A generalized kinetic model with variable octane number for engine knock prediction

Fuel 188 (2017) 489–499

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Full Length Article

A generalized kinetic model with variable octane number for engine knock prediction Zhi Wang ⇑, Fubai Li, Yingdi Wang State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, China

h i g h l i g h t s
A reduced and generalized model for gasoline knocking prediction was developed.
GRON can present gasoline fuels with various octane numbers.
GRON was validated over a wide range of temperature, pressure and equivalence ratio.
Pressure oscillations and important radicals during knocking was captured with CFD.
GRON model significantly reduces computational time.

a r t i c l e

i n f o

Article history: Received 13 June 2016 Received in revised form 9 October 2016 Accepted 12 October 2016 Available online 17 October 2016 Keywords: Kinetic model Engine knock Octane number CFD

a b s t r a c t A generalized research octane number (GRON) model, including 22 species and 21 reactions, has been developed to simulate the hydrocarbon oxidation with the goal of predicting engine knock. The simplicity of the model enables to represent gasoline with different octane numbers by adjusting the global lowtemperature reaction rate. The model was validated against shock tube experimental data obtained over a wide range of conditions, including equivalence ratios from 0.5 to 2.0, initial pressures from 13 to 55 bar, and initial temperatures from 700 to 1250 K. Both gasoline engine knock and normal combustion were investigated using Computational Fluid Dynamics (CFD) couple with the present GRON. The numerical results proved to be in good agreement with the experimental data. Both the cylinder pressure traces and the distribution of important radical species (CHO and OH) during knocking combustion can be predicted reasonably well. Compared to the CFD calculations using detailed mechanisms, the generalized kinetic model enables a reduction of the computational time by more than 90%. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Fuel consumption regulation are driving the technical development of internal combustion engines worldwide. The required CO2 reductions between 2014 and 2020 are 17%, 24%, 30%, and 28% for Japan, Europe, USA, and China, respectively [1]. In the recent decades, China initiated a ‘‘863” project aiming at achieving less than 200 g/kW h fuel consumption for gasoline engines. Japan started a project named Research Association of Automotive Internal Combustion Engines (AICE), aiming at improving gasoline engine thermal efficiency to an unprecedented level of 50% by 2020. In Europe, the highly downsized gasoline engines with ultra-boost have been investigated intensively [2]. Improving compression ratio and boost ratio are the two major approaches for gasoline ⇑ Corresponding author at: Automobile Research Institute, Tsinghua University, Beijing 100084, China. E-mail address: [email protected] (Z. Wang). http://dx.doi.org/10.1016/j.fuel.2016.10.067 0016-2361/Ó 2016 Elsevier Ltd. All rights reserved.

spark ignition engines to meet the stringent fuel consumption regulations. However, the obstacle for further increasing compression ratio and boost ratio is engine knock. Accurate predictions of knocking combustion in spark ignition engines are critical for developing future high efficiency IC engines. Based on a literature review, five categories of models employed for engine knock prediction were identified and are listed in Table 1 by increasing order of complexity. Table 1 also indicates the advantages, drawbacks and applicability of the different models. For gasoline engine knock prediction, the first model proposed was the Livengood-Wu correlation [3], which is based on ignition delay time calculation using a global reaction model in a zero-dimensional (0D) reactor. The quasi-dimensional model described the combustion chamber as a two-zone reactor composed of a burned zone and an unburned zone [4]. Noda et al. [5] accurately observed the engine knock onset using a quasi-dimensional two-zone model with a detailed primary

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Table 1 Comparisons of engine knock models. Knock model

Reaction number of mechanism

Advantages

Disadvantages

Applications

Calculation time (min)

0D single-zone [3]

Global reaction to 8-step reaction

Simple, ignition delay predication with low computational cost

HC and CO incapable Pressure oscillation can’t be simulated

Fast predication of knock onset

<1

Quasi-dimensional twozone with detailed chemistry [4,5]

102–103

End gas auto-ignition process can be described accurately before knock onset

Combustion chamber geometry is neglected

HC, CO and NOx emissions as well as heat release rate prediction

<10

1D CFD with detailed chemistry [5–8]

102–103

Aero-thermo-chemistry interaction with high calculation efficiency

Turbulence-combustion interaction is neglected

Combustion mode identification

<102

Multi-D CFD with simplified chemistry [10–13]

8–102

Fuel spray, flow and turbulence, mixture formation considered

Simplified pre-reaction and post-oxidation process

Optimization of SI combustion system

102–103

Multi-D CFD with detailed chemistry [14–17]

102–103

Detailed fluid dynamics, chemical kinetics and emission formation considered

High computational cost

HC, CO, NOx, Soot, heat release and pressure oscillation prediction

103–105

reference fuel (PRF) mechanism. Bradly et al. [6,7], Dai et al. [8], Wang et al. [9] employed one-dimensional (1D) computational fluid dynamics (CFD) with detailed syngas, n-heptane and isooctane mechanisms in order to capture the auto-ignition and pressure wave in HCCI and super-knock conditions. However, 0D or 1D models could only capture the ignition delay time or heat release induced pressure rise. Since knock is a spatial-temporal combustion process, multi-dimensional model have been widely applied to analyze engine knock [10–17]. Using three-dimensional CFD with detailed chemistry, turbulent flame propagation, autoignition induced pressure oscillation as well as emissions could be predicted [13–16]. As seen from Table 1, the tendency in researches on knock modeling is from 0D to 3D models, with simple reaction models being substituted by detailed chemical kinetics. The challenges are the greatly increased calculation time and the uncertainty associated with the complex composition of the real gasoline fuel. In recent years, a series of gasoline surrogate mechanisms have been developed, such as iso-octane and n-heptane [18,19]; iso-octane, n-heptane and toluene [20,21]; iso-octane, n-heptane, toluene and 2-pentene [22]; iso-octane, n-heptane, toluene, 1-pentene, methyl cyclohexane [23]; iso-octane, n-heptane n-hexadecane and iso-cetane [24]; iso-octane, n-heptane, ethanol, toluene, and diisobutylene (DIB) [25,26]. Although these mechanisms enable an increasingly accurate description of the gasoline main components, they are still far away representing the gasoline characteristics in detail because real gasoline fuel is composed of hundreds of hydrocarbon species with different chemical and physical properties. In addition, the computational time is extremely long when coupling multi-dimensional CFD with these surrogate mechanisms which include hundreds or even thousands of reactions. Even with a parallel computing approach, single working cycle simulation of internal combustion engine necessitates more than 100 h [27]. This limits the practical application of multi-dimensional CFD in internal combustion engine simulation, especially for engine knock prediction. For engineering application of engine knock prediction, the most important factors of gasoline surrogate model are carbon/hydrogen ratio, ignition delay time, heat release rate, concentration of important radicals, and the main pollutant emissions. To capture knocking combustion in gasoline engines, the model needs to focus on the following four aspects: (1) Ignition delay. The uncertainties of ignition delay time should be less than 0.1 ms (about 1 °CA at 1666 rpm) to capture engine knock under stoichiometric conditions; (2) Concentration of crucial radicals,

such as CHO and OH distribution; (3) Size of mechanism. Appropriate amount of reactions and species are needed for reasonable computational time, usually less than 8 h for engineering application; (4) Capability of representing gasolines with different octane numbers, for example, RON can be varied from 0 to 100. The objective of the study was to develop a practical and generalized gasoline oxidation model that enables computationally inexpensive multi-dimensional SI engines CFD simulations under conditions of both normal and knocking combustion of gasolines with various RONs. 2. Model construction Gasoline fuels are typically composed of three main hydrocarbon families, alkanes, alkenes and aromatics. As for alkanes, significant differences in terms of reactivity exist between n-alkanes and branched alkanes. Generally, the oxidation of hydrocarbons can be divided into three temperature ranges: low temperature range (less than 850 K), intermediate temperature range (about 850–1050 K), and high temperature range (above 1050 K). Despite the difference of reactivity between the hydrocarbon families, the dominant chemical pathways are essentially similar in the lowtemperature range are similar, as shown in Fig. 1 [28]. Under IC engine-like conditions, hydrocarbon fuel oxidize very slowly during the early stage of the process (often below 600 K). During the process of compression, temperature increases promptly, stepping into the low temperature reaction range (600–850 K). In this stage, reaction is initiated by the abstraction of H from a hydrocarbon fuel by O2 to form an R radical and HO2 (R1). Following H abstraction, the R radical undergoes successive O2 addition and isomerization to form a QOOH radical (R2). The QOOH radical undergoes a second O2 addition (R3) followed by OH elimination (R4) which leads to the formation of ketohydroperoxide species. OH radical further reacts with the fuel molecule to form R radical and H2O (R5). The chemical sequence R2–R5 is exothermic and induces low temperature heat release. The initiation reaction (R1) controls the total reaction process whereas (R2) controls the low temperature heat release rate.

RH þ O2 ¼ R þ HO2 R þ O2 ()  QOOH  

ðR1Þ ðR2Þ

QOOH þ O2 ()  OOQOOH

ðR3Þ



OOQOOH ¼ R ket þ OH

ðR4Þ

RH þ  OH ¼ R þ H2 O

ðR5Þ

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Fig. 1. Schematic mechanism for low-temperature hydrocarbon oxidation and auto-ignition chemistry [28].

Fig. 2. Schematic reaction pathways of GRON (generalized research octane number) model.

As the temperature increases to the intermediate temperature range (about 850–1050 K), low temperature reaction (R2) is overcome by R6. As a result, the rate of R7 becomes higher and the stable species H2O2 is formed. As a consequence, the oxidation process slows down as temperature increases. This is the negative temperature coefficient (NTC) characteristic.

R þ O2 ¼ Olefin þ HO2 RH þ HO2 ¼ R þ H2 O2

ðR6Þ ðR7Þ

In order to describe the decomposition of ketohydroperoxide and olefin to small hydrocarbon molecules and CO, the irreversible reaction R8 and R9 were introduced.

R ket ) Cx Hy þ CO þ CH2 O þ  OH

ðR8Þ

Olefin þ O2 ) Cx Hy þ CH2 O þ HCO

ðR9Þ

CxHy represents an alkyl molecule which is formed through ethylene abstraction from R.

As the temperature continues to increase to high temperature range (above 1050 K), H2O2 becomes thermally unstable and initiates a thermal runaway through the sequence: H2O2 = OH + OH, CO + OH = CO2 + H. In summary, low-intermediate temperature reactions of hydrocarbon fuel can be generalized as R1–R9. As for high temperature reactions, the oxidation of alkene is important to combustion chemistry because alkenes are major intermediates of combustion. They are often formed as the result of b-scission reactions of larger alkyl radicals [29]. The high temperature oxidation process proves insensitive to the chemical structure of the hydrocarbon molecule and thus can be considered very similar for alkanes, alkenes and aromatics. After pyrolysis, only ethylene (C2H4), formaldehyde (CH2O) and carbon monoxide (CO) are considered for high temperature oxidation as listed in R10–R21 in this work. As a result, the generalized kinetic model with skeleton reaction pathways was constructed as shown in Fig. 2, which contains 22 species and 21 reactions, named GRON, as shown in Table 2.

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Table 2 The chemical kinetics model of GRON. No.

Reaction 

HO2

A (s1)

n

E (kcal mol1)

Reference

2.00e+15 1.00e+12

0.00 0.00

4.60e+04 0.00e+00

This work

R01

RH + O2 = R + rev

R02

R + O2 = QOOH rev

5.50e+10 2.80e+14

0.00 0.00

0.00e+00 2.74e+04

This work

R03



QOOH + O2 = OOQOOH rev

3.16e+11 2.51e+13

0.00 0.00

0.00e+00 2.74e+04

[30]

R04 R05 R06 R07



OOQOOH ) R_ket + OH R_ket ) CxHy + CO + CH2O + OH RH + OH ) R + H2O R + O2 = Olefin + HO2 rev

8.91e+10 3.98e+15 6.00e+13 3.16e+11 3.16e+11

0.00 0.00 0.00 0.00 0.00

1.70e+04 4.30e+04 3.00e+03 6.00e+03 1.95e+04

[30] [30] [30,31] [30]

R08 R09 R10 R11 R12 R13 R14 R15 R16 R17 R18 R19 R20 R21

Olefin + O2 ) CxHy + CH2O + HCO RH + HO2 = R + H2O2 R ) CxHy + C2H4 CxHy = C3H7 + C3H6 C3H7 + O2 = C3H6 + HO2 C3H6 + C3H6 ) C2H4 + C2H4 + C2H4 CH2O + OH = HCO + H2O HCO + O2 = CO + HO2 CO + OH = CO2 + H H2O2 + OH = HO2 + H2O H + O2 + M = HO2 + M HO2 + HO2 = H2O2 + O2 H2O2 + M = OH + OH + M C2H4 + O2 ) CH2O + CH2O

3.16e+13 1.00e+13 3.61e+17 7.20e+13 3.00e+11 3.16e+13 2.43e+10 1.35e+13 6.00e+06 1.00e+13 2.80e+18 1.30e+11 1.20e+17 3.00e+13

0.00 0.00 1.27 0.03 0.00 0.00 1.20 0.00 1.30 0.00 0.90 0.00 0.00 0.00

1.00e+04 1.69e+04 2.97e+04 2.79e+04 3.00e+03 1.00e+04 4.47e+02 4.00e+02 7.58e+02 1.80e+03 0.00e+00 1.63e+03 4.60e+04 3.00e+04

[31] [32] [33] [31,33] [34] [31] [32] [35] [31,32] [32] [35] [35] [36] [19,31,32]

rev means the reverse reaction rate.

Fig. 3. Sensitivity result on ignition delay at different temperatures, p = 40 bar, u = 1.0.

Chemkin-Pro [37] was employed to calculate the ignition delays in the 0D adiabatic combustion process under adiabatic constant volume conditions. Ignition delays of gasoline fuels under different initial pressures, temperatures and equivalence ratios were calculated with GRON, PRF [30] and LLNL [33] mechanisms respectively, and the calculated results were validated against reference data. The ignition delay was defined as the time to 400 K temperature increase [19]. To accurately represent gasoline with different RONs, kinetics parameters in the model should be adjusted to optimize the agreement with experimental data. This was achieved by modifying the pre-exponential factor A for key reactions. A factor sensitivity analysis was performed to investigate specific reaction sensitivities to ignition delay time for iso-octane oxidation as a function of tem-

perature using Canterà [38]. Fig. 3 depicts sensitivity coefficients for a stoichiometric iso-octane/air mixture at 750, 850 and 950 K and at a pressure of 40 bar. The 10 most sensitive reactions are displayed in Fig. 4 depicts the result of the same stoichiometric isooctane/air mixture at 40 bar and 1000 K, which is representative of the high-temperature sensitivity. As the substantial reactions are rather clear in this region, top five of them are shown. The reaction rates of those specific reactions were changed by multiplying or dividing the pre-exponential factor by a factor of 2, with sensitivities expressed using the formula:

ln S ¼

ln sþ  ln s lnðsþ =s Þ ¼ ln kþ  ln k lnð2=0:5Þ

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Fig. 4. Sensitivity result on ignition delay at T = 1000 K, p = 40 bar, u = 1.0.

Table 3 Pre-exponential factors adjusted for different RONs. RON0

RON60

RON80

RON90

RON100

R1

Aforward

1.00e+16

6.00e+15

5.00e+15

4.00e+15

2.00e+15

R2

Aforward Areverse

2.00e+11 3.00e+13

1.30e+11 9.00e+13

9.00e+10 1.05e+14

7.50e+10 2.00e+14

5.50e+10 2.80e+14

where k+(k) indicated that the target rate constant was multiplied (divided) by 2 and s+(s) represented the corresponding ignition delay time. After sensitivity analysis of these 21 reactions, it can be seen that the pathways relevant to QOOH and OH mainly influence the intermediate temperature region behaviors, whereas the HO2 pathways show an increasing effect with temperature increase. The result is consistent with previous studies in NTC region, i.e. the competition between low temperature chain branching from QOOH and HO2 chain propagation causes the NTC behavior. The negative values in the figures indicate an acceleration of combustion process when increasing the reaction rate. Consequently, higher forward pre-exponential factors (Aforward) of R2, R3, R6, R9, R20, R21 lead to shorter ignition delay at intermediate temperature range, while increasing A for R7, R10, R14, R19 has opposite effect. Because R2 controls the low temperature reactivity but has no impact on the kinetics at higher temperature, both the forward and inverse reaction rate of R2 can be used to match various NTC behaviors. In contrast, R1 is important only in the high temperature region while the other four reactions in Fig. 4 significantly affect both the high temperature and intermediate temperature regions. Therefore, RON characteristics of gasoline can be presented using various Aforward and Areverse in R1 and R1. The preexponential factors for reactions R1 and R1 were adjusted to give the best fit to the experimental data from Refs. [19,39]. The preexponential factors for gasoline with the different RONs are shown in Table 3.

Fig. 5. Experimental [40] and calculated ignition delay for various RONs at u = 1.0, p = 40 bar.

3. Model validations

equivalence ratios under thermodynamics conditions relevant to IC engine operation. These experimental data were used to validate the ignition delay predictions using the present GRON model under various initial conditions. Fig. 5 shows the comparison of calculated and experimental results of ignition delay for stoichiometric fuel-air mixtures of RON 100, RON 90, RON 80, RON 60 and RON 0 at 40 bar, from 700 to 1250 K. The calculated ignition delay times are in good agreement with the experimental data, namely, ignition delay time becomes shorter with decreasing RON. The generalized mechanism also reproduces well the NTC behavior in the temperature range of 750–900 K.

3.1. Calculated ignition delay for various RONs

3.2. Calculated ignition delay for various equivalence ratios

Fieweger et al. [40] employed the shock tube technique to measure the ignition delay-time of PRF-air mixtures with different

Fig. 6 shows the calculated ignition delay and experimental data [40] for various equivalence ratios at the initial pressure of 40 bar.

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Fig. 6. Experimental [40] and calculated ignition delay for iso-octane and n-heptane at u = 0.5, 1.0, 2.0, p = 40 bar.

Fig. 7. Experimental [40] and calculated ignition delay for iso-octane at u = 1.0 and pressures range from 13 to 55 bar.

Fig. 8. Ignition delay of RON0 at 40 bar computed using the detailed mechanism of Curran et al. [33], reduced PRF mechanism of Ra et al. [19] and Tanaka et al. [30].

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Fig. 9. Ignition delay of RON100 at 40 bar computed using the detailed mechanism of Curran et al. [33] and reduced PRF mechanism of Ra et al. [19] and Tanaka et al. [30].

Fig. 10. Schematic diagram of optical apparatus [41] and KIVA-mesh for spark ignition combustion.

The data at different equivalence ratios (u = 0.5, 1.0, and 2.0) are plotted. Overall, a good agreement between the calculated results and the experimental data is observed.

Table 4 Specification of CNR engine.

3.3. Calculated ignition delay for various pressures The GRON model at various initial pressures was validated using the data from Ref. [40] as shown in Fig. 7. For all pressure conditions cases, the NTC behavior is well reproduced.

Characteristic

Value

Bore (mm) Stroke (mm) Connecting rod (mm) Displacement (L) Compression ratio Engine speed (r/min) Fuel Equivalence ratios

79.0 81.3 143 0.4 10.0:1 1000 PRF(ic8h18,nc7h16) Stoichiometric

3.4. Comparison with detailed and reduced PRF mechanism After validation with ignition delay measurements, predictions of the GRON model were also compared with other gasoline surrogate mechanisms. Figs. 8 and 9 show the comparisons of ignition delay using the mechanisms of Tanaka et al. [30], Ra et al. [19] and Curran et al. [33] at lean, stoichiometric, and rich equivalence ratios for n-heptane and iso-octane oxidation. Fig. 8 compares the performance of ignition delay between the RON0 using GRON model and other mechanisms. It indicates that the temperature intervals for the NTC regime are similar for four mechanisms. However, the present GRON model tends to predict

Table 5 The computational sub-models applied in the simulations. Phenomenon

Model

Reference

Turbulence Spark kernel Flame front Wall heat transfer Gasoline auto-ignition

RNG k-e DPIK G-equation Pressure oscillations enhanced GRON

Han et al. [42] Fan et al. [43] Peters et al. [44] Wang et al. [45] This study

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Fig. 11. Measured [41] and predicted cylinder pressure at 13 °CA BTDC spark timing with PRF100 and PRF90.

longer ignition delay-time as compared to Tanaka’s and Ra’s models but is consistent with Curran’s model in the low-temperature range. Fig. 9 compares the predictions of ignition delay between the RON100 using GRON model and other mechanisms. It indicates that similar NTC regions are predicted by the GRON model and the other mechanisms at lean (u = 0.5) and stoichiometric (u = 1.0) conditions. The predictions of the GRON model are closest to that of Ra’s mechanism. 4. Application to gasoline knocking simulation 4.1. Simulation model description An optical gasoline engine studied by Vaglieco et al. [41] is shown in Fig. 10. The specifications are listed in Table 4 and a KIVA mesh for spark ignition combustion of the engine is presented in Fig. 10. Images were taken through a flat transparent piston. Radical species were measured using filters of specific wavelength ranges (HCO, 330 nm; OH, 310 nm). The KIVA-3V code was used to simulate the engine combustion process. The sub-models used in this study are listed in Table 5. The G-equation model was used [46] to track the flame front. The standard model constants cm1 = 2.0 and cm2 = 2.0 in the G-equation model were used in all simulated cases for the in-cylinder process. The initial temperature is 780 K and initial pressure is 1.36 MPa at 15 °CA before top dead center (BTDC) based on a 1D engine simulation. Outside the flame front, including in the burned zone and the unburned zone, the computational cells were treated as homogeneous reactors in which the chemical source term is calculated using the CHEMKIN-II library [47]. The generalized GRON model was used in the chemical calculations. Therefore, the end gas auto-ignition caused by the combined effects of piston and flame front propagation compression could be calculated. In the simulations, a measure point, MP1, was set in the cylinder near the wall on the intake side to detect pressure, as shown in Fig. 10. 4.2. Comparison of simulated results and experimental data Fig. 11 shows the simulated and experimental pressures at a spark timing of 13 °CA BTDC fueled with PRF100 and PRF90, respectively. It can be seen that the PRF100 fuel does not exhibit

engine knock, but both the simulated results and experimental data using PRF90 presents appreciable engine knock behavior. Comparison between two different mechanisms, the simulated pressure traces of GRON match slightly better than that of PRF. This can be explained by the slight difference in ignition delays of the two mechanisms at stoichiometric conditions as shown in Fig. 9. Pressure oscillations occur during the combustion period. Both the two simulated results present auto-ignition properties of the fuel. However, the calculated knocking onset is slightly earlier than that of experimental result. This can be explained by cycle-to-cycle variations and the uncertain boundary conditions in the optical engine. The experimental data in Fig. 11(b) is a single-cycle cylinder pressure trace taken from the fifty engine cycles under engine knock conditions [40]. Fig. 12 shows the simulated results and experimental measurements of intermediate species in cylinder at knock onset fueled with PRF90 with sparking timing of 13 °CA BTDC. It shows that the cylinder has been divided into the burned and unburned regions by flame front marked as a purple1 circle. A high concentration of OH radicals was formed in the center of the cylinder trapped by flame front at the time of initial knock for 10.2 °CA after top dead center (ATDC). It is consistent with the predictions by Ra et al. with a time of initial knock for 8.2 °CA ATDC [26]. This high concentration of OH indicates that the burned zone has reached the postoxidation stage. A high concentration of HCO radicals, which is characteristic of low temperature reactivity, had been formed on the intake side of the engine outside of the flame front with both GRON and Ra’s mechanism, which indicates end gas auto-ignition. Because the spark is 2 mm offset with respect to the cylinder center toward exhaust valves, the end gas auto-ignition tends to occur near the intake side more easily. However, GRON mechanism shows lower OH concentration at the center of the cylinder than the simulations performed with the Ra’s mechanism. This is due to auto-ignition occurrence at different crank angles. For the GRON case, the time elapsed between the spark and the auto-ignition event is of 23.2 crank angles whereas it is only 21.2 for the Ra’s model case. This difference of timing has several consequences: (i) It influences the dynamics of OH radicals in the burnt gas region. For the GRON case, the concentration of OH radical decreases due to post-combustion reactions whereas it continues to increase in the Ra’s model case. 1 For interpretation of color in Fig. 12, the reader is referred to the web version of this article.

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Fig. 12. Predicted active species distribution at engine knock occurrence with PRF90 fuel (13 °CA BTDC spark timing with PRF90 fuel).

(ii) It modifies the shape of the flame front and of the region of high HCO and OH concentration in the end gas. (iii) It modifies the pressure in the end gas when auto-ignition occurs. For the GRON model case, the longer period of compression results in higher end-gas pressure at knock onset. The end-gas auto-ignition with higher pressure has higher energy density, which results in larger volume expansion. Thus, the flame front was pushed back at knock onset. Overall, the calculation results indicate the mechanism of GRON is capable to capture the formation and evolution of active species in the cylinder at the knocking onset and predict engine knock effectively as well. 4.3. Analysis of auto-ignition and pressure oscillation Fig. 13 shows the knock evolution process of PRF90 under the condition of 13 °CA BTDC spark timing. The average pressure in the cylinder appears smooth but exhibits a two-stage behavior. The solid line indicates the local cylinder pressure near the wall

at the position of the measurement point, MP1 (shown in Fig. 10). The images above the curve display the distribution of temperature, concentration of the active radicals and pressure respectively at critical timing during the knocking combustion process. It is seen that the stage of flame propagation is from spark timing to 9.0 °CA ATDC. The image at 6.0 °CA ATDC shows the temperature distribution. The flame surface separates the combustion chamber into two zone, the central burned zone (about 2600 K) and the surrounding unburned zone with the temperature about 900 K. The image at 10.2 °CA ATDC presents the spatial distribution of CHO radical before pressure oscillation, which is also the peak CHO concentration during the combustion process. It can be seen that CHO radicals accumulated to a maximum of 6 ppm on the intake side area between flame front and wall, then it was rapidly consumed which indicates the occurrence of auto-ignition. The rapid local heat release led to a rapid pressure rise at the measure point at 10.5 °CA ATDC, the first obvious pressure wave generated between the flame front and cylinder wall at intake side. Then the

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Z. Wang et al. / Fuel 188 (2017) 489–499 Table 6 Sizes of the four models in this simulation. Model

Species

Reactions

Curran et al. [33] Tanaka et al. [30] Ra et al. [19] GRON

860 32 41 22

3600 55 130 21

5. Conclusions A simple and useful gasoline oxidation model, GRON, including 22 species and 21 reactions, was developed in this study. The results show that the present mechanism well predicts the ignition delay and heat release, while significantly improving computational efficiency. The major conclusions are:

Fig. 13. Engine knock evolution process of PRF90 under the condition of 13 °CA BTDC spark timing.

pressure wave propagated and reflected in cylinder, and coupled with the 2nd pressure peak produced by auto-ignition near wall at exhaust side, resulting in strong pressure oscillation, as shown in the 3rd image of cylinder pressure distribution with high local pressure rise at 11 °CA ATDC. 4.4. Comparison of calculation efficiency Fig. 14(a) gives the comparison of calculation time between GRON model and Ra’s mechanism in predicting engine knock cases. It shows that the calculation time using Ra’s mechanisms is 30 times longer than the GRON, which suggests that GRON significantly improves the computational efficiency without compromising the accuracy in predicting knock behavior. In addition, Fig. 14(b) compares the time of calculating ignition delay of iso-octane/air mixture using four different mechanisms at stoichiometric condition with an initial pressure at 40 bar, a temperature range from 700 K to 1250 K using Chemkin-Pro [37]. The sizes of these mechanisms are listed in Table 6. Similarly, GRON model reduced the computational time by more than an order of magnitude compared to the other mechanisms.

(1) GRON (generalized research octane number) model is presented for auto-ignition and knocking combustion predictions. The good agreement in prediction of the ignition characteristics of gasolines with RON between 0 and 100 suggests that the current model can be used for gasoline engine knock in practical applications. (2) Comparisons with various experiment data from shock tube indicate reliable performance of this mechanism over a wide range of temperatures from 700 to 1250 K, pressures from 1.3 to 5.5 MPa, and equivalence ratios of 0.5, 1.0 and 2.0. An approximation was derived through comparison of ignition delay time simulation between GRON and other mechanisms. (3) The proposed GRON model has also been applied to simulate the knocking combustion in gasoline sparking ignition engine with different fuel with various RONs. The simulations are able to capture both end gas auto-ignition and pressure oscillation. Moreover, simulated results of the pressure oscillations, flame structures and oxidation processes show good agreements with the measured pressure traces, combustion images and active radical locations (HCO, OH) under engine knock conditions. (4) Compared with more detailed mechanisms, the GRON mechanism reduces the computational time by more than 90% without sacrificing accuracy.

Fig. 14. Calculation time of different model on predicting engine knock and ignition delay.

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