Numerical investigations on the effects of turbulence intensity on knocking combustion in a downsized gasoline engine

Accepted Manuscript Numerical investigations on the effects of turbulence intensity on knocking combustion in a downsized gasoline engine

Lin Chen, Haiqiao Wei, Ceyuan Chen, Dengquan Feng, Lei Zhou, Jiaying Pan PII:

S0360-5442(18)32048-6

DOI:

10.1016/j.energy.2018.10.058

Reference:

EGY 13955

To appear in:

Energy

Received Date:

12 March 2018

Accepted Date:

10 October 2018

Please cite this article as: Lin Chen, Haiqiao Wei, Ceyuan Chen, Dengquan Feng, Lei Zhou, Jiaying Pan, Numerical investigations on the effects of turbulence intensity on knocking combustion in a downsized gasoline engine, Energy (2018), doi: 10.1016/j.energy.2018.10.058

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ACCEPTED MANUSCRIPT

Numerical investigations on the effects of turbulence intensity on knocking combustion in a downsized gasoline engine Lin Chen, Haiqiao Wei*, Ceyuan Chen, Dengquan Feng, Lei Zhou, Jiaying Pan* State Key Laboratory of Engines, Tianjin University, Tianjin 300072, P. R. China

* Corresponding author. Tel.: +86-22-27402609; fax: +86-22-27402609; E-mail address: [email protected] (H. Q. Wei), [email protected] (JY Pan)

Abstract In this work, the influence of turbulence intensity on knocking characteristics was studied. Different levels of initial swirl ratio inside cylinder were firstly performed to investigate the effect of turbulence intensity on combustion process. The results show that the enhanced turbulence intensity with increasing initial swirl ratio accelerates the spark-ignited flame (main flame) propagation, resulting in a shortage of combustion phasing (or an advance combustion phasing) and a faster flame speed. Under low turbulence intensity, the faster flame propagation can facilitate knocking combustion because of the enhanced compression of SI flame on the improvement of end-gas thermodynamic conditions. However, further increases in turbulence intensity and flame speed suppress the knocking combustion due to the insufficient time for end-gas autoignition occurrence. Further analysis shows that knock intensity mainly depended on the Unburned Mass Fraction (UBMF). Under lower levels of initial swirl ratios, the enhanced compression of SI flame with the increase of turbulence intensity induces an advanced knock onset, which leads to a larger UBMF and heavier knock intensity. However, 1

ACCEPTED MANUSCRIPT under higher swirl ratio scenarios, UBMF and knock intensity exhibited an opposite trend because the consumption of end-gas by the fast main flame played a dominating role. Keywords: Turbulence intensity; Swirl ratio; Flame speed; Knock intensity; Unburned mass fraction

1. Introduction Downsizing and supercharging have become the mainstream technologies for modern spark-ignition (SI) engines thanks to their higher thermal efficiency and lower CO2 emissions. However, the severe thermodynamic conditions of in-cylinder mixture under large load conditions may induce knocking combustion [1]. Generally, engine knock is considered as a consequence of local mixture autoignition before the SI flame front arrival [2]. When engine knock occurs, extremely rapid heat release in end-gas region causes strong local over-pressure, followed by the propagation of pressure waves with substantial amplitude and thereby obvious pressure oscillations [3], leading to engine body damage [4, 5]. Therefore, further investigations on knocking combustion are crucially important because it determines the durability, fuel consumption and engine performance. Theoretically, engine knock involves complex competition between the SI flame propagation and end-gas autoignition. Based on Livengood-Wu integration [6], it is commonly believed that engine knock can be suppressed when the SI flame speed is increased and consumes more end-gas mixture before autoignition occurrence. Therefore, there are many studies about increasing the flame speed to suppress engine knock such as high turbulence intensity or the addition of hydrogen [7-10]. Based on high turbulence intensity strategies, Vafamehr et al. [11] studied the effect of different injection strategy and Taiga et al. [12] 2

ACCEPTED MANUSCRIPT investigated different in-cylinder compression flow field, they found that knocking characteristics were significantly affected by in-cylinder turbulence intensity and knock was suppressed with the increase of turbulence intensity and flame speed. Besides, though onedimensional LES simulation, the formation of end-gas autoignition was found to be inhibited with increased turbulence intensity [13]. The addition of hydrogen is also an effective way to increase flame speed. Using a gasoline engine [14, 15], Heywood study the effect of hydrogen on the knock and he thought that the knock suppression is due to the fast flame speed of H2. Different from above conclusions, however, there are contradictions on whether increasing flame speed can reduce knock intensity and there is a viewpoint that fast flame speed can induce higher end-gas temperature and pressure, which may promote the possibility of engine knock [16, 17]. Using a turbocharged SI engine, Gersen et al. [18] studied the variations of end-gas autoignition delay time under different flame speed conditions, and they found that higher flame speed was able to induce more severe knocking events. Chen et al. [19] further found that the contributions of burning rate to the knock were categorized by two factors described as ‘‘predominant’’ steps and ‘‘post-dominant’’ steps, and severe knock intensity could be observed under increased burning rate conditions. Despite the numerous studies devoted, there are still many ambiguities regarding knocking combustion, especially for modern gasoline directinjection engines [20]. What’s more, how turbulence intensity and turbulent flame speed affect knock intensity and corresponding critical conditions also remain unclear. Practically, in-cylinder airflow is controlled by complex turbulence motions such as swirl, squish and tumble inside the cylinder [21]. In previous researches, the tumble flow has been studied extensively in order to investigate knocking scenarios in port-injection and direct3

ACCEPTED MANUSCRIPT injection gasoline engines. However, the work on swirl flow in direct-injection gasoline engine and its effect on combustion characteristics are scarcely studied. Chen et al. [22] implemented an experiment with high-speed particle image velocimetry to measure in-cylinder airflow field at five different intake swirl ratios, and found that turbulence intensity increased with swirl ratio linearly, and the main flame propagation speed increased obviously under higher swirl ratio condition. Shao et al. [23] used KIVA-3V to investigate different methods for suppressing engine knock, and they found that higher flame propagation speed was achieved with higher swirl ratio, such that more fuel/air mixture available in end-gas region was consumed before autoignition occurrence and thereby engine knock was suppressed. Despite the numerous studies on turbulent combustion, the influence of turbulence flow characterized by intake swirl flow on knocking combustion is scarcely studied. With the above considerations, the current work aims to clarify the influence of turbulence intensity, especially for in-cylinder swirl flow, on knocking characteristics in a downsized gasoline direct-injection SI engine. Large Eddy Simulation (LES) was carried out as it can well predict the stochastic behavior of local autoignition and cyclic variations of combustion process [24, 25]. Different turbulence intensities were achieved through changing the values of initial swirl ratio. Variations of the main flame propagation, knock intensity and local autoignition under different turbulence intensities were discussed. Current study can provide insights into intake system optimization and knocking suppression in modern downsized gasoline engines.

2. Methodology and model descriptions 2.1 Experiment setup A single-cylinder, two-valve and direct-injection SI engine was used for the experiments. 4

ACCEPTED MANUSCRIPT A flattop piston and a pent-roof cylinder head compose the combustion chamber. The combustion chamber is 80 mm in bore, 100 mm in stroke, 500 cc in displacements and 10.0 in compression ratio. More details for the SI engine can be found in Table 1. Engine speed was maintained 1600±5 round/min through DZC-20 power control system. Homogeneous combustion conditions were achieved by an early-injection at 60 CAD after the Top Dead Center (TDC) at intake stroke, and the test fuel was #92 gasoline provided by Shell China. Homogeneous mixture is chosen so as to exclude the influence of different fuel distribution. All the tests were run on the condition of the air–fuel mixture equivalence ratio of 1 ± 0.01,which was determined by adjusting the injection pulse-width based on the wideband lambda sensor. The room air temperature was maintained at 25 ± 3°C by air conditioning system to avoid intake air temperature fluctuations. The combustion chamber was equipped with a Kistler 6041A water-cooled cylinder pressure sensor to measure the in-cylinder pressure data. Then the signals were acquired by a National Instruments PC-6123 data acquisition card through a Kistler 5018 charge amplifier and stored in a computer. The resolution of pressure transducer is 0.1 CAD, which corresponds to a sampling frequency of 96 kHz under 1600 rpm engine speed. Details for the engine operation conditions and data acquisition can be found in previous work [26]. Table 1 Main specifications for the experimental SI engine Parameters

Value

Engine type

Single cylinder, 4-stroke

Bore×stroke

80×100mm

Sweep volume

0.5L

Compression ratio

10:1

Valve mechanism

VVA, 2-valve 5

ACCEPTED MANUSCRIPT Intake valve close timing (IVC)

128 CAD bTDC

Intake valve open timing (IVO)

364 CAD bTDC

Exhaust valve close timing (EVC)

154 CAD aTDC

Exhaust valve open timing (EVO)

364 CAD aTDC

2.2 Numerical methodology The CONVERGE was used in this study because of its capability of solving complex geometries by incorporating various physical transient flows with stationary or moving surfaces. Because the SAGE solver allows for detailed chemical kinetics in combustion simulations with a set of CHEMKIN-formatted input files and calculates the reaction rate of each elementary reaction. Therefore, the SAGE solver is applied to accurately capture the stochastic autoignition and engine knock. An innovative modified cut cell Cartesian method called Adaptive Mesh Refinement (AMR) was also utilized for local refinement of mesh grid generation. The applications of AMR technique are important because it can capture important flow features without huge number of grids. Furthermore, the state-of-the-art spray and wall heat transfer models were also incorporated in the CONVERGE. The model constants/parameters of each of these models have well been calibrated through the experimental results. In the calculation of CONVERGE, the pressure is calculated in energy equation, given by: ∂𝑢𝑗𝜌𝑒 ∂𝑢𝑗 ∂𝑢𝑖 ∂𝜌𝑒 ∂ + =‒ + ∂𝑥 𝑃 + 𝜎 ∂𝑥𝑗 ∂𝑥𝑗 ∂𝑥𝑗 ∂𝑡 𝑗 𝑖𝑗

( ) ∂𝑇

∂

(

∂𝛾𝑚

)

K∂𝑥 + ∂𝑥 ρD∑𝑚ℎ𝑚 ∂𝑥 + 𝑆 𝑗

𝑗

𝑗

(1)

where ρ is density, 𝛾𝑚 is the mass fraction of species m, D is the mass diffusion coefficient, P is the pressure, e is the specific internal energy, K is the conductivity, ℎ𝑚 is the species enthalpy, 𝜎𝑖𝑗 is the stress tensor, T is the temperature, and S is the energy source term. The pressurevelocity coupling is achieved using a modified Pressure Implicit with Splitting of Operators (PISO) method [27]. Further, in order to capture the gas dynamics (i.e. pressure oscillations) in the cylinder during the knock combustion, the max speed of sound CFL number (max_cfl_mach) 6

ACCEPTED MANUSCRIPT was adjusted from 50 to 1.75 to reduce time-step once combustion starts. The CFL number estimates the number of cells through which the related pressure will move in a single timestep and the max_cfl_mach number is given as: ∆𝑡

𝑐𝑓𝑙𝑚𝑎𝑐ℎ = c∆𝑥

(2)

where ∆𝑡 is the time-step, ∆𝑥 is the grid spacing and c is the speed of local sound. Turbulence has a significant effect on the mixing rate of mixing of momentum, energy and species, so an accurate turbulence model is of great importance to model the turbulence effects. In this work, large eddy simulation with the sub-model of one-equation viscosity model was adopted here. The one-equation viscosity model adds a transport equation for the sub-grid kinetic energy and then the turbulent viscosity was modeled by using the sub-grid kinetic energy [28, 29]. The governing equations for the sub-grid kinetic energy is ∂𝜇𝑖 ∂𝑘 ∂ 𝑣𝑡 ∂𝑘 ∂k + 𝜇𝑖∂𝑥 =‒ 𝜏𝑖𝑗∂𝑥 ‒ 𝜀 + ∂𝑥 (𝜎 ∂𝑥 ) ∂𝑡 𝑘 𝑖 𝑛 𝑖 𝑖

(3)

in which the superscripts “-” is respective the filtered quantity. The unclosed terms in the governing equations presented here are sub-grid kinetic energy 𝑘 , sub-grid stress tensor τ𝑖𝑗 and sub-grid dissipation ε , which are given by： 𝑘 = 0.5(𝑢𝑖𝑢𝑛𝑗 ‒ 𝑢𝑖𝑢𝐽) 2

τ𝑖𝑗 =‒ 2𝑣𝑡𝑘𝑆𝑖𝑗 + 3𝑘𝛿𝑖𝑗

(4) (5)

3 2

ε=

𝐶𝜀𝑘

(6)

∆

where the turbulent viscosity, v𝑡𝑘, for the one-equation model is given as: 12

v𝑡𝑘 = 𝐶𝑘𝑘

∆

(7)

2.3 Model specifications In order to capture more knocking combustion information especially pressure oscillation, 7

ACCEPTED MANUSCRIPT eight monitor points (P1-P8) were set up evenly at the edge of the combustion chamber. Different temperature distributions in the cylinder according to the experiments were also considered, where the temperature of the intake valves is 500 K, the cylinder head and piston is 575 K, and the exhaust valves is 600 K. Figure 1 shows the physical model and monitor points employed in the current study. In our previous work, numbers of calculation with different uniform cell sizes were carried out, and it shows that a uniform cell size of 2.0 mm was sufficient for knocking study combined with the AMR and fixed embedding strategies [30]. The AMR and fixed embedding strategies were employed here to maintain a good balance between the computational efficiency and accuracy based on mixture fraction and temperature. With the AMR, when the absolute value of the sub-grid is above a certain value, the cell will be embedded. Consequently, the cell size was dx = 0.1 – 0.5 mm around the spark plug and end-gas region when the combustion happened, and it was close to dx = 0.5 – 2.0 mm for the cells at other regions, which is sufficient to resolve most of turbulent kinetic energy throughout the whole field [31]. Therefore, the mesh independency was verified and the uniform cell size of 2.0 mm is sufficient for the current study. In order to improve computation efficiency, a reduced Primary Reference Fuel (PRF) mechanism developed by Liu et al. [33–34] was adopted here rather than detailed chemical kinetics. The chemical kinetic mechanism has been validated and tested against a wide range of engine combustion conditions.

8

ACCEPTED MANUSCRIPT

Fig. 1 Physical model of the SI engine and monitor points in the combustion chamber

2.4 Model validation To validate the CFD model, Figure 2 shows a comparison of the pressure traces between the simulation and experimental results under no-knock condition. The measured data of incylinder pressure for 200 continuous engine cycles was obtained at the spark timing of -18 CAD bTDC. It is observed that under the current Spark Timing, there is nearly no knock happened and the in-cylinder pressure curve is relatively smooth without obvious pressure oscillation. The calculation results are obtained at the same spark timing as shown by red thick line, which possesses a peak pressure of Pmax = 4.17 MPa at 22.5 CAD. Although the simulated peak pressure is a little lower, a good match can be observed in terms of combustion phasing and pressure amplitude when considering the cycle-to-cycle variations in the gasoline engine. So the combustion characteristics are well captured under normal condition.

9

ACCEPTED MANUSCRIPT

Fig. 2 Measured cylinder pressure traces and validation of the CFD model under normal condition For a more convincing validation and studying the knocking phenomenon, Fig. 3 shows a comparison of the pressure traces under different spark timings. As shown in Fig. 3, the experimental data is from 800 continuous engine cycles operated at ST = -18 to -24 CAD with an interval of 2 CAD. When the simulated ST is advanced pressure peak and pressure rise rate significantly increase. At ST = -24 CAD, the advance of combustion phasing is followed by an apparent pressure oscillation superimposing on in-cylinder pressure traces, which suggests the occurrence of engine knock. From the calculations of normal and knocking cycles, it is seen that current LES results yield good agreement with experimental data under different spark timings. As an extension of research scope, knocking characteristics under different turbulence intensity is further numerically investigated based on current downsized engine configuration.

10

ACCEPTED MANUSCRIPT

Fig. 3 Validation of the CFD model under different spark timings

3. Results and Discussion 3.1 Turbulence intensity In the current work, different levels of in-cylinder turbulence intensity were obtained through varying the values of initial 𝑠𝑤𝑖𝑟𝑙_𝑟𝑎𝑡𝑖𝑜 at the Bottom Dead Center (BDC i.e. -180 CAD). The 𝑠𝑤𝑖𝑟𝑙_𝑟𝑎𝑡𝑖𝑜 is a preset input value in the calculating files of CONVERGE and 𝑠𝑤𝑖𝑟𝑙_𝑟𝑎𝑡𝑖𝑜 is the ratio of the angular speed of the flow to the angular speed of the crankshaft. Initially, several continuous complete cycles (Figure 3) were calculated, and then the swirl ratio and hence turbulence intensity were extracted at the BDC for reference. Specifically, the other thermophysical parameters of the subsequent calculation cases were also extracted from the complete cycles at the BDC, mainly the pressure, wall temperature, mixture, etc. Moreover, research octane number of the PRF was maintained RON = 90, the Spark Timing was advanced to −30 CAD, and the initial temperature of mixture was increased to 400 K. Therefore, the enhanced mixture reactivity was able to promote local autoignition and severe knock events under the same flow dynamics conditions. Subsequently, the effect of turbulence intensity on 11

ACCEPTED MANUSCRIPT knocking characteristics was studied by varying the values of initial swirl ratio at the BDC and such methodology can effectively facilitate the study in the paper. To investigate the effect of different turbulence intensity, the initial swirl ratio is set to 0.6,1, 2, 3, 4 and 5 at the BDC and 0.6 is reconstructed from the case of Fig. 3. The ranges are considered to cover the typical range of 0.55 - 5 under engine-like conditions [35,39]. The rough swirl flow field distribution is shown in Fig. 4a. For the following section, the initial swirl ratio of 0.6 is recommended as Case 1 whereas 1 to 5 are recommended as Cases 2 to 6. First, the influence of the initial swirl ratio on in-cylinder instantaneous swirl ratio and turbulent kinetic energy (TKE) before combustion is discussed here. Figure 4b shows the in-cylinder instantaneous swirl ratio during the compression stroke before spark. In this transient flow condition, the instantaneous swirl ratio is almost unchanged irrespective of the crank angle since the start of the compression for all cases. However, there is a slight downtrend under high initial swirl ratio condition especially for case6. The tendency is the same as the experimental results reported in [36]. In Fig 4c, the turbulence intensity, in terms of TKE, increased obviously with the increase of initial swirl ratio during the whole compression stroke. For example, the TKE is about 2.2 m2/s2 for case 6 while the values is about 1.0 m2/s2for case 1. This result illustrates increasing initial swirl ratio can increase turbulence intensity inside the cylinder under current model and the conclusion is also found in previous results [37-40]. Therefore, the influence of different turbulence intensities on combustion characteristics and engine knock can be studied by varying the values of initial swirl ratio.

12

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Fig. 4 (a) swirl flow field distribution, (b) instantaneous swirl ratio vs. crank angle and (c) instantaneous TKE vs. crank angle under different initial swirl ratios

3.2 Flame propagation Figure 5 shows the variations of burned mass fraction (BMF) and the corresponding heat release rate (HRR) under different turbulence intensities. It is observed that the phasing of the BMF is gradually advanced as the turbulence intensity increases. To better understand the effect of turbulence intensity on the combustion phasing, BMF70 is calculated according to the BMF profiles, and BMF70 represents the crank angle from Spark Timing to the instant of BMF=70%. This parameter can represent the main flame speed under engine knock conditions [19]. It is observed that BMF70 gradually decreases from 30.93 CAD to 22.16 CAD with the increase of turbulence intensity. This indicates that the increase in turbulence intensity can strongly promote flame propagation and advance the combustion phasing. Meanwhile, it is observed 13

ACCEPTED MANUSCRIPT that under knocking combustion, the heat release rate curves experience obvious two stages (the main flame propagation and end-gas autoignition), and the second one is featured by the sharp rise owing to the occurrence of end-gas autoignition. However, it is noted that there is a trend of increase first and then decrease for the peak HRR, and the peak HRR in hot spots can be used as an indicator in the determination of knock intensity. That’s to say, as the increases of initial swirl ratio, engine knock becomes more severe; while further increases in initial swirl ratio, engine knock starts to be suppressed.

Fig. 5 Predicted burned mass fraction, heat release rate and combustion phasing under different turbulence intensities Figure 6 shows the evolutions of the main flame propagation represented by temperature isosurface of 2000 K for Cases #2-4. It is observed that after the spark (-30 CAD), there is an obvious flame center induced by the spark ignition, and the initial flame area is almost the same for the three cases at -25 CAD. As the piston travels upward, the spark induced flame propagates to the surrounding. The flame front is stretched and wrinkled, which is affected by 14

ACCEPTED MANUSCRIPT the in-cylinder turbulence flow. However, when the piston moves to −3 CAD, the flame almost fully occupies the cylinder in Case 4, whereas there remains a significant amount of unburned mixture for Case 2 and 3. In other words, the flame speed increases with the increase in turbulence intensity, which is consistent with the results in Fig. 5. Moreover, as shown by the yellow dotted lines for -3 CAD, there is a trend that the flame front propagates along the counter-clockwise direction, and it becomes more obvious with the increase of swirl ratio, which proves that the swirl flow filed can also strangely affect the direction of flame propagation.

15

ACCEPTED MANUSCRIPT Case 3

Case 4

-5 CAD

-10 CAD

-15 CAD

-20 CAD

-25 CAD

Case 2

-3 CAD

Flame propagation direction

Isosurface T = 2000 K

Fig. 6 Evolutions of spark-ignited flame propagation under different turbulence intensities

3.3 Knocking characteristics and local autoignition The effects of different turbulence intensities on the knocking characteristics and local autoignition are further discussed in this section. Figure 7 shows the traces of in-cylinder pressure and corresponding pressure oscillation at different turbulence intensities for Cases #1– 6, and the pressure oscillation is obtained by filtering the pressure at a band frequency of 4 – 16

ACCEPTED MANUSCRIPT 25 kHz. For Cases #1–4 corresponding to initial swirl ratios of 0.6 to 3, knock happened with obvious pressure oscillation. In the early stage of the knocking combustion, the pressure rises gradually. Then there is a sudden pressure rise due to the rapid heat release when end-gas autoignition occurs. After the sharp pressure rise, the pressure wave propagates back-and-forth in the closed chamber and pressure oscillation appears with obvious attenuation. Moreover, the combustion phasing and timing of knock onset (defined as the timing of a sharp increase in the first derivative of the pressure signal) significantly advance with the increase of turbulence intensity. Figure 7 also shows that knock can be prevented when the turbulence intensity is sufficiently large or the flame speed is sufficiently fast, as shown by Cases 5 and 6 which corresponds to initial swirl ratios of 4 and 5, respectively. Otherwise, the knock intensity will be facilitated as shown from Cases 1 to Case 3.

Fig. 7 Predicted pressure and pressure oscillation under different turbulence intensities In order to further study the effects of turbulence intensities on local autoignition, the evolutions of flame propagation and end-gas autoignition represented by the temperature and 17

ACCEPTED MANUSCRIPT corresponding pressure difference are shown in Figure 8. As the piston travels upward nearly the TDC at compression stroke, the SI flame propagates towards the cylinder wall, and all of the flame front are stretched and wrinkled with a turbulent behavior. In Case 2, there is a single hot-spot induced autoignition center happened at -0.84 CAD around point P6. Subsequently, the autoignition center propagates to the surrounding mixture in the end-gas. Within approximately 0.2 CAD, the unburned mixture is consumed and the corresponding flame speed is several meters per second. As a result, an intense overpressure with the amplitude of approximately 3 MPa happens, and the corresponding pressure wave propagates back and forth in the cylinder, resulting in an obvious pressure oscillating behavior. Compared with Case 2, the autoignition timing of Case 3 is advanced owing to the fast flame speed and enhancement of compression heating effect. When the piston moves to −1.99 CAD, an autoignition center appears around point P4. With the increase in turbulence intensity, the effects of fast flame fronts on the autoignition timing become more evident. As shown by the mass fraction burned by autoignition at −1.95 and −1.90 CAD, the autoignition center consumes more mixture compared with Case 2. Consequently, the autoignition produces a fast propagating reaction front and this autoignition front is accompanied by a stronger oscillation with the pressure amplitude of approximately 5 MPa, as shown by the pressure difference counters at −1.90 CAD. When further increase in the turbulence intensity of Case 4, there are some new observations. The position of autoignition changes along the direction of the swirl flow, from P6 for Case 2 to P2 for Case 4. Furthermore, the timing of autoignition is advanced but the mass burned by autoignition is less compared with Case 3. From the tendency of knock intensity and the mass burned by autoignition in the three cases, knock intensity seems to be 18

ACCEPTED MANUSCRIPT related to the unburned mass fraction (UBMF, the mass fraction of unburned gas at the moment of end-gas autoignition). -0.84 CAD

-0.80 CAD

-0.75 CAD

Case 2

Isosurface T = 2000 K

-0.88 CAD

Autoignition

-1.99 CAD

Local over-pressure

-1.95 CAD

-1.90 CAD

Case 3

Isosurface T = 2000 K

-2.04 CAD

Autoignition

-2.95 CAD

Local over-pressure

-2.90 CAD

-2.85 CAD

Autoignition

Case 4

Isosurface T = 2000 K

-2.99 CAD

Local over-pressure Fig. 8 Evolutions of flame propagation and end-gas autoignition under different turbulence intensities Figure 9 further shows the temperature of the autoignition points in Case #2-4 and the closet monitor points are selected to represent the autoignition points for each case. It is 19

ACCEPTED MANUSCRIPT observed that with the increase of turbulence intensity, the compression heating effect of the main flame propagation on end-gas mixture becomes enhanced, characterized by the obvious rise in the temperature and pressure of end-gas mixture. Consequently, the corresponding autoignition delay is largely reduced and knock onset is advanced. This contributes to the variations of knock intensity from Case 2 to Case 4, consisting with Fig.7 and 8.

Fig. 9 Predicted temperature and pressure under different turbulence intensities

3.4 Correlations of knock intensity and unburned mass fraction Figure 7 shows that the knock intensity increases initially and thereafter decreases with the increase in turbulence intensity and Figure 8 shows that knock intensity seems to be related to the UBMF. To further illustrate the underlying reasons, the correlations between the knock intensity and UBMF are further explored under different turbulence intensities. Figure 10 shows the knock intensity and the corresponding UBMF under different turbulence intensities, while two more cases are studied as a supplement: Case 7 with the initial swirl ratio of 3.2 and Case 8 with the initial swirl ratio of 3.4. It can be observed that both of the UBMF and knock 20

ACCEPTED MANUSCRIPT intensity increase first and thereafter decreases with the increase in turbulence intensity, and the turning point exists at swirl ratio of 2~3. In region A, knock intensity increases from 0.88 MPa to 4.43 MPa as the initial swirl ratio is increased from 0.6 to 2; However, in region B, knock intensity decreases to 0.36 MPa and even be suppressed as the swirl ratio further increases. Knock intensity is closely related to the quantity and energy density of end-gas mixture and involves complex competition between the main flame propagation and end-gas autoignition. On the one hand, the flame speed increases as the turbulence intensity and increasing heating effect makes the end-gas mixture more likely to accumulate in the autoignition condition, therefore the knock intensity increases; On the other hand, increasing flame speed consumes more in-cylinder mixture and hence less quantity is left for the end-gas autoignition, thus knock intensity decreases.

Fig. 10 Predicted knock intensity and unburned mass fraction for different turbulence intensities 21

ACCEPTED MANUSCRIPT In region A, assuming that the flame propagation and end-gas autoignition is 1D in the engine knock combustion, besides, the mixture gases behave as ideal gases and the unburned gas is compressed isentropically. When the autoignition happened at the main flame radius of 𝑅𝑖, we can get a relationship between flame radius and relative knock pressure [41,42]: 𝑃𝑚𝑎𝑥 ‒ 𝑃𝑖

𝑅𝑖 = [1 ‒ 𝑃

𝑚𝑎𝑥 ‒ 𝑃𝑜

∙

𝑃𝑜 1/𝛾 1/2

() 𝑃𝑖

]

∙𝑅

(8)

where 𝑃𝑖 is the knock pressure when autoignition happened, 𝑃𝑜 is the initial pressure, 𝑃𝑚𝑎𝑥 is the equilibrium pressure when the mixture is all burned, R is radius of combustion chamber and γis the ratio of specific heat (γ>1). From equations (8), it can be seen that knock pressure 𝑃𝑖 increases with flame radius 𝑅𝑖. So the results that the knock intensity is increased as the turbulence intensity (flame speed) is proved as shown from Case 1 to Case 3 in Fig. 10; In region B, on the one hand: based on Livengood–Wu integral [6]: end-gas autoignition will occur if the Livengood–Wu integral reaches unity before the flame front reaches the wall. That is to say, end-gas autoignition can be prevented if the flame speed is sufficiently fast to reach the wall. So increasing turbulence intensity makes the flame speed fast enough to consume the UBMF such that knock intensity decrease (Case 4, 7 and 8) and even is suppressed (Cases 5 and 6). On the other hand, the mass and heat transfer is enhanced under high turbulence intensity [13], so that the formation of autoignition kernels is delayed and knock is suppressed. Hence, under the knocking condition studied herein, increasing the turbulence intensity will promote the knock first, whereas knock intensity will be weakened and even engine knock can be avoided when the turbulence intensity and flame speed reach a sufficiently high level.

4. Conclusions In this work, the influence of different turbulence intensities on knocking characteristics 22

ACCEPTED MANUSCRIPT was studied using CONVERGE simulation coupled with a detailed chemistry solver in a highly downsized spark-ignition engine. Different values of initial swirl ratios were used in the simulation to change the in-cylinder turbulence intensity, and the effects of turbulence intensity on knocking characteristics were discussed, with addressing knock intensity and local autoignition. With the increases of initial swirl ratio, in-cylinder turbulence intensity increases obviously during the compression stroke. The increases in turbulence intensity can strongly promote the flame propagation and therefore the shortage of combustion phasing. However, the faster main flame propagation has a higher compression heating effect on the end-gas and can advance the timing of knock onset. Meanwhile, the direction of flame propagation and autoignition location is significantly influenced by the swirl flow filed with counter-clockwise direction. Further analysis on knocking characteristics shows that faster main flame propagation at higher turbulence intensity facilitates knock intensity because of the higher compression heating effect. However, if the turbulence intensity is sufficiently large or the flame speed is sufficiently fast, knocking event will be suppressed (or is even prevented) due to the insufficient time for end-gas autoignition. The correlations between knock intensity and unburned mass fraction show that knock intensity mainly depends on unburned mass fraction. Fast flame speed decreases the unburned mass fraction whereas advanced timing of knocking onset increases the unburned mass fraction. Therefore, the competition between the main flame propagation and end-gas autoignition determine the eventual knock intensity. Under low levels of swirl ratio, knock intensity is increased with turbulence intensity due to the enhanced compression heating 23

ACCEPTED MANUSCRIPT effect from the main flame. Whereas further increase in initial swirl ratio, the end-gas mixture consumed by the fast main flame has a dominating effect and thus the unburned mass fraction exhibits an opposite trend. Therefore, knock intensity is significantly decreased and even suppressed. The current study can help to clarify the contradiction on whether faster turbulent flame propagation promotes or suppresses knock intensity, and highlights the combustion variations through increasing turbulence intensity under heavy knocking conditions. Further studies will focus on the knocking combustion (i.e. conventional knock and super-knock) of downsized SI engines involving turbulent combustion and fuel property interactions.

Acknowledgements This work was supported by Major Research Plan of National Natural Science Foundation of China (91641203), National Natural Science Foundation of China (Grant No. 51476114, 51706152), and Tianjin Natural Science Foundation (17JCZDJC31500, 18JCQNJC07500 ).

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ACCEPTED MANUSCRIPT HIGHLIGHTS ►Effects of swirl flow on flame speed and engine knock were numerically studied. ►In-cylinder turbulence intensity increased with the increase of initial swirl ratio. ► Knock intensity behaves a non-monotonic correlation with turbulence intensity ►Knock intensity mainly depends on the Unburned Mass Fraction.