Emiliano PipitoneDepartment of Industrial

and Digital Innovation (DIID),

University of Palermo,

Palermo 90128, Italy

e-mail: emiliano.pipitone@unipa.it

Stefano BeccariDepartment of Industrial

and Digital Innovation (DIID),

University of Palermo,

Palermo 90128, Italy

e-mail: stefano.beccari@unipa.it

A Comprehensive Model for theAuto-Ignition Prediction in SparkIgnition Engines Fueled WithMixtures of Gasoline andMethane-Based FuelThe introduction of natural gas (NG) in the road transport market is proceeding throughbifuel vehicles, which, endowed of a double-injection system, can run either with gasolineor with NG. A third possibility is the simultaneous combustion of NG and gasoline, calleddouble-fuel (DF) combustion: the addition of methane to gasoline allows to run theengine with stoichiometric air even at full load, without knocking phenomena, increasingengine efficiency of about 26% and cutting pollutant emissions by 90%. The introductionof DF combustion into series production vehicles requires, however, proper engine cali-bration (i.e., determination of DF injection and spark timing maps), a process which isdrastically shortened by the use of computer simulations (with a 0D two zone approachfor in-cylinder processes). An original knock onset prediction model is here proposed tobe employed in zero-dimensional simulations for knock-safe performances optimizationof engines fueled by gasoline-NG mixtures or gasoline-methane mixtures. The modeltakes into account the negative temperature coefficient (NTC) behavior of fuels and hasbeen calibrated using a considerable amount of knocking in-cylinder pressure cyclesacquired on a Cooperative Fuel Research (CFR) engine widely varying compressionratio (CR), inlet temperature, spark advance (SA), and fuel mixture composition, thus giv-ing the model a general validity for the simulation of naturally aspirated or superchargedengines. As a result, the auto-ignition onset is predicted with maximum and mean errorof 4.5 and 1.4 crank angle degrees (CAD), respectively, which is a negligible quantityfrom an engine control standpoint. [DOI: 10.1115/1.4041675]

Keywords: spark ignition engine, natural gas, methane, knock modeling, auto-ignition

Introduction

The influence of anthropic pollution on global warming is agreatly debated topic in the scientific community. Internal com-bustion engines play indeed a relevant role in urban pollution[1,2]; Diesel vehicles are deemed to be the main responsible forthe unsustainable level of particulate matter and NOx in urbanarea, so much that some of the world’s biggest cities alreadyplanned to ban diesel vehicles from their centers by 2025.Gaseous fuels, such as natural gas (NG) or liquefied petroleumgas (LPG), are the most environmental friendly fuels for roadtransport applications, due to several reasons: their unparalleledmixing capabilities allow to obtain almost complete combustionswith low levels of unburned hydrocarbon emissions in cold andtransient operation, and almost null emissions of particulate mat-ter; their superior knock resistance (i.e., motor octane number(MON), of NG is about 120, while gasoline MON is about 85) notonly allows to adopt higher compression ratio (CR) and bettercombustion phase but, above all, allows to run spark ignition (SI)engines with stoichiometric air–fuel mixture even at full load: thiscrucial advantage leads to great fuel economy and minimum levelof unburned hydrocarbons (HC), carbon monoxide (CO), and car-bon dioxide (CO2) emissions if compared with the use of commongasoline which, instead, requires very rich mixtures to preventfrom dangerous knocking phenomena in full load operation, thuscausing high fuel consumption and heavy CO and HC emissions

(also due to the consequent poor catalyst conversion efficiency).A further significant advantage of gaseous fuels is their lower costcompared to gasoline or diesel fuel, resulting in a valuable moneysaving for end users. In spite of these economic and environmen-tal advantages, the diffusion of gaseous fuel is still marginal: inEuropean Union, as example, the market penetration of LPGvehicles results 3%, while natural gas vehicles represent only 1%of the market, even if a peak of 14% NG vehicles is reported forItaly [3], where advanced powertrain systems are hardly spreading[4]. Outside the European Union, the countries with the highestlevels of market development for natural gas vehicles are Argen-tina, Brazil, India, Iran, and Pakistan. In particular, Brazil repre-sents today the non-EU country with the highest market share ofNG vehicles (5%), while India is forecast to become the world’slargest natural gas vehicle market. The share of natural gasvehicles is 1.5% in China, while results lower than 1% in U.S. andRussia. Although the use of natural gas in road transportation isstill marginal in all but a few countries, it has been worldwide rec-ognized as a strategic alternative to replace oil-derived fuels andmitigate pollutant emissions from the transport sector, and its usewill, therefore, be actively promoted all over the world. As exam-ple, the European Union, through the Clean Power for Transport(CPT) package, plans the creation of an alternative fuels infra-structure, with a network of refueling stations for natural gasvehicles in cities and densely populated areas, ports, and along theTrans-European-Network for Transport (TEN-T).

A first step toward the diffusion of natural gas in the road trans-port market is represented by bifuel engines, i.e., engines endowedof two separate injection systems that can run either with gasoline

Manuscript received June 7, 2018; final manuscript received October 1, 2018;published online November 16, 2018. Assoc. Editor: Nadir Yilmaz.

Journal of Engineering for Gas Turbines and Power APRIL 2019, Vol. 141 / 041009-1Copyright VC 2019 by ASME

or with gas; this kind of engines equip almost every NG vehiclecurrently available in the market. These engines usually exploitthe high knock resistance of methane, by the use of properly highcompression ratios, optimal combustion phases, and stoichiomet-ric air/fuel (A/F) mixtures. When running with gasoline, however,the effective compression ratio of these engines must be reduced(e.g., through Miller implementation or by intake air throttling)and abundantly rich mixtures must be employed to prevent thealready mentioned knocking phenomena, thus drastically increas-ing both fuel consumption and pollutant emissions. However, asalready shown by the authors in previous works [5,6], besides thestandard operation either with gasoline or with natural gas, theseengines also allow to adopt an innovative operation mode, calleddouble-fuel (DF) combustion, consisting in the simultaneous com-bustion of gasoline and gaseous fuel (natural gas or LPG) homo-geneously mixed with air;1 this third combustion mode permits tosimultaneously exploit the best characteristics of each fuel, i.e.,the good volumetric efficiency provided by gasoline, and the highknock resistance ensured by natural gas (or LPG), thus allowingto adopt stoichiometric proportion with air even at full load; thisbrings considerable advantages with respect to both pure fuels: ineffect, the experimental tests carried out showed, with respect topure gasoline operation, an higher engine efficiency (þ26%)with negligible power loss (�4%), thanks to the stoichiometricproportion with air and to the better combustion phase, togetherwith a drastic cut (�90%) to pollutant emissions of unburnedhydrocarbon and carbon monoxide, which amply profited fromthe maximized catalyst conversion efficiency due to the overallstoichiometric air–fuels mixture; with respect to pure natural gasoperation, instead, the advantage connected to DF combustionrelies in the engine power, which in the test performed reached a13% increase. It is worth to mention that maximizing the energyefficiency conversion with gasoline means also to extend the vehi-cle operating range.

The undeniable advantages of DF combustion induced otherresearchers to perform test [7–9], both in naturally aspirated andsupercharged SI engines. The general result was always an engineefficiency increase and pollutant emissions reduction, with respectto pure gasoline operation, and an engine power increase withrespect to pure gas operation.

The aspect which makes DF combustion particularly attractiveis represented by its easy implementation in current productionbifuel engines: in effect, it requires only a simple programing ofthe electronic control unit (ECU), which should be endowed ofthe adequate maps for DF operation, i.e., injection times map andknock-safe spark advance map; this ECU calibration process canbe accomplished carrying out a considerable amount of experi-mental tests on the engine test bed, or by computer simulations,which allow to obtain fast and reliable ECU maps, thus stronglylimiting the need of experimental test. Several simulation toolsare available on the market, generally coupling the one-dimensional (1D) approach, adopted for inlet and exhaust flows,to the two-zone zero-dimensional (0D) approach followed insteadfor the in-cylinder processes, where the burned and unburned gasare separately treated (i.e., two-zone), both considered in a zero-dimensional perspective.

However, to be sufficiently reliable and accurate, these simula-tion tools should be endowed with proper submodels capable toadequately predict turbulent flame propagation and auto-ignitionin DF condition. Knocking is, in effect, a crucial issue when deal-ing with spark advance (SA) control in SI engines; hence, a reli-able knock onset prediction submodel is mandatory whenthermodynamic simulations are employed to obtain a knock-safeECU calibration for the DF operation.

Given the total absence of auto-ignition submodels for the zero-dimensional simulation of DF combustion in the current scientific

literature, the authors carried out a wide series of experimentaltests on a properly equipped bifuel engine test bed, thus develop-ing a simple yet accurate submodel for the prediction of unburnedgas auto-ignition in 0D simulations involving the combustion ofgasoline-LPG mixtures and gasoline-propane mixtures [10] inspark ignition (SI) engines; the aim of the present paper is then todevelop a submodel also for the auto-ignition prediction of bothmethane-gasoline mixtures and natural gas-gasoline mixtures inspark ignition engines. Even if pure methane is not commerciallyavailable as natural gas, it is commonly employed by engine man-ufacturer in the development and optimization process, wherenumerical simulations and experimental tests are performed usingreference fuels, whose known properties allow to trace repeatableand comparable results: this is the reason why the methane-gasoline mixture has been included in this study. The first innova-tion that characterize this paper with respect to previous works ofthe same authors [10,11] is the use of fuel mixtures composed bygasoline and methane based fuel.

Knock Prediction Model

According to the current scientific literature, two differentapproaches may be followed for auto-ignition prediction in ther-modynamic simulations: the detailed chemical kinetic approachand the auto-ignition delay approach. The first takes into accountthe basic reaction steps that occur during combustion [12–15] but,due to the great number of reactions to consider, these modelsrequire a great computational effort and are often difficult toimplement. The auto-ignition delay approach, instead, is based onthe unburned gas pressure and temperature history [16–20] and,although less accurate than the first approach, is quite easy toimplement in zero-dimensional simulations; for this reason, thisapproach is often preferred for the estimation of the auto-ignitiontime of fuel–air mixtures.

The auto-ignition delay approach originates from measure-ments and observation made through the use of rapid compressionmachines (RCM) [16,21,22], where a rapid compression strokebrings the fuel-air mixture to a certain pressure and temperaturecondition, which is maintained almost constant until auto-ignition.The auto-ignition delay time s (s) is measured between the end ofthe rapid compression (the start of constant pressure condition)and the auto-ignition (detected by the rapid pressure increase dueto combustion), as can also be observed in Ref. [10]

The experimental data obtained by RCM (pressures, tempera-tures, and auto-ignition times) have been used to calibrate simpleauto-ignition models based on Arrhenius type equations:

s ¼ Ap�neE

RT ¼ Ap�neBT (1)

where p (bar) and T (K) are the constant pressure and temperatureof the air–fuel mixture inside the RCM, B¼E/R (K) is the ratiobetween the fuel activation energy E (J/mol) and the universal gasconstant R (J/mol K), while A and n are fuel dependent coeffi-cients, determined by statistical regression of the experimentaldata. When the fuel activation energy is unknown, the coefficientB is usually determined by statistical regression [18,23].

The simple model reported in Eq. (1), however, poses someproblems for the application to SI engine thermodynamic simula-tions, since pressure and temperature of the unburned gas are farfrom being constant; an evolution of Eq. (1) is represented by theknock integral (KI) approach [16,18–20,24,25] that can beexpressed as follows:

KI tð Þ ¼ðt

tIVC

dt

s(2)

were KI(t) is evaluated from tIVC (inlet valve closure (IVC) time)to the generic time t. According to this approach, the knock inte-gral reaches the value of 1 when auto-ignition occurs (i.e., when

1Quite different from the known dual fuel combustion, where the two fuels arenot homogeneously mixed and the auto-ignition of one acts as starter for thecombustion of the second.

041009-2 / Vol. 141, APRIL 2019 Transactions of the ASME

the radical species in the unburned gas reach the critical concen-tration), hence

KI tKOð Þ ¼ðtKO

tIVC

dt

s¼ 1 (3)

Equation (3), together with Eq. (1), allows to determine the timetKO at which knock occurs (once the model coefficients A, B, andn have been properly determined) using the nonconstant pressurep and temperature T of the unburned gas.

Negative Temperature Coefficient Zone and

Auto-Ignition Model

It is worth to point out that according to Eq. (1), a pressure and/or temperature increment causes a reduction of auto-ignition time;this has a general validity, even if several experimental datacollected on rapid compression machines or shock tubes[14,21,22,26,27] reveal that, at temperatures between 650 and1200 K, many hydrocarbon fuels exhibit a reverse dependence,i.e., an increase of the auto-ignition time (s in Eq. (1)) for increas-ing temperatures, as, for example, reported in Fig. 1 [21].

This phenomenon is known as negative temperature coefficient(NTC) behavior, and the temperatures range of its existence mayvary from one fuel to another, also as function of pressure. Asshown in Fig. 1, the auto-ignition of gasoline-air mixtures reveals,regardless of the equivalence ratio / [21], an NTC behaviorbetween 700 and 850 K, which is quite consistent with the typicaltemperature reached by unburned gas during the combustion pro-cess in SI engines. Some fuels exhibit a near-NTC behavior zone,i.e., a temperature range where the overall reaction rate has aweak dependence on temperature [14,15,22,26,27], thus resultingin a roughly constant auto-ignition time. However, whether thefuel exhibits a pronounced NTC or a near-NTC behavior, Eq. (1)is not adequate to represent the auto-ignition delay as function oftemperature: it would produce a simple straight line in Fig. 1. Thesimple correlation of Eq. (1) remains, however, valid for unburnedgas temperatures outside the NTC range. The data available in the

scientific literature [21] revealed that, for a stoichiometric mixtureof air and gasoline, the NTC behavior exists between 713 and873 K (as shown in Fig. 1). As regards methane, very few data areavailable in literature concerning the application to spark ignitionengines, i.e., with reasonable pressure levels and mixturestrengths: the data reported in Ref. [28] allowed to estimate theexistence of the NTC zone between 1090 and 1190 K, for a stoi-chiometric mixture with air and for absolute pressures between 17and 40 bar. Being methane the main component of the natural gasused in the tests (86% Vol as reported in Table 1), the same tem-peratures range can be assumed for the NTC zone of natural gas.As regards the simultaneous combustion of gasoline and naturalgas (or gasoline and methane), an introductory consideration isnecessary. The strong knock resistance increase recorded evenwith the addition of small amount of natural gas, as reported inprevious works [6,33] and confirmed by the data reported in thepresent paper, can be justified through a chemical interactionbetween the intermediate products of the pre-ignition reactions ofboth fuels. During the combustion process, in effect, each fuel inthe unburned mixture is characterized by several pre-ignition reac-tions, essentially controlled by the radicals produced by each sin-gle component of the fuel. Due to the very different compositionof gasoline (a mixture of C4–C12 hydrocarbons [29,34]) and natu-ral gas (whose main component is methane), the radicals involvedin the chain-branching reactions of gasoline are quite differentfrom those produced by natural gas (or methane), which are char-acterized by lower reaction rate and longer lives [21]. This clari-fies the higher knock resistance of NG and methane (whose MONis 123 and 140, respectively, as reported in Table 1) with respectto gasoline (MON 84). A possible explanation of the strongknocking resistance increment obtained by adding even smallquantities of NG or methane to gasoline may, hence, be given bysupposing that the intermediate products of methane interact withgasoline radicals, slowing down their reactions and hence theoverall auto-ignition process (i.e., increasing the auto-ignitiondelay time s). According to this interpretation, in the simultaneouscombustion of gasoline and natural gas (or gasoline and methane),the auto-ignition process is promoted by the lower knock resistantfuel (gasoline) and slowed down by the higher resistant (NG ormethane): this led to consider that, in the combustion of gasoline-natural gas and gasoline-methane mixtures, it is always the lessresistant fuel (i.e., gasoline) to undergo auto-ignition and startknocking phenomena. According to this consideration, and withthe aim to preserve the model simplicity and its ease of implemen-tation, the authors assumed the same NTC temperatures of gaso-line, i.e., 713 and 873 K, also for the DF combustion.

In the test performed by the authors, the temperature reachedby the unburned gas obviously depended on the inlet temperatureand on the compression ratio adopted. Table 2 reports, for each of

Fig. 1 Auto-ignition delay obtained by rapid compressionmachine test [21] (gasoline surrogate, 20 bar, three differentequivalence ratios /)

Table 1 Main properties of the fuels employed

Properties Gasoline Natural gas Methane

Composition (% Vol) mixture of C4–C12 hydrocarbon 86% CH4, 8.3% C2H6, 1.5% C3H8, 1.3% CO2, 2.3% N2, 0.6% other �99% CH4

Molar mass (g/mole) 103–114 [29–31] 18.3 16Motor octane number (MON) 84 123 140 [32]Lower heating value (MJ/kg) 43.4 46.2 50Stoichiometric air–fuel ratio 14.7 16.9 17.2

Table 2 End-gas temperatures and NTC zone limiting tempera-tures for each fuel (fuel mixture) tested

Fuel TEnd-gas (K) TNTC1 (K) TNTC2 (K)

Gasoline 860–1070 713 873Double-fuel 878–1250 713 873Natural gas 1020–1260 1090 1190Methane 1010–1330 1090 1190

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the fuel (or fuel mixture) employed, the measured range of varia-tion of the end-gas2 temperatures before knocking events (i.e., themaximum unburned gas temperature), together with the limitingtemperatures of the NTC zone: as can be deduced, in the test per-formed, the unburned gas temperature always reached, and some-times crossed, the fuel NTC zone.

This observation induced the authors to adopt a modified ver-sion of the auto-ignition time model of Eq. (1), with the aim totake into account the NTC behavior of each fuel and improve themodel reliability in knock onset prediction; the auto-ignition timemodel proposed by the authors is resumed in the followingequation:

s ¼

Ap�neBT T < TNTC1

Ap�neB

TNTC1 TNTC1 � T � TNTC2

Ap�neB

½T�ðDTNTCÞ� T > TNTC2

8>>>>><>>>>>:

(4)

where TNTC1 and TNTC2 represent the minimum and maximumtemperature of the NTC zone of the fuel (as also represented inFig. 2), and DTNTC is their difference

DTNTC ¼ TNTC2 � TNTC1 (5)

The parameters A, n, and B, have the same meaning alreadypresented in Eq. (1). Figure 2 reports a graphical representation ofthe proposed model, compared with the experimental datareported in Ref. [21].

As is clear, in the auto-ignition delay model proposed bythe authors, the Arrhenius approach expressed by Eq. (1) isconsidered valid until the beginning of the NTC zone (i.e.,with T< TNTC1); for temperatures inside the NTC zone (i.e.,TNTC1 � T � TNTC2), the auto-ignition delay is assumed to remainconstant at given pressure, while, for temperature exceeding theNTC zone (T>TNTC2) the auto-ignition delay resumes thedecreasing trend of Eq. (1). The use of two different temperaturesto delimit the fuel NTC zone, and then Eq. (4), is a refinement ofthe model proposed by the authors in previous works [10,11] andrepresents the second innovation of the present paper.

The calculation of the auto-ignition delay s from Eq. (4)requires the evaluation of the unburned gas temperature T (accord-ing to the zero-dimensional approach, one single value is adoptedfor the whole unburned gas mass). From IVC up to the spark igni-tion (i.e., the start of combustion), this temperature was evaluatedusing the perfect gas law

T ¼ TIVC �p � V

pIVC�VIVC

(6)

where p and V are the gas pressure and in-cylinder volume whilepIVC, VIVC, and TIVC indicate pressure, volume, and temperatureof the gas at IVC. Eq. (6) is clearly based on the assumption of nogas leakage from the cylinder: this assumption is fairly acceptableconsidering that, at the test engine speed of 900 rpm, the compres-sion stroke takes 33.3 ms, which is quite near to the 30 msemployed in some rapid compression machine [21] for the estima-tion of fuel auto-ignition delay. Furthermore, the authors also con-sidered negligible the heat transfer during the intake stroke, thusassuming TIVC¼ TIN.

During the combustion process, the unburned gas mass is pro-gressively reduced by the flame front propagation, and Eq. (6)cannot be used anymore. The evaluation of the unburned gas tem-perature T after spark ignition was then made considering a poly-tropic law, as usually done both in RCM calculations [21,22] andin zero-dimensional engines simulations

T ¼ TIGN �p

pIGN

� �m�1m

(7)

here pIGN is the in-cylinder pressure at spark ignition time, TIGN isthe corresponding unburned gas temperature, evaluated throughEq. (6), while m is the polytropic coefficient: this has been eval-uated as the opposite slope of least square regression line repre-senting Log p as function of Log V, from 80 to 40 crank angledegrees (CAD) before top dead center (BTDC) (i.e., excluding thecombustion phase). This procedure, applied to each singlesampled pressure cycle, allowed to account for the different heattransfer levels related to the several different compression ratiosand intake temperatures adopted in the tests (see Tables 3 and 4).

The authors implemented Eq. (4) using the knock integralapproach of Eq. (3), and tuned the model parameters A, B, and n,employing a great number of experimental data collected on aproperly instrumented engine test bed: this allowed to obtain anaccurate and reliable tool for the prediction of auto-ignition occur-rence in SI engines fueled with every possible mixture of gasolineand methane, or gasoline and natural gas.

Experimental Setup

As mentioned earlier, the aim of this research is to produce asimple yet reliable auto-ignition prediction submodel to beemployed in zero-dimensional thermodynamic simulations dedi-cated to spark advance calibration of engines fueled withgasoline–methane mixtures or gasoline–natural gas mixtures.With the aim to make the model proposed safely predictive eventoward the first incipient knocking phenomena, a set of unburnedgas pressure and temperature curves obtained under light knockcondition was employed for model calibration. Moreover, sincethe prediction capability of a model is strongly consolidated bythe heterogeneity of the experimental data used for its calibration,the authors greatly diversified the set of in-cylinder pressure andtemperature curves employed for model calibration thanks to theuse of a Cooperative Fuel Research (CFR) engine (whose maincharacteristics are resumed in Table 5), which, being prescribedfor fuel octane rating, is properly designed to run under knockingconditions and is endowed of proper systems for a wide variationof volumetric compression ratio, inlet temperature, and sparkadvance; these properties allowed to obtain a widely differentiatedset of pressure and temperature histories, fully representative ofthe in-cylinder thermodynamic conditions obtainable in sparkignition engines of different kind (i.e., naturally aspirated orsupercharged with or without intercooler) and geometry.

Once properly calibrated, the auto-ignition prediction modelcan be implemented in zero-dimensional simulations involvingthe combustion of every gasoline-methane mixture (or

Fig. 2 Graphical representation of the model proposed versusexperimental data [21]

2The portion of unburned gas most distant from the ignition point, whichundergoes auto-ignition if not promptly reached by the flame front.

041009-4 / Vol. 141, APRIL 2019 Transactions of the ASME

gasoline–natural gas mixture) in almost every kind of engines,since the model parameters depend only on the fuel type [18],while the in-cylinder pressure and temperature histories aremostly influenced by the engine and by the operative conditions.

In order to realize each desired fuel mixture and perform anaccurate control on the overall air/fuel ratio, the CFR engineemployed in the test was equipped with two independent digitallycontrolled injection systems: a complete and detailed descriptionof both modified CFR engine and experimental setup is given inRef. [13]

Test Method

Two different kind of fuel mixtures were taken into considera-tion: gasoline–natural gas and gasoline–methane. For each testperformed, the mixture composition was identified by the gaseousfuel mass fraction xgas (i.e., the ratio of the gaseous fuel mass tothe total fuel mass in the mixture). The gas mass fraction xgas wasvaried from 0% (which means pure gasoline operation) to 100%(i.e., pure gaseous fuel) with steps of 20%. The overall air/fuelratio was maintained at the stoichiometric value in all the test

performed, in order to calibrate the model in the condition whichallows to minimize pollutant emissions. The properties of thefuels employed (gasoline, natural gas, and methane) are listed inTable 1, while Table 6 resumes the operative conditions of thetest performed.

In order to obtain the mentioned widely differentiated set ofunburned gas pressure and temperature histories, both SA andinlet temperature (TIN) were fixed for each test conditionexplored, while the engine compression ratio was increased untillight knocking occurrence; this was assumed by the authors asthe condition for which at least 10% of the sampled pressurecycles exhibit knocking oscillations with peak to peak value notlower than 0.2 bar. With the aim to employ only light knockingcycles for calibration, the pressure traces with peak to peak oscil-lations higher than 0.8 bar (i.e., too strong knock phenomena)were excluded from the experimental data employed for themodel calibration: this procedure led to the exclusion of about20% of the recorded pressure cycles and allows the model to

Table 4 Compression ratios adopted to induce light knocking in the gasoline–methane tests

Methane mass fraction (xGAS)

SA (CAD BTDC) TIN (�C) 0% 20% 40% 60% 80% 100%

15 50 7.00 8.09 9.04 10.50 11.80 15.5080 6.70 7.57 8.50 9.57 11.00 14.50

110 6.49 7.21 8.04 8.89 10.20 13.30140 6.23 7.00 7.70 8.50 9.69 12.10

25 50 6.17 6.84 7.43 8.13 8.83 10.8080 6.00 6.56 7.00 7.57 8.50 10.00

110 5.74 6.23 6.70 7.21 8.09 9.33140 5.57 6.00 6.51 7.00 7.72 9.18

35 50 5.95 6.45 6.91 7.57 8.31 9.5680 5.71 6.08 6.56 7.00 7.82 8.96

110 5.39 5.86 6.23 6.62 7.43 8.50140 5.19 5.57 6.00 6.49 7.21 8.20

Table 5 Specifications of the CFR engine employed [35]

Compression ratio 4.5� 16

Bore 82.6 (mm)Stroke 114.3 (mm)Connecting rod length 254.0 (mm)Displacement 611.2 (cm3)

Table 6 Test conditions

Engine speed 900 (RPM)

Inlet temperature (TIN) 50, 80, 110, 140 (�C)Engine load condition full loadCompression ratio determined to induce light knockingOverall air/fuel ratio stoichiometricSpark advance (SA) 15, 25, 35 (CAD BTDC)Gas mass fraction (xgas) from 0% to 100% with step of 20%

Table 3 Compression ratios adopted to induce light knocking in the gasoline–natural gas tests

Natural gas mass fraction (xGAS)

SA (CAD BTDC) TIN (�C) 0% 20% 40% 60% 80% 100%

15 50 7.00 8.14 9.18 10.04 11.80 13.7080 6.70 7.74 8.63 9.64 11.00 13.00

110 6.49 7.43 8.20 8.89 10.00 11.70140 6.23 7.06 7.92 8.50 9.33 10.70

25 50 6.17 7.00 7.57 8.12 8.77 9.8280 6.00 6.62 7.08 7.67 8.21 9.18

110 5.74 6.38 6.81 7.21 7.81 8.77140 5.57 6.10 6.51 7.00 7.56 8.26

35 50 5.95 6.48 7.00 7.43 7.81 8.8780 5.71 6.15 6.62 7.00 7.51 8.26

110 5.39 5.89 6.17 6.62 7.12 7.84140 5.19 5.62 6.00 6.36 6.84 7.59

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safely delimit the knock-free region of any fuel mixture (i.e., foreach given gas fraction xgas from 0 to 100%), thus enablingengine designers and testers to perform safe and reliable engineperformance optimization involving the combustion of mixturesof gasoline and methane based fuel. Both the mentioned thresh-olds (0.2 and 0.8 bar) were experimentally determined throughsome preliminary tests carried out on the same engine test bench,by inducing both light knocking phenomena (whose suppressionrequired a spark advance reduction of only 2 CAD) and heavyknocking phenomena (requiring instead a spark advance reduc-tion of 6 CAD).

For each light knocking condition, the authors sampled 50 con-secutive pressure cycles. This procedure was repeated for all thespark advances and all the inlet temperatures considered. In orderto reproduce combustion and knocking phenomena plausible foractual SI engines, the spark advances adopted in the tests were 15,25, and 35 CAD before TDC (BTDC), while the four inlet temper-atures (50, 80, 110, and 140 �C) were selected to take into accountthe inlet conditions that can be realized in both naturally aspiratedand supercharged engines, with and without intercooler. It israther obvious that some nonknocking cycles were also recorded,being, as already mentioned, the light knocking condition adoptedbased on a statistical approach. As discussed further on, some ofthe recorded nonknocking cycles were employed in the parametercalibration procedure to make the model safe also against false-positive.

As an overall resume (see Table 6), the operative conditionsexplored in this paper include eleven different fuel mixtures (puregasoline, gasoline-methane, gasoline-NG mixtures, pure methane,and pure natural gas), four inlet temperatures and three sparkadvances, which means a total of 132 operative conditions tested,resulting in a total amount of 6600 pressure cycles sampled.

As also observed in the previous works [10,11], the mainresonant knocking frequency of the CFR engine is around 6 kHz,as also confirmed by the theoretical solution of Draper’sequation [36]

f ¼ k1;0;0 � CS

p � B (8)

which, being k1,0,0¼ 1.841 the wave number for the first radialmode of vibration, CS the speed of sound (approximately 850 m/sconsidering a mean gas temperature of 2000 K) and B¼ 82.6 mmthe engine bore, yields f¼ 6.03 kHz.

According to this resonant knocking frequency, all the sampledpressure curves were filtered using a second order 3–20 kHz band-pass Butterworth filter with phase shift compensation, with theaim to highlight the knocking pressure oscillations and to removeunwanted noise.

For each single knocking pressure cycle recorded, the realcrank position at which auto-ignition occurred (indicated as#K,exp) was located at the position of the first filtered pressurepeak with amplitude higher or equal to 0.1 bar, as illustrated inFig. 3: here the knock onset position #K,exp is highlighted by theblack point.

Experimental Results and Discussion

Table 3 reports the compression ratios adopted to induce lightknocking in the gasoline–natural gas test, while Table 4 reportsthe data related to the gasoline–methane test.

It is worth to remind that the compression ratios in the first col-umn of both tables (i.e., related to 0% gas mass fraction) refers topure gasoline operation; the data shown, hence, allow to estimatethe strong effect played by the addition of even a small quantityof methane (Table 4) or natural gas (Table 3) to gasoline: asexample, considering the spark advance of 25 CAD BTDC andthe inlet temperature of 50 �C, the addition of only 20% in massof natural gas caused an increase of the light knocking compres-sion ratio in the order of 13%.

For any given set of model parameters (A, B, and n) and for anypressure/temperature history, the model proposed evaluateswhether the unburned gas undergoes auto-ignition, and the crankposition at which auto-ignition occurs, i.e., #K,mod. To this pur-pose the knock condition of Eq. (3) must be solved, using the igni-tion delay time model of Eq. (4), in the crank angle domain. Theauto-ignition condition hence becomes

ð#K;mod

#IVC

d#

x � s ¼ 1 (9)

where #IVC is the crank position at intake valve closure (IVC) andx is the engine angular velocity. For each single pressure trace,the knock onset position evaluated by the model #K,mod can bethen compared with the experimental measure, and their differ-ence assumed as the error produced by the model

e ¼ #K;mod � #K;exp (10)

For each set of model parameters (A, B, and n), the mean absoluteerror eMA can be evaluated as mean value over the total number ofpressure cycles N available for the fuel

eMA ¼

XN

i¼1

eij j

N(11)

where ei is the auto-ignition position error determined for the ithknocking pressure cycle using Eq. (10). For each fuel mixturetested, hence, the authors identified the model parameters, whichbest fitted the experimental data minimizing the mean absoluteerror eMA. The error minimization process was carried out usingthe Downhill simplex searching algorithm [37], whose searchingdomain was previously restricted by excluding all the parametersset which produced the following knocking condition with any ofthe nonknocking cycles:

ðMFB100

#IVC

d#

x � s ¼ 1 (12)

being MFB100 the crank position at which the mass fractionburned is 100%, and hence, the combustion is complete. This pre-liminary domain limiting procedure allowed to make the modelsafe against false-positive and represents the third important inno-vation of this work with respect to previous papers [10,11].

Table 7 resumes the results of the minimization algorithmapplied to the data regarding the three pure fuels, i.e., gasoline,methane, and natural gas. For each of the three fuels, the best fit

Fig. 3 Raw and filtered in-cylinder pressure signal with #K,exp

evaluation (methane mass fraction 60%, SA 5 35 CAD BTDC,TIN 5 140 �C)

041009-6 / Vol. 141, APRIL 2019 Transactions of the ASME

model coefficients are reported together with both mean and max-imum knock onset position error, i.e., eMA and jeMAXj.

It can be noted the relevant difference between the valuesassumed by model parameters determined for gasoline withrespect to the values obtained with natural gas or with methane,above all in terms of A and B, which is quite consistent with thehigh knock resistance difference between gasoline and methane ornatural gas.

According to the observation already made on the strong knockresistance increase obtained even with small addition of methaneor natural gas to gasoline (as also confirmed by the knocking com-pression ratio increments in Tables 3 and 4) and on the consequentconsideration that the knocking events produced during the com-bustion of gasoline-methane mixtures (or gasoline-natural gasmixtures) are always started by the auto-ignition of gasoline, theauthors supposed that, for the DF operation, the coefficients n andB (which characterize the fuel sensitivity to pressure and tempera-ture) assume the same values determined for pure gasoline opera-tion, thus entirely ascribing to the parameter A the increased auto-ignition retard due to the addition of methane (or natural gas); thesame assumption was made in Ref. [18] for the simultaneous com-bustion of n-heptane and isooctane. Employing the alreadydescribed minimum search algorithm to the mean absolute errordefined in Eq. (11), the authors determined the best fit values ofthe model parameter A for all the gasoline-methane mixtures andall the gasoline-natural gas mixtures tested (already listed inTables 3 and 4), i.e., for gas mass fraction ranging from 20% to80%: the results are listed in Table 8 together with the correspond-ing mean and maximum knock onset position errors. As can beobserved from both Tables 7 and 8, the error caused by the cali-brated model in the evaluation of the auto-ignition start is charac-terized by a mean absolute value lower than 1.5 CAD, while themaximum error ranges from less than 2 (DF operation) to 4.5CAD (for NG). It is also worth to point out that the highest valuesof the maximum error are obtained with the higher knock resistantfuels, as can be deduced by both Tables 7 and 8; this can beexplained considering that the lower reactive fuels (i.e., NG andmethane) required higher compression ratios to cause knocking,resulting in higher in-cylinder pressure and temperature values,and hence a rapid increase of the KI as function of crank position,which crossed the value of 1 (i.e., the auto-ignition condition)with high gradients. Due to the sampling resolution of the

experimental data recorded (i.e., 1 KI value for each CAD), theexact position at which the KI reached the value of 1 was obtainedinterpolating the two KI values closer to 1; it is clear, hence, that ahigher KI gradient involves a higher distance between the twointerpolated values, and hence a less accurate result of theinterpolation.

Figures 4 and 5 give a graphical representation of the agree-ment between the auto-ignition positions evaluated by the modelon the basis of the experimental data, and the direct measurement.As can be observed, a good agreement was found for each fuelmixture tested, being the model predicted values well gatheredaround the bisecting line, with R2 values higher than 0.95; thesame diagrams also report the amplitudes of the data dispersion,whose semivalues are related to the maximum absolute errorsreported in Table 8.

The results obtained demonstrate that, once properly calibrated,the model is able to predict the knock onset position with a

Table 8 Best fit values of model coefficient A determined forboth gasoline-methane and gasoline-NG mixtures tested(n 5 2.25, B 5 3800, TNTC1 5 713 K, TNTC2 5 873 K)

A eMA (CAD) jeMAXj (CAD)

NG mass fraction (%)20 0.0232 0.472 1.8640 0.0310 0.571 1.9860 0.0438 0.774 1.8780 0.0640 1.030 2.34

Methane mass fraction (%)20 0.0232 0.453 1.7840 0.0322 0.495 2.2260 0.0468 0.631 2.5080 0.0850 0.863 2.12

Fig. 4 Gasoline–natural gas test: comparison between esti-mated and experimental auto-ignition onset position (operativeconditions reported in Table 3, xGAS from 20% to 80%)

Fig. 5 Gasoline–methane test: comparison between estimatedand experimental auto-ignition onset position (operative condi-tions reported in Table 4, xGAS from 20% to 80%)

Table 7 Model parameters together with mean and maximumerror, determined for gasoline, NG, and methane

Fuel A n B eMA (CAD) jeMAXj (CAD)

Gasoline 0.0193 2.25 3800 0.569 2.93NG 0.00142 2.25 8906 1.38 4.46Methane 0.00560 3.25 11875 1.00 3.90

Journal of Engineering for Gas Turbines and Power APRIL 2019, Vol. 141 / 041009-7

maximum error of about 4.5 crank angle degrees, which is a verysatisfactory result from an engine optimization point of view,above all if the wide variety of pressure and temperature historiesused for model calibration is considered; as already mentioned,the experimental data used may represent, in effect, a variety ofengine geometries and thermodynamic conditions (thanks to theseveral different compression ratios and inlet temperaturesemployed), and many different fuel compositions (greatly variedwithin the tests executed, as resumed in Tables 3 and 4).

A Comprehensive Model for Gasoline–Gaseous

Fuel Mixtures

The graph reported in Fig. 6 reports the best fit values assumedby the model parameter A, as function of the gas mass fractionxgas, for three different DF mixtures: two of these mixtures weretested in the present work, i.e., gasoline-natural gas and gasoline-methane, while the third mixture, gasoline–propane, was tested ina previously published work [10]. The graph in Fig. 6 also showsthat, for each fuel mixture, the coefficient A can be expressed asfunction of the gas mass fraction xgas by the use of a fitting curve,as reported in the following equations:

AG�M ¼ 0:014 � EXP 2:223 � xgasð Þ

AG�N ¼ 0:016 � EXP 1:705 � xgasð Þ (13)

AG�P ¼ 0:019 � EXP 0:914 � xgasð Þ

here AG–M and AG–N represent the functions valid for thegasoline–methane and gasoline–natural gas mixture, obtained byinterpolation of the data listed in Table 8, while AG–P representsthe function valid for the gasoline–propane mixtures, evaluatedon the basis of the measurement performed in the previouswork [10] and considering the same DF auto-ignition parame-ters reported in Table 8 (i.e., n¼ 2.25, B¼ 3800, TNTC1¼ 713K, TNTC2¼ 873 K).

As a result, the very simple mathematical expressions inEq. (13) allow to obtain the values of the parameter A (and hencethe auto-ignition time using Eq. (4)) of a DF mixture composedby gasoline and a gaseous fuel (natural gas, methane, or propane)for any proportion between gasoline and the gaseous fuel in themixture. It must be remarked that each value in Fig. 6 refers to aDF mixture and cannot include the 100% gaseous fuel because,according to the assumption made, it was computed consideringthe gasoline sensitivity to pressure and temperature, i.e., all thedata in Fig. 6 have been obtained adopting the values of n and Band the NTC limit temperatures related to pure gasoline.

As far as the knock resistance of the fuel mixture is concerned,a correlation between the coefficient A and the fuel mixture MONis useful, as stated also by other authors [18].

On the other hand, the experimental activities previously car-ried out by the authors allowed to trace a correlation betweenMON and xgas not only for mixtures involving gasoline and natu-ral gas or methane [33] but also for the gasoline-propane mixtures[10], as reported in Fig. 7. According to these correlations, theauthors evaluated the MON of each fuel mixture reported inFig. 6, thus obtaining the representation of the model parameter Aas function of the mixture MON of Fig. 8.

As can be noted, the very interesting result in Fig. 8 is that,regardless of the gaseous fuel considered, it is possible to trace aunique simple correlation between the parameter ADF (valid forDF operation) and the fuel mixture MON

ADF ¼1

2754� eMON

21:18 (14)

with MON values ranging from 84 to 115.Remembering that, in DF operations, except for A, all the other

model parameters (B, n, and the NTC temperatures) assume thesame values valid for pure gasoline, Fig. 8 demonstrates that thesingle exponential correlation of Eq. (14) allows to predict theauto-ignition time delay for each possible fuel mixture composedby gasoline and a gaseous fuel of whatever composition, withknock resistance up 115 MON. This is the fourth innovation ofthe present paper with respect to previous works [10,11] and rep-resents also the most remarkable conclusion. With the aim toassess the reliability of this new correlation, the values adopted bythe coefficient ADF (determined by Eq. (14)) were introduced inthe model (Eqs. (4) and (9)) for the evaluation of the auto-ignitiononset of each fuel mixture reported in Fig. 6; the results were thencompared to the experimental measured values, thus re-evaluatingboth mean and maximum errors, as reported in Table 9 togetherwith the values assumed by ADF.

Fig. 7 Fuel mixture MON as function of xgas

Fig. 8 Model coefficient A as function of the mixtures MON

Fig. 6 Model coefficient A as function of the gaseous fuelmass fraction xGAS

041009-8 / Vol. 141, APRIL 2019 Transactions of the ASME

It can be noted that both mean and maximum errors obtainedusing the DF coefficient ADF revealed similar to the values previ-ously obtained for each single fuel mixtures (e.g., reported inTable 8): this confirms the reliability and accuracy of the new cor-relation expressed in Eq. (14), which can be then used to evaluatethe parameter A for each DF mixture whose knock resistance(MON) is known, regardless of gaseous fuel composition andmass fraction.

Conclusions

In this paper, the authors present an original model for theauto-ignition prediction of unburned gas in zero-dimensional ther-modynamic simulations of spark ignition engines fueled withgasoline–methane mixtures or gasoline–natural gas mixtures. Theoriginal aspect of the proposed model consists in its capability totake into account the NTC behavior exhibited by hydrocarbonsfuels such as gasoline and methane. The model was calibrated ona CFR engine properly equipped with a double-injection system,thus testing fuel mixtures with methane (or natural gas) contentranging from 0% to 100%. Moreover, the use of a CFR enginemade possible a large variation of inlet temperature and volumet-ric compression ratio, thus allowing to calibrate the model throughthousands of widely differentiated in-cylinder pressure (and tem-perature) curves, and making hence the model suitable for 0Dthermodynamic simulations of both naturally aspirated and super-charged spark ignition engines, with or without intercooling,fueled with gasoline–methane or gasoline–natural gas mixtures ofevery composition.

Once calibrated, the model revealed a very good accuracy inpredicting the onset of auto-ignition, with maximum errors in theorder of 4.5 CAD, and mean absolute error of 1.4 CAD, which arequite consistent for engine spark timing calibration purpose. Thereliability of the model against false-positive was also improvedby properly employing the available nonknocking cycles.

A very interesting result is also constituted by a further repre-sentation of the proposed model, which is valid only for the simul-taneous combustion of gasoline and a gaseous fuel (which couldbe methane, natural gas, LPG, propane, etc.) and allows to deter-mine the auto-ignition onset on the basis of the MON of the fuelmixture only. The accuracy of this last model representationrevealed as good as the others, with mean and maximum absoluteerror of 1 CAD and 3 CAD, respectively. This final correlationmay greatly facilitate engine designers in their knock-safespark timing calibration process by means of thermodynamic

simulations when gasoline–gaseous fuel mixtures of known MONare considered.

Symbols and Abbreviation

A, B, n ¼ fuel dependent model parametersADF ¼ model parameter A for DF operationA/F ¼ air to fuel ratio

(A/f)ST ¼ stoichiometric air to fuel ratioBTDC ¼ before top dead center

CAD ¼ crank angle degreesCFR ¼ cooperative fuel research

CR ¼ compression ratioE ¼ fuel activation energy

IVC ¼ intake valve closureKI ¼ knock integral

LPG ¼ liquefied petroleum gasm ¼ polytropic law coefficient

MON ¼ motor octane numberMFB100 ¼ crank position at which the mass fraction burned is

100% (complete combustion)N ¼ total number of pressure cycles acquired for each

operative conditionNG ¼ natural gas

NTC ¼ negative temperature coefficientp ¼ unburned gas pressure

pIGN ¼ unburned gas pressure at spark ignition timepIVC ¼ unburned gas pressure at IVC

pm ¼ experimental mean unburned gas pressureR ¼ universal gas constant

RCM ¼ rapid compression machinesRPM ¼ revolutions per minute

SA ¼ spark advanceSI ¼ spark ignition

t ¼ timeT ¼ unburned gas temperature

tIVC ¼ inlet valve closure timetKO ¼ knock onset time

TEnd-gas ¼ temperature of the end-gasTIGN ¼ unburned gas temperature at spark ignition time

TIN ¼ engine inlet temperatureTIVC ¼ unburned gas temperature at IVC

Tm ¼ experimental mean unburned gas temperatureTNTC1 ¼ lowest temperature of the fuel NTC zoneTNTC2 ¼ highest temperature of the fuel NTC zone

V ¼ in-cylinder volumeVIVC ¼ unburned gas in-cylinder volume at IVCxgas ¼ gaseous fuel mass fraction

DTNTC ¼ temperature variation of the fuel NTC zonee ¼ model error¼#K,mod�#K,exp

eMA ¼ model mean absolute erroreMAX ¼ model maximum absolute error

s ¼ ignition delayx ¼ engine angular velocity/ ¼ equivalence ratio¼ (A/F)ST/(A/F)

#IVC ¼ crank angle at inlet valve closure#K,mod ¼ auto-ignition crank position estimated by the model#K,exp ¼ experimental auto-ignition crank position

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