Effects of Flame Propagation Velocity and Turbulence Intensity On

energies

Article Eﬀects of Flame Propagation Velocity and Turbulence Intensity on End-Gas Auto-Ignition in a Spark Ignition Gasoline Engine

Lei Zhou *, Xiaojun Zhang, Lijia Zhong and Jie Yu

State Key Laboratory of Engines, Tianjin University, Tianjin 300072, China; [email protected] (X.Z.); [email protected] (L.Z.); [email protected] (J.Y.) * Correspondence: [email protected]; Tel.: +86-22-27402609

Received: 30 August 2020; Accepted: 22 September 2020; Published: 24 September 2020

Abstract: Knocking is a destructive and abnormal combustion phenomenon that hinders modern spark ignition (SI) engine technologies. However, the in-depth mechanism of a single-factor influence on knocking has not been well studied. Thus, the major aim of the present study is to study the effects of flame propagation velocity and turbulence intensity on end-gas auto-ignition through a large eddy simulation (LES) and a decoupling methodology in a downsized gasoline engine. The mechanisms of end-gas auto-ignition as well as strong pressure oscillation are qualitatively analyzed. It is observed that both flame propagation velocity and turbulence have a non-monotonic effect on knocking intensity. The competitive relationship between flame propagation velocity and ignition delay of the end gas is the primary reason responding to this phenomenon. A higher flame speed leads to an increase in the heat release rate in the cylinder, and consequently, quicker increases in the temperature and pressure of the unburned end-gas mixture are obtained, leading to end-gas auto-ignition. Further, the coupling of a pressure wave and an auto-ignition flame front results in super-knocking with a maximum peak of pressure of 31 MPa. Although the turbulence indirectly influences the end-gas auto-ignition by affecting the flame propagation velocity, it can accelerate the dissipation of radicals and heat in the end gas, which significantly influences knocking intensity. Moreover, it is found that the effect of turbulence is more pronounced than that of flame propagation velocity in inhibiting knocking. It can be concluded that the intensity of the pressure oscillation depends on the unburned mixture mass as well as the local thermodynamic state induced by flame propagation and turbulence, with mutual interactions. The present work is expected to provide valuable perspective for inhibiting super-knocking of an SI gasoline engine.

Keywords: knocking mechanism; ﬂame propagation velocity; turbulence; auto-ignition; pressure oscillation

1. Introduction The increasing severity of the current energy crisis and environmental pollution are leading to technical downsizing and turbocharging in spark ignition (SI) engines due to their superior economy and power performance [1]. Theoretically, the engine performance, such as the torque and fuel consumption rate, is positively related to the fuel compression ratio; however, knocking, which is a devastating and abnormal combustion phenomenon, occurs under critically constrained conditions in the development of high-efficiency engine [2]. This trade-off makes it difficult to achieve the theoretical maximum combustion efficiency in practical engines. Finding a balance between improved engine performance and knocking inhibition has thus become a perpetual challenge to the engine manufacturing industry and researchers.

Energies 2020, 13, 5039; doi:10.3390/en13195039 www.mdpi.com/journal/energies Energies 2020, 13, 5039 2 of 23

Because end-gas auto-ignition is the first stage of knocking, whose subsequent development determines the knocking occurrence and intensity, in general, it can be concluded that knocking in SI engines is induced by auto-ignition occurring in the end gas [3,4], which has been extensively and comprehensively investigated. Many excellent studies have contributed to exploring the method of inhibiting such knocking, and several potential means have been discovered, including changing the flame propagation speed [5], increasing the in-cylinder turbulence [6,7], split injection strategies [8], octane number [9,10], and EGR (Exhaust Gas Recirculation) strategies [11]. For instance, Yang et al. [12] found a higher tumble rate can lead to the increase of flame speed through by facilitating the interaction between the fuel spray and air flow and the heat-mass transfer between the unburnt and burnt zone. Kim [13] studied the effects of hydrogen on a gasoline direct injection engine and found that hydrogen addition can inhibit the propensity of knocking combustion under high-load conditions because of its high flame velocity. However, the decelerated flame propagation velocity induced by cooler EGR [11] accompanied by reduced end-gas temperature could also mitigate knock occurrence. Yue et al. [14] found that increasing flame speed shows a negative impact on knock mitigation, but provides improvement on thermal efficiency by shortening the combustion duration. However, some research [15,16] shows that relatively low turbulence intensity gives the longer residence time for end-gas auto-ignition occurrence, thus knock is intensified. This contrast manifests that the underlying mechanism of the effects of flame propagation speed on auto-ignition is unclear. In fact, there are disagreeing opinions among researchers regarding whether an increase in the flame speed is capable of inhibiting knocking. Kee et al. [5] developed a rapid compression/expansion device to explore the essential phenomenon of knocking. Their results indicate that increasing the laminar flame speed inhibits the knocking because a fast propagation decreases the time required for low-temperature reactions in the end gas. Hirooka et al. [17] believe that increasing the burn rate is also effective in improving the knocking characteristics. However, many studies have indicated the opposite [18,19]. For instance, Chen and Raine [19] proposed a multi-step adiabatic constant-volume zero-dimensional (MACZ) model to calculate the chemical reaction of an unburned air-fuel mixture and pointed out that increasing the burning rate promotes knocking through two factors, namely, “pre-dominant” steps and “post-dominant” steps. Furthermore, Yu et al. [20] conducted a 1D simulation regarding the effects of the flame propagation velocity on the end-gas auto-ignition in a constant volume combustion chamber by introducing artificial mass diffusivity. They found that increasing the flame propagation can suppress the knocking occurrence if the chamber size is sufficiently small. In our previous work [21], the knock phenomenon under the influence of different acceleration flame is investigated by conducting a series of 2D DNS (Direct Numerical Simulation) investigation. Three modes were found to exist, namely auto-ignition promoted by strong flame acceleration, auto-ignition suppressed by weak flame acceleration, and auto-ignition independent of flame acceleration. Such studies clearly show how our understanding of the effect of the flame propagation velocity has changed, whereas the knock mode transition from inhibition to promotion has not been understood, which is very important to suppress knock in SI engines. It is generally accepted that turbulence intensity influences the end gas properties. Mastorakos et al. [22] conducted a two-dimensional direct numerical simulation on the auto-ignition of laminar and turbulent mixing layers. They found that the auto-ignition time in the turbulent flows is longer than the ignition delay time of homogeneous mixtures. Juan et al. performed an experimental investigation regarding the turbulence intensity on knock tendency in a SI engine. It was found that increased turbulence intensity increased the knocking tendency. Besides, the turbulent flame propagation investigations associated with pressure oscillation [23], flame-shock interaction [24], and flame acceleration [25] were wildly conducted. Those work observed the auto-ignition process visually, yet the fundamental auto-ignition mechanism of how the turbulence influences the end gas auto-ignition is still less understood. Therefore, the major objective of the present study is to comprehensively study the effects of the flame propagation velocity and turbulence intensity on the end-gas auto-ignition in a downsized Energies 2020, 13, 5039 3 of 23

SI gasoline engine, as well as the pressure oscillation through a large eddy simulation coupling with a decoupling methodology. The SAGE solver coupling with a detailed chemistry mechanism of the PRF (Primary Reference Fuel) is employed to capture the detailed reaction process as the end-gas auto-ignition occurrence. Note that, using flame models such as G-equation model to mimic laminar flame comprise the ability to mutually decouple flame propagation and end-gas auto-ignition. By modifying the coefficient in the G-equation, the flame speed is changed. Consequently, a quantitative analysis regarding the effects of the flame propagation velocity on the knocking occurrence was conducted in this study. Furthermore, the turbulence intensity is achieved by rescaling the in-cylinder flow velocity. The effects are further understood in terms of the pressure wave, HCO, flame front velocity, and unburned temperature distributions. The present study will deliver valuable and new perspectives for inhibiting the knocking and improving the performance in SI gasoline engines. The remainder of the present paper is structured as follows: The experimental setting is briefly presented in Section2. The numerical settings including the LES equations, combustion model, numerical model, model validation, and parameter setting are provided in Section2. The e ffects of the flame propagation velocity and turbulence are discussed in Section3. Finally, the concluding remarks are given in Section4. The model validation is presented in AppendixA.

2. Numerical Setting

2.1. Combustion Model The G-equation-based turbulent combustion model [26] is utilized to capture the turbulent ﬂame propagation in the partially pre-mixed combustions. SAGE solver coupling with detailed chemistry mechanism of the PRF [27] is used to capture the detailed reaction process as the end-gas auto-ignition occurrence. Here, a simple description of G-equation is listed below. The G-equation is [28]:

∂Ge e ρu + (v→ →v vertex) Ge = st Ge DtekM Ge , (1) ∂t f − ·∇ ρ ∇ − ∇

e where Ge is the Favre-averaged G, v→f is the Favre mean bulk fluid velocity in the flame front, →v vertex is the mesh vertex velocity, ρu is unburned mixture density, ρ is the mean gas density of a turbulent flame, Dt is the turbulent diffusivity,ekM is the mean flame curvature, and st is the turbulent flame speed. Here, st is the function of the laminar flame speed (sl), and is expressed as follows [28]:

 1    2  2   a b2  a b2    4 3  4 3  2   st = sl + v0 Da +  Da + a4b3Da , (2) − 2b1  2b1      where v0 is the turbulence intensity; a4, b1, and b3 are constants; and Da is the Damköhler number, which establishes the relationship between the chemical kinetic and ﬂame development. In the present work, a4, b1, and b3 are optimized trying to well reproduce the combustion characteristic such as cylinder pressure and heat release rate. To obtain the laminar ﬂame speed, the Metghalchi and Kech correlation [29] is adopted in this study: !α !β Tu P sl = sl re f (1 2.1Ydil). (3) − Tu,re f Pre f −

Here, Tu is the unburnt mixture temperature, Tu,re f is 298.0 K, P is the unburnt mixture pressure, Pre f is 1.01 bar, Ydil is the mass fraction of the dilution species, and α and β are the temperature and pressure exponents: α = 2.18 0.8(φ 1), (4) − − Energies 2020, 13, 5039 4 of 23

β = 0.16 0.22(φ 1), (5) − − − where sl re f is obtained using the Gülder correlations [30]: Energies 2020− , 13, x FOR PEER REVIEW 4 of 23

η h 2i sl re f = ωφ exp ξ(φ σ) . (6) − − − 𝑠 =𝜔𝜙 𝑒𝑥 𝑝−𝜉𝜙−𝜎 . (6) Here, ω, η, ξ, and σ are the modeling constant coefficients for an iso-octane–air mixture. Here, 𝜔, 𝜂, 𝜉, and 𝜎 are the modeling constant coefficients for an iso-octane–air mixture. To reproduce the experimental and suitable length and time scales of laminar flames, the model To reproduce the experimental and suitable length and time scales of laminar flames, the model coefficients are calibrated and optimized, as shown in Table1. It can be seen from Figure1 that, coefficients are calibrated and optimized, as shown in Table 1. It can be seen from Figure 1 that, for for primary reference fuels with octane numbers varying from 85 to 95, the laminar flame speeds primary reference fuels with octane numbers varying from 85 to 95, the laminar flame speeds are are quite close under different equivalence ratios. It is reasonable to speculate PRF92 behaves a quite close under different equivalence ratios. It is reasonable to speculate PRF92 behaves a similar similar curve in the laminar flame speed—equivalence ratio diagram. Comparing with Guler line curve in the laminar flame speed—equivalence ratio diagram. Comparing with Guler line and and Metghalchi line, we can conclude that by adopting the revised coefficients, agreement with the Metghalchi line, we can conclude that by adopting the revised coefficients, agreement with the experimental data can be obtained. experimental data can be obtained. Table 1. Fitting coefficients of the laminar flame speed. Table 1. Fitting coefficients of the laminar flame speed. ω η ξ σ γ β ω η ξ σ γ β Gülder 0.4658 0.326 4.48 1.075 1.56 0.22 Gülder 0.4658− −0.326 4.48 1.075 1.56 −0.22− Present work 0.35 0.1 4.5 1.075 1.8 0.22 Present work 0.35 0.1 4.5 1.075 1.8 −0.22−

0.6 Iso-octane, Davis, 1998 T = 298 K, P = 1 atm n-heptane, Davis, 1998 0 0 Iso-octane, Huang, 2004 0.5 PRF85, Huang, 2004 PRF90, Huang, 2004 PRF95, Huang, 2004 0.4 Iso-octane, Kumar, 2007 Metghalchi, 1982 Gulder, 1984 present work 0.3

0.2

Laminar flame speed (m/s) 0.1

0.0 0.51.01.52.0 Φ equivalence ratio FigureFigure 1. 1. ComparisonComparison of of the the fitting ﬁtting cu curvesrves and and experimental experimental data data of of laminar laminar flame ﬂame speed. speed.

2.2.2.2. Numerical Numerical Models Models TheThe 3D 3D methodology ofof aa LESLES coupled coupled with with a G-equationa G-equation and and a chemical a chemical kinetic kinetic model model for thefor PRFthe PRFoxidation oxidation in the in CONVERGE the CONVERGE CFD codeCFD iscode applied is applied to the simulationto the simulation used in used this study.in this Thestudy. reacting The reactingflow problems flow problems are described are described in terms of in the terms mass, of energy, the mass, species energy, conservation, species conservation, and the Navier–Stokes and the Navier–Stokesequations [31– 33equations]. The detailed [31–33]. numerical The detailed models numeri can becal foundmodels in can Ref. be [34 found–36]. Thein Ref. geometry [34–36]. model, The geometrywhich consists model, of awhich combustion consists chamber, of a combustion an inlet port, cham andber, an an outlet inlet port, port, together and an withoutlet its port, grid together splitting, withcan be its found grid splitting, in Figure 2can. The be ignition found in process Figure is 2. initiated The ignition by a spark process located is initiated opposite by the a spray,spark whichlocated is supposed to ignite a flame core at ST 18. A base grid size of 1 mm is utilized, with a fixed embedding opposite the spray, which is supposed− to ignite a flame core at ST −18. A base grid size of 1 mm is utilized,around thewith spark a fixed plug andembedding spray to around meet the the required spark meshplug resolution.and spray Meanwhile,to meet the an required adaptive mesh mesh resolution.refinement Meanwhile, (AMR) is adopted. an adaptive During mesh combustion, refinement the (AMR) average is grid adopted. size in theDuring flame combustion, front is 0.5 mm,the averageand is on grid the size order in the of 0.125 flame mm front around is 0.5 mm, the spark and is plug on the during order the of 0.125 spark mm process around and the 0.25 spark mm plug near duringthe spray the duringspark process the injection. and 0.25 A maximummm near the of spra 4 milliony during cells the is achieved.injection. A Note maximum that, according of 4 million to a cells is achieved. Note that, according to a previous study, the present grid resolution can predict the occurrence of super-knocking [37]. The time step adjusts itself according to the CFL (Courant– Friedrichs–Lewy) number, which varies from 1×10 to 1×10 s.

Energies 2020, 13, 5039 5 of 23 previous study, the present grid resolution can predict the occurrence of super-knocking [37]. The time 8 step adjusts itself according to the CFL (Courant–Friedrichs–Lewy) number, which varies from 1 10− 6 × to 1 10− s. Energies× 2020, 13, x FOR PEER REVIEW 5 of 23

Figure 2. Schematic of the model structure and grid splitting.

2.3. Different Diﬀerent Case Settings

2.3.1. Effects Effects of Flame Propagation Velocity In practical engines, the flame flame propagation veloci velocityty is physically under the joint action of the laminar flameflame speed, turbulent flameflame speed, and in-cylinderin-cylinder turbulent flow.flow. Hence, Hence, it it is tricky to directly changechange flameflame propagationpropagation velocity. velocity. Keeping Keeping in in mind mind that that turbulent turbulent flame flame speed speed is ais functiona function of laminarof laminar flame flame speed speed and turbulenceand turbulence intensity intensity as Equation as Equation (3) implied, (3) we implied, find a solution. we find Furthermore, a solution. accordingFurthermore, to an according Equation to (6) an proposed Equation by (6) Gülder proposed [30], theby laminarGülder flame[30], the speed laminar has a flame linear speed relationship has a ω withlinear coe relationshipfficient ,with which coefficient means thatω, which a monotonically means that a increasing monotonicall ofy laminar increasing flame of laminar speed would flame bespeed observed wouldwhen be observed other parameters when other are parameters identical. Thus,are identical. we can Thus, decouple we can the flamedecouple velocity the flame from thevelocity end-gas from auto-ignition. the end-gas auto-ignition. Table2 lists Table the operating 2 lists the parameters operating parameters for studying for the studying e ffects the of effects flame propagationof flame propagation velocities. velocities.

Table 2. Operating parameters. Table 2. Operating parameters.

ParameterParameter Value Value OnsetOnset ofof calculationcalculation timetime −3030 CAD CAD aTDC aTDC − SparkSpark timingtiming −1818 CAD CAD aTDC aTDC (ST-18) (ST-18) − BaselineBaseline case:case: ωω 0.360.36 Cases:Cases: ωω 0.4,0.4, 0.5, 0.5, 0.6, 0.6, 0.7, 0.7, 0.8 0.8

2.3.2. Effects Effects of Turbulence IntensityIntensity Figure3 3 illustrates illustrates thethe variationsvariations ofof thethe coldcold flowflow atat −18 CAD aTDC (after top dead center) and − TDC after amplifying the flowflow velocity at −30 CAD aTDC. It can be seen that present setting has the − ability toto capturecapture the the turbulence turbulence dissipation dissipation as as the th vortexe vortex structure structure breaks breaks up andup and disappears disappears over time.over Thetime. vortex The vortex structure structure becomes becomes more more obvious obvious and complicatedand complicated as u /asu 0𝑢/𝑢increases, increases, and and remains remains to the to TDC.the TDC. These These results results indicate indicate that thethat method the method of amplifying of amplifying the flow the velocity flow velocity enhances enhances the in-cylinder the in- turbulencecylinder turbulence intensity. intensity. The evolution The ofevolution the TKE of (Turbulent the TKE kinetic(Turbulent energy) kinetic after energy) scaling theafter flow scaling velocity the flow velocity at different times is illustrated in Figure 4. It can be seen that the TKE increases first as the flow velocity increases, but subsequently decreases owing to the viscous dissipation. However, the TKE maintains a proportional relationship with 𝑢/𝑢. Figure 5 shows the variation of TKE with 𝑢/𝑢 at −18 CAD (spark timing) and TDC. At −18 CAD aTDC, the TKE and 𝑢/𝑢 basically exhibit a linearly positive relationship regardless of the timing of the scaling; however, the situation at the TDC is different. At the TDC, owing to viscous dissipation, the attenuation of TKE is positively related to the flow velocity and mapping timing. For instance, in the case of map −120 CAD and map −60 CAD,

Energies 2020, 13, 5039 6 of 23 at different times is illustrated in Figure4. It can be seen that the TKE increases first as the flow velocity increases, but subsequently decreases owing to the viscous dissipation. However, the TKE maintains a proportional relationship with u/u . Figure5 shows the variation of TKE with u/u at 18 CAD 0 0 − (spark timing) and TDC. At 18 CAD aTDC, the TKE and u/u basically exhibit a linearly positive − 0 relationship regardless of the timing of the scaling; however, the situation at the TDC is different. At the TDC, owing to viscous dissipation, the attenuation of TKE is positively related to the flow velocity andEnergies mapping 2020, 13, timing. x FOR PEER For REVIEW instance, in the case of map 120 CAD and map 60 CAD, the TKE6 of is23 not Energies 2020, 13, x FOR PEER REVIEW − − 6 of 23 linearly related to u/u0, whereas in the case of map 30, this linear relationship remains well owing to the TKE is not linearly related to 𝑢/𝑢, whereas in− the case of map −30, this linear relationship thethe lesser TKEdecay. is not Therefore,linearly related map to30 𝑢/𝑢 CAD, whereas is utilized. in the Detailed case of operating map −30, parameters this linear canrelationship be found in − Tableremainsremains3. wellwell owingowing toto thethe lesserlesser decay.decay. Therefore,Therefore, mapmap −−3030 CADCAD isis utilized.utilized. DetailedDetailed operatingoperating parametersparameters cancan bebe foundfound inin TableTable 3.3.

Figure 3. Evolution of different initial velocity fields. FigureFigure 3.3. Evolution of of different diﬀerent initial initial velocity velocity fields. ﬁelds.

5050

u/u0=1 u/u0=1 u/u =2 u/u0 =2 4040 0 u/u0=3 u/u0=3 u/u0=4 u/u0=4 3030 TKE TKE 2020

10 10 mapmap -120-120 mapmap -60-60 mapmap -30-30 00 -120-120 -90 -90 -60 -60 -30 -30 0 0 30 30 Crank Angle (CAD) Crank Angle (CAD) Figure 4. Evolution of averaged TKE after scaling the flow velocity at different times. FigureFigure 4. 4.Evolution Evolution of averaged TKE TKE after after scaling scaling the the flow ﬂow velocity velocity at atdifferent diﬀerent times. times.

Energies 2020, 13, 5039 7 of 23 Energies 2020, 13, x FOR PEER REVIEW 7 of 23

26 18 0 CAD 24 -18 CAD 16 22 map -120 CAD map -120 CAD 20 map -60 CAD 14 map -60 CAD map -30 CAD 18 map -30 CAD 12 16

TKE 10 TKE 14 12 8

10 6 8 4 6 1.0 1.5 2.0 2.5 3.0 3.5 4.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 u/u u/u 0 0 (a) (b)

FigureFigure 5. 5. ValuesValues of of TKE TKE for for different diﬀerent 𝑢/𝑢u/u at the instant of (a) −1818 CAD CAD aTDC and ( b)) TDC. TDC. 0 − TableTable 3. 3. OperatingOperating parameters parameters in in the the analysis analysis of of the the effects eﬀects of of turbulence turbulence intensity. intensity.

Parameters Value Value OnsetOnset of calculation timing −3030 CAD CAD aTDC aTDC − SparkingSparking timing −1818 CAD CAD aTDC aTDC (ST-18) (ST-18) − BaseBase case: case: 𝒖/𝒖u/u𝟎0 1.01.0 Ratios:Ratios: 𝒖/𝒖u/u𝟎0 1.5,1.5, 2.0, 2.0, 2.5, 2.5, 3.0, 3.0, 4.0 4.0

3.3. Results Results and and Discussion Discussion

3.1.3.1. Effects Eﬀects of of Flame Flame Propagation Propagation Velocity Velocity

3.1.1.3.1.1. Analysis Analysis of of Cylinder Cylinder Pressure Pressure and and HRR HRR FigureFigure 66 demonstrates demonstrates the the pressure pressure profiles profiles and filteredand filtered pressure pressure oscillations oscillations a ffected affected by different by differentlaminar flamelaminar speeds. flame Inspeeds. addition, In addition, Figure7 demonstratesFigure 7 demonstrates the MAPO the (Maximum MAPO (Maximum Amplitude Amplitude Pressure PressureOscillation) Oscillation) and onset and of auto-ignitiononset of auto-ignition with different with flamedifferent speeds. flame The speeds. peak pressureThe peak and pressure amplitude and amplitudeof the pressure of the oscillation pressure first oscillation increase andfirst then increa decreasese and as then increasing decrease the flameas increasing propagation the velocity. flame propagationHowever, the velocity. onset of auto-ignition However, the advances onset as of increasing auto-ignition the flame advances propagation as increasing velocity. The the strongest flame propagationknocking intensity velocity. with The astrongest peak pressure knocking of 35intens MPaity appears with a peak at ω pressure= 0.5, whereas of 35 MPa another appears pressure at ω =oscillation 0.5, whereas of highanother amplitude pressure with oscillation a peak valueof high of amplitude approximately with a 25 peak MPa value appears of approximately at ω = 0.6. Thus, 25 MPait can appears be implied at ω that= 0.6. super-knocking Thus, it can be occursimplied under that supe bothr-knocking conditions. occurs A further under increase both conditions. in the flame A furtherpropagation increase velocity in the flame leads propagation to a cliff-like velocity decrease leads in theto a pressure cliff-like profiledecrease and in the knocking pressure intensity; profile andfor instance,knocking the intensity; pressure for oscillation instance, amplitude the pressure is below oscillation 0.5 MPa amplitude at ω = 0.7 is andbelowω =0.50.8 MPa, which at ω means = 0.7 andthe knockingω = 0.8, which or pressure means oscillation the knocking disappears. or pressure This oscillation in-depth mechanism disappears. can This be demonstratedin-depth mechanism through can3D images,be demonstrated as discussed through later. 3D The images, evolutions as discus of HRRsed (Heatlater. The Release evolutions Rate) and of HRR BMF (Heat (burned Release mass Rate)fraction) and withBMF di(burnedfferent mass flame fraction) propagation with different speeds areflame plotted propagation in Figure speeds8a. At areω plotted= 0.36 inand Figureω = 8a.0.4 , Atthe ω profile = 0.36 of and the ω HRR = 0.4, exhibits the profile a bimodal of the shape. HRR Meanwhile,exhibits a bimodal as the flame shape. propagation Meanwhile, speed as the increases, flame propagationthe onset of AIspeed (auto increases, ignition) advancesthe onset andof AI the (auto peak ignition) value of HRRadvances increases, and the whereas peak thevalue heat of release HRR increases,duration decreases.whereas the These heat release results duration indicate decrease that twos. individual These results AIs indicate occur in that an two unburned individual mixture. AIs occurThe higher in an theunburned flame speedmixture. is, theThe closer higher is the the flam overalle speed combustion is, the closer process is tothe the overall TDC, combustion resulting in processhigher averageto the TDC, temperature resulting and in higher pressure. average As a te result,mperature auto-ignition and pressure. in the end-gasAs a result, region auto-ignition is prone to inoccur. the end-gas In addition, region higher is prone thermodynamics to occur. In providesaddition, favorablehigher thermodynamics conditions for a provides higher combustion favorable conditionsrate after the for occurrence a higher combustion of AI. However, rate after pressure the occurrence oscillation isof weak. AI. However, Furthermore, pressure a unimodal oscillation shape is weak.of HRR Furthermore, with higher a unimodal peak pressure shape is of exhibited HRR with with higher an peak increase pressure in the is exhibited flame propagation with an increase speed. inThe the unimodal flame propagation shape of HRR speed. implies The that unimodal an individual shape hotof HRR spot implies or auto-ignition that an individual occurs in the hot unburned spot or auto-ignition occurs in the unburned gas. Consequently, the auto-ignition flame completely consumes the residual unburned gas in the end-gas region at a speed close to the CJ velocity.

Energies 2020, 13, 5039 8 of 23

gas. Consequently, the auto-ignition ﬂame completely consumes the residual unburned gas in the Energies 2020, 13, x FOR PEER REVIEW 9 of 23 Energiesend-gas 2020, region13, x FOR at PEER a speed REVIEW close to the CJ velocity. 9 of 23

20 20 40 40 ω = ω 0.36 = 0.36 ω = 30 30 ω = 0.4 0.4 ω = ω 0.5 = 0.5

20 15 15 20 ω = ω 0.6 = 0.6 10 10 ω = ω 0.7 = 0.7 ω = 0 ω = 0.8 0.8 0 -10 -5 0 5 10 15 20 10 -10 -5 0 5 10 15 20 10 Pressure (MPa) Pressure (MPa) 5 5

0 0 -20-20 -10 -10 0 0 10 10 20 20 CrankCrank Angle Angle (CAD) (CAD) (a)( Pressurea) Pressure

6 6 ω =ω = 0.36 ω =ω 0.4 = 0.4 3 3 0.36 Knocking Onset 0 0 Knocking Onset -3 -3 -6 -6 30 30 ω =ω 0.5 = 0.5 ω =ω 0.6 = 0.6 20 20 10 10 0 0 -10-10 6 6 ω =ω 0.7 = 0.7 ω =ω 0.8 = 0.8 3 3 0 0 Pressure Oscillation (MPa) Pressure Oscillation (MPa) -3 -3 -6 -6 -30-30 -20 -20 -10 -10 0 0 10 10 20 20 30 30-20-20 -10 -10 0 0 10 10 20 20 30 30 Crank Angle (CAD) Crank Angle (CAD)

(b)( bPressure) Pressure oscillation oscillation

FigureFigureFigure 6. Pressure6. 6. PressurePressure profiles profiles profiles and and and filtered filtered filtered pressure pressure oscillations o oscillationsscillations with with different different different flame flameflame velocities. velocities.velocities.

30 30 SuperSuper knocking knocking 12 12

25 25 10 MAPO MAPO 10 Onset Onset of auto-ignition of auto-ignition 20 20 8 8

15 15 6 6

10 4 10MAPO (MPa) 4 MAPO (MPa) GeneralGeneral 5 5 combustioncombustion2 2 Onset of auto-ignition (CAD) auto-ignition of Onset Onset of auto-ignition (CAD) auto-ignition of Onset

0 0 0 0

0.30.3 0.4 0.4 0.5 0.5 0.6 0.6 0.7 0.7 0.8 0.8 ω ω FigureFigure 7. MAPO7. MAPOMAPO and and and onset onset onset of auto-ignitionof of auto-ignition auto-ignition with with different different diﬀerent flame flame ﬂame velocities. velocities.

Energies 2020, 13, 5039 9 of 23

Energies 2020, 13, x FOR PEER REVIEW 10 of 23

1.0 ω = 0.36 0.8 ω = 0.4 ω = 0.5 0.6 ω = 0.6 ω = 0.7 0.4 ω = 0.8 BMF Onset of auto-ignition 0.2

0.0

750

600

450

300

HRR (J/CAD) HRR 150

0 -20 -15 -10 -5 0 5 10 15 20 Crank Angle (CAD) (a) HRR and BMF profiles

200 HRR Onset of Onset of End of first AI Second AI Second AI 150 Second AI heat release 100 First AI heat release

HRR (J/CAD) 50 Heat release Heat release Heat release before during first AI during second AI end-gas AI 0 First AI duration Second AI duration 2CAD 1.8 CAD 10 12 14 16 Crank Angle (CAD) (b) HRR at ω = 0.36 800 HRR

600 Onset of AI End of AI

400

Heat release by AI

HRR (J/CAD) 200 HRR peak in ω = 0.5

Heat release before AI 0 AI Duration(0.9 CAD)

246 Crank Angle (CAD) (c) HRR at ω = 0.5

Figure 8. ((aa)) HRR HRR and and BMF BMF profiles profiles with with different different flame flame velocities velocities and and amplified amplified HRR HRR profile profile of ( ofb) (ωb )=ω 0.36= 0.36 and and(c) ω (c )= ω0.5.= 0.5.

Energies 2020, 13, 5039 10 of 23

To clearly demonstrate the heat release process under different conditions, the HRR profiles at ω = 0.36 and ω = 0.5 are amplified, as shown in Figure8b,c, respectively. At ω = 0.36, the HRR increases gradually before the onset of the first AI, after which it experiences a steep lift. Together with the subsequent decrease, the enclosed yellow area can be plotted to represent the heat release process by the first AI flame. At 13.8 CAD aTDC, the HRR increases again with a fast growth rate, which indicates the occurrence of a second AI. Similarly, the green area represents the heat released by the second AI flame. Durations of 2 CAD aTDC and 1.8 CAD aTDC for the two AIs can be observed. For the case at ω = 0.5, a single peak of HRR 4-times that of HRR at ω = 0.36 is observed, whereas the fast heat release duration is approximately half of the heat release for two AIs at ω = 0.36. No obvious peak in the HRR is observed because of the absence of the AI when the flame propagation speed is further increased by increasing the coefficient to ω = 0.7 and ω = 0.8. Furthermore, the BMF diagram reveals that the mass fraction of unburned gas consumed by the AI decreases gradually as the flame propagation speed increases. For instance, 97.5% of the mixture is consumed by the main flame at ω = 0.7, whereas at ω = 0.8, the main flame has already swept the entire combustion chamber before auto-ignition occurs owing to a very fast flame propagation speed, resulting in the absence of auto-ignition at ω = 0.8. Slight pressure oscillations can still be observed under the two conditions. It is worth mentioning that Rober et al. [38] presented that the pressure wave intensity is proportional to the burned mass by AI, and they also suggested that AI location and the coupling between the pressure wave and the AI flame propagation are also probably factors to control knock intensity. However, the present results demonstrate the non-monotonic relationship between the flame propagation velocity or BMF and the knock intensity. Such phenomena can be clearly explained by the detailed flame propagation process under different conditions, as shown in the latter figures. To summarize, increasing the flame propagation velocity will first strengthen the knocking intensity and then weaken it. There are two aspects to this. On the one hand, a higher flame velocity results in an increase of the heat release rate in the cylinder, consequently obtaining quicker increases of temperature and pressure at the end-gas region. Therefore, the ignition delay time of the unburned end-gas mixture is shortened, which can promote a hot-spot formation or the occurrence of auto-ignition. On the other hand, the higher the flame propagation velocity is, the shorter the time required for the main flame propagating from the spark to the end-wall. If all fuel-air mixtures are consumed by the main flame before an auto-ignition occurs, the auto-ignition will not appear. The competitive relationship between the flame propagation velocity and end-gas auto-ignition brings about a non-monotonic relationship between the flame propagation speed and knocking intensity. Meanwhile, the intensity of the knocking does not depend solely on the flame propagation velocity, but also on the mass of the unburned mixture when auto-ignition occurs. The most intense knocking is observed when both the flame propagation velocity and mass of the unburned mixture are significant. However, a sufficiently high flame propagation velocity will decrease the knocking intensity as a result of the absence of the AI or an insufficient unburned mixture as auto-ignition occurrence. This phenomenon is consistent with the 1D DNS results from Yu et al. [20].

3.1.2. Analysis of Combustion Process To further study the influence of the different flame velocities on the end-gas auto-ignition and pressure oscillation, the effects of the flame propagation velocities at ω = 0.5 and ω = 0.8 are considered.

(1). Combustion characteristics at ω = 0.5

Figure9 shows the evolution of the main flame propagation and end-gas auto-ignition at ω = 0.5. Noted that, the isosurface for G = 0, marked by the red color, indicates the main flame front [28]. The onset of an auto-ignition is localized by the isosurface of HCO with a mass fraction of 3.0 ppm [39], and the isosurface of the unburned mixture at a temperature of 1600 K at the end-gas region represents the flame front induced through an auto-ignition. The distribution of the local pressure fluctuation (∆P), which is calculated by the difference between the local pressure and the average pressure in the cylinder, Energies 2020, 13, x FOR PEER REVIEW 11 of 23

3.1.2. Analysis of Combustion Process To further study the influence of the different flame velocities on the end-gas auto-ignition and pressure oscillation, the effects of the flame propagation velocities at ω = 0.5 and ω = 0.8 are considered. (1). Combustion characteristics at ω = 0.5 Figure 9 shows the evolution of the main flame propagation and end-gas auto-ignition at ω = 0.5. Noted that, the isosurface for G = 0, marked by the red color, indicates the main flame front [28]. The onset of an auto-ignition is localized by the isosurface of HCO with a mass fraction of 3.0 ppm [39], and

Energiesthe isosurface2020, 13, 5039of the unburned mixture at a temperature of 1600 K at the end-gas region represents11 of 23 the flame front induced through an auto-ignition. The distribution of the local pressure fluctuation (ΔP), which is calculated by the difference between the local pressure and the average pressure in the iscylinder, also demonstrated. is also demonstrated. An obvious An auto-ignition obvious auto-ignition spot appears spot at appears 4.5 CAD at aTDC 4.5 CAD near aTDC the bottom near leftthe wallbottom under left awall large under accumulation a large accumulation of HCO owing of HC to low-temperatureO owing to low-temperature reactions, which reactions, is immediately which is consumedimmediately by consumed the subsequent by the high-temperature subsequent high-tempe reactions,rature forming reactions, a stable forming flame. a Under stable this flame. condition, Under althoughthis condition, only one although auto-ignition only one spot auto-ignition occurs, the mutual spot interactionoccurs, the between mutual theinteraction developed between flame front the induceddeveloped by flame AI and front a pressure induced wave by AI leads and a to pressure a much wave higher leads explosive to a much pressure, higher which explosive finally pressure, results inwhich violent finally knocking results combustion.in violent knocking Figure combustion.10 shows the Figure distribution 10 shows of thethe pressuredistribution fluctuation, of the pressure HCO, and unburned temperature (UT) on a horizontal plane with z = 3 mm. The purple line indicates the fluctuation, HCO, and unburned temperature (UT) on a horizontal− plane with z = −3 mm. The purple mainline indicates flame front the bymain the flame contour front of Gby= the0. It contour can be clearlyof G = seen0. It can from be the clearly pressure seen fluctuation from the pressure that the flamefluctuation front generatedthat the flame by the front AI on generated the right sideby the is atAI the on same the right position side as is the at pressurethe same wave position during as the periodpressure of wave 4.9 CAD during to 5.1 the CAD period aTDC. of 4.9 In CAD addition, to 5.1 the CAD pressure aTDC. fluctuation In addition, at the flamepressure front fluctuation achieves theat the peak flame value. front The achieves flame propagation the peak value. speed onThe the flame right propagation side is approximately speed on 1.7the km right/s, which side is closeapproximately to the Chapman–Jouguet 1.7 km/s, which (CJ) is detonationclose to the velocity Chapman–Jouguet and confirms the(CJ) occurrence detonation of velocity a detonation and here.confirms The the present occurrence result agreesof a detonation with the resulthere. The by Robert present et result al. [37 agrees], which with confirmed the result the by hypothesis Robert et proposedal. [37], which in the confirmed previous works the hypothesis [40] that super-knock proposed in is the characterized previous works by a deflagration [40] that super-knock to detonation is (DDT).characterized In addition, by a deflagration recently, the to super-knock detonation (DDT). with DDT In addition, phenomenon recently, also the can super-knock be distinctly with observed DDT byphenomenon an optically also rapid can compression be distinctly machineobserved (RCM) by an optically [41]. The rapid present compression flame propagation machine as(RCM) shown [41]. in FigureThe present9 is similar flame to propagation the detonation as shown propagation in Figure in [941 is]. similar to the detonation propagation in [41].

Figure 9. Evolution of main ﬂameflame propagation andand end-gasend-gas auto-ignitionauto-ignition atatω ω == 0.5 by 3D isosurfaces Energies 2020, 13, x FOR PEER REVIEW 12 of 23 of G = 0 and mass fraction of HCO = 33 ppm; ppm; the the bac backgroundkground color color indicates indicates the the pressure pressure evolution.

FigureFigure 10. 10. EvolutionEvolution of of Δ∆P,P, mass mass fraction fraction of ofHCO, HCO, and and unburned unburned temperature temperature after after the initial the initial auto- auto-ignitionignition at ωat = 0.5.ω = 0.5.

In [37], a circular 1D profile is extracted from the periphery of the combustion chamber to quantitatively analyze the cause of knock mechanism by comparing the pressure profile and auto- ignition reaction rate at every angular degree. This method describes the super-knocking mechanism well. Therefore, to further investigate the coupling between the flame and pressure wave, a path, as shown in Figure 11, is applied by extracting the 1D profiles of the pressure, unburned temperature, and mass fraction of HCO, and the profiles along with 2D images are illustrated in Figure 12. It can be seen from the 4.7 CAD to 4.8 CAD aTDC that a large amount of HCO is generated on the right side of the auto-ignition flame, indicating that sequential AIs occur in the region. During this period, the AI flame propagates with a deflagration velocity of approximately 730 m/s, exceeding the local acoustic speed. In addition, at 4.8 CAD aTDC, the pressure peak at the right side of the auto-ignition flame clearly increases. At this time, the auto-ignition flame speed is approximately 1.3 km/s, which is slightly lower than the CJ velocity. Owing to the fast heat release, the intensity of the pressure wave continues to enhance, and the pressure wave reaches a peak of 28 MPa at 4.9 CAD aTDC. It should be noted that, at this time, a coupling between the auto-ignition flame and pressure wave is formed, and the combustion mode completes the transitions from auto-ignition to a deflagration flame to detonation, which consequently generates the occurrence of super-knocking. This process is consistent with the work in [37]. Next, the subsequent detonation combustion wave proceeds to consume the unburned gas at a speed of 1.7 km/s, and the maximum pressure reaches 31 MPa. It is not until the unburned mixture on of left side of the flame is completely consumed at 5.1 CAD aTDC that the pressure wave detaches from the flame front, indicating the end of the detonation combustion. On the left side of the auto-ignition flame, the propagation speed remains at approximately 240 m/s, which is clearly inferior to the speed of the pressure wave, and thus a coupling between the auto-igntion flame and pressure wave does not appear here.

Figure 11. Schematic of trace from which the 1D profile is extracted.

Energies 2020, 13, x FOR PEER REVIEW 12 of 23

EnergiesFigure2020, 13 10., 5039 Evolution of ΔP, mass fraction of HCO, and unburned temperature after the initial auto-12 of 23 ignition at ω = 0.5.

In [37], a circular 1D profile is extracted from the periphery of the combustion chamber In [37], a circular 1D profile is extracted from the periphery of the combustion chamber to to quantitatively analyze the cause of knock mechanism by comparing the pressure profile and quantitatively analyze the cause of knock mechanism by comparing the pressure profile and auto- auto-ignition reaction rate at every angular degree. This method describes the super-knocking ignition reaction rate at every angular degree. This method describes the super-knocking mechanism mechanism well. Therefore, to further investigate the coupling between the flame and pressure wave, well. Therefore, to further investigate the coupling between the flame and pressure wave, a path, as a path, as shown in Figure 11, is applied by extracting the 1D profiles of the pressure, unburned shown in Figure 11, is applied by extracting the 1D profiles of the pressure, unburned temperature, temperature, and mass fraction of HCO, and the profiles along with 2D images are illustrated in and mass fraction of HCO, and the profiles along with 2D images are illustrated in Figure 12. It can Figure 12. It can be seen from the 4.7 CAD to 4.8 CAD aTDC that a large amount of HCO is generated on be seen from the 4.7 CAD to 4.8 CAD aTDC that a large amount of HCO is generated on the right the right side of the auto-ignition flame, indicating that sequential AIs occur in the region. During this side of the auto-ignition flame, indicating that sequential AIs occur in the region. During this period, period, the AI flame propagates with a deflagration velocity of approximately 730 m/s, exceeding the AI flame propagates with a deflagration velocity of approximately 730 m/s, exceeding the local the local acoustic speed. In addition, at 4.8 CAD aTDC, the pressure peak at the right side of the acoustic speed. In addition, at 4.8 CAD aTDC, the pressure peak at the right side of the auto-ignition auto-ignition flame clearly increases. At this time, the auto-ignition flame speed is approximately flame clearly increases. At this time, the auto-ignition flame speed is approximately 1.3 km/s, which 1.3 km/s, which is slightly lower than the CJ velocity. Owing to the fast heat release, the intensity of the is slightly lower than the CJ velocity. Owing to the fast heat release, the intensity of the pressure wave pressure wave continues to enhance, and the pressure wave reaches a peak of 28 MPa at 4.9 CAD aTDC. continues to enhance, and the pressure wave reaches a peak of 28 MPa at 4.9 CAD aTDC. It should It should be noted that, at this time, a coupling between the auto-ignition flame and pressure wave be noted that, at this time, a coupling between the auto-ignition flame and pressure wave is formed, is formed, and the combustion mode completes the transitions from auto-ignition to a deflagration and the combustion mode completes the transitions from auto-ignition to a deflagration flame to flame to detonation, which consequently generates the occurrence of super-knocking. This process detonation, which consequently generates the occurrence of super-knocking. This process is is consistent with the work in [37]. Next, the subsequent detonation combustion wave proceeds to consistent with the work in [37]. Next, the subsequent detonation combustion wave proceeds to consume the unburned gas at a speed of 1.7 km/s, and the maximum pressure reaches 31 MPa. It is not consume the unburned gas at a speed of 1.7 km/s, and the maximum pressure reaches 31 MPa. It is until the unburned mixture on of left side of the flame is completely consumed at 5.1 CAD aTDC that not until the unburned mixture on of left side of the flame is completely consumed at 5.1 CAD aTDC the pressure wave detaches from the flame front, indicating the end of the detonation combustion. that the pressure wave detaches from the flame front, indicating the end of the detonation On the left side of the auto-ignition flame, the propagation speed remains at approximately 240 m/s, combustion. On the left side of the auto-ignition flame, the propagation speed remains at which is clearly inferior to the speed of the pressure wave, and thus a coupling between the auto-igntion approximately 240 m/s, which is clearly inferior to the speed of the pressure wave, and thus a flame and pressure wave does not appear here. coupling between the auto-igntion flame and pressure wave does not appear here.

FigureFigure 11. 11.Schematic Schematic of of trace trace from from which which the the 1D 1D proﬁle profile is is extracted. extracted.

(2). Combustion characteristics at ω= 0.8

Figure 13 demonstrates the evolution of the main flame propagation and end-gas auto-ignition at ω = 0.8. Under this condition, the auto-ignition does not occur. As the figure indicates, the main flame has already swept the entire combustion chamber at 1 CAD aTDC, leading to the suppression − of the end-gas AI. Similar results can be concluded from the distribution of HCO and UT. No obvious accumulation of HCO or an increase of UT occurs, as shown in Figure 14. However, the pressure oscillation with an amplitude of approximately 3 bar can still be observed from the distribution of the pressure fluctuation. This phenomenon implies that the in-cylinder pressure wave oscillation can not only be induced by auto-ignition, but can also be caused by a fast heat release or accelerated flame if it is sufficiently fast to induce a local pressure increase, which was confirmed in previous studies [42–44]. Meanwhile, it can be seen that multiple pressure waves are generated during the flame propagation. The pressure waves continuously compress the unburned mixture, increasing the local temperature and pressure, which in turn enhances the flame propagation. It should be noted that the pressure oscillation induced by the main flame is far lower than that by the end-gas auto-ignition. Therefore, knocking can be inhibited by increasing the flame propagation velocity; however, it can be reasonably Energies 2020, 13, 5039 13 of 23 predicted that a further increase in the flame velocity will cause higher pressure oscillations owing to the increase in HRR. Overall, for a quickly accelerating flame, the interactions between the flame, compress wave, and auto-ignition dominate the occurrence of knocking combustion. Energies 2020, 13, x FOR PEER REVIEW 13 of 23

FigureFigure 12.12. Evolution of 2D patternpattern ofof ∆ΔPP inin thethe horizontalhorizontal cross-sectioncross-section ((leftleft),), pressure,pressure, unburnedunburned temperature,temperature, andand massmass fractionfraction ofof HCOHCO onon thethe 1D1D proﬁleprofile ((middlemiddle)) andand 2D2D patternpattern ofof unburnedunburned temperaturetemperature inin thethe horizontalhorizontal cross-sectioncross-section ((rightright)) underunder thethe conditioncondition ofofω ω == 0.5.

(2). Combustion characteristics at ω= 0.8

Figure 13 demonstrates the evolution of the main flame propagation and end-gas auto-ignition at ω = 0.8. Under this condition, the auto-ignition does not occur. As the figure indicates, the main flame has already swept the entire combustion chamber at −1 CAD aTDC, leading to the suppression of the end-gas AI. Similar results can be concluded from the distribution of HCO and UT. No obvious accumulation of HCO or an increase of UT occurs, as shown in Figure 14. However, the pressure oscillation with an amplitude of approximately 3 bar can still be observed from the distribution of the pressure fluctuation. This phenomenon implies that the in-cylinder pressure wave oscillation can not only be induced by auto-ignition, but can also be caused by a fast heat release or accelerated flame if it is sufficiently fast to induce a local pressure increase, which was confirmed in previous studies [42–44]. Meanwhile, it can be seen that multiple pressure waves are generated during the flame propagation. The pressure waves continuously compress the unburned mixture, increasing the local temperature and pressure, which in turn enhances the flame propagation. It should be noted that the

Energies 2020, 13, x FOR PEER REVIEW 14 of 23 Energies 2020, 13, x FOR PEER REVIEW 14 of 23

pressure oscillation induced by the main flame is far lower than that by the end-gas auto-ignition. pressure oscillation induced by the main flame is far lower than that by the end-gas auto-ignition. Therefore, knocking can be inhibited by increasing the flame propagation velocity; however, it can be Therefore, knocking can be inhibited by increasing the flame propagation velocity; however, it can be reasonably predicted that a further increase in the flame velocity will cause higher pressure oscillations reasonably predicted that a further increase in the flame velocity will cause higher pressure oscillations owing to the increase in HRR. Overall, for a quickly accelerating flame, the interactions between the owingEnergies 2020to the, 13 ,increase 5039 in HRR. Overall, for a quickly accelerating flame, the interactions between14 ofthe 23 flame, compress wave, and auto-ignition dominate the occurrence of knocking combustion. flame, compress wave, and auto-ignition dominate the occurrence of knocking combustion.

Figure 13. Evolution of 3D in-cylinder combustion process at ω = 0.8. Figure 13. Evolution of 3D in-cylinder combustion process at ω = 0.8.0.8.

FigureFigure 14. 14. Evolution of of Δ∆P,P, mass mass fraction fraction of of HCO, HCO, and and unburned unburned temperature temperature after after the initial the initial auto- Figure 14. Evolution of ΔP, mass fraction of HCO, and unburned temperature after the initial auto- auto-ignitionignition at ω at = ω0.8.= 0.8. ignition at ω = 0.8. 3.2. Effects of Turbulence Intensity 3.2. Effects of Turbulence Intensity 3.2. Effects of Turbulence Intensity Unlike the effects of the turbulent flame velocity on the end-gas auto-ignition and knocking Unlike the effects of the turbulent flame velocity on the end-gas auto-ignition and knocking occurrence,Unlike increasingthe effects theof the turbulence turbulent intensity flame veloci mustty simultaneously on the end-gas change auto-ignition the flame and propagation knocking occurrence, increasing the turbulence intensity must simultaneously change the flame propagation occurrence,and thermodynamic increasing state the involvingturbulence the intensity temperature must simultaneously and compositions change in the the end-gas flame region.propagation Here, and thermodynamic state involving the temperature and compositions in the end-gas region. Here, andthe ethermodynamicffects of the turbulence state involving intensity the by temperature changing the and flow compositions velocity on the in end-gasthe end-gas auto-ignition region. Here, and the effects of the turbulence intensity by changing the flow velocity on the end-gas auto-ignition and thepressure effects oscillation of the turbulence are determined. intensity by changing the flow velocity on the end-gas auto-ignition and pressure oscillation are determined. pressure oscillation are determined. 3.2.1. Analysis of Cylinder Pressure and HRR 3.2.1. Analysis of Cylinder Pressure and HRR 3.2.1.Figure Analysis 15 showsof Cylinder the pressure Pressure profiles and HRR and filtered pressure oscillations with different turbulence Figure 15 shows the pressure profiles and filtered pressure oscillations with different turbulence intensities.Figure 15 Similar shows to the the pressure effects ofprofiles the flame and filtered velocity pressure on the knockingoscillations intensity, with different a non-monotonic turbulence intensities. Similar to the effects of the flame velocity on the knocking intensity, a non-monotonic intensities.relationship Similar between to the the effects turbulence of the intensity flame velocity and the on pressure the knocking oscillation intensity, is observed a non-monotonic from the relationship between the turbulence intensity and the pressure oscillation is observed from the flame- relationshipflame-turbulence between interaction. the turbulence The combustion intensity and phenomenon the pressure isoscillation consistent is withobserved the results from the obtained flame- turbulence interaction. The combustion phenomenon is consistent with the results obtained from a turbulencefrom a 1D simulation interaction. described The combustion in previous phenomenon studies [45 ,is46 ].consistent On the one with hand, the theresults increased obtained turbulence from a 1D simulation described in previous studies [45,46]. On the one hand, the increased turbulence 1Dintensity simulation can promote described important in previous intermediate studies [45, radicals46]. On and the heat one dispersions, hand, the increased which finally turbulence retards the onset of the AI and reduces the AI kernel size [47]. On the other hand, increasing the turbulence

intensity can also increase the wrinkled flame surface and burning rate, which results in an increase in the flame propagation velocity. As discussed above, the effects of the flame propagation speed on the end-gas auto-ignition are also non-monotonic. Both causes will ultimately influence the knocking Energies 2020, 13, x FOR PEER REVIEW 15 of 23

intensity can promote important intermediate radicals and heat dispersions, which finally retards the onset of the AI and reduces the AI kernel size [47]. On the other hand, increasing the turbulence intensity can also increase the wrinkled flame surface and burning rate, which results in an increase in the flame propagation velocity. As discussed above, the effects of the flame propagation speed on the end-gas auto-ignition are also non-monotonic. Both causes will ultimately influence the knocking tendency and intensity. However, the previous studies neglected the effects of flame propagation and compression wave. It is worth noting that the MAPO under enhanced turbulence intensity conditions is generally lower than that under the flame speed cases. In addition, none of the MAPOs here exceeds 1.5 MPa, as shown in Figure 16. The more intense the turbulence is, the faster the main flame propagates, which promotes the pressure increase and advances the onset of the pressure oscillation. As a result, the mean in-cylinder pressure is also high as a pressure oscillation occurs. Compared to the effect of the flame speed, the effect of the turbulence on the pressure oscillation is more complicated, as discussed above. Therefore, to further decouple the flame acceleration from the end gas auto-ignition, applying the mean combustion rate (BMF when auto-ignition occurs is divided by the difference of auto-ignition timing and spark timing) before the auto-ignition occurrence is proposed to indicate the main flame propagation speed. Similarly, the effect of different flame speeds on the end-gas auto- ignition is also determined using the same method as a comparison. Figure 17 demonstrates the relationship between the MAPO and the combustion rate before the AI in terms of the increase in flame speed and an increase in turbulence intensity, respectively. By comparison, under the same mean combustion rate, the MAPO obtained by changing the turbulence intensity is far lower than that obtained by increasing the flame speed, which indicates that increasing the turbulence can effectively suppress the auto-ignition. The HRR and BMF profiles at different turbulent intensities are plotted in Figure 18. The bimodal curve of the HRR reveals the occurrence of two individual AIs. As the turbulence intensity increases, the first peak by the first AI is gradually inhibited, whereas the second peak first increases and then decreases. This indicates that the turbulence first leads to a more homogenous reactivity and an increase in the thermodynamic state in unburned gas for the second AI spot. Thus, the heat release rate increases. In contrast, a further increase of the turbulence intensity will increase the propagation Energiesvelocity2020 of ,the13, 5039main flame as well as the ignition delay of the end gas, which means a reduction 15of ofthe 23 unburned mixture when an auto-ignition occurs. As a result, the HRR gradually decreases. For instance, approximately 97.1% of the fuel-air mixture is consumed by the main flame when auto-ignition occurs tendency and intensity. However, the previous studies neglected the eﬀects of ﬂame propagation and at 𝑢/𝑢 = 4.0, and therefore the amplitude of the pressure oscillation under this condition is only 0.27 compression wave. MPa, which is even smaller than the case of ω = 0.8 where no auto-ignition is observed.

u/u0 = 1.0 u/u = 1.5 8 0 u/u0 = 2.0

u/u0 = 2.5 u/u = 3.0 6 0

u/u0 = 4.0

Pressure (MPa) Pressure 4

-20 -10 0 10 20 Crank Angle (CAD) Energies 2020, 13, x FOR PEER REVIEW (a) Cylinder pressure 16 of 23

2 1 u/u0 = 1.0 u/u0 = 1.5 Knocking onset 0 -1 -22 1 u/u0 = 2.0 u/u0 = 2.5 0 -1 -22 u/u = 4.0 1 u/u0 = 3.5 0 0 Pressure Oscillation (MPa) Oscillation Pressure -1 -2 -30 -20 -10 0 10 20 30 -20-100 102030 Crank Angle (CAD) (b) Filtered pressure oscillation

FigureFigure 15. 15. PressurePressure traces traces and and filtered ﬁltered pressure pressure oscilla oscillationstions with with different diﬀerent turbulence turbulence intensities. intensities.

It is worth noting that the1.6 MAPO under enhanced turbulence intensity14 conditions is generally MAPO lower than that under the flame1.4 speed cases. In addition, none of the12 MAPOs here exceeds 1.5 MPa, Onset of auto-ignition as shown in Figure 16. The more intense the turbulence is, the faster the main flame propagates, 1.2 10 which promotes the pressure increase and advances the onset of the pressure oscillation. As a result, 1.0 the mean in-cylinder pressure is also high as a pressure oscillation8 occurs. Compared to the effect 0.8 of the flame speed, the effect of the turbulence on the pressure oscillation6 is more complicated, as

discussed above. Therefore,(MPa) MAPO 0.6 to further decouple the flame acceleration from the end gas auto-ignition, applying the mean combustion rate (BMF when auto-ignition occurs4 is divided by the difference of 0.4 auto-ignition timing and spark timing) before the auto-ignition occurrence2 Onset of auto-ignition (CAD) is proposed to indicate the main flame propagation0.2 speed. Similarly, the effect of different flame speeds on the end-gas 0 auto-ignition is also determined1.0 using 1.5 the 2.0 same 2.5 method 3.0 as 3.5 a comparison. 4.0 Figure 17 demonstrates u/u the relationship between the MAPO and the combustion0 rate before the AI in terms of the increase in flame speedFigure and 16. an MAPO increase and inonset turbulence of auto-ignition intensity, with respectively. different turbulence By comparison, intensities. under the same mean combustion rate, the MAPO obtained by changing the turbulence intensity is far lower than that obtained by increasing the flame speed, which indicates that increasing14 the turbulence can effectively 30 Effect of turbulence intensity suppress the auto-ignition. 12 Effect of flame speed 25 10

20 8

6 15 4 10 MAPO (MPa) 2 5 0 Onset of auto-ignition (CAD) of auto-ignition Onset

0 -2

0.02 0.03 0.04 0.05 0.06 Combustion rate before AI (1/CAD) Figure 17. Relationship between MAPO and the combustion rate before auto-ignition as increasing the flame speed and increasing the turbulence intensity.

Energies 2020,, 13,, xx FORFOR PEERPEER REVIEWREVIEW 16 of 23

2 u/u = 1.0 u/u = 1.5 1 u/u00 = 1.0 u/u00 = 1.5 Knocking onset 0 -1-1 -2-22 u/u = 2.0 u/u = 2.5 1 u/u00 = 2.0 u/u00 = 2.5 0 -1-1 -2-22 u/u = 3.5 u/u == 4.04.0 1 u/u00 = 3.5 00 0 Pressure Oscillation (MPa) Oscillation Pressure Pressure Oscillation (MPa) Oscillation Pressure -1-1 -2-2 -30-30 -20 -20 -10 -10 0 0 10 10 20 20 30 30 -20-100-20-100 102030 102030 Crank Angle (CAD) (b) Filtered pressure oscillation Energies 2020, 13, 5039 (b) Filtered pressure oscillation 16 of 23 Figure 15. Pressure traces and filtered pressure oscillationstions withwith differentdifferent turbulenceturbulence intensities.intensities.

1.61.6 1414

MAPOMAPO 1.41.4 1212 OnsetOnset ofof auto-ignitionauto-ignition 1.2 1.2 1010

1.01.0 88

0.80.8 66 MAPO (MPa) MAPO MAPO (MPa) MAPO 0.60.6 44 0.40.4 Onset of auto-ignition (CAD) 22 Onset of auto-ignition (CAD) 0.20.2 00 1.01.0 1.5 1.5 2.0 2.0 2.5 2.5 3.0 3.0 3.5 3.5 4.0 4.0 u/u 00 FigureFigure 16. 16. MAPOMAPO and and onset onset of of auto-ignition auto-ignition with with different diﬀerent turbulence intensities.

1414 30 30 EffectEffect ofof turbulenceturbulence intensityintensity 1212 EffectEffect ofof flameflame speedspeed 25 25 1010

2020 88

66 1515 44 10

MAPO (MPa) 10 MAPO (MPa) 22 55 0

0 (CAD) of auto-ignition Onset Onset of auto-ignition (CAD) of auto-ignition Onset

00 -2-2

0.020.02 0.03 0.03 0.04 0.04 0.05 0.05 0.06 0.06 Combustion rate before AI (1/CAD)

Figure 17. Relationship betweenbetween MAPOMAPO and and the the combustion combustion rate raterate before beforebefore auto-ignition auto-ignitionauto-ignition as increasingasas increasingincreasing the theﬂamethe flameflame speed speedspeed and andand increasing increasingincreasing the turbulencethethe turbulenceturbulence intensity. intensity.intensity.

The HRR and BMF profiles at different turbulent intensities are plotted in Figure 18. The bimodal curve of the HRR reveals the occurrence of two individual AIs. As the turbulence intensity increases, the first peak by the first AI is gradually inhibited, whereas the second peak first increases and then decreases. This indicates that the turbulence first leads to a more homogenous reactivity and an increase in the thermodynamic state in unburned gas for the second AI spot. Thus, the heat release rate increases. In contrast, a further increase of the turbulence intensity will increase the propagation velocity of the main flame as well as the ignition delay of the end gas, which means a reduction of the unburned mixture when an auto-ignition occurs. As a result, the HRR gradually decreases. For instance, approximately 97.1% of the fuel-air mixture is consumed by the main flame when auto-ignition occurs at u/u0 = 4.0, and therefore the amplitude of the pressure oscillation under this condition is only 0.27 MPa, which is even smaller than the case of ω = 0.8 where no auto-ignition is observed. Energies 2020, 13, 5039 17 of 23

Energies 2020, 13, x FOR PEER REVIEW 17 of 23

1.0 u/u0 = 1.0

0.8 u/u0 = 1.5

u/u0 = 2.0 0.6 u/u0 = 2.5 u/u = 3.0 0.4 0 BMF u/u = 4.0 0 Onset of auto-ignition 0.2

0.0 400 350 300 250 200 150 100

HRR (J/CAD) HRR 50 0 -50 -20 -15 -10 -5 0 5 10 15 20 Crank Angle (CAD) Figure 18. HRR and BMF curves with different diﬀerent turbulence intensities.

3.2.2. Analysis of Combustion Process The profileprofile of the HRR under different different turbulence intensities can be divided into into two two categories. categories. The cases of u/u = 1.5, 2.0, and 2.5 share similar bimodal curves of the HRR, which means they have a The cases of 𝑢/𝑢0 = 1.5, 2.0, and 2.5 share similar bimodal curves of the HRR, which means they have similar combustion process. For u/u = 3.0 and 4.0, the curves of the HRR are unimodal evolutions. a similar combustion process. For 𝑢/𝑢0 = 3.0 and 4.0, the curves of the HRR are unimodal evolutions. Based on this, the two turbulence intensities at u/u = 1.5 and u/u = 4.0 are adopted to analyze the Based on this, the two turbulence intensities at 𝑢/𝑢0 = 1.5 and 𝑢/𝑢0 = 4.0 are adopted to analyze the in-cylinder combustion processprocess aaffectedffected byby thethe turbulenceturbulence intensity.intensity.

(1). CombustionCombustion characteristics characteristics at at u𝑢/𝑢/u0=1.5= 1.5

Figure 19 shows the in-cylinder combustion characteristics for 𝑢/𝑢 = 1.5. In addition, for the Figure 19 shows the in-cylinder combustion characteristics for u/u0 = 1.5. In addition, for the evolution of ΔP, the mass fraction of the HCO and the unburned temperature at 𝑢/𝑢 = 1.5 are evolution of ∆P, the mass fraction of the HCO and the unburned temperature at u/u0 = 1.5 are illustrated in Figure 20. As the figure indicates, auto-ignition first occurs near the bottom left wall at illustrated in Figure 20. As the figure indicates, auto-ignition first occurs near the bottom left wall 7.3 CAD aTDC with a large amount of HCO accumulated around the initial auto-ignition kernel, at 7.3 CAD aTDC with a large amount of HCO accumulated around the initial auto-ignition kernel, denoting the occurrence of sequential auto-ignitions in this region. The fast heat release generated by denoting the occurrence of sequential auto-ignitions in this region. The fast heat release generated the AI results in a local pressure increase and triggers the pressure waves. However, the pressure by the AI results in a local pressure increase and triggers the pressure waves. However, the pressure waves have a higher propagation velocity than the AI flame speed. In addition, the limited mass of waves have a higher propagation velocity than the AI flame speed. In addition, the limited mass of the the unburned mixture around the AI spots further prevents the coupling between the flame and unburned mixture around the AI spots further prevents the coupling between the flame and pressure pressure wave, which does not lead to a strong pressure oscillation according to a previous study. wave, which does not lead to a strong pressure oscillation according to a previous study. Affected by Affected by the compression effects of both the main flame and the auto-ignition flame, a second the compression effects of both the main flame and the auto-ignition flame, a second auto-ignition auto-ignition appears on the right side of the combustion chamber at 8.3 CAD aTDC. The in-cylinder appears on the right side of the combustion chamber at 8.3 CAD aTDC. The in-cylinder pressure and pressure and temperature are further increased compared to the first auto-ignition, which leads to a temperature are further increased compared to the first auto-ignition, which leads to a more intense heat more intense heat release, generating stronger pressure waves. As shown in [45,46], the increased release, generating stronger pressure waves. As shown in [45,46], the increased turbulence intensity turbulence intensity has the capability of delaying the onset of the AI formation and shrinks the has the capability of delaying the onset of the AI formation and shrinks the kernel size at the onset of AI kernel size at the onset of AI because of turbulence stirring and subsequently the enhance localized because of turbulence stirring and subsequently the enhance localized energy and radicals dissipation, energy and radicals dissipation, which results in the decrease of unburned mixture amount if AI which results in the decrease of unburned mixture amount if AI occurs. The in-depth analysis of the occurs. The in-depth analysis of the similar work is confirmed by the work of Wu et al. [48]. However, similar work is confirmed by the work of Wu et al. [48]. However, as pointed out by Wei et al. [46], as pointed out by Wei et al. [46], the increased turbulence stirring results in the increases of mean the increased turbulence stirring results in the increases of mean temperature and pressure of the temperature and pressure of the unburnt mixture. Furthermore, the increased turbulence also can unburnt mixture. Furthermore, the increased turbulence also can promote flame propagation induced promote flame propagation induced by the AI due to increasing the turbulent flame surface. As a by the AI due to increasing the turbulent flame surface. As a consequence, although the remaining consequence, although the remaining unburned mixture when auto-ignition occurs is less than that unburned mixture when auto-ignition occurs is less than that for the baseline case, noted that, the mean for the baseline case, noted that, the mean thermodynamic states involving the temperature and thermodynamic states involving the temperature and pressure are higher, which introduces a more pressure are higher, which introduces a more intense heat release and strengthens the pressure intense heat release and strengthens the pressure oscillation ultimately. The present result indicates that oscillation ultimately. The present result indicates that the thermodynamic states dominate the the thermodynamic states dominate the combustion intensity and not only the unburned mixture mass. combustion intensity and not only the unburned mixture mass.

Energies 2020, 13, 5039 18 of 23 Energies 2020, 13, x FOR PEER REVIEW 18 of 23 Energies 2020, 13, x FOR PEER REVIEW 18 of 23

FigureFigure 19.19. EvolutionEvolution ofof 3D3D in-cylinderin-cylinder combustioncombustion processprocess atatu 𝑢/𝑢/u0= =1.5. 1.5. Figure 19. Evolution of 3D in-cylinder combustion process at 𝑢/𝑢 = 1.5.

FigureFigure 20.20. EvolutionEvolution of of ΔP,∆P, mass mass fraction fraction of ofHCO, HCO, and and unburned unburned temperature temperature after after the initial the initial auto- Figureauto-ignition 20. Evolution at u/u of= 1.5.ΔP, mass fraction of HCO, and unburned temperature after the initial auto- ignition at 𝑢/𝑢 = 1.5.0 ignition at 𝑢/𝑢 = 1.5. (2). Combustion characteristics at u/u0 = 4.0 (2). Combustion characteristics at 𝑢/𝑢 = 4.0 (2). Combustion characteristics at 𝑢/𝑢 = 4.0 FigureFigure 21 21 demonstrates demonstrates thethe evolutionevolution ofof thethe mainmain flame,flame, auto-ignitionauto-ignition flame,flame, andand pressurepressure wave wave Figure 21 demonstrates the evolution of the main flame, auto-ignition flame, and pressure wave basedbased onon 2D2D imagesimages asas auto-ignitionauto-ignition occurs,occurs, respectively.respectively. OnlyOnly oneone auto-ignitionauto-ignition isis observedobserved onon thethe based on 2D images as auto-ignition occurs, respectively. Only one auto-ignition is observed on the rightright sideside of of the the combustion combustion chamber chamber where where a seconda second AI AI was was found found in previousin previous cases. cases. The The absence absence of right side of the combustion chamber where a second AI was found in previous cases. The absence AIof inAI the in firstthe first AI position AI position mentioned mentioned above above can be can attributed be attributed to the to increase the increase in flame in propagationflame propagation speed of AI in the first AI position mentioned above can be attributed to the increase in flame propagation andspeed the and dissipation the dissipation of heat andof heat intermediate and intermediate radicals radicals generated generated by low-temperature by low-temperature reactions reactions around speed and the dissipation of heat and intermediate radicals generated by low-temperature reactions thearound AI kernel. the AI These kernel. impacts These substantially impacts substantially retard the ignition retard delay,the ignition resulting delay, in the resulting consumption in the of around the AI kernel. These impacts substantially retard the ignition delay, resulting in the theconsumption unburned of mixture the unburned by the main mixture flame by beforethe main auto-ignition. flame before Compared auto-ignition. to the Compared case of u to/u the= case1.5, consumption of the unburned mixture by the main flame before auto-ignition. Compared to the0 case theof increased𝑢/𝑢 = 1.5, flame the increased speed dominates flame speed the combustion dominates processthe combustion and suppresses process the and end-gas suppresses auto-ignition the end- of 𝑢/𝑢 = 1.5, the increased flame speed dominates the combustion process and suppresses the end- duegas toauto-ignition the distinct due effect to of the enhanced distinct turbulenceeffect of enhanced intensity. turbulence At 1.5 CAD intensity. aTDC, theAt 1.5 AI occursCAD aTDC, with thethe gas auto-ignition due to the distinct effect of enhanced turbulence intensity. At 1.5 CAD aTDC, the consumptionAI occurs with of the the consumption remaining unburned of the remaining gas during unburned 0.4 CAD. gas Limitedduring 0.4 by CAD. the mass Limited of the by available the mass AI occurs with the consumption of the remaining unburned gas during 0.4 CAD. Limited by the mass unburnedof the available mixture, unburned the auto-ignition mixture, the does auto-ignition not produce do stronges not pressure produce oscillations.strong pressure Note oscillations. that, under Note this of the available unburned mixture, the auto-ignition does not produce strong pressure oscillations. Note condition,that, under a this pressure condition, wave a with pressure a slight wave intensity with a can slight be observedintensity can at 1.3 be CAD observed aTDC, at even1.3 CAD before aTDC, the that, under this condition, a pressure wave with a slight intensity can be observed at 1.3 CAD aTDC, occurrenceeven before of the auto-ignition. occurrence Thisof auto-ignition. phenomenon This can bephenomenon explained by can the be intense explained combustion by the processintense even before the occurrence of auto-ignition. This phenomenon can be explained by the intense andcombustion fast heat process release and rate fast induced heat release by the fastrate propagationinduced by the speed fast ofpropagation the main flame. speed of the main flame. combustion process and fast heat release rate induced by the fast propagation speed of the main flame.

Energies 2020, 13, 5039 19 of 23 Energies 2020, 13, x FOR PEER REVIEW 19 of 23

Figure 21. EvolutionEvolution of ofΔP,∆ P,mass mass fraction fraction of HCO, of HCO, andand unburned unburned temperature temperature after afterthe initial theinitial auto- auto-ignition at u/u0 = 4.0. ignition at 𝑢/𝑢 = 4.0. 4. Conclusions 4. Conclusions The major objective of the present work is to investigate the effects of the flame propagation velocity The major objective of the present work is to investigate the effects of the flame propagation and turbulence intensity on the end-gas auto-ignition as well as pressure oscillation through an LES velocity and turbulence intensity on the end-gas auto-ignition as well as pressure oscillation through and a decoupling methodology applied in a downsized SI gasoline engine. The mechanisms of end-gas an LES and a decoupling methodology applied in a downsized SI gasoline engine. The mechanisms auto-ignition and a strong pressure oscillation were qualitatively analyzed. In this work, it should be of end-gas auto-ignition and a strong pressure oscillation were qualitatively analyzed. In this work, noted that, based on the G-equation model and SAGE solver, a decoupling of the relationship of the it should be noted that, based on the G-equation model and SAGE solver, a decoupling of the flame propagation velocity and the thermodynamics of the end-gas mixture was achieved. A validation relationship of the flame propagation velocity and the thermodynamics of the end-gas mixture was of the pressure evolution and HRR was conducted under different combustion conditions, and the achieved. A validation of the pressure evolution and HRR was conducted under different combustion results indicate that the present model is capable of capturing the combustion characteristics under conditions, and the results indicate that the present model is capable of capturing the combustion wide operating conditions. The following remarkable results were found: characteristics under wide operating conditions. The following remarkable results were found: 1. The knocking intensity or maximum pressure oscillation, as well as the MAPO, first experiences 1. The knocking intensity or maximum pressure oscillation, as well as the MAPO, first experiences an increase and then a decrease as the flame propagation speed increases, which presents a an increase and then a decrease as the flame propagation speed increases, which presents a non- non-monotonic relationship with the flame propagation velocity. The competitive relationship monotonic relationship with the flame propagation velocity. The competitive relationship between the flame propagation velocity and the ignition delay of the end gas is responsible for between the flame propagation velocity and the ignition delay of the end gas is responsible for this phenomenon. The higher flame speed leads to an increase in the heat release rate in the this phenomenon. The higher flame speed leads to an increase in the heat release rate in the cylinder, and consequently, quicker increases in the temperature and pressure of the unburned cylinder, and consequently, quicker increases in the temperature and pressure of the unburned end-gas mixture are obtained, leading to an end-gas auto-ignition. However, the sufficiently high end-gas mixture are obtained, leading to an end-gas auto-ignition. However, the sufficiently propagation velocity of the flame will reduce the mass fraction of the unburned mixture consumed high propagation velocity of the flame will reduce the mass fraction of the unburned mixture by the AI, thus ultimately decreasing the knocking intensity. Furthermore, the coupling of the consumed by the AI, thus ultimately decreasing the knocking intensity. Furthermore, the pressure wave and AI flame front results in super-knocking with a maximum peak in pressure of coupling of the pressure wave and AI flame front results in super-knocking with a maximum 31 MPa. peak in pressure of 31 MPa. 2. TheThe non-monotonic non-monotonic relationship between the end- end-gasgas auto-ignition and turbulence intensity was alsoalso observed. observed. On On the the one one hand, hand, an an increased increased turb turbulenceulence intensity can accelerate the dissipation ofof the key intermediate radicals and and heat energy, which finallyfinally retards the AI formationformation and shrinksshrinks the the kernel kernel size size of the AI. AI. On the other ha hand,nd, increasing the turbulence intensity can also wrinkle the flame flame surface and increase the burning rate, which results in an increase in the flameflame propagation velocity. It can be concluded that the turbulence intensity has a more complicatedcomplicated effecteffect on the knocking compared to the flameflame propagation velocity. 3. TheThe evolutions of thethe mainmain flameflame propagation propagation velocity velocity and and end-gas end-gas auto-ignition auto-ignition and and a profilea profile of ofthe the HRR HRR revealed revealed that that the the influence influence of both of both the the flame flame speed speed and and the turbulencethe turbulence intensity intensity can lead can leadto two to ditwofferent different combustion combustion modes. modes. The unimodalThe unimodal and bimodaland bimodal shapes shapes of the of heat the heat release release rate rateare obtained,are obtained, which which is strongly is strongly dependent dependent on the mainon the flame main propagation flame propagation velocity, unburned velocity, unburnedmixture mass, mixture and mass, thermodynamic and thermody statenamic in the state end-gas in the region. end-gas region. In the present work, the LES method is selected to simulate the turbulence evolution. However, the present work only focuses on the quantitative analysis of effects of turbulence intensity and flame

Energies 2020, 13, 5039 20 of 23

In the present work, the LES method is selected to simulate the turbulence evolution. However, the present work only focuses on the quantitative analysis of effects of turbulence intensity and flame propagation velocity on the super-knock by conducting a series of parameter studies under given settings conditions, thus the effects of the cycle-to-cycle cannot be achieved, which is unignorable in practical engines. Therefore, the cycle-to-cycle variations should be taken into consideration, and the simulation should be expanded to multi-cycles conditions. Meanwhile, effects of temperature and reactivity inhomogeneities on knock combustion are supposed to be conducted as those two parameters are closely related to the knock phenomenon in practical engines.

Author Contributions: Data curation, L.Z. (Lei Zhou) and X.Z.; formal analysis, L.Z. (Lei Zhou); funding acquisition, X.Z.; investigation, L.Z. (Lei Zhou) and L.Z. (Lijia Zhong); methodology, L.Z. (Lei Zhou) and J.Y.; software, X.Z., L.Z. (Lijia Zhong) and J.Y.; writing—original draft, L.Z. (Lei Zhou). All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China, grant number 91741119 and 91641203. Acknowledgments: This work was supported by the National Natural Science Foundation of China (Grant Nos. 91741119 and 91641203). This work is also supported by National Key R&D Program of China (2017YFB0103400). Conﬂicts of Interest: The authors declare no conﬂict of interest.

Abbreviations aTDC after top dead center AMR adaptive mesh refine AI auto-ignition BMF burned mass fraction CFD computational fluid dynamics CFL Courant–Friedrichs–Lewy CJ Chapman–Jouguet DNS direct numerical simulation DDT deflagration to detonation transition FFT fast Fourier transform GDI gasoline direct injection HCCI homogeneous charge compression ignition HRR heat release rate KH Kelvin–Helmholtz instability LEM linear Eddy model LES large Eddy simulation MAPO maximum amplitude of pressure oscillation RT Rayleigh–Taylor instability PRF primary reference fuels SI spark ignition RCM rapid compression machine UT unburned temperature TKE turbulent kinetic energy

Appendix A

Model Validation In our previous works [34–36], we have comprehensively validated the present models in terms of pressure profiles and heat release rate. The numerical pressure evolution agrees well with the experimental results, both in ST-10 case and ST-18 cases. Noted that, our present numerical model not only captures the knocking phenomenon but also captures the combustion mode transition as spark timing from the ST-10 to ST-18. It should be noted that in the present paper, we only focus on the quantitative analysis of effects of turbulence intensity and the flame propagation velocity on Energies 2020, 13, 5039 21 of 23 the super-knock through a series of given settings as a fundamental study of knocking combustion, and thus the effects of the cycle-to-cycle variations cannot be achieved in the present model.

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