hydrocarbons (UHC) reduction increasing the ethanol content in the blend [9–17]. The impact of gasoline-ethanol mixtures on NOx emissions still requires deeper investigations since no clear trends emerge from literature. In fact, while in [12,17] higher NOx emissions were registered increasing ethanol content, opposite results were found in [13,15]. Contradictory trends shown by the different experimental tests can be explained considering the high sensitivity exhibited by nitrogen oxides to the specific engine OP and ethanol content, as shown in [11,14]. With respect to soot emissions, several studies clearly demonstrated that soot mass can be strongly decreased if gasoline is blended with ethanol and the reduction is proportional to the ethanol content [18–21]. Despite gasoline-ethanol blends constitute a promising solution to lower the environmental impact of ICEs, further efforts in terms of control strategy optimization are mandatory in order to extend their benefits over a wider range of OPs. Although oxygenates are not naturally present in relevant percentage in crude oil, this molecular class is blended with gasoline [22] to improve combustion and thermodynamic efficiency. In fact, as shown by Di Iorio et al. [23], ethanol addition increases the octane number, thus allowing greater spark advances and/or higher compression ratios. This in turn confirms the reduced emissions in terms of carbon monoxide CO, unburned hydrocarbons (UHC) and particulate matter [24,25]. However, Sarathy et al. [26] pointed out that the addition of oxygenates produces a decrease in the (mass based) Lower Heating

Value (LHV) of the blend, as fuel oxygen atoms do not contribute to heat production; therefore the reduction of the LHV is proportional to the mass percentage of oxygen. 3D-CFD simulations represent a powerful tool to optimize the use of ethanol-gasoline blends in internal combustion engines. In fact, numerical analyses offer a deep comprehension of the phenomena responsible for the overall behavior of the engine observed by the experiments. As for combustion simulation in SI engines, flamelet combustion models are widely adopted in the scientific community. Among them, the ECFM-3Z [27] and the G-equation [28] are the most diffused ones. Despite the representation of the combustion process is based on different approaches, both models require the laminar flame speed (LFS) sL as an input to properly estimate the turbulent burn rate. In most of the CFD codes, sL is obtained using correlations derived via fitting of experimental data related to a wide range of conditions. For example, Metghalchi and Keck’s [29] or even Gülder’s correlations [30] are widely diffused for Isooctane. LFS is a characteristic of the mixture and it is directly influenced by the chemical nature of the fuel, hence the air-to-fuel-ratio (AFR) of the burning mixture. It is straightforward that dedicated correlations are needed to describe the flame propagation characteristics for a given fuel. Gülder in [31] and Broustail et al. in [32] derived LFS correlations for isooctane-ethanol blends by experiments at ambient pressure. Such correlations are useful to evaluate the impact of ethanol content on flame propagation, but they are not suitable to quantitatively predict LFS at engine-relevant conditions. In fact, a non-negligible error is introduced adopting the correlations out of their validity range. For this reason, Vancoillie et al. [33] derived correlations for ethanol and methanol LFS through chemistry-based calculations at several conditions, covering the entire operating range of alcohol-fueled spark-ignition engines. Similarly, Syed at al. [34] used numerical simulations to investigate gasoline-ethanol blend LFS for different pressures, temperatures and ethanol contents. A correlation was derived, to predict gasoline-ethanol blend LFS up to an ethanol 2

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liquid volume content equal to 85%, a pressure of 8 bar and a temperature of 600 K. As a result, most of the correlations available in literature are not suitable to reliably predict LFS of gasoline-ethanol blends, with a generic ethanol content, at chemical-thermal conditions of interest for SI engines. This is particularly true at full-load operations.

works by the authors [35,36], two different fuel surrogates, to be used with different chemical kinetics mechanisms, were chosen to compute LFS of a typical European gasoline. As reported in [47], refined fuels are complex mixtures of hydrocarbons that often vary based on both geographic location and season. Therefore, a statistically representative “average gasoline”, denoted as ULG 95 [37], is here considered for the formulation of gasoline-ethanol blends. The ULG 95 emulates an unleaded gasoline, according to the EN228 specification. A new methodology based on the work proposed by Pera et al. [37] is here used to formulate surrogates able to represent the main chemical-physical properties, the auto-ignition tendency and the flame propagating characteristics of the investigated fuel blends. Since no data on the ULG 95 LFS are available in literature, the dataset provided by Jerzembeck et al. in [45] for a generic commercial gasoline at 373 K and engine-like pressure conditions is considered for validation. Among the different chemical-physical properties of a fuel, the H/C ratio plays a fundamental role as able to remarkably affect LHV, density, stoichiometric AFR and boiling point [37]. A proper estimation of the stoichiometric AFR is crucial, as the LFS correlation requires the mixture equivalence ratio as an input parameter. A mismatch in terms of stoichiometric AFR between the actual fuel and the surrogate could potentially introduce a non-negligible error in the sL estimation. Finally, in order to have a surrogate which is representative of the autoignition characteristics, the Research Octane Number (RON ) is selected as a further constraint. The methodology proposed by Pera et al. [37] is suitable to generate a surrogate matching many different properties, such as H/C ratio, O/C ratio, RON and MON , solving a simple linear system. Unfortunately, no information on the surrogate capability to represent the laminar propagating characteristics of the fuel are provided. Therefore, an improved methodology to generate a surrogate able to match the LFS of the actual fuel is presented hereafter. In [46], Sileghem et al. demonstrated that a mixing rule applied to the components of a TRF surrogate can be used to predict the LFS of a commercial gasoline over a given temperature range. In [48], the same authors investigated the capability of simple mixing rules applied to ETRF components to predict LFS of gasoline-ethanol blends. The results proved that simple mixing rules considering only the ethanol-hydrocarbon blend composition are sufficiently accurate to predict sL . In literature, several mixing rules are available but, for the present study, only Le Chatelier’s one is considered. The latter was successfully used by Sarli et al. [49] to predict hydrogen-methane blend sL up to 10 bar and 400 K. Eq.1 reports Le Chatelier’s mixing rule, in which the LFS of a blend is estimated based on the mole fractions (xi ) and the LFSs (sL,i ) of the pure components.

1.2. Current analysis In the present work, Toluene Reference Fuel surrogates with addition of Ethanol (ETRF) are used, as suitable for representing gasolineethanol blends up to 85% of ethanol volume content. Such surrogates are formulated with a methodology developed by the authors and, to assess their validity, the combustion-relevant properties are compared with a wide literature dataset. In the following paragraph, a recently proposed methodology [35,36] to formulate LFS correlations is briefly recalled and results from chemistry-based 1D premixed flame simulations are presented for five selected engine-relevant blends (E0, E5, E10, E20, and E85). The methodology is used to derive correlations, providing an accurate estimation of LFS for gasoline-ethanol blends at typical full-load conditions of GDI engines, to be implemented in 3DCFD codes. 2. Methods 2.1. Gasoline-ethanol fuel surrogate formulation Detailed chemical kinetics calculations rely on the definition of a proper fuel model to give a quantitative description of specific fuel characteristics (e.g. ignition delay,sL , sooting tendency, etc.) at given thermodynamic and mixture quality conditions. A fuel model is defined when both a fuel surrogate and a chemical kinetics mechanism are defined. The first must be suitable to mimic a set of specific chemical and physical fuel properties relevant for combustion simulations (e.g. H/C ratio, O/C ratio, density, LHV , RON , MON , etc.). The second must include the main oxidation pathways to obtain combustion products from reactants. In order to formulate a surrogate, both the chemical and the physical properties of the targeted fuel are needed [37]. When referring to a generic gasoline-ethanol blend, the integer number following the capital letter “E” indicates the ethanol content by volume [38]. Once a gasoline-ethanol blend is considered, its ethanol content is uniquely defined (e.g. for E5 it is 5 vol%), while a suitable fuel surrogate is required for describing the properties of the base gasoline, that is a complex mixture of different hydrocarbon classes. Several studies showed that a mixture of isooctane, n-heptane and toluene, known as Toluene Reference Fuel (TRF ), can represent, with a high degree of accuracy, both auto-ignition delays and premixed flame propagating characteristics of a commercial gasoline such as a RON 87 or a RON95 [37,39,40–44]. In addition, Jerzembeck et al. [45] and Sileghem et al. [46] demonstrated that a TRF fuel surrogate approach is suitable to retain a good accuracy also for lean and rich mixtures. In previous Isooctane

80

1

sL,blend ( ) =

n xi i = 1 SL,i ( )

(1)

where n is the number of the blend components. As stated earlier, many other mixing rules (even more complex) are available in literature [48–50]. All can be used in the methodology proposed in the present work, if analytical equations are based on the pure component

n-Heptane

Toluene

Mole fraction [%mol]

70 60 50 40 30 20 10 0

1

2

3

4

5

6

7

8

9

10

Fig. 1. TRF surrogate compositions (x

11 m,corr

12 13 Solutions

14

15

16

17

18

19

20

) for the m conditions targeted in the present study. 3

21

22

23

24

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Table 1 Comparison in terms of properties between the actual gasoline and the formulated surrogate. (*) indicates the targeted properties.

ULG95 TRF

ACA [–]

AHA [–]

AOA [–]

RON* [–]

MON [–]

AKI [–]

Sensitivity [–]

H/C* [–]

O/C [–]

6.760 7.409

12.480 13.207

0.080 0.000

95 95.12

85 87.67

90 91.39

10 7.45

1.801 1.782

0.011 0.000

concentrations, as Eq. (1). Similarly, a mathematical formulation is needed to estimate the auto-ignition characteristics of a fuel blend. Despite several studies indicated complex mathematical formulations [51–55], Pera et al. [37] suggested a simpler linear approach proven to be effective for surrogates having an aromatic content (toluene) up to 35 vol%. For this reason, a linear weighted average approach, using molar fractions as weights, is used to quantitatively evaluate the auto-ignition characteristics in the present study. Such an approach, represented by Eq.2, is as accurate as more elaborate expressions such as the ones proposed in [41,52] and it is able to replicate the non-linear blending effects due to n-heptane and toluene [37]. As previously highlighted, it is recommended to properly represent the H/C ratio of the fuel and this can be done by means of Eq.3. Finally, a constraint must be imposed on the sum of the individual molar fractions, as reported in Eq. (4).

xiRONi i=1

H/Cblend =

n i=1 n i=1

xi = 1

42.801 42.714

749.00 752.57

E0

E5

E10

E20

E85

E100

Isooctane n-Heptane Toluene Ethanol

40.94 13.91 45.15 0.00

36.49 12.40 40.24 10.87

32.56 11.07 35.91 20.47

25.92 8.81 28.59 36.67

2.90 0.98 3.20 92.92

0.00 0.00 0.00 100.00

1 Ciso

( )

H Hnhept C blend

1 Cnhept

( )

1

H Htol C blend

Ctol

( )

H C blend

RONiso

RONnhept

RONtol

sL,nhept sL,tol

sL,iso sL,tol

sL,iso sL,nhept

1 xiso 0 xnhept = RON gas xtol sL,gas

(5)

sL,iso , sL,nhept and sL,tol are the LFS of isooctane, n-heptane and toluene respectively, estimated via chemical kinetics calculations at specific conditions. The ternary surrogate representative of the gasoline and obtained solving the linear system satisfies Eq. (1) on a single experimental condition. In order to extend the validity of the ternary surrogate for sL calculations over a wider range of experimental conditions, the entire dataset (consisting of 24 points) provided by Jerzembeck et al. [45] is targeted in the present study. Therefore, 24 different linear systems are solved, obtaining as many TRF surrogates. From a general standpoint, when a fuel blend using n components is used to target m LFS experimental conditions, the proposed methodology will produce m solutions in the n-dimensional component space. Despite the additional condition xi 0 , where xi is the mole fraction of the ith component, the linear system (Eq. (5)) is over-determined. m Therefore, the generic solution x must be intended as the one minimizing m the squares of the residuals. This means that x does not perfectly meet the

(2)

(3

n i= 1

ρ at 298 K [kg/m3]

[%mol]

Hiso

xiHi x iC i

14.254 14.416

LHV [MJ/kg]

Table 2 Formulated gasoline-ethanol blend surrogate compositions.

n

RONblend =

s [–]

(4)

Collecting Eqs. (1)–(4) for the estimation of the target blend properties (H/C , RON and sL ), a linear system is obtained. The latter is overdetermined as four equations are available for only three unknowns. Nonetheless, it can still be solved using a least-squares method. In particular, a non-negative linear least-squares solver is used, to ensure that the resulting single component concentrations of the blend are strictly non-negative. ¯ x¯ = b¯ can be written for a Therefore a linear system in the form A given gasoline as reported in Eq. (5), targeting the experimental LFS at a specific condition sL,gas = sL (p , T , , EGR ) , a research octane number RONgas and a mole-based hydrogen to carbon ratio H/Cgas .

m

constraints expressed by b . While a deviation from H/Cgas , RONgas and m sL,gas is acceptable, a further correction to the generic x solution must be undertaken if the constraint of total molar fraction equal to unity is not met. m Thus, the n components of x are scaled in proportion, according to the m,corr formulation reported in Eq. (6), to obtain a corrected solution x :

Fig. 2. LFS as a function of Φ at 373 K and four pressures (10, 15, 20 and 25 bar). Dots and solid black line represent experiments and Le Chatelier’s mixing rule, while green, blue, and dashed red lines depict Andrae, Creck and the average of 1D simulation results respectively. Error bars in the experiments stand for the measurement errors. 4

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Table 3 Formulated gasoline-ethanol blend surrogate properties.

E0 E5 E10 E20 E85 E100

x m,corr = i

Eth [%vol]

ACA [–]

AHA [–]

AOA [–]

RON* [–]

MON [–]

H/C* [–]

O/C [–]

0 5 10 20 85 100

7.409 6.822 6.302 5.426 2.383 2.000

13.207 12.424 11.732 10.564 6.510 6.000

0.000 0.109 0.205 0.367 0.929 1.000

95.12 96.52 97.75 99.84 107.09 108.0

87.67 87.92 88.14 88.52 89.83 90.00

1.782 1.821 1.862 1.947 2.732 3.000

0.000 0.016 0.032 0.068 0.390 0.500

|x m i | n xm i=1 i

s [–]

14.416 14.133 13.850 13.289 9.755 8.967

LHV [MJ/kg]

ρ at 298 K [kg/m3]

Tb [K]

42.714 40.984 39.456 36.878 27.927 26.800

752.57 754.19 755.81 759.06 780.14 785.00

377.31 374.50 372.03 367.85 353.35 351.52

the final TRF surrogate can be calculated as reported in Eq. (7).

(6)

f x iso =

In Fig. 1, the TRF surrogates constituting the m corrected solutions m,corr x are reported in the form of a bar graph. m,corr need to be reduced to As a last step, the m corrected solutions x f a single reference surrogate. In order to minimize the error, the final x surrogate is calculated as the least square of the m solutions in the nf dimensional fuel component space. Graphically x represents the centroid of the m solution points. Since the centroid in a n-dimensional space is the mean position of all the points in the different directions,

f x nhept = f x tol =

m i,corr i = 1 x iso

m

;

m i,corr i = 1 x nhept

m m i,corr i = 1 xtol

m

; (7)

A comparison between ULG95 gasoline properties [37,44] and the ones of the proposed TRF surrogate is summarized in Table 1. ACA , AHA and AOA are the average atom numbers of carbon, hydrogen and oxygen of the surrogate, respectively. Moreover, it is

Fig. 3. (a) Density at ambient conditions: present study compared to the average value and its variance (reported as error bar) for each ethanol vol%, (b) Stoichiometric AFR, (c) H/C ratio and (d) O/C ratio. Dotted lines report values from literature, while solid ones represent properties calculated with the proposed methodology. 5

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Fig. 4. (a) Research Octane Number, (b) Motor Octane Number, (c) Lower Heating Value at ambient conditions, (d) Boiling point. Dotted lines report values from literature, while solid ones represent properties calculated with the proposed methodology.

useful to remember that only the quantities marked by “*” were effectively targeted. The resulting surrogate exhibits a satisfactory agreement with the actual fuel. The difference in terms of stoichiometric AFR (-1.12%) is acceptable as no significant impact in the LFS prediction is expected. In order to further assess the capability of the methodology to generate a surrogate able to represent the premixed flame propagating characteristics of a given fuel, 1D sL calculations were carried out using the methodology proposed by the authors in [36]. Both the CRECK-MECH chemical kinetics mechanism [56] and the Andrae’s one [43] were used along with the proposed TRF surrogate, in order to minimize the error related to the use of a specific mechanism beyond its validation range, as discussed in [35,36]. Then, the final sL is obtained via a linear averaging of the two resulting datasets. A

comparison between experiments, Le Chatelier’s mixing rule and 1D simulations is reported in Fig. 2. sL values predicted by the proposed methodology and by Le Chatelier’s formula are almost coincident and both closely agree with the targeted experimental dataset, proving that mixing rules can provide quantitative information on the LFS of a given surrogate. Concluding, the TRF surrogate f f f f x = |x iso , x nhept , x tol | = |0.4094, 0.1391, 0.4515| (with quantities expressed as molar fractions) is able to match the chemico-physical properties, the auto-ignition tendency and the premixed flame propagating characteristics of the ULG95 gasoline. At this point, a family of gasoline-ethanol blend surrogates can be generated, as ethanol content in volume is imposed by definition and TRF components are scaled accordingly. The compositions of the 6

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resulting ETRF surrogates are reported in Table 2 and their corresponding properties are reported in Table 3. Tb is the average boiling point of the mixture, which affects the distillation characteristics of the blend, according to [57]. Tb is obtained as weighted average, whose weights are the surrogate molar fractions. In order to further validate the proposed methodology and the formulated surrogates, in Figs. 3 and 4 the properties reported in Table 3 are compared with the ones provided by a wide dataset available in literature [7–15,17,18,58,59,60–68]. It must be underlined that most of the aforementioned studies are based on experimental measurements of several gasoline-ethanol blends using base gasolines with different properties. In Fig. 3(a), the liquid density of the surrogates at ambient conditions is compared with the experimental dataset. The generated surrogate family shows an increasing trend for increasing ethanol contents, in agreement with the experiments. It is interesting to note that the higher is the ethanol content, the lower is the data dispersion, which is

due to the different gasolines (E0) used to generate the blends. For increased ethanol content, the fuel mixture properties depicted in Fig. 3(a)–(d) present a less remarked data scatter. The reason of this behavior is barely due to decreased influence of the base gasoline properties as the ethanol content of the mixture increases. Similarly, the stoichiometric AFRs reported in Fig. 3(b) are closely matched by the generated surrogates, which is important to have coherent equivalence ratios between actual fuels and surrogates. Any misalignment leads to non-negligible deviations in terms of sL prediction. The H / C and O/ C ratios are in good agreement as well, as visible in Fig. 3(c) and (d). As for real gasoline-ethanol blend, data dispersion for the H / C ratio is higher for poorly oxygenated blends, similarly to liquid density data from literature depicted in Fig. 3(a). Conversely, an opposite trend is found for the O/ C ratio, which exhibits higher dispersion for higher ethanol contents. This behavior can be explained considering the slight differences in the ethanol content, compared to the nominal values, in the commercial blends. Moving to the auto-ignition tendency of the surrogates, a wide RON dataset of gasoline-ethanol blends is available for validation. The dataset includes several engine-based experiments (dotted lines) and a few data coming from previous studies (solid lines) [66–68], aiming at formulating multicomponent surrogates able to predict gasolineethanol blend auto-ignition tendency. Such a goal is not straightforward, as ethanol acts synergistically with isooctane and toluene and antagonistically with n-heptane, in terms of octane numbers [66]. This motivates the non-linear increase of the RON with increasing ethanol content, as shown in Fig. 4(a). Generated surrogates are able to reproduce this non-linear behavior consistently. Although [53–55] proposed a detailed approach for targeting octane numbers non-linear behavior when ethanol is added to hydrocarbon mixtures, Pera et al. [37] demonstrated that a linear mole-weighted mixing rule is able to provide very close estimations of RON and MON compared to the nonlinear approaches proposed in [41,52–55]. This comparison carried out by Pera et al. [38], highlighted a negligible deviation of the linear rule within 35%vol content, which is the standard aromatic content for commercial gasoline. As for the literature data dealing with the octane numbers, the higher data dispersion for poorly oxygenated blends is due to different gasolines for the blend formulations. The non-linear increase of the MON with ethanol is qualitatively captured as well. In this case, a quantitative misalignment is noticed, due to the overestimation of the gasoline MON , which is an intrinsic limitation of the ternary approach to formulate a gasoline surrogate. A better estimation

(a)

(b)

Fig. 5. Dots represent experimental sL for different isooctane/ethanol blends [46]. Numerical sL values obtained with the proposed methodology are reported with the solid lines.

Fig. 6. Average values of LFS evaluated via DARS simulations are reported for E0, E5, E10, E20, E85 surrogates at 30 bar (a) and 100 bar (b), for different temperatures and equivalence ratio equal to 1. 7

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Fig. 7. Effect of the ethanol content by volume on the sL values calculated at 30 bar (a) and 100 bar (b) and different temperatures.

of the MON could be obtained formulating the gasoline surrogate with a higher number of components. Fig. 4(c) shows LHV , which decreases increasing the ethanol content. 1D outcomes match satisfactorily the experimental data. Finally, an estimation of the blend boiling point can be obtained via the simple approach proposed in [57]. Fig. 4(d) reveals that the proposed methodology is qualitatively able to match the decreasing trend of Tb as a function of the ethanol content, but the absolute value is generally over-predicted. In particular, for ethanol content higher than 40 vol%, the hydrocarbon and ethanol mixture exhibits an azeotropic behavior [69]. Ignoring this effect leads to a higher reckoned mixture boiling temperature. In the present study, this facet is neglected since boiling temperature is not among the targeted properties. However, due to the importance of fuel evaporation induced mixture cooling, a better estimate of the boiling point is highly desirable, and it will be one of the key topics for further development of the methodology.

a brief validation in terms LFS of both the blend surrogates and their respective mechanisms, the methodology proposed by the authors in [35,36] to obtain LFS correlations is recap. Unfortunately, LFS experiments are poorly available, especially at engine-relevant conditions and for high ethanol contents. For this reason, at first the approach proposed by the authors for the calculation of the LFS of gasoline-ethanol blends is validated against experimental data of isooctane-ethanol blends at ambient pressure and 358 K [46]. Similarly to paragraph 2.1, both the previously mentioned chemical kinetics mechanisms (the CRECK-MECH [54] and the Andrae’s one [43]) are used to calculate LFS, whose final value is obtained as arithmetical average. Hence, even the fitting procedure described afterwards is carried out on a unique (average) set of sL data. Simulations are performed using DARS v4.30 licensed by SIEMENS PLM. A comparison between experimental and calculated sL values is reported in Fig. 5. Numerical results show good agreement with the experimental data. In order to double-check calculated sL values, sensitivity analyses to pressure, temperature and dilution rate (EGR content) are performed. The EGR constituents are the primary combustion products, namely H2O, CO2 and the unburned reactants, the fuel and the oxidant species O2 and N2. A set of chemical kinetic simulations is carried out for a stoichiometric mixture and the results are reported in Fig. 6. Comparing Fig. 6(a) and (b), it is evident that LFS increases with temperature while

2.2. LFS correlations In the previous paragraph, different gasoline-ethanol blend surrogates were formulated. Their capability to match the pure gasoline (E0) LFS and to mimic the main chemico-physical properties of the different blends was validated against experimental data. In this section, besides

8

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Fig. 8. Comparison between experimental and numerical sL values at different conditions: (a) 1 bar-473 K, (b) 2 bar-473 K, (c) 3 bar-473 K, (d) 5 bar-473 K. Table 4 Composition of the actual commercial gasoline (whose RON, MON and ethanol content by volume are 96, 86.2 and 5%, respectively) and of its surrogate ETRF, both investigated in [70]. Also, the composition of the E5 surrogate formulated in the present study is reported. Gasoline (RON96/MON86.2/Ethanol content 5% vol) [70]

ETRF surrogate [70]

Ethanol (%vol) n-Heptane (%vol) Olefin (%vol) Aromatic (%vol) Benzene (%vol) Methyl-cyclohexane (%vol)

Ethanol (%vol) n-Heptane (%vol) Iso-Octane (%vol) Toluene (%vol)

5.00 3.60 6.20 33.70 0.10 1.50

it decreases for increasing pressure. Similar trends are visible also in Fig. 6(c), where E85 is separately reported for the sake of clarity. Moreover, the higher the ethanol content is, the faster the flame results for a given thermodynamic condition (in terms of p, T and Φ). Such trends obtained via 1D simulations appear as reasonable, thus confirming the validity of both the surrogates and the mechanisms. The accelerating effect due to the ethanol presence is shown in

E5 (ETRF surrogate of ULG95) 5.00 15.00 44.00 36.00

Ethanol (%vol) n-Heptane (%vol) Iso-Octane (%vol) Toluene (%vol)

5.00 14.24 47.20 33.50

Fig. 7(a) and (b). Blends with an ethanol content ranging from 5% to 20% by volume exhibit similar values ofsL , while a remarkable difference can be noticed for E85. As the temperature increases, such gap broadens. 1D chemistry-based simulations are in reasonable agreement with the observations by Syed at al. [36]. In Fig. 7(a), (b) laminar burning velocities of this study are compared with those of Di Lorenzo et al. [70]

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These ECs, represented by blue dots in Fig. 9, were chosen in order to cover any possible thermodynamic state of the unburned mixture, based on a wide dataset of SI engines characterized by different architectures, specific powers and operating conditions (in terms of revving speed and load). It is useful to point out that a temperature interval of 200K was considered for each pressure level, allowing broad variations the unburned temperature Tu . Despite several studies demonstrated the increasing cooling effect due to higher and higher ethanol contents [71,72], Kasseris et al. [73] estimated a temperature reduction equal to 35 K moving from pure gasoline to E85. Therefore, ECs reported in Table 5 can be considered still reasonably representative even in the case of extremely high ethanol contents. Once the fuel model and the reference thermodynamic states were identified, chemical kinetics calculations were carried out. For each of the 33 selected ECs, 1D LFS calculations were carried out over a wide range of equivalence ratios (in order to account for the mixture inhomogeneity in the combustion chamber due to direct-injection) and dilution rates: ranges from 0.4 to 2.0 , while EGR mass fraction from 0 to 20 . A numerical methodology, extensively discussed by the authors in [35,36], was used to fit the sL dataset calculated at the ECs. In the present study, the latest version of the methodology [37] is used to derive the sL correlations. Although such methodology is of general validity regardless of the ethanol content, correlations are derived only for E0, E5, E10, E20 and E85, which are the most widespread fuels on the market. In particular, E5 is currently the standard reference blend for a commercial gasoline [37]. E20 is expected to replace E10 in the near future, since the latter does not contain the required amount of ethanol necessary to meet the constraints in terms of renewable energy imposed by the regulations coming into force in 2020 [3]. Finally, E85 is the leading blend for flex-fuel vehicles (FFV) [15], which are vehicles equipped with an internal combustion engine able to run with more

Table 5 Representative engine conditions at medium-to-high loads. Engine Condition (EC)

Pressure [bar]

Temperature [K]

EC-1-2-3 EC-4-5-6 EC-7-8-9 EC-10-11-12 EC-13-14-15 EC-16-17-18 EC-19-20-21 EC-22-23-24 EC-25-26-27 EC-28-29-30 EC-31-32-33

30 40 50 60 70 80 90 100 110 120 130

700 750 775 800 825 850 875 900 925 950 975

± ± ± ± ± ± ± ± ± ± ±

100 100 100 100 100 100 100 100 100 100 100

A further validation of the proposed methodology is carried out against experimental data provided by Di Lorenzo et al. [70], which investigated a commercial Gasoline (whose RON, MON and ethanol content by volume are 96, 86.2 and 5%, respectively) and its ETRF surrogate, whose compositions are reported in Table 4. Fig. 8 compares experimental data reported in [70] and the average values of the LFS calculated using the two aforementioned chemical kinetics mechanisms. Outcomes of the 1D chemical kinetic simulations using the E5 surrogate formulated in this study closely match the experiments. In the light of the presented results, the chemical kinetics mechanisms as well as the formulated surrogates constitute a solid basis to provide a chemistry-grounded LFS estimation at engine-relevant conditions. In [35], the authors identified a set of representative thermodynamic conditions, hereafter called “Engine Conditions” (ECs) and reported in Table 5, potentially experienced by a flame propagating in a cylinder of a current production ICE operated at medium-to-high loads.

Fig. 9. Pressure-Temperature curves describing the thermodynamic state of the unburned mixture during compression and combustion for several SI engines operated at medium-to-high loads are depicted with solid lines. Reference engine conditions considered to compute chemistry-based laminar sL are reported with red dots.

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(a)

(b)

Fig. 10. Accuracy of sL values predicted by correlations, around stoichiometry, for E20 (a) and E85 (b), E10 (c), E20 (d) and E85 I fuels for (a) E20 and (b) E85 surrogates.

Fig. 11. sL correlation accuracy. Lean range: (a) E20, (c) E85. Rich range: (b) E20, (d) E85. 11

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Fig. 12. sL for E0, E5, E10, E20, and E85, at different conditions. “DARS” refers to DARS 1-D simulation results, while “Fit” stands for the lsL values predicted by correlations.

than one fuel, usually gasoline-ethanol blends with different ethanol contents. The key points of the developed methodology are briefly summarized hereafter. Further details can be found in [36]. The relationship presented in Eq. (8) is used to model the dependency on pressure p, unburnt temperature Tu and equivalence ratio . In order to properly fit the calculated sL dataset, fifth order logarithmic polynomials, are used for sL,0 , and , as shown in Eq. (9).

Tu T0

sL = sL,0 sL,0 = = =

5 i=0 5 i=0 5 i=0

p p0

(1

fres Yres)

The coefficients ai , bi , and c i describe sL dependency on equivalence ratio, temperature and pressure at the reference condition (T0 = 850K and p0 = 80bar ). The (eighteen) coefficients ai , bi , and c i must be determined using a least-squares minimization approach. As visible in Eq. (8), the dependency on a diluent mass fraction Yres is included and assumed as linear. The fres factor (considered as constant in the present study) is introduced and calculated using the results obtained via the 1D simulations at different EGR levels. The outcome of the fitting procedure is the correlation presented in Eq. (10), which can be implemented in any CFD solver.

(8)

sL,res =

ai log( ) i ;

bi log(

)i;

c i log( ) i

5 i= 0

ai log( )i

T T0

5 b log( )i i= 0 i

p p0

5 c log( )i i= 0 i

(1

fres Yres)

(10) (9)

The LFS correlations proposed in this paper cover a wide range of 12

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gasoline-ethanol blends is reported to estimate the accuracy of sLn, lean and sLn, rich , both based on a temperature–pressure scaling (TPS) methodology. Details on the latter and, in general, on this second fitting procedure can be found in [36]. In Fig. 11 only E20 and E85 are shown, while remaining blends are reported in Appendix A.4. Target sL values are obtained from 1D chemistry-based simulations, while predicted ones come from correlations at the same reference condition. Similarly to the correlation used to fit sL around stoichiometry, both rich and lean extensions exhibit a high degree of accuracy. 3. Results and discussion 3.1. LFS of the formulated Gasoline-Ethanol surrogates A comparison between the raw sL values computed by the chemistrysolver and those provided by the fitting correlation is depicted in Fig. 12 for a subset of the conditions reported in Table 5. The latter are purposely selected since representative of the unburned mixture state during compression stroke and combustion in one of the analyzed GDI engines, as visible in Fig. 13 [74,75]. As reported by Meng et al. [76] in their experimental measurements, no remarkable difference in terms of sL between E0, E5, E10, and E20 is visible. Conversely, E85 shows a non-negligible increase of LFS at stoichiometric and rich conditions, while lower values are found on the lean range. Such behavior may be explained considering the high O/C ratio of the mixture resulting from the combination of the rich-inoxygen blend with a lean (i.e. rich-in-oxygen) mixture. Results for all the other conditions available in Table 5 are reported in Appendix A.1. Finally, it is interesting to compare the outcomes of the proposed methodology with values coming from well-established correlations available in literature. In particular, Rhodes and Keck’s, [77], Metghalchi and Keck’s [29] and Gülder’s [30] correlations for gasoline are compared in Fig. 14 with the one formulated in the present paper for E0, at different conditions. The same comparison is carried out for E5 in Fig. 15. In this case, Di Lorenzo’s correlation [70] and the application of Eq. (1) to Gülder’s one are shown. Both in Figs. 14 and 15 1D raw data are reported as well. As for the E0, compared to the 1D chemical kinetics simulations, both Rhodes and Keck’s and Metghalchi and Keck’s correlations provide a remarkable LFS overestimation, while better prediction is obtained using Gülder’s one, at least in the lean-to-stoichiometric range; in the

Fig. 13. Actual mean in-cylinder pressure and unburned temperature traces of a GDI engine. Both experimental data and 3D-CFD simulation results are reported.

2.0) , typical of GDI engines. equivalence ratios (0.4 In order to reduce the fitting error, ai , bi , and c i coefficients are computed limiting the range from 0.7 to 1.4. In Fig. 10, the fitting relative error over the different ECs is presented in the form of maps. For the sake of brevity, only the error maps for the E20 and E85 surrogates are reported. For the other gasoline-ethanol blends, maps are reported in Appendix A.3. Then, a second fitting procedure is introduced, to extend sL correlations to extremely lean ( lean = 0.4–0.7) and rich ( rich = 1.4–2) ranges. The aim of this further procedure is to generate a formulation for both sLn, lean ( ) and sLn, rich ( ) , whose definition are reported in Eq. (11) and (12), respectively. In fact, once inverted, the latter represent scaling laws able to provide sL (for given p and Tu ) for very lean and very rich mixtures starting from the values obtained via the original fitting at = 0.7 and = 1.4 , if sLn, lean ( ) and sLn, rich ( ) are known. sLn,lean ( ) =

sL ( ) sL, = 0.7

(11)

sLn,rich ( ) =

sL ( ) sL, = 1.4

(12)

In Fig. 11, the coefficient of determination R2 for each of the

(a)

(b)

(c)

Fig. 14. Comparison between raw DARS data, fitting of the latter and correlations form literature for E0 and different conditions. (a) 40 bar and 750 K; (b) 80 bar and 850 K; (c) 120 bar and 950 K.

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Fig. 15. Comparison between raw DARS data, fitting of the latter and correlations form literature for E5 and different conditions. (a) 40 bar and 750 K; (b) 80 bar and 850 K; (c) 120 bar and 950 K.

field of rich mixtures, Gülder’s correlation leads to a non-negligible under-estimation. As for the E5, a slight underestimation of the LFS for nearly stoichiometric conditions is obtained with Di Lorenzo’s correlation. The latter widely under-estimates sL for lean and rich mixtures. This behavior can be motivated considering that such correlation was validated for low pressures and temperatures and for a limited range of the equivalence ratio (0.8 < < 1.3), i.e. conditions far from the investigated ones typical of ICEs. Conversely, Gülder’s formulation provides LFS values in good agreement with the 1D outcomes, especially for lean-to-stoichiometric mixtures. Before concluding, it is worthwhile to remember that the proposed procedure, combining the definition of a suitable fuel model (intended as surrogate and related mechanism) with the formulation of a fitting correlation for sL , results in a set of coefficients which can be easily implemented in any 3D-CFD code to replicate a fuel-tailored laminar burning velocity for combustion models. For the sake of clarity, the eighteen input coefficients to Eq. (10) (ai , bi , and c i ) are listed for all the gasoline-ethanol blend surrogates in Appendix A.2.

conditions (p = 30 ÷ 130 bar, Tu = 600 ÷ 1075 K, Φ = 0.4 ÷ 2.0 and EGR = 0%÷ 20%). Comparing fitting correlations and 1D chemical kinetics simulations raw data on a set of selected engine-like conditions the relative error is always lower than 4%, except for few cases showing higher errors, but never exceeding 10%. Exploiting the proposed methodology to derive LFS correlations tailored on the chemical nature of the reference fuel surrogates, it is therefore possible to improve the representation of the flame propagation characteristics in engines fueled with gasoline-ethanol blends. A sensitivity to thermodynamic and mixture quality variations on sL have been investigated, resulting in good agreement with experimental evidences previously reported in literature. As a final remark, the present study aims to provide chemistry-grounded information for CFD simulations involving the use of highly oxygenated gasoline-ethanol blends in current production internal combustion engines. Credit authorship contribution statement M. Del Pecchia: Conceptualization, Methodology, Software, Validation, Investigation, Resources, Writing - original draft, Writing review & editing, Visualization. V. Pessina: Validation, Formal analysis, Investigation, Resources, Writing - review & editing, Visualization. F. Berni: Writing - review & editing, Supervision. A. d’Adamo: Writing - review & editing, Supervision. S. Fontanesi: Writing - review & editing, Supervision.

4. Conclusions In the present study, a set of chemistry-based LFS correlations for different gasoline-ethanol fuel blends (E0, E5, E10, E20, and E85) is derived. Such correlations are of practical use for researchers in the engine community, since they can be straightforwardly implemented in any CFD solver exploiting a flamelet combustion model. To this aim, adhoc fuel surrogates are generated at first, matching the main chemical characteristics and combustion-related fuel properties. Secondly, correlations are formulated fitting a dataset of LFS values provided by 1D chemical kinetics simulations. These calculations are performed using two different chemical kinetics mechanisms, to reduce uncertainties. Resulting correlations are fitted onto a wide range of engine-like

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A.1 Comparison, in terms of laminar flame speed, between the values predicted by the logarithmic polynomial fitting correlations and the ones provided by DARS

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Fig. A.1. LsL comparison: solid lines represent values obtained with poly-logarithmic fitting correlations, while dots depict DARS results.

A.2 Coefficients of the LFS fitting correlations The correlations derived in the present study are intended to be adopted in the following ranges of the mixture properties:

• Pressure: 30 bar p 130 bar; • Unburnt Temperature: 600 K T • Equivalence Ratio: 0.4 Φ 2.0; • EGR: 0 EGR% 20; u

1075 K;

15

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M. Del Pecchia, et al. E0-Polynomial Fitting Coefficients A

Pressure Scaling Lean-side Extension Fitting Coefficients

Pressure Scaling Rich-side Extension Fitting Coefficients

B

C

l3

4.180515E + 00

r3

−8.815310E-01

1 8.684906E + 01 2 5.480633E + 01 3 −2.453949E + 02 4 −4.074860E + 02 5 2.743065E + 02 6 1.080072E + 03 αst Kegr

2.665919E + 00 −2.423410E-01 5.066840E + 00 5.928647E + 00 −8.483957E + 00 −3.388884E + 01 14.416 2.24

−2.773052E-01 −3.691900E-03 −4.056873E-01 3.663628E-01 3.687658E + 00 4.803771E + 00

l2 l1 l0 m2

−6.898785E-01 −2.694727E + 00 1.000000E + 00 1.311908E-01

r2 r1 r0 m1

1.637995E + 00 −1.341685E + 00 9.998374E-01 1.716769E-01

p0_fit T0_fit

8.0E + 06 850.00

Temperature Scaling Rich-side Extension Fitting Coefficients

4 3 2 1 0

m LOW (rml)

q LOW (rql)

m MED (rmm)

q MED (rqm)

m HIGH (rmh)

q HIGH (rqh)

−4.270104E + 00 3.130788E + 01 −8.617967E + 01 1.058728E + 02 −4.876696E + 01

6.144492E + 00 −4.556492E + 01 1.272775E + 02 −1.595215E + 02 7.622910E + 01

−3.133542E-01 3.133317E + 00 −1.161852E + 01 1.872206E + 01 −1.072339E + 01

1.254521E + 00 −1.098716E + 01 3.661789E + 01 −5.482206E + 01 3.115995E + 01

3.534458E + 00 −2.482474E + 01 6.404297E + 01 −7.165339E + 01 2.939951E + 01

−5.032566E + 00 3.457004E + 01 −8.622439E + 01 9.124992E + 01 −3.337720E + 01

Temperature Scaling Lean-side Extension Fitting Coefficients

2 1 0

m LOW (lml)

q LOW (lql)

m MED (lmm)

q MED (lqm)

m HIGH (lmh)

q HIGH (lqh)

−7.541445E + 00 7.760682E + 00 −1.725389E + 00

1.246271E + 01 −1.028477E + 01 2.102660E + 00

−3.475354E + 00 3.870882E + 00 −9.102542E-01

6.504110E + 00 −4.533464E + 00 8.765270E-01

−2.547370E + 00 2.643662E + 00 −4.886068E-01

4.821078E + 00 −2.672221E + 00 3.527148E-01

Temperature- Pressure Scaling Coefficients pressure weight Temperature weight Total weight pref_fit Tref_fit

E85

1.00 5.00 6.00 8.00E + 06 600.00

E85-Polynomial Fitting Coefficients

1 2 3 4 5 6

A 1.009623E + 02 8.114265E + 01 −3.307984E + 02 −7.158979E + 02 4.189288E + 02 2.422162E + 03

B 2.718921E + 00 −5.443706E-01 6.180692E + 00 1.010163E + 01 −1.435391E + 01 −6.368069E + 01

C −2.889658E-01 5.176360E-02 −4.658047E-01 5.374411E-01 4.848613E + 00 6.666948E + 00

αst Kegr

9.755 2.07

p0_fit T0_fit

8.00E + 06 850.00

Pressure Scaling Lean-side Extension Fitting Coefficients

Pressure Scaling Rich-side Extension Fitting Coefficients

13 l2 l1 l0 m2

r3 r2 r1 r0 m1

6.068968E + 00 9.544402E-01 −3.489660E + 00 1.000000E + 00 4.682530E-01

16

−1.045214E + 00 1.689523E + 00 −1.338939E + 00 9.942390E-01 2.301505E-01

Fuel xxx (xxxx) xxxx

M. Del Pecchia, et al. Temperature Scaling Rich-side Extension Fitting Coefficients

4 3 2 1 0

m LOW (rml)

q LOW (rql)

m MED (rmm)

q MED (rqm)

m HIGH (rmh)

q HIGH (rqh)

−2.894646E + 00 2.147954E + 01 −6.031420E + 01 7.614266E + 01 −3.618666E + 01

4.433458E + 00 −3.324583E + 01 9.452988E + 01 −1.214530E + 02 5.992599E + 01

−1.808167E + 00 1.341226E + 01 −3.812400E + 01 4.933375E + 01 −2.415342E + 01

3.088075E + 00 −2.349130E + 01 6.844413E + 01 −9.100407E + 01 4.677931E + 01

3.592250E + 00 −2.497154E + 01 6.346575E + 01 −6.908535E + 01 2.712505E + 01

−5.462787E + 00 3.700372E + 01 −9.076880E + 01 9.333645E + 01 −3.244142E + 01

Temperature Scaling Lean-side Extension Fitting Coefficients

2 1 0

m LOW (lml)

q LOW (lql)

m MED (lmm)

q MED (lqm)

m HIGH (lmh)

q HIGH (lqh)

−6.285140E + 00 6.186889E + 00 −1.241555E + 00

1.347990E + 01 −1.101462E + 01 2.123534E + 00

−4.378305E + 00 4.003308E + 00 −6.803398E-01

1.091458E + 01 −8.026481E + 00 1.345030E + 00

−4.950865E + 00 3.779165E + 00 −2.994363E-01

1.123173E + 01 −7.125334E + 00 6.477671E-01

Temperature- Pressure Scaling Coefficients Pressure weight Temperature weight Total weight pref_fit Tref_fit

1.00 5.00 6.00 8.00E + 06 600.00

A.3 Error maps of the laminar flame speed values predicted by correlations compared to the 1D simulation results

10 8 6 4 2 0 -2 -4 -6 -8 -10

(a)

(b)

(c)

Fig. A.3. Accuracy of sL values predicted by correlations, around stoichiometry, for E0 (a), E5 (b) and E10 (c) surrogates.

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A.4 Accuracy for all the surrogate blends, for rich and lean mixtures

Fig. A.4. Accuracy of sL normalized values predicted by correlations for lean and rich mixtures.

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