An empirical modeling approach for the ignition delay of fuel blends based on the molar fractions of fuel components

Fuel 164 (2016) 305–313

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An empirical modeling approach for the ignition delay of fuel blends based on the molar fractions of fuel components Jianan Ma 1, Kyoung Hyun Kwak 2, Byungchan Lee 3, Dohoy Jung ⇑ University of Michigan-Dearborn, 4901 Evergreen Rd, Dearborn, Michigan 48128, USA

a r t i c l e

i n f o

Article history: Received 7 April 2015 Received in revised form 24 September 2015 Accepted 25 September 2015 Available online 9 October 2015 Keywords: Auto-ignition Ignition delay model Fuel blend Negative temperature coefficient (NTC) Knock

a b s t r a c t An empirical ignition delay model has been developed for the fuel blends of isooctane, n-heptane, toluene and ethanol based on their molar fractions in the stoichiometric condition. The model employs traditional Arrhenius type correlation and cool-flame temperature rise correlations to describe the negative temperature coefficient (NTC) region for the fuel blends. The overall ignition delay of a fuel blend is correlated with individual ignition delay information based on the molar fraction of the fuel component in the mixture. The proposed model is successfully validated against the published experimental ignition delay data using various binary, ternary and quaternary fuel blends of isooctane, n-heptane, toluene and ethanol. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Engine knock in spark ignition (SI) engines is characterized by the noise that is transmitted through the engine structure when auto-ignition of unburned end gas ahead of flame front occurs [1]. Knock in SI engine is one of factors that limits higher compression ratio, spark advance, and intake boost level. An accurate and efficient numerical engine combustion model with a capability of predicting the auto-ignition phenomenon can be a powerful engine development tool during the early engine development stage by reducing prototype based experimental development cost and time. Auto-ignition is affected by the fuel properties as well as the cylinder temperature and pressure evolution during the combustion process. Since commercially available fuel is a complex blend of hydrocarbons, the characteristics of the auto-ignition of the fuel is strongly influenced by its composition. Ideally, chemical kinetics models would provide good prediction, but current researches on these chemical kinetics models are only available for a limited number of fuel components. In addition, the complexity and huge computational time make it impractical to incorporate them directly into an engine system level simulation. Reduced and

skeletal chemical kinetics models are more suitable for this type of application, but they still need calibration using experimental data and computation load can be still problematic depends on the type of simulation. Therefore, empirical auto-ignition correlations have been developed and widely used for variety of engine system simulations. The auto-ignition of hydrocarbon fuel is governed by fundamental chemical reaction principles and the ignition delay can be described by an Arrhenius type correlation. Livengood and Wu [2] developed the classic Knock-Integral approach using the data from a rapid compression machine to predict the time of knock occurrence. In their model, the auto-ignition is presumed to occur when the integral of the inverse of ignition delay correlation becomes unity over a period of time using the pressure and temperature history of the fuel–air mixture in the cylinder. The knock integral method has been widely used for knock predictions due to its concept of calculating ignition delay when charge conditions are not steady state [3–5]. An adaptable correlation developed by Douaud and Eyzat [6] includes octane number to an ignition delay correlation and had been validated for various commercially available fuels:

s ¼ 17:68ðON=100Þ3:402 p1:7 expð3800=T Þ ⇑ Corresponding author. Tel.: +1 (313)436 9137. E-mail addresses: [email protected] (J. Ma), [email protected] (K.H. Kwak), [email protected] (B. Lee), [email protected] (D. Jung). 1 Tel.: +1 (313)930 0626. 2 Tel.: +1 (734)239 5252. 3 Tel.: +1 (734)205 7530. http://dx.doi.org/10.1016/j.fuel.2015.09.069 0016-2361/Ó 2015 Elsevier Ltd. All rights reserved.

ð1Þ

where s is ignition delay (ms), p and T are pressure (atm) and temperature (K), and ON is the octane number. This single stage Arrhenius type model was validated by Kim and Ghandhi [7] by comparing the simple correlation model with detailed chemical kinetics model in predicting knock. They concluded that the Douaud

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Nomenclature Notation [A] [F] A C CCP Cp F K N n ON p P R T t VFA Y

a

b

concentration of air (mol/cm3) concentration of fuel (mol/cm3) air calibration coefficient coefficients for specific heat correlation constant pressure specific heat (J/K) fuel reaction rate constant total number of pure components in the fuel blend mole number octane number pressure (bar) product of pre-ignition reaction universal gas constant (J/mol K) temperature (K) time (ms) volume of fuel air mixture (cm3) molar fraction precursor species for ignition proportionality constant

and Eyzat Arrhenius correlation is as accurate as the chemical kinetics model in some specific regions. However, it is not able to describe the two-stage ignition and deflagration with a single Arrhenius type correlation. It does not capture the cool flame phenomenon [8], which paraffin class fuels with the form of CnH2n+2(n > 2) exhibit during the ignition delay period. Cool flame phenomena are usually associated with so called negative temperature coefficient (NTC) behavior of the reaction rate in low and intermediate temperature regions, and are characterized by an abrupt temperature rise after the pre-cool flame delay period. An example of such ignition delay is shown in Fig. 1. The cool flame region is shown in the upper right corner of the plot, where twostage ignition with cool flame phenomenon takes place. The cool flame releases heat which increases temperature and such effect shortens overall ignition delay. In the intermediate temperature region, an evidence of the NTC behavior can be observed. As initial temperature increases, cool flame reaction slows down and eventually shuts off [9]. Therefore, cool flame temperature rise effect degrades and ignition delay becomes longer as initial temperature

Ignition delay (ms)

100

n-heptane/air at 13.5 bar, =1 [10]

Low Temperature Region (Cool Flame Region)

10

Intermediate Temperature Region

1 High Temperature Region

0.1 0.68

0.88

1.08

1.28

1.48

1.68

1000/T (1/K) Fig. 1. Shock tube ignition delay versus reciprocal temperature profiles extracted from Ciezki and Adomeit [10] for n-heptane with stoichiometric fuel/air equivalent ratio.

ma s sb sc shCF shi /

x

volume fraction of alcohol characteristic ignition delay (ms) ignition delay of blend fuel (ms) cool flame ignition delay (ms) exothermic reaction delay at post cool flame condition (ms) exothermic reaction delay at pre-cool flame condition (ms) equivalence ratio reaction rate (mol/s)

Subscripts b blend CF evaluated at post cool flame condition cc coefficient correlation F fuel i evaluated at initial condition ign evaluated at ignition j fuel component in blend MEOH methanol PRF primary reference fuel

increases. In the high temperature region, ignition delay shows positive temperature coefficient behavior again. In order to model the two-stage ignition and capture the NTC region, Yates and Viljoen [11] developed an Arrhenius type two stage ignition delay model. The model was calibrated with results from more than 1500 detailed chemical kinetics simulations to fit a wide range of temperatures, pressures, fuel–air equivalent ratios and octane numbers. It predicts the time delay before the cool flame, abrupt temperature rise and overall ignition delay for primary reference fuel (PRF) and methanol blends by employing the Knock-Integral method explained in Livengood and Wu [2] and expanding it to a two-stage integration by integrating different correlations in different temperature regions. This model describes the trend of the NTC region in a reasonable manner. Iqbal et al. [12] also employed the model and calibrated it using detailed CHEMKIN chemical kinetics model for toluene reference fuel 91 (TRF91: 53.8% isooctane, 13.7% n-heptane, 32.5% toluene). The fuel is regarded as a better representative of the gasoline than PRF because TRF exhibits similar octane sensitivity as commercial gasoline does. In their research, the octane number was not used but exhaust gas recirculation (EGR) rate was taken into account. He et al. [13] and Walton et al. [14] incorporated oxygen fraction and fuel air equivalent ratio in their correlation for the ignition delay of isooctane. Then Goldsborough [15] improved it based on the functional behavior exhibited by a detailed chemical kinetics to capture the NTC region. The correlation employs a single Arrhenius type power law formulation including equivalence ratio, temperature, pressure, and oxygen concentration. The coefficients of the Arrhenius type correlation are expressed as a combination of two quadratic terms with respect to temperature and pressure to calculate the NTC behavior. Syed et al. [16] developed a simple correlation for the ignition delay of gasoline-ethanol blend fuel. The model was calibrated using the result from a CHEMKIN closed homogeneous reactor model with a validated semi-detailed chemical kinetics mechanism consisting of 142 species and 672 reactions. It employed pre-defined coefficient tables corresponding different temperatures, equivalence ratios and ethanol volume fractions in order to describe appropriate ignition delay behaviors in wide range of conditions.

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J. Ma et al. / Fuel 164 (2016) 305–313

Calibration process of the previous models for two-stage ignition is complex and requires extensive experimental or numerical data in wide range of temperature, pressure and equivalence ratio conditions. The calibration obtained from these data is typically limited to a specific fuel. When these models are used for various fuels with different ignition delay characteristics, distinctive calibrations for each fuel are necessary. To reduce intensive effort on the calibration process, octane number is adapted in the model [1,11], volume fraction of fuel additive [11,16] or empirical coefficient correlations [11] are used to extend model validity on different fuel kinds. In practice however, octane number of a specific fuel is often unknown and additional model for octane number [17,18] might be needed. This brings another level of complexity to the model. In addition, using additive volume fraction or building empirical coefficient requires even more data and effort to begin with. Meanwhile, the majority of the researches [12–16,19] have been performed on gasoline surrogates instead of the commercially available fuels with complex and inconsistent composition. Ignition delays for the various gasoline surrogates, such as 35% n-heptane/63% toluene [19], 63% isooctane/20% toluene/17% n-heptane [20] and 37.8% isooctane/10.2% n-heptane/12% toluene/40% ethanol [21], have been measured in shock tubes and rapid compression machines. The results of surrogates are widely used to develop empirical correlations and chemical kinetics models for real fuels. Although many researchers have worked on the analysis of the influences of additives such as ethanol [18] and toluene [22] on PRFs, they have not found simple governing principles on how each constituent in the blend affects the overall ignition delay of the mixture. Therefore, the goal of this study is to develop a predictive empirical modeling approach to calculate the ignition delay of a fuel blend including the gasoline surrogates. By developing a blending rule based on fuel composition, the individual ignition delay of fuel component can be appropriately used to calculate total ignition delay of a surrogate blend. In addition, the proposed model is able to capture the NTC region of a fuel blend adequately for practical applications. It also provides high computational efficiency and can be directly incorporated into an engine combustion simulation. The developed model was validated with experimental data of binary, ternary and quaternary blends from literatures. The details of the model development and validation are explained in the following sections.

Z

t CF

dt

sc

0

¼1

ð3Þ

where sc is the characteristic time of pre-cool flame ignition delay which is the time interval between the start of reaction and the appearance of cool flame temperature rise evaluated at the initial temperature and pressure condition. Yates and Viljoen [11] proposed simpler form of overall ignition delay using Eqs. (2) and (3) for the condition where pressure and temperature can be assumed constant during the initial stage of ignition process. In such condition, Eq. (2) can be simplified as

tCF

shi

þ

t ign  tCF

shCF

¼1

ð4Þ

Furthermore, tCF equals to sc from Eq. (3). By rearranging Eq. (4) and substituting tCF with sc, overall two-stage ignition delay can be obtained by the following equation.

 tign ¼ sc þ shCF 1 

sc shi

 ð5Þ

Each of the characteristic exothermic reaction delay and the pre-cool flame ignition delay can be described by an Arrhenius type equation. Thus, sc, shi and shcf are expressed as follows.

 C id;4 Ti   C id;8 C id;7 C id;5 shi ¼ / C id;6 pi exp Ti   C id;8 C id;7 C id;5 shCF ¼ / C id;6 pCF exp T i þ DT CF

sc ¼ /Cid;1 C id;2 pCi id;3 exp



ð6Þ ð7Þ ð8Þ

where / is the fuel–air equivalence ratio, pi is the initial pressure, Ti is the initial temperature, pCF is the post cool flame pressure which can be calculated based on the ideal gas law using the post cool flame temperature, Ti + DTCF, and DTCF is cool flame temperature rise. A termination function was introduced by Yates and Viljoen [11] to prevent DTCF from becoming a negative value at high temperature as follows.

 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DT CF ¼ 0:5C CF;1 DT þ DT 2 þ 4750

ð9Þ

where

"

2. Two-stage ignition delay model

C

DT ¼ C CF;2 T i  C CF;3 pi CF;4 /CCF;5

The ignition delay correlation introduced by Yates and Viljoen [11] predicts the trend of the two-stage ignition with the cool flame phenomenon reasonably well. Initially, the model evaluates ignition delay with initial conditions. Then, cool flame temperature rise and time are calculated. After cool flame temperature rise, characteristic ignition delay time need to be evaluated with new conditions. Thus by employing the ignition delay integral method of Livengood and Wu [2], the overall two-stage ignition delay can be described as

Z 0

t CF

dt

shi

Z þ

t ign

t CF

dt

shCF

¼1

ð2Þ

where tCF is defined as the time at the appearance of the cool flame temperature rise, tign is the time at ignition, shi is the characteristic time of exothermic reaction delay evaluated at the initial condition, and shCF represents the characteristic time of exothermic reaction delay evaluated at the post cool flame condition. For engine-like condition where pressure and temperature changes, the time at cool flame temperature rise, tCF, need to be calculated using ignition delay integral method.

CCF;6 # 100 99 þ /



ð10Þ

In Eqs. (6) though (10), Cid,1 through Cid,8 and CCF,1 through CCF,6 are coefficients varying from fuel to fuel. In Yates and Viljoen [11], the coefficients for different grades of PRF are obtained using numerical simulations. Then empirical coefficient correlation is constructed as as a second-order polynomial with respect to the octane number.

 C PRF ¼ C cc;1 þ C cc;2

  2 ON ON þ C cc;3 100 100

ð11Þ

where Ccc,1, Ccc,2, and Ccc,3 are the coefficients of the empirical correlation and ON is the octane number. For the case of methanol-PRF blend, Yates and Viljoen modified the coefficients for the post cool flame ignition (Cid,5, Cid,6, Cid,7 and Cid,8) by linear interpolation based on a volume fraction of methanol additive.

C b ¼ C PRF ð1  v a Þ þ C MEOH v a

ð12Þ

where Cb is the calibration coefficient for the methanol-PRF blend and CMEOH is the calibration coefficient for pure methanol and ma is the volume fraction of methanol in the mixture. In addition,

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J. Ma et al. / Fuel 164 (2016) 305–313

following modification were applied for the coefficients Cid,3, CCF,1 and CCF,2.

  C b ¼ C PRF 1  C cc;4 v a þ C cc;5 v a 2

ð13Þ

Since the coefficient correlations described in Eqs. (11)–(13) are in functions of the octane number and the methanol additive volume fraction, it does not have enough sensitivity to the fuels with different ignition delay characteristics other than the fuels used to calibrate these correlations (methanol-PRF blend). In case of particular fuel of interest do not show similar ignition behavior to PRF and its blend with methanol additive, Eqs. (11)–(13) need to be reformulated. This reformulation requires calibrated coefficients of Eqs. (6)–(8) and (10) using either intensive experimental data or validated results from detailed chemical kinetic model. In this study, a new modeling approach is developed for various fuel mixtures to avoid the reformulation and calibration process of the coefficient correlations which only works for a particular fuel. In the new approach, a new blending rule to predict ignition delay of fuel blend is derived using the characteristic delay of different pure fuels. A new ignition delay model is derived from Eqs. (4)– (10) based on molar fractions of pure fuel components in the blend. In this way, ignition delay of fuel surrogates of various pure fuels can be predicted without immense effort to develop or calibrate new coefficient correlations for different fuel blends. The details of formula derivation are described in the following section. 3. Ignition delay modeling approach for fuel blends The auto-ignition reaction mechanism of a fuel can be described by a global pre-ignition chemistry. For one mole of fuel, the reaction can be expressed as

F þ A!a þ P K

ð14Þ

where F and A are fuel and air respectively, a is a precursor for autoignition and P represents remainder of radicals produced from the pre-ignition reaction. The precursor a represents the radicals involved in the initiation of auto-ignition. When the molar concentration of a reaches a critical value, auto-ignition is assumed to occur. Since this global reaction ends at time of ignition, reaction rate is proportional to the inverse of ignition delay. Therefore,

x¼

d½F 1 ¼b dt s

ð15Þ

where x is the reaction rate, and [F] is the concentration of fuel in fuel–air mixture, s is the ignition delay and b is a proportionality constant which is expressed in the unit of concentration (mol/cm3). By integrating Eq. (15) from zero to the time of ignition, the proportionality constant becomes equal to the fuel concentration. Then, the reaction rate can be written as

1

x ¼ ½F s

N X 1 j¼1

1

sb

¼

N 1 X 1 ½F j  ½F b  j¼1 sj

sj

½F j  ¼

1

sb

½F b 

ð17Þ

where [Fj] is the molar concentration of the fuel component j in the blend, [Fb] is the molar concentration of the entire fuel blend, and N

ð18Þ

The molar concentration of fuel in Eq. (18) is evaluated for the fuel–air mixture. Thus it changes as equivalence ratio changes. To avoid this, the molar fraction of fuel component in the fuel blend can be used instead of the molar concentration. By definition, the molar fraction is expressed using the molar concentration of individual fuel component and the mixture.

Y F;j ¼ nF;j =nF ¼

nF;j =V FA ¼ ½F i =½F b  nF =V FA

ð19Þ

where YF,j is the molar fraction of the fuel component j in the fuel blend, nF,j is the number of moles of the fuel component j in the fuel blend, nF is the total number of moles of the fuel blend, and VFA is the total volume of the fuel–air mixture. Then, Eq. (18) can be rewritten in terms of molar fraction using Eq. (18).

1

sb

¼

N X 1

ð20Þ

Y F;j

sj

j¼1

Eq. (20) is the governing equation that correlates the characteristic ignition delays of the individual fuel components to the characteristic ignition delay of the mixture. The blending rule for the two stage ignition delay model is developed using Eq. (20). The two-stage ignition model of Yates and Viljoen describes the pre-cool flame ignition delay (sc) and the characteristic exothermic reaction delays of pre and post cool flame rise (shi and shCF). Each delay can be described as the result of semi-global reactions in terms of Eq. (14). For the individual fuel component j in the fuel blend, the individual characteristic delays are expressed as follows.

 C id;4;j Ti   C id;8;j C id;7;j C id;5;j shi;j ¼ / C id;6;j pi exp Ti   C id;8;j shCF;j ¼ /Cid;5;j C id;6;j pCCFid;7;j exp T i þ DT CF

sc;j ¼ /Cid;1;j C id;2;j pCi id;3;j exp



ð21Þ ð22Þ ð23Þ

Then, the characteristic delays of the fuel blend can be written as

sc;b ¼

!1

N X 1

sc;j

j¼1

shi;b ¼

ð16Þ

A global pre-ignition reaction mechanism of a blend of N number of fuels assumed as the sum of N number of semi-global prereactions for each fuel component which produces the precursor a and does not consumes. By assuming fuel components do not react with each other and that the individual fuel contributes a specific reaction rate for the precursor generation, the reaction rate of the global pre-ignition reaction for the fuel blend can be described as the summation of the individual reaction rates.

xb ¼

is the total number of fuel components in the blend. Then, the ignition delay of the fuel blend can be expressed as

N X 1 j¼1

shCF;b ¼

shi;j

!1 ð25Þ

Y F;j

N X 1 j¼1

ð24Þ

Y F;j

shCF;j

!1 ð26Þ

Y F;j

The cool flame temperature rise, DTCF in Eq. (23) is a global value which needs to be evaluated based on the temperature rises of individual fuel components. The global cool flame temperature rise of the fuel can be calculated by the specific heat weighted average temperature.

DT CF;b ¼

N X j¼1

!,

DT CF;j cp;j Y F;j

N X cp;j Y F;j

! ð27Þ

j¼1

where DTCF,j is the cool flame temperature rise of the fuel component j and cp,j is the specific heat of the fuel component j.

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J. Ma et al. / Fuel 164 (2016) 305–313

The specific heat can be calculated using empirical correlation given in Heywood [1] as follow.

ð28Þ

where Ccp,1 through Ccp,5 are empirical coefficients. The characteristic delay times described in Eqs. (23)–(26) and the global cool flame temperature rise in Eq. (27) are used for calculating overall ignition delay of a fuel blend. Depending on the circumstances of pressure and temperature changes, the integral forms in Eqs. (2) and (3) or the simple form in Eq. (5) can be used.

isooctane / air, =1 * data are scaled with p-0.79 Ignition delay (ms)

cp 1 ¼ C cp;1 þ C cp;2 T þ C cp;3 T 2 þ C cp;4 T 3 þ C cp;5 2 R T

100

10

1

Exp. 40 bar [23]

0.1 Exp. 40 bar [24] * Exp. 41 bar ±2.1 bar [22]

0.01 0.7

0.85

1

4. Results and discussions

1.15

1.3

1.45

1.6

1000/T (1/K)

(a) Isooctane ignition delay comparison

4.1. Model calibration

100

Ignition delay (ms)

n-heptane/ air, =1 * data are scaled with p-1.64 10

1 Exp. 13.5 bar [10] Exp. 13.5 bar [20] * Exp. 42 bar [10] Exp. 40 bar [23] Exp. 40 bar [22] Exp. 40 bar [20] *

0.1

0.01 0.7

0.85

1

1.15

1.3

1.45

1.6

1000/T (1/K)

(b) n-heptane ignition delay comparison 10

toluene / air, =1 * data are scaled with p-0.93 Ignition delay (ms)

In this study, model coefficients in Eqs. (6)–(10) were calculated and the coefficient library was developed for four pure fuels (isooctane, n-heptane, toluene and ethanol) using the least square method with the experimental data from the shock tube experiments [10,22–26]. Then, to validate the proposed model capabilities, the predicted ignition delays of different binary mixtures, ternary mixtures and quaternary mixtures were compared with experimental data obtained from the literatures [19–23,27,28]. All the experimental data used were measured from three different shock tube facilities. A summary of the experimental data sources used in this study is presented in Table 1. To confirm the compatibility of using the data from different setups, selected pure fuel data from each experimental setup were compared and examined for any significant deviations between test setups and the comparisons are presented in Fig. 2. In the comparison, pressure dependency is scaled as pn with an exponent, n, which is provided with experimental data from each literature, except for ethanol. For ethanol, the exponent was determined by a linear regression analysis of experimental data. The comparisons of pure fuels from different test setups show that the test results are reasonably consistent with each other thus the data from different test setups can be used for the validation of the proposed model.

1

Exp. 40 bar [24] * Exp. 40 bar [22]

Using the least square method, model coefficients in Eqs. (6)–(10) were calculated for each pure fuel. In this study, all comparisons are accomplished at stoichiometric condition thus

0.1 0.7

0.85

1

1.15

1.3

1000/T (1/K)

(c) Toluene ignition delay comparison 10

Table 1 Summary of experimental data and test setups from literatures [10,19–28]. Pure fuels

Blended fuels

RWTH Aachen University

Isooctane [23] n-heptane [10] n-heptane [23] Ethanol [26]a

Isooctane/n-heptane [23]

University of Duisburg-Essen

Isooctane [22] n-heptane [22] Toluene [22] Ethanol [25]

Isooctane/toluene [22] n-heptane/toluene [22] n-heptane/toluene [19] Isooctane/ethanol [28] Isooctane/n-heptane/ethanol [27] Quaternary mixture [21]

Isooctane [24] n-heptane [20] Toluene [24]

Isooctane/n-heptane/toluene [20]

Stanford University

a Test data is obtained using a different shock tube setup from [10] and [21], but test results are comparable.

ethanol / air, =1 * dataare scaled with p-0.77 Ignition delay (ms)

Test setups

1

0.1

Exp. 30 bar [25] * Exp. 30 bar [26] *

0.01 0.7

0.85

1

1.15

1.3

1000/T (1/K)

(d) Ethanol ignition delay comparison Fig. 2. Comparison of pure fuel ignition delay data from different experimental setups.

J. Ma et al. / Fuel 164 (2016) 305–313 100

isooctane / air, =1 Ignition delay (ms)

the coefficients, Cid,1, Cid,5, CCF,5 and CCF,6 are not used. Table 2 shows the coefficient library for different fuel component and the calibration results are given in Fig. 3. The experimental data of isooctane in Fig. 3(a) show a weak but noticeable NTC behavior. In Fig. 3(b), a typical NTC behavior of paraffin fuels can be observed for n-heptane. The results of the calibrated model follow the characteristics of both fuels remarkably well. Toluene and ethanol data in Fig. 3(c) and (d) rarely show the NTC behavior. Thus the auto-ignition characteristic of these fuels can be modeled with a single stage auto-ignition. In the blending rule, the format of correlations should be the same for both single and two-stage ignition fuels. To retain the same format for a single-stage ignition fuel, the coefficients for Eqs. (21)–(23) are kept the same and coefficients regarding cool flame temperature increase (CCF,1 through CCF,6) are set all zero. Then the characteristic delays described in Eqs. (21)–(23) are effectively the same for single-stage ignition fuels. Therefore, single-stage ignition fuels contribute uniform characteristic ignition delays in post cool flame period of the fuel blend. The results of the calibration also show good agreements with the experimental trends of toluene and ethanol. Overall, the calibrations for pure fuels give satisfactory results. The coefficients of determination for the calibrated models are 0.9501, 0.9347, 0.9351 and 0.8136 for isooctane, n-heptane, toluene and ethanol respectively.

10

1 Exp. 13 bar [23] Exp. 17 bar [23] Exp. 34 bar [23] Exp. 40 bar [23] Current model 13 bar Current model 17 bar Current model 34 bar Current model 40 bar

0.1

0.01 0.7

0.85

1

1.15

n-heptane / air, =1 10

1 Exp. 13.5 bar [10] Exp. 19.3 bar [10] Exp. 40 bar [23] Current model 13.5 bar =1 Current model 19.3 bar =1 Current model 40 bar =1

0.1

0.01 0.7

Isooctane

n-heptane

Toluene

Ethanol

5.05E06 1.758 14,165 2.52E06 1.103 17,115 3.418 0.513 664.6 0.048

1.69E08 0.377 14,169 2.48E05 1.100 14,378 1.440 1.050 800.1 0.052

2.27E03 0.866 9,391 2.27E03 0.866 9,391 0 0 0 0

7.00E06 0.770 14,000 7.00E06 0.770 14,000 0 0 0 0

Note that the coefficients Cid,1, Cid,5, CCF,5 and CCF,6 are not used at stoichiometric condition, thus they are not listed in the table.

0.85

1

1.15

1.3

1.45

1.6

1000/T (1/K)

(b) n-heptane calibration results 100

Ignition delay (ms)

toluene/ air, =1 * data are scaled with p-0.93 10

1 Exp. 16 bar [24] * Exp. 40 bar [22] Exp. 50 bar [24] * Current model 16 bar Current model 40 bar Current model 50 bar

0.1

0.01 0.7

0.85

1

1.15

1.3

1000/T (1/K)

(c) Toluene calibration results 100

ethanol /air, Ignition delay (ms)

Coefficient Cid,2 Cid,3 Cid,4 Cid,6 Cid,7 Cid,8 CCF,1 CCF,2 CCF,3 CCF,4

1.6

100

For the validation of proposed model, ignition delays of various fuel blends of the four pure fuels are calculated and compared with experimental data. Blend ratio of the mixtures is given by % of liquid volume. The calibrated coefficients of the pure fuels are maintained the same for the validation.

Table 2 Calibration result for different fuel component.

1.45

(a) Isooctane calibration results

4.2. Model validation

4.2.1. Binary mixture Comparisons of predicted ignition delays by the proposed model with experimental data for various binary mixtures are presented in Figs. 4–7. Fig. 4 shows the comparison of various blend ratios of isooctane and n-heptane at the stoichiometric equivalence ratio and 40 bar condition. The blend ratios for the comparison are 100%/0%, 90%/10%, 60%/40% and 0%/100% of isooctane/n-heptane. In the figure, the ignition delay predictions trace the experimental data accurately in a wide range of temperature variations. The NTC behaviors of two different blends (90% and 60% of isooctane) are properly captured. The results of 10% of toluene mixed with 90% of isooctane or 90% of n-heptane are shown in Fig 5. In the figure, the NTC behaviors of toluene-doped isooctane and n-heptane are precisely

1.3

1000/T (1/K)

Ignition delay (ms)

310

=1

10

1 Exp. 10 bar [25] Exp. 19 bar [26] Exp. 40 bar [26] Exp. 50 bar [25] Current model 10 bar Current model 19 bar Current model 40 bar Current model 50 bar

0.1

0.01 0. 7

0.85

1

1.15

1.3

1000/T (1/K)

(d) Ethanol calibration results Fig. 3. Comparison of experimental data and calibrated model results for isooctane, n-heptane, toluene, and ethanol.

311

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captured by the model predictions. In Fig. 6, results of 65% of toluene mixed with 35% of n-heptane in various pressure conditions are presented. The experimental result shows less pronounced NTC behavior due to high content of toluene in the mixture. The model predictions are agreed with experiment very well at higher temperature above 870 K (1000/T of 1.15 and below)

100

isooctane + n-heptane 40 bar, ϕ =1

Ignition delay (ms)

10

1 Exp. 100% isooctane [23] Exp. 90% isooctane [23] Exp. 60% isooctane [23] Exp. 100% n-heptane [23] Current model 100% isooctane Current model 90% isooctane Current model 60% isooctane Current model 100% n-heptane

0.1

0.01 0.7

0.85

1

1.15 1.3 1000/T (1/K)

1.45

1.6

Fig. 4. Comparison of experimental data and the model results for isooctane and n-heptane mixture.

while the model overpredicts slightly at lower temperature below 800 K (1000/T of 1.25 and above). However it is worth nothing that the calibration of toluene in this study was made with the experimental data in relatively narrow temperature range (1000/T of 0.8–1.2) compared to isooctane and n-heptane as seen in Fig. 3 (c). In addition, 65% of toluene content in this case is much larger than the case shown in Fig 5. Therefore, effect of toluene to mixture ignition delay becomes larger and the deviations are more noticeable. In Fig. 7, the comparison for 75% of isooctane and 25% of ethanol mixture is presented. Temperature range of the experimental data does not reach into low temperature where isooctane shows the NTC behavior more noticeably. Thus the mixture shows no NTC behavior. The model predicts the experimental data trend fairly well and shows relatively weak NTC behavior in just outside of low temperature bound of experimental data. 4.2.2. Ternary mixture Three different gasoline surrogates are used for the validation of the proposed model for ternary mixtures and the comparisons are presented in Figs. 8 and 9. Fig. 8 is the case of a mixture with 62% of isooctane, 18% of n-heptane and 20% of ethanol. The experimental data is obtained in wide range of temperature and minor NTC behavior is observed. The model show moderate underpredictions, but the general trends of experimental data are captured. In Fig. 9 (a) and (b), two different blend ratio of isooctane, n-heptane and

10

10

75% isooctane + 25% ethanol 30 bar, =1

10% toluene mixed with 90% isooctane or 90% n-heptane 40 bar, =1

Ignition delay (ms)

Ignition delay (ms)

100

1 Exp. isooctane 90% [22]

0.1

1

0.1

Exp. isooctane 75% [28]

Exp. n-heptane 90% [22]

Current model 75% isooctane

Current model isooctane 90 %

0.01 0.7

Current model n-heptane 90 %

0.01 0.7

0.85

1

1.15

1.3

1.45

0.85

1000/T (1/K) Fig. 5. Comparison of experimental data and the model results for isooctane/toluene and n-heptane/toluene mixtures.

100

Ignition delay (ms)

Ignition delay (ms)

35% n-heptane + 65% toluene =1

1

Exp. 10 bar [19] Exp. 30 bar [19] Exp. 50 bar [19] Current model 10 bar Current model 30 bar Current model 50 bar

0.1

0.7

0.85

1

1.15 1.3 1000/T (1/K)

1.45

1.3

Fig. 7. Comparison of experimental data and the model results for isooctane and ethanol mixture.

100

10

1.15

1 1000/T (1/K)

1.6

10

62% isooctane + 18% n-heptane + 20% ethanol =1

1 Exp. 30 bar [27] Exp. 50 bar [27]

0.1

Current model 30 bar Current model 50 bar

1.6

Fig. 6. Comparison of experimental data and the model results for n-heptane and toluene mixture in various pressures.

0.01 0.7

0.85

1

1.15

1.3

1.45

1.6

1000/T(1/K) Fig. 8. Comparison of experimental data and the model results for isooctane, nheptane and ethanol mixture.

J. Ma et al. / Fuel 164 (2016) 305–313

toluene mixtures are used for comparisons. The temperature range of experimental data for these two fuel blends are focused on mid to high temperature ranges. Mixture A contains 63% of isooctane, 17% of n-heptane and 20% of toluene and mixture B contains 69% of isooctane, 17% of n-heptane and 14% of toluene. For both blends, the model predictions agree with the experimental results with a remarkable accuracy. 4.2.3. Quaternary mixture In Fig. 10, the comparison for a quaternary mixture (37.8% of isooctane, 10.2% of n-heptane, 12% of toluene and 40% of ethanol) is presented. In the figure, the experimental data for 30 bar and 50 bar conditions at low temperature range are scattered and difficult to differentiate them from each other. The model prediction for the quaternary mixture lies within the distribution of experimental data which is acceptable. 4.3. Fuel blend NTC behavior The comparisons presented in Section 4.2 show that NTC behavior of a fuel blend generally becomes stronger as the fraction of a certain fuel components with strong NTC behavior increases. The proposed model captures these NTC behavior changes of fuel blends properly by calculating the cool flame temperature rise of the mixtures using Eq. (27). As a demonstration of the model capability, the ignition delay and the cool flame temperature rise are presented in Fig. 11 for various blend ratios of n-heptane and toluene mixture. Fig. 11(a) shows diminishing NTC behavior as

100

10

1

Exp. 10 bar [21] Exp. 30 bar [21] Exp. 50 bar [21] Current model 10 bar Current model 30 bar Current model 50 bar

0.01 0.7

0.85

1

1.15

1.3

Fig. 10. Comparison of experimental data and the model results for quaternary mixture.

100

Exp. 16.8 -19.9 bar [20] Exp. 49.3-52.8 bar [20] Current model 18 bar

n-heptaneand toluene 40 bar, =1

10

1 Model 90% n-heptane Model 60% n-heptane Model 30% n-heptane Model 10% n-heptane

0.1

Current model 51.5 bar

0.85

1

1.6

1000

1

0.01 0.7

1.45

1000/T (1/K)

63% isooctane + 17% n-heptane + 20% toluene =1

0.1

37.8% isooctane + 10.2% n-heptane + 12% toluene + 40% ethanol =1

0.1

Ignition delay (ms)

Ignition delay (ms)

10

the fraction of n-heptane reduces in the mixture. Fig. 11(b) shows the cool flame temperature rise which drops significantly with reduced n-heptane fraction at low temperature region. Weak NTC behavior of mixture containing low n-heptane is due to the lower cool flame temperature rise which causes slower ignition. The trend of cool flame temperature rise of the proposed model is physically viable, since less exothermic reactions of cool flame phenomenon happen as the fraction of n-heptane decreases.

Ignition delay (ms)

312

1.15

0.01 0.7

1.3

1000/T (1/K)

0.85

1

1.15

1.3

1.45

1.6

1000/T (1/K)

(a) Isooctane/n-heptane/toluene mixture A

(a) Ignition delay comparison of various blend ratios 500

69% isooctane + 17% n-heptane +14% toluene =1

Cool flame temperature rise (K)

Ignition delay (ms)

10

1

Exp. 24.9 -25.3 bar [20]

0.1 Exp. 49.9 -59.7 bar [20] Current model 25 bar Current model 54 bar

0.01 0.7

0.85

1

1.15

1.3

1000/T (1/K)

(b) Isooctane/n-heptane/toluene mixture B Fig. 9. Comparison of experimental data and the model results for isooctane, n-heptane and toluene mixture.

450

Model 90% n-heptane

400

Model 60% n-heptane Model 30% n-heptane

350

Model 10% n-heptane

300 250 200 150 100 50 0 0.7

0.85

1

1.15

1.3

1.45

1.6

1000/T (1/K)

(b) Cool flame temperature rise for various blend ratios Fig. 11. Comparison of ignition delay calculation for n-heptane and toluene mixtures.

J. Ma et al. / Fuel 164 (2016) 305–313

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4.4. Benefit of the blending rule approach of the proposed model

References

In this study, the proposed model successfully demonstrated its capability to calculate various blends only with the model calibration coefficients for fuel components. The calibration process is reasonably simple because the model does not require extensive experimental or numerical data of any fuel blend. Therefore the expense of calibration process is greatly reduced compared to previous empirical ignition delay models for two-stage ignition delay. Generally, the previous models are not designed for generic fuel blend and limited to a specific fuel. Thus, they require distinctive calibrations for each fuel blend. Several models tried to extend their model for various blend ratios of a specific fuel by including a volume fraction of a fuel additive in the correlations. In few other models, empirical coefficient correlation is used as well. However they are still limited to a specific fuel blend, therefore recalibration or reformulation of the correlation is required for different fuels. The cost and time consumption of this process is excessive because a huge data set is required over full range of blend ratio, temperature and pressure. The approach of current study requires calibrations of only pure components for the various blends of fuels, which are clearly much simpler tasks.

[1] Heywood JB. Internal combustion engine fundamentals. New York: McGrawHill; 1988. [2] Livengood JC, Wu PC. Correlation of auto-ignition phenomena in internal combustion engines and rapid compression machines. Proc Combust Inst 1955:347–56. [3] Soylu S, Van Gerpen J. Development of an autoignition submodel for natural gas engines. Fuel 2003;82:1699–707. [4] Shahbakhti M, Lupul P, Koch CR. Predicting HCCI auto-ignition timing by extending a modified knock-integral method. SAE paper no. 2007-01-0222; 2007. [5] Elmqvist C, Lindstrom F, Angstrom H-E, Grandin B, Kalghatgi G. Optimizing engine concepts by using a simple model for knock prediction. SAE paper no. 2003-01-3123; 2003. [6] Douaud AM, Eyzat P. Four-octane-number method for predicting the antiknock behavior of fuels and engines. SAE paper no. 780080; 1978. [7] Kim KS, Ghandhi J. Preliminary results from a simplified approach to modeling the distribution of engine knock. SAE paper no. 2012-32-0004; 2012. [8] Glassman I, Yetter RA. Combustion. 4th ed. CA: Academic Press; 2008. [9] Law CK. Combustion physics. NY: Cambridge University Press; 2006. p. 113–5. [10] Ciezki HK, Adomeit G. Shock-tube investigation of self-ignition of n-heptaneair mixtures under engine relevant conditions. Combust Flame 1993;93: 421–33. [11] Yates ADB, Viljoen CL. An improved empirical model for describing autoignition. SAE paper no. 2008-01-1629; 2008. [12] Iqbal A, Selamet A, Reese R, Vick R. Ignition delay correlation for predicting autoignition of a toluene reference fuel blend in spark ignition engines. SAE paper no. 2011-01-0338; 2011. [13] He X, Donovan MT, Zigler BT, Palmer TR, Walton SM, Wooldridge MS, et al. An experimental and modeling study of iso-octane ignition delay times under homogeneous charge compression ignition conditions. Combust Flame 2005;142:266–75. [14] Walton SM, He X, Zigler BT, Wooldridge MS, Atreya A. An experimental investigation of iso-octane ignition phenomena. Combust Flame 2007;150:246–62. [15] Goldsborough SS. A chemical kinetically based ignition delay correlation for iso-octane covering a wide range of conditions including the NTC region. Combust Flame 2009;156:1248–62. [16] Syed IZ, Mukherjee A, Naber JD. Numerical simulation of autoignition of gasoline-ethanol/air mixtures under different conditions of pressure, temperature, dilution, and equivalence ratio. SAE paper no. 2011-01-0341; 2011. [17] Ghosh P, Hickey KJ, Jaffe SB. Development of a detailed gasoline compositionbased octane model. Ind Eng Chem Res 2006;45:337–45. [18] Anderson JE, Leone TG, Shelby MH, Wallington TJ, Bizub JJ, Foster M, et al. Octane numbers of Ethanol–Gasoline blends: measurements and novel estimation method from molar composition. SAE paper no. 2012-01-1274; 2012. [19] Herzler J, Fikri M, Hitzbleck K, Starke R, Schulz C, Roth P, et al. Shock-tube study of the autoignition of n-heptane/toluene/air mixtures at intermediate temperatures and high pressures. Combust Flame 2007;149:25–31. [20] Gauthier BM, Davidson DF, Hanson RK. Shock tube determination of ignition delay times in full-blend and surrogate fuel mixtures. Combust Flame 2004;139:300–11. [21] Cancino LR, Fikri M, Oliveira AAM, Schulz C. Autoignition of gasoline surrogate mixtures at intermediate temperatures and high pressures: experimental and numerical approaches. Proc Combust Inst 2009;32:501–8. [22] Hartmann M, Gushterova I, Fikri M, Schulz C, Schießl R, Maas U. Auto-ignition of toluene-doped n-heptane and iso-octane/air mixtures: High-pressure shock-tube experiments and kinetics modeling. Combust Flame 2011;158:172–8. [23] Fieweger K, Blumenthal R, Adomeit G. Self-ignition of S.I. engine model fuels: a shock tube investigation at high pressure. Combust Flame 1997;109: 599–619. [24] Davidson DF, Gauthier BM, Hanson RK. Shock tube ignition measurements of iso-octane/air and toluene/air at high pressures. Proc Combust Inst 2005;30:1175–82. [25] Cancino LR, Fikri M, Oliveira AMM, Schulz C. Ignition delay times of ethanolcontaining multi-component gasoline surrogates: shock-tube experiments and detailed modeling. In: 27th International symposium on shock waves, St. Petersburg, Russia; 2009. [26] Heufer KA, Olivier H. Determination of ignition delay times of different hydrocarbons in a new high pressure shock tube. Shock Waves 2010;20:307–16. [27] Fikri M, Herzler J, Starke R, Schulz C, Roth P, Kalghatgi GT. Autoignition of gasoline surrogates mixtures at intermediate temperatures and high pressures. Combust Flame 2008;152:276–81. [28] Cancino LR, Fikri M, Oliveira AAM, Schulz C. Ignition delay times of ethanolcontaining multi-component gasoline surrogates: shock-tube experiments and detailed modeling. Fuel 2011;90:1238–44.

5. Summary and conclusion In this study, a novel method was developed to correlate the ignition delay of a fuel blend to those of the individual fuel component in the mixture without referring to any specific chemical reactions. The ignition delay model is designed to capture the cool flame phenomena of two-stage ignition fuels and predicts the ignition delay with good accuracy for the fuel blend with both tow stage and single stage ignition fuels. The experimental data of shock tube ignition delay from various literatures are used in the model calibration and validation. These data are measured from three different shock tube facilities. The compatibility of the experimental data is examined and confirmed consistency between different test setups. Calibrations of four pure fuels (isooctane, n-heptane, toluene and ethanol) were conducted at various temperatures and pressures for stoichiometric fuel–air mixtures. Validation of the model was accomplished using various fuel blends including binary, ternary and quaternary mixtures for wide ranges of temperature and pressure and the predictions were agreed with experimental data successfully. NTC behavior changes of mixture with two-stage ignition fuels and single stage ignition fuels were properly captured by the proposed model using specific heats of fuel components. In the model, the cool flame temperature rise is progressively reduced as the fraction of two-stage fuels decreases, thus the NTC behavior becomes less noticeable. The proposed model offers a method to predict the ignition delay of various fuel blends only with simple calibrations of pure fuel components for a desired mixture. In addition, the model is fast and reliable because it is based on Arrhenius equations. These characteristics of the model are highly preferred for practical applications such as an engine combustion simulation. In the model, the developed blending rule enables to utilize fuel surrogates instead of real fuels. Since the compositions of commercially available fuels are complex and inconsistent, using a surrogate is more favorable approach to draw a consistent result and improve accuracy while maintaining a simple practical form of the model. In the blending rule, the specific heat weighted average temperature is used to calculate the global cool flame temperature rise of a fuel blend. This method is physically viable and predicts correct NTC behavior change of various blend ratios.