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Numerical Investigation of the Knocking Combustion Characteristics of the N-Butanol/N-Octanol RCCI Engine

: The n-butanol/n-octanol fueled reactivity-controlled compression ignition engine was numerically studied based on the KIVA-CHEMKIN code. First, the knocking combustion characteristics were analyzed while functioning with a premixed n-butanol percentage of 20% (B20), since it exhibited the most severe knocking. Ten local regions were monitored to obtain local data, such as pressure and heat release rate. The local pressure oscillation was quantiﬁed by a band-pass ﬁlter. Second, the premixed n-butanol percentage and the intake valve close (IVC) timing were varied to investigate their effects on the combustion characteristics and emissions formations, as well as their potential for mitigating knocking. The results showed that a strong pressure oscillation was observed for B20 near the cylinder wall, which indicates severe knocking. This consequence is mainly caused by the low-temperature combustion of the n-octanol/n-butanol/air mixture near the cylinder-wall region. Increasing premixed n-butanol percentage and retarding IVC timing could result in an extended ignition delay, lowered peak pressure, and reduced maximum pressure rise rate (PRR). Condition B80 with an IVC timing of − 126 ◦ ATDC could improve the indicated mean effective pressure by 11.7% and reduce the maximum PRR by 63.4% when compared to condition B20.


Introduction
Environmental pollution and the energy crisis are two of the main reasons driving researchers to find renewable and clean energy sources and new combustion technologies. To improve the combustion efficiency and reduce the emissions of internal combustion engines (ICE), many innovative combustion strategies for ICEs have been proposed, such as homogeneous charge compression ignition (HCCI), premixed charge compression ignition (PCCI), and reactivity-controlled compression ignition (RCCI) technologies [1,2]. In particular, both HCCI and PCCI employ a single fuel, which consequently results in the disadvantage of being poorly controlled since the ignition point depends on the chemical kinetics of fuels [3,4]. In contrast, the RCCI mode, which belongs to the dual-fuel combustion mode, regulates the ratio of two fuels with different reactivity, and in conjunction with an appropriate direct injection strategy, can achieve the aim of controlling the ignition point and combustion process [5]. Hence, the RCCI mode has received widespread attention.
One of the key challenges confronting RCCI engines is the tendency of knocking under high loads [6]. Karim and Liu [7] studied the knock phenomenon in a natural gas/diesel dual-fuel engine. The results showed that the knock generally occurs during the combustion of natural gas and is more pronounced at high loads. Berenjestanaki et al. [8] suggested that the knocking phenomenon in the dual-fuel combustion mode at high loads is mainly caused by the ignition and combustion of the premixed mixture in the end gas region. To mitigate knocking, different techniques have been considered in various kinds of RCCI engines [9]. Yousefi et al. [10] studied the effect of the double injection strategy on the knocking combustion of a natural gas/diesel RCCI engine. They found that the double injection strategy could lower the speed of flame propagation which would consequently

Experimental Data
In this study, two types of engines were used to validate the models in the KIVA-CHEMKIN code. One is the HCCI engine fueled with neat n-butanol. The other is the conventional compression ignition (CCI) engine fueled with neat n-octanol. The experimental data of the HCCI engine and CCI engine for validation were taken from the published results reported by Han et al. [22] and Kerschgens et al. [17], respectively. Table 1 lists the specifications of the HCCI and CCI engines. Table 1. Engine specifications [17,22].

Grid Generation
Based on the information from the HCCI and CCI engines, grids were generated individually. Assuming that both geometric and flow symmetries exist in the cylinder, the sector mesh method, which could save much computational time, was adopted in this study. By conducting the grid convergence test, the average cell size of 2.0 mm was chosen [23]. Figure 1 demonstrates the generated sector meshes at the top dead-center (TDC) for the HCCI and CCI engines. It should also be noted that with the use of sector mesh, the closed-cycle simulation should be performed from the IVC timing to the exhaust valve open (EVO) timing for both engines. developed by the authors' group. The adopted skeletal reaction mechanism, including nbutanol and n-octanol, consists of 121 species and 623 reactions [16]. The formation process of NOx was also embedded in this reaction mechanism. Apart from the chemical reaction mechanism of the fuels, their thermophysical properties need to be added to the fuel library of the KIVA code. Therefore, the thermophysical properties of n-butanol and n-octanol, such as boiling point, critical properties, vapor pressure, latent heat of vaporization, density, viscosity, thermal conductivity, gas diffusion coefficient, and surface tension, were calculated based on the methods stated in reference [21]. Then the calculated data were updated in the KIVA fuel library.

Experimental Data
In this study, two types of engines were used to validate the models in the KIVA-CHEMKIN code. One is the HCCI engine fueled with neat n-butanol. The other is the conventional compression ignition (CCI) engine fueled with neat n-octanol. The experimental data of the HCCI engine and CCI engine for validation were taken from the published results reported by Han et al. [22] and Kerschgens et al. [17], respectively. Table 1 lists the specifications of the HCCI and CCI engines.

Grid Generation
Based on the information from the HCCI and CCI engines, grids were generated individually. Assuming that both geometric and flow symmetries exist in the cylinder, the sector mesh method, which could save much computational time, was adopted in this study. By conducting the grid convergence test, the average cell size of 2.0 mm was chosen [23]. Figure 1 demonstrates the generated sector meshes at the top dead-center (TDC) for the HCCI and CCI engines. It should also be noted that with the use of sector mesh, the closed-cycle simulation should be performed from the IVC timing to the exhaust valve open (EVO) timing for both engines.   Table 2 shows the operating conditions for the validation cases. As can be seen from the table, the n-butanol-fueled HCCI engine was operated at a speed of 1500 rpm with different EGR rates. The n-octanol-fueled CCI engine was operated at different speeds with various EGR rates. The properties of n-butanol and n-octanol are given in Table 3. In comparison to n-octanol, n-butanol has a lower cetane number, which suggests that it is also less reactive. Additionally, the lower heating value of n-butanol is marginally smaller than that of noctanol. In terms of oxygen content, the value of n-butanol is almost two times higher than that of n-octanol. Table 3. Properties of n-butanol and n-octanol [15,24].  Figure 2 compares the simulated in-cylinder pressure and heat release rate (HRR) with the experimental data for both HCCI and CCI engines fueled with n-butanol and n-octanol, respectively. As is shown, the simulated in-cylinder pressure and HRR of the n-butanol fueled HCCI engine can accurately reproduce the experimental data, except that the peak HRR is marginally higher. As for the n-octanol fueled CCI engine, though the simulated ignition time is earlier than the experimental results, the discrepancies are still within an acceptable level. In summary, the models and reaction mechanism adopted in this study are reliable.

Local Regions Analysis
It is common to adopt mean pressure and HRR to analyze the combustion characteristics of engines. For RCCI engines, the end-gas autoignition may occur. It would be very helpful to detect the occurrence of the end-gas autoignition with the aid of the local region analysis technique. In this study, the n-butanol/n-octanol RCCI combustion was realized by premixing n-butanol in the n-octanol fueled CCI engine. That is, the RCCI combustion was modeled based on the CCI engine given in Table 1. Therefore, to realize the local analysis, ten local regions (R1-R10) were defined in the geometry of the CCI engine, as illustrated in Figure 3. Among the ten local regions, R1-R5 are located in the piston bowl area, R6-R8 are on the top of the piston crown, and R9 and R10 are near the cylinder wall. By defining the regions, information such as pressure and HRR of the local regions can be extracted for detailed analysis.

Local Regions Analysis
It is common to adopt mean pressure and HRR to analyze the combustion characteristics of engines. For RCCI engines, the end-gas autoignition may occur. It would be very helpful to detect the occurrence of the end-gas autoignition with the aid of the local region analysis technique. In this study, the n-butanol/n-octanol RCCI combustion was realized by premixing n-butanol in the n-octanol fueled CCI engine. That is, the RCCI combustion was modeled based on the CCI engine given in Table 1. Therefore, to realize the local analysis, ten local regions (R1-R10) were defined in the geometry of the CCI engine, as illustrated in Figure 3. Among the ten local regions, R1-R5 are located in the piston bowl area, R6-R8 are on the top of the piston crown, and R9 and R10 are near the cylinder wall. By defining the regions, information such as pressure and HRR of the local regions can be extracted for detailed analysis.

Knocking Identification
In this study, the analysis of local in-cylinder pressure was carried out to identify the onset of knocking [25]. A fourth-order Butterworth band-pass filter was used to process the pressure data; as a result, the peak-to-peak PPmax can be obtained to quantify pressure oscillation. First, using the analytical solution of the wave equation for a closed cylinder with two flat ends, the resonant knocking frequencies were calculated to determine the Butterworth band-pass filter cut-off frequency. The resonant frequency is calculated by Equation (1).
where , is the wave number determined employing Bessel's equation; m and n are the numbers of radial and circumferential pressure nodes, respectively; cs represents the

Knocking Identification
In this study, the analysis of local in-cylinder pressure was carried out to identify the onset of knocking [25]. A fourth-order Butterworth band-pass filter was used to process the pressure data; as a result, the peak-to-peak PPmax can be obtained to quantify pressure oscillation. First, using the analytical solution of the wave equation for a closed cylinder with two flat ends, the resonant knocking frequencies were calculated to determine the Butterworth band-pass filter cut-off frequency. The resonant frequency is calculated by Equation (1).
where α m,n is the wave number determined employing Bessel's equation; m and n are the numbers of radial and circumferential pressure nodes, respectively; c s represents the speed of sound; and B stands for the bore of a cylinder. The calculated theoretical values at different vibration modes are given in Table 4. As can be seen, when the high-cutoff and low-cutoff Butterworth filter frequencies were set to 5 kHz and 25 kHz, respectively, the main spectral components associated with knocking could be identified while maintaining a reasonable signal-to-noise ratio. In this study, the analysis of local in-cylinder pressure was carried out to identify the onset of knocking [25]. A fourth-order Butterworth band-pass filter was used to process the pressure data; as a result, the peak-to-peak PPmax can be obtained to quantify pressure oscillation. First, using the analytical solution of the wave equation for a closed cylinder with two flat ends, the resonant knocking frequencies were calculated to determine the Butterworth band-pass filter cut-off frequency. The resonant frequency is calculated by Equation (1).
where , is the wave number determined employing Bessel's equation; m and n are the numbers of radial and circumferential pressure nodes, respectively; cs represents the speed of sound; and B stands for the bore of a cylinder. The calculated theoretical values at different vibration modes are given in Table 4. As can be seen, when the high-cutoff and low-cutoff Butterworth filter frequencies were set to 5 kHz and 25 kHz, respectively, the main spectral components associated with knocking could be identified while maintaining a reasonable signal-to-noise ratio.

Study Cases
Based on validation condition 4, the EGR rate was changed to 0%, and the percentage of n-butanol varied from 0% to 90%. According to the n-butanol percentage, the corresponding working conditions are designated as B0 to B90. When varying the premixed nbutanol percentage, the total energy input was kept constant. The premixed n-butanol percentage can be determined by Equation (2): where Mbut means the mass of n-butanol (kg); Moct means the mass of n-octanol (kg); LHVbut means the lower heating value of n-butanol (MJ/kg); and LHVoct means the lower heating value of n-octanol (MJ/kg). Besides premixing n-butanol, the start of injection (SOI) timing was advanced to −20 °ATDC to realize the RCCI combustion. Then, knocking combustion

Knocking Identification
In this study, the analysis of local in-cylinder pressure was carried out to identify the onset of knocking [25]. A fourth-order Butterworth band-pass filter was used to process the pressure data; as a result, the peak-to-peak PPmax can be obtained to quantify pressure oscillation. First, using the analytical solution of the wave equation for a closed cylinder with two flat ends, the resonant knocking frequencies were calculated to determine the Butterworth band-pass filter cut-off frequency. The resonant frequency is calculated by Equation (1).
where , is the wave number determined employing Bessel's equation; m and n are the numbers of radial and circumferential pressure nodes, respectively; cs represents the speed of sound; and B stands for the bore of a cylinder. The calculated theoretical values at different vibration modes are given in Table 4. As can be seen, when the high-cutoff and low-cutoff Butterworth filter frequencies were set to 5 kHz and 25 kHz, respectively, the main spectral components associated with knocking could be identified while maintaining a reasonable signal-to-noise ratio.

Study Cases
Based on validation condition 4, the EGR rate was changed to 0%, and the percentage of n-butanol varied from 0% to 90%. According to the n-butanol percentage, the corresponding working conditions are designated as B0 to B90. When varying the premixed nbutanol percentage, the total energy input was kept constant. The premixed n-butanol percentage can be determined by Equation (2): where Mbut means the mass of n-butanol (kg); Moct means the mass of n-octanol (kg); LHVbut means the lower heating value of n-butanol (MJ/kg); and LHVoct means the lower heating value of n-octanol (MJ/kg). Besides premixing n-butanol, the start of injection (SOI) timing was advanced to −20 °ATDC to realize the RCCI combustion. Then, knocking combustion

Knocking Identification
In this study, the analysis of local in-cylinder pressure was carried out to identify the onset of knocking [25]. A fourth-order Butterworth band-pass filter was used to process the pressure data; as a result, the peak-to-peak PPmax can be obtained to quantify pressure oscillation. First, using the analytical solution of the wave equation for a closed cylinder with two flat ends, the resonant knocking frequencies were calculated to determine the Butterworth band-pass filter cut-off frequency. The resonant frequency is calculated by Equation (1).
where , is the wave number determined employing Bessel's equation; m and n are the numbers of radial and circumferential pressure nodes, respectively; cs represents the speed of sound; and B stands for the bore of a cylinder. The calculated theoretical values at different vibration modes are given in Table 4. As can be seen, when the high-cutoff and low-cutoff Butterworth filter frequencies were set to 5 kHz and 25 kHz, respectively, the main spectral components associated with knocking could be identified while maintaining a reasonable signal-to-noise ratio.

Study Cases
Based on validation condition 4, the EGR rate was changed to 0%, and the percentage of n-butanol varied from 0% to 90%. According to the n-butanol percentage, the corresponding working conditions are designated as B0 to B90. When varying the premixed nbutanol percentage, the total energy input was kept constant. The premixed n-butanol percentage can be determined by Equation (2): where Mbut means the mass of n-butanol (kg); Moct means the mass of n-octanol (kg); LHVbut means the lower heating value of n-butanol (MJ/kg); and LHVoct means the lower heating value of n-octanol (MJ/kg). Besides premixing n-butanol, the start of injection (SOI) timing was advanced to −20 °ATDC to realize the RCCI combustion. Then, knocking combustion

Knocking Identification
In this study, the analysis of local in-cylinder pressure was carried out to identify the onset of knocking [25]. A fourth-order Butterworth band-pass filter was used to process the pressure data; as a result, the peak-to-peak PPmax can be obtained to quantify pressure oscillation. First, using the analytical solution of the wave equation for a closed cylinder with two flat ends, the resonant knocking frequencies were calculated to determine the Butterworth band-pass filter cut-off frequency. The resonant frequency is calculated by Equation (1).
where , is the wave number determined employing Bessel's equation; m and n are the numbers of radial and circumferential pressure nodes, respectively; cs represents the speed of sound; and B stands for the bore of a cylinder. The calculated theoretical values at different vibration modes are given in Table 4. As can be seen, when the high-cutoff and low-cutoff Butterworth filter frequencies were set to 5 kHz and 25 kHz, respectively, the main spectral components associated with knocking could be identified while maintaining a reasonable signal-to-noise ratio.

Study Cases
Based on validation condition 4, the EGR rate was changed to 0%, and the percentage of n-butanol varied from 0% to 90%. According to the n-butanol percentage, the corresponding working conditions are designated as B0 to B90. When varying the premixed nbutanol percentage, the total energy input was kept constant. The premixed n-butanol percentage can be determined by Equation (2): where Mbut means the mass of n-butanol (kg); Moct means the mass of n-octanol (kg); LHVbut means the lower heating value of n-butanol (MJ/kg); and LHVoct means the lower heating value of n-octanol (MJ/kg). Besides premixing n-butanol, the start of injection (SOI) timing was advanced to −20 °ATDC to realize the RCCI combustion. Then, knocking combustion

Knocking Identification
In this study, the analysis of local in-cylinder pressure was carried out to identify the onset of knocking [25]. A fourth-order Butterworth band-pass filter was used to process the pressure data; as a result, the peak-to-peak PPmax can be obtained to quantify pressure oscillation. First, using the analytical solution of the wave equation for a closed cylinder with two flat ends, the resonant knocking frequencies were calculated to determine the Butterworth band-pass filter cut-off frequency. The resonant frequency is calculated by Equation (1).
where , is the wave number determined employing Bessel's equation; m and n are the numbers of radial and circumferential pressure nodes, respectively; cs represents the speed of sound; and B stands for the bore of a cylinder. The calculated theoretical values at different vibration modes are given in Table 4. As can be seen, when the high-cutoff and low-cutoff Butterworth filter frequencies were set to 5 kHz and 25 kHz, respectively, the main spectral components associated with knocking could be identified while maintaining a reasonable signal-to-noise ratio.

Study Cases
Based on validation condition 4, the EGR rate was changed to 0%, and the percentage of n-butanol varied from 0% to 90%. According to the n-butanol percentage, the corresponding working conditions are designated as B0 to B90. When varying the premixed nbutanol percentage, the total energy input was kept constant. The premixed n-butanol percentage can be determined by Equation (2): where Mbut means the mass of n-butanol (kg); Moct means the mass of n-octanol (kg); LHVbut means the lower heating value of n-butanol (MJ/kg); and LHVoct means the lower heating value of n-octanol (MJ/kg). Besides premixing n-butanol, the start of injection (SOI) timing was advanced to −20 °ATDC to realize the RCCI combustion. Then, knocking combustion

Knocking Identification
In this study, the analysis of local in-cylinder pressure was carried out to identify the onset of knocking [25]. A fourth-order Butterworth band-pass filter was used to process the pressure data; as a result, the peak-to-peak PPmax can be obtained to quantify pressure oscillation. First, using the analytical solution of the wave equation for a closed cylinder with two flat ends, the resonant knocking frequencies were calculated to determine the Butterworth band-pass filter cut-off frequency. The resonant frequency is calculated by Equation (1).
where , is the wave number determined employing Bessel's equation; m and n are the numbers of radial and circumferential pressure nodes, respectively; cs represents the speed of sound; and B stands for the bore of a cylinder. The calculated theoretical values at different vibration modes are given in Table 4. As can be seen, when the high-cutoff and low-cutoff Butterworth filter frequencies were set to 5 kHz and 25 kHz, respectively, the main spectral components associated with knocking could be identified while maintaining a reasonable signal-to-noise ratio.

Study Cases
Based on validation condition 4, the EGR rate was changed to 0%, and the percentage of n-butanol varied from 0% to 90%. According to the n-butanol percentage, the corresponding working conditions are designated as B0 to B90. When varying the premixed nbutanol percentage, the total energy input was kept constant. The premixed n-butanol percentage can be determined by Equation (2): where Mbut means the mass of n-butanol (kg); Moct means the mass of n-octanol (kg); LHVbut means the lower heating value of n-butanol (MJ/kg); and LHVoct means the lower heating value of n-octanol (MJ/kg). Besides premixing n-butanol, the start of injection (SOI) timing was advanced to −20 °ATDC to realize the RCCI combustion. Then, knocking combustion

Study Cases
Based on validation condition 4, the EGR rate was changed to 0%, and the percentage of n-butanol varied from 0% to 90%. According to the n-butanol percentage, the corresponding working conditions are designated as B0 to B90. When varying the premixed n-butanol percentage, the total energy input was kept constant. The premixed n-butanol percentage can be determined by Equation (2): Premixed fuel percentage = M but LHV but M oct LHV oct + M but LHV but (2) where M but means the mass of n-butanol (kg); M oct means the mass of n-octanol (kg); LHV but means the lower heating value of n-butanol (MJ/kg); and LHV oct means the lower heating value of n-octanol (MJ/kg). Besides premixing n-butanol, the start of injection (SOI) timing was advanced to −20 • ATDC to realize the RCCI combustion. Then, knocking combustion characteristics were investigated under the B20 condition. At last, the potential of varying premixed fuel percentage and IVC timing on knocking mitigation was examined.

Characteristics of Knocking Combustion
The local pressures in the ten regions of the cylinder were acquired through simulation. The Butterworth Filter was employed to quantify pressure oscillation, and the local maximum pressure PPmax was then determined in different regions; the region with the most tendency of knocking can then be determined. Figure 4 shows the pressure and its local PPmax for the ten regions under B20 working conditions. As can be seen from the graph, the in-cylinder pressure curves of the R2-R6 regions are relatively smooth. Fluctuations in the process of pressure rising become obvious in R1 and R7-R10. Furthermore, fluctuations become stronger in regions R9 and R10, which indicates that the knocking tends to happen in the vicinity of the cylinder wall.    Figure 5 compares the PPmax of the ten regions under B20 working conditions. When PPmax is less than 10 bar, the engine is considered to be under normal combustion conditions [26]. Therefore, regions R3-R6 exhibit normal combustion. R1, R2, R7 and R8 regions show a moderate knocking phenomenon. Noticeably, severe knocking is produced in the vicinity of the cylinder wall (R9 and R10), since an obvious pressure oscillation phenomenon is observed.

Temperature and Radical Concentration Analysis
Analyzing the concentration of radicals is an effective method to determine whether auto-ignition occurs in the end gas. In this study, OH concentration and ROOH concentration are used as the basis for high-temperature and low-temperature combustion evaluation, respectively. Figure 6 compares the spatial distribution of temperature, OH and ROOH concentrations at different crank angles for the B20 condition. When the crank angle is −10 °ATDC, the in-cylinder temperature is around 1000 K. At this moment, OH radicals have not yet been generated; however, ROOH radicals associated with n-butanol and n-octanol, respectively, have been generated in the bowl region of the combustion chamber. This result indicates that low-temperature combustion occurs in the bowl region of the combustion chamber at this moment. This is attributed to the injection of n-octanol into the combustion chamber bowl region. In more detail: n-octanol

Temperature and Radical Concentration Analysis
Analyzing the concentration of radicals is an effective method to determine whether auto-ignition occurs in the end gas. In this study, OH concentration and ROOH concentration are used as the basis for high-temperature and low-temperature combustion evaluation, respectively. Figure 6 compares the spatial distribution of temperature, OH and ROOH concentrations at different crank angles for the B20 condition.

Temperature and Radical Concentration Analysis
Analyzing the concentration of radicals is an effective method to determine whether auto-ignition occurs in the end gas. In this study, OH concentration and ROOH concentration are used as the basis for high-temperature and low-temperature combustion evaluation, respectively. Figure 6 compares the spatial distribution of temperature, OH and ROOH concentrations at different crank angles for the B20 condition. When the crank angle is −10 °ATDC, the in-cylinder temperature is around 1000 K. At this moment, OH radicals have not yet been generated; however, ROOH radicals associated with n-butanol and n-octanol, respectively, have been generated in the bowl region of the combustion chamber. This result indicates that low-temperature combustion occurs in the bowl region of the combustion chamber at this moment. This is attributed to the injection of n-octanol into the combustion chamber bowl region. In more detail: n-octanol When the crank angle is −10 • ATDC, the in-cylinder temperature is around 1000 K. At this moment, OH radicals have not yet been generated; however, ROOH radicals associated with n-butanol and n-octanol, respectively, have been generated in the bowl region of the combustion chamber. This result indicates that low-temperature combustion occurs in the bowl region of the combustion chamber at this moment. This is attributed to the injection of n-octanol into the combustion chamber bowl region. In more detail: n-octanol is injected into the n-butanol/air mixture, and fuel spray and mixing processes occur, followed by the low-temperature combustion of both fuels.
When the crank angle is −5 • ATDC, the temperature in the bowl region can reach more than 2000 K. At this time, the ROOH radicals generated by the two fuels in the bowl region have been completely consumed, while a large amount of OH radicals have also been generated. This indicates that high-temperature combustion occurs in the bowl region of the cylinder at this time. Simultaneously, a considerable amount of n-octanol ROOH and n-butanol ROOH are produced adjacent to the cylinder wall and the centerline of the combustion chamber, implying that low-temperature combustion occurs in these regions. This reveals that the low-temperature combustion of n-octanol and n-butanol starts from the bowl region and then gradually propagates to the two sides, that is, there are two development directions: one is "from bowl to centerline", and the other is "from bowl to cylinder wall". When the piston reaches the TDC, the ROOH radicals are completely consumed, and the OH radicals are still mainly distributed in the vicinity of the bowl region. The temperature distribution also indicates that high-temperature combustion is mostly concentrated in the bowl region, and it is not observed in the vicinity of the cylinder wall.
From the pressure oscillation curves in the R9 and R10 regions in Figure 4, it can be seen that the more intense pressure oscillation produced in the vicinity of the cylinder wall also occurs at the crank angle of −5 • ATDC, which is consistent with the moment when low-temperature combustion of n-octanol and n-butanol occurs in the vicinity of the cylinder wall. Therefore, it can be inferred that the severe knocking in the vicinity of the cylinder wall is caused by the low-temperature combustion of the fuels. Figure 7 demonstrates the total HRR and local HRR of the ten regions. It can be seen that the total HRR curve starts to rise around −13 • ATDC and reaches a peak at around −8 • ATDC. In conjunction with the analysis of Figure 6, it is clear that the heat generated before −10 • ATDC originates from the low-temperature combustion of n-butanol and n-octanol in the bowl region of the combustion chamber. is injected into the n-butanol/air mixture, and fuel spray and mixing processes occur, followed by the low-temperature combustion of both fuels. When the crank angle is −5 °ATDC, the temperature in the bowl region can reach more than 2000 K. At this time, the ROOH radicals generated by the two fuels in the bowl region have been completely consumed, while a large amount of OH radicals have also been generated. This indicates that high-temperature combustion occurs in the bowl region of the cylinder at this time. Simultaneously, a considerable amount of n-octanol ROOH and n-butanol ROOH are produced adjacent to the cylinder wall and the centerline of the combustion chamber, implying that low-temperature combustion occurs in these regions. This reveals that the low-temperature combustion of n-octanol and n-butanol starts from the bowl region and then gradually propagates to the two sides, that is, there are two development directions: one is "from bowl to centerline", and the other is "from bowl to cylinder wall". When the piston reaches the TDC, the ROOH radicals are completely consumed, and the OH radicals are still mainly distributed in the vicinity of the bowl region. The temperature distribution also indicates that high-temperature combustion is mostly concentrated in the bowl region, and it is not observed in the vicinity of the cylinder wall.

Local HRR
From the pressure oscillation curves in the R9 and R10 regions in Figure 4, it can be seen that the more intense pressure oscillation produced in the vicinity of the cylinder wall also occurs at the crank angle of −5 °ATDC, which is consistent with the moment when low-temperature combustion of n-octanol and n-butanol occurs in the vicinity of the cylinder wall. Therefore, it can be inferred that the severe knocking in the vicinity of the cylinder wall is caused by the low-temperature combustion of the fuels. Figure 7 demonstrates the total HRR and local HRR of the ten regions. It can be seen that the total HRR curve starts to rise around −13 °ATDC and reaches a peak at around −8 °ATDC. In conjunction with the analysis of Figure 6, it is clear that the heat generated before −10 °ATDC originates from the low-temperature combustion of n-butanol and noctanol in the bowl region of the combustion chamber. Furthermore, the heat generated from regions R2, R3, and R5 is also substantially higher than that from the other regions after −8 °ATDC. This result indicates that the hightemperature combustion occurs in the bowl area of the combustion chamber and generates a large amount of heat. This phenomenon is consistent with the temperature Furthermore, the heat generated from regions R2, R3, and R5 is also substantially higher than that from the other regions after −8 • ATDC. This result indicates that the high-temperature combustion occurs in the bowl area of the combustion chamber and generates a large amount of heat. This phenomenon is consistent with the temperature distribution shown in Figure 6, i.e., the region where more heat is released is at a higher temperature. However, the peak heat release rate is lower near the cylinder wall (R7-R10). Based on the analysis in Section 3.1.2, it can be inferred that the relatively small amount of heat released comes mainly from the regions near the cylinder wall and near the centerline of the combustion chamber where the low-temperature combustion happens. Figure 8 compares the PRR of the ten regions under B20 working conditions. As shown in the figure, when the crank angle is −8 • ATDC, the peak PRR is relatively lower in the region adjacent to the cylinder wall (R9 and R10). In contrast, the highest peak PRR occurs in the bowl area of the combustion chamber. This would be mainly due to the high-temperature combustion occurring in the bowl area and the low-temperature combustion occurring near the cylinder wall. However, there is a further sharp increase in the PRR at the region near the cylinder wall (R9 and R10) at the crank angle of roughly −5 • ATDC. This crank angle coincides with the presence of a large amount of n-butanol ROOH and n-octanol ROOH in the region near the cylinder wall, as illustrated in Figure 6. Therefore, it can be inferred that the high PRR around the crank angle of −5 • ATDC is caused by the occurrence of low-temperature combustion of the fuels. of heat released comes mainly from the regions near the cylinder wall and near the centerline of the combustion chamber where the low-temperature combustion happens. Figure 8 compares the PRR of the ten regions under B20 working conditions. As shown in the figure, when the crank angle is −8 °ATDC, the peak PRR is relatively lower in the region adjacent to the cylinder wall (R9 and R10). In contrast, the highest peak PRR occurs in the bowl area of the combustion chamber. This would be mainly due to the hightemperature combustion occurring in the bowl area and the low-temperature combustion occurring near the cylinder wall. However, there is a further sharp increase in the PRR at the region near the cylinder wall (R9 and R10) at the crank angle of roughly −5 °ATDC. This crank angle coincides with the presence of a large amount of n-butanol ROOH and n-octanol ROOH in the region near the cylinder wall, as illustrated in Figure 6. Therefore, it can be inferred that the high PRR around the crank angle of −5 °ATDC is caused by the occurrence of low-temperature combustion of the fuels.

Local PRR
In addition, R9 and R10 display higher PPmax compared with other regions ( Figure  5), and the pressure curves of R9 and R10 exhibit significant pressure oscillation around −5 °ATDC (Figure 4). Hence, it can also be inferred that the high PPmax in the region near the cylinder wall is caused by the low-temperature combustion occurring in the end gas region where the combustion of n-octanol/n-butanol/air mixture occurs.

Effects of Premixed Fuel Percentage
In this section, the combustion characteristics and emissions formation are analyzed by varying the percentage of n-butanol from 0% to 90%. Figure 9 shows the comparison of in-cylinder pressure and HRR with different premixed n-butanol percentages. As can be seen from the in-cylinder profiles, the increased n-butanol percentage leads to an increased ignition delay. For B10 to B50, the ignition points are all relatively close to each other, which implies that the effect of fuel percentage on the ignition delay is small under these conditions. However, when the premixed percentage of n-butanol is increased to 60% and above, a significant impact on the ignition In addition, R9 and R10 display higher PPmax compared with other regions (Figure 5), and the pressure curves of R9 and R10 exhibit significant pressure oscillation around −5 • ATDC ( Figure 4). Hence, it can also be inferred that the high PPmax in the region near the cylinder wall is caused by the low-temperature combustion occurring in the end gas region where the combustion of n-octanol/n-butanol/air mixture occurs.

Effects of Premixed Fuel Percentage
In this section, the combustion characteristics and emissions formation are analyzed by varying the percentage of n-butanol from 0% to 90%. Figure 9 shows the comparison of in-cylinder pressure and HRR with different premixed n-butanol percentages. As can be seen from the in-cylinder profiles, the increased n-butanol percentage leads to an increased ignition delay. For B10 to B50, the ignition points are all relatively close to each other, which implies that the effect of fuel percentage on the ignition delay is small under these conditions. However, when the premixed percentage of n-butanol is increased to 60% and above, a significant impact on the ignition delay can be observed. Especially for the B90 condition, the ignition point has been retarded after the TDC. This is mainly associated with the reactivity of the fuels. As is known, the reactivity of n-butanol is lower than that of n-octanol. Therefore, the global reactivity in the dual-fuel engine would be reduced by increasing the premixed percentage of n-butanol. Consequently, the ignition point gradually moves backward as more n-butanol is premixed. creases and then decreases, and its position gradually shifts backward. This phenomenon is primarily caused by the interaction of the fuel oxygen content and the in-cylinder reactivity gradient. It is known that n-butanol contains more oxygen than n-octanol does. The higher the n-butanol percentage, the higher the oxygen content of the fuel mixture in the cylinder, which benefits the combustion process. As a result, the peak HRR is initially increased gradually for the conditions of B10 to B40.  Figure 10 compares the maximum PRR for various n-butanol percentages. As can be seen from the graph, as the percentage of n-butanol increases, the maximum PRR increases and then decreases. The trend of maximum PRR correlates with the HRR. The higher the peak HRR, the faster the pressure rises. It is known that the PRR is an indicator of engine knock. The threshold is 10 bar/degree. Therefore, all the working conditions explored in this study experienced the knock phenomenon, with B20 experiencing the most intense knocking. It should also be noted that this result is inconsistent with one of a gasoline/biodiesel RCCI engine discussed in the literature [27]. Li et al. found that premixing more gasoline resulted in a higher maximum PRR [27], whereas, in this study, premixing more n-butanol was beneficial in reducing the PRR. This may be due to the lower reactivity of n-butanol compared to gasoline. It can be observed from the HRR curves that increasing the premixed n-butanol could slow the HRR and extend the combustion duration. Meanwhile, the peak HRR first increases and then decreases, and its position gradually shifts backward. This phenomenon is primarily caused by the interaction of the fuel oxygen content and the in-cylinder reactivity gradient. It is known that n-butanol contains more oxygen than n-octanol does. The higher the n-butanol percentage, the higher the oxygen content of the fuel mixture in the cylinder, which benefits the combustion process. As a result, the peak HRR is initially increased gradually for the conditions of B10 to B40. Figure 10 compares the maximum PRR for various n-butanol percentages. As can be seen from the graph, as the percentage of n-butanol increases, the maximum PRR increases and then decreases. The trend of maximum PRR correlates with the HRR. The higher the peak HRR, the faster the pressure rises. It is known that the PRR is an indicator of engine knock. The threshold is 10 bar/degree. Therefore, all the working conditions explored in this study experienced the knock phenomenon, with B20 experiencing the most intense knocking. It should also be noted that this result is inconsistent with one of a gasoline/biodiesel RCCI engine discussed in the literature [27]. Li et al. found that premixing more gasoline resulted in a higher maximum PRR [27], whereas, in this study, premixing more n-butanol was beneficial in reducing the PRR. This may be due to the lower reactivity of n-butanol compared to gasoline. 3.2.3. Temperature Distribution Figure 11 shows the simulated evolution of spatial temperature (K) distributions under conditions of B20 and B80. The figure shows that B20 starts high-temperature com-  Figure 11 shows the simulated evolution of spatial temperature (K) distributions under conditions of B20 and B80. The figure shows that B20 starts high-temperature combustion at −5 • ATDC, and the high-temperature combustion area is widely distributed. In contrast, B80 is currently just starting to ignite, and the combustion initiation is in the bowl-shaped area. From 5 • to 15 • ATDC, B80 has fewer areas with a high temperature (T > 2200 K) in the cylinder than B20, but it has a higher temperature close to the cylinder wall. This implies that the temperature distribution of B80 is more homogeneous. At 20 • ATDC, the in-cylinder temperature of B80 is below 2000 K, while the B20 still shows some areas with a temperature above 2000 K, indicating a shorter combustion duration of B80. 3.2.4. IMEP Figure 12 compares the IMEP for various n-butanol percentages. As can be seen, with the increase in n-butanol percentage, IMEP shows a trend of first decreasing and then increasing. The maximum IMEP is observed for B90. It can also be found that the IMEPs of B0~B50 are between 8.5~9.0 bar. This can be implied from the in-cylinder pressure curves. As is demonstrated in Figure 9, the pressure curves of B0~B50 do not differ much; in addition, their start of combustion timings are all before TDC, which makes the engine work less efficient. In contrast, the IMEP is significantly improved when the percentage of n-butanol is raised to more than 60%. This is mainly due to the longer ignition delay for these conditions. As a result, the start of combustion timing is closer to the TDC, which  Figure 12 compares the IMEP for various n-butanol percentages. As can be seen, with the increase in n-butanol percentage, IMEP shows a trend of first decreasing and then increasing. The maximum IMEP is observed for B90. It can also be found that the IMEPs of B0~B50 are between 8.5~9.0 bar. This can be implied from the in-cylinder pressure curves. As is demonstrated in Figure 9, the pressure curves of B0~B50 do not differ much; in addition, their start of combustion timings are all before TDC, which makes the engine work less efficient. In contrast, the IMEP is significantly improved when the percentage of n-butanol is raised to more than 60%. This is mainly due to the longer ignition delay for these conditions. As a result, the start of combustion timing is closer to the TDC, which is advantageous for the efficient operation of the engine.  Figure 13 compares the NOx and CO emissions with different n-butanol percentages. As can be observed, with the increase of n-butanol percentage, NOx emission is significantly reduced. This is because a high percentage of premixed n-butanol leads to a longer ignition delay period. Therefore, the fuel and air have sufficient mixing time and can achieve low-temperature combustion. As for CO emission, a first increasing and then decreasing trend can be seen as more n-butanol is premixed. Figure 14 demonstrates the spatial distribution of CO under conditions of B20 and B80. Due to the premixed n-butanol, CO is formed in the region near the cylinder wall. What's more, B80 produces much more CO near the cylinder wall. However, the CO of B80 is eventually oxidized due to a higher combustion temperature near the cylinder wall ( Figure 11). Another reason is that the oxygen content of n-butanol is higher than that of n-octanol, leading to better oxidation of CO when premixing more nbutanol.  Figure 13 compares the NOx and CO emissions with different n-butanol percentages. As can be observed, with the increase of n-butanol percentage, NOx emission is significantly reduced. This is because a high percentage of premixed n-butanol leads to a longer ignition delay period. Therefore, the fuel and air have sufficient mixing time and can achieve low-temperature combustion.  Figure 13 compares the NOx and CO emissions with different n-butanol percentages. As can be observed, with the increase of n-butanol percentage, NOx emission is significantly reduced. This is because a high percentage of premixed n-butanol leads to a longer ignition delay period. Therefore, the fuel and air have sufficient mixing time and can achieve low-temperature combustion. As for CO emission, a first increasing and then decreasing trend can be seen as more n-butanol is premixed. Figure 14 demonstrates the spatial distribution of CO under conditions of B20 and B80. Due to the premixed n-butanol, CO is formed in the region near the cylinder wall. What's more, B80 produces much more CO near the cylinder wall. However, the CO of B80 is eventually oxidized due to a higher combustion temperature near the cylinder wall ( Figure 11). Another reason is that the oxygen content of n-butanol is higher than that of n-octanol, leading to better oxidation of CO when premixing more nbutanol. As for CO emission, a first increasing and then decreasing trend can be seen as more nbutanol is premixed. Figure 14 demonstrates the spatial distribution of CO under conditions of B20 and B80. Due to the premixed n-butanol, CO is formed in the region near the cylinder wall. What's more, B80 produces much more CO near the cylinder wall. However, the CO of B80 is eventually oxidized due to a higher combustion temperature near the cylinder wall ( Figure 11). Another reason is that the oxygen content of n-butanol is higher than that of n-octanol, leading to better oxidation of CO when premixing more n-butanol. In summary, B80 can achieve high IMEP with low NOx and CO emissions. The maximum PRR is marginally higher than the critical value (10 bar/degree). Hence, B80 is selected as the benchmark for the following study on the effects of IVC timing.

Effects of IVC Timing
In this section, the combustion characteristics and emissions formation are analyzed with the IVC timings of −134, −130, −126, −122, and −118 °ATDC. Figure 15 illustrates the comparison of in-cylinder pressure and HRR with different IVC timings. It can be observed that retarding IVC timing could lead to a longer ignition delay and a lower peak pressure. The main reason is that retarding IVC timing reduces the effective compression ratio and is not favorable for ignition. In addition, the reduced effective compression ratio can lower the back pressure of the cylinder, which is not beneficial to the air-fuel mixing process.  In summary, B80 can achieve high IMEP with low NOx and CO emissions. The maximum PRR is marginally higher than the critical value (10 bar/degree). Hence, B80 is selected as the benchmark for the following study on the effects of IVC timing.

Effects of IVC Timing
In this section, the combustion characteristics and emissions formation are analyzed with the IVC timings of −134, −130, −126, −122, and −118 • ATDC. Figure 15 illustrates the comparison of in-cylinder pressure and HRR with different IVC timings. It can be observed that retarding IVC timing could lead to a longer ignition delay and a lower peak pressure. The main reason is that retarding IVC timing reduces the effective compression ratio and is not favorable for ignition. In addition, the reduced effective compression ratio can lower the back pressure of the cylinder, which is not beneficial to the air-fuel mixing process. In summary, B80 can achieve high IMEP with low NOx and CO emissions. The maximum PRR is marginally higher than the critical value (10 bar/degree). Hence, B80 is selected as the benchmark for the following study on the effects of IVC timing.

Effects of IVC Timing
In this section, the combustion characteristics and emissions formation are analyzed with the IVC timings of −134, −130, −126, −122, and −118 °ATDC. Figure 15 illustrates the comparison of in-cylinder pressure and HRR with different IVC timings. It can be observed that retarding IVC timing could lead to a longer ignition delay and a lower peak pressure. The main reason is that retarding IVC timing reduces the effective compression ratio and is not favorable for ignition. In addition, the reduced effective compression ratio can lower the back pressure of the cylinder, which is not beneficial to the air-fuel mixing process.  From HRR curves, two-stage combustion, including low-temperature and hightemperature combustion stages, can be observed for the n-butanol/n-octanol RCCI engine. This low-temperature stage combustion, around −10 • ATDC, is caused by the negative temperature coefficient behavior of n-octanol [28]. Another phenomenon that can be seen is that the peak HRR decreases with the delay of the IVC timing. This result is correlated with the phenomenon observed in the cylinder pressure curve. This is also mainly caused by the decrease in the effective compression ratio. Figure 16 shows the maximum PRR of the RCCI engine with various IVC timings. As can be seen, the maximum PRR decreases significantly with the delay of IVC timing, showing a linear relationship. Hence, it can be inferred that reducing the effective compression ratio is a promising method for mitigating the knocking phenomenon of the dual-fuel engine. When the IVC timing is retarded after −126 • ATDC, the maximum PRR could be reduced below 10 bar/degree, which can mitigate the knocking phenomenon. From HRR curves, two-stage combustion, including low-temperature and high-temperature combustion stages, can be observed for the n-butanol/n-octanol RCCI engine. This low-temperature stage combustion, around −10 °ATDC, is caused by the negative temperature coefficient behavior of n-octanol [28]. Another phenomenon that can be seen is that the peak HRR decreases with the delay of the IVC timing. This result is correlated with the phenomenon observed in the cylinder pressure curve. This is also mainly caused by the decrease in the effective compression ratio. Figure 16 shows the maximum PRR of the RCCI engine with various IVC timings. As can be seen, the maximum PRR decreases significantly with the delay of IVC timing, showing a linear relationship. Hence, it can be inferred that reducing the effective compression ratio is a promising method for mitigating the knocking phenomenon of the dual-fuel engine. When the IVC timing is retarded after −126 °ATDC, the maximum PRR could be reduced below 10 bar/degree, which can mitigate the knocking phenomenon.  Figure 17 displays the simulated evolution of spatial temperature (K) distributions under conditions with IVC timings of −134° and −118 °ATDC. With the IVC timing of −134 °ATDC, high-temperature combustion regions already appear at −5 °ATDC. At the TDC, the temperature reaches more than 1000 K at all locations in the cylinder. As for the IVC timing of −118 °ATDC, the high-temperature combustion regions only appear around the TDC. Meanwhile, the temperature at the bowl region is always lower than that with IVC timing of −134 °ATDC. This phenomenon is consistent with the results for in-cylinder pressure and HRR, mainly because the IVC timing of −118 °ATDC has a low effective compression ratio, which is not beneficial for high-temperature combustion. Figure 18 compares the IMEP for various IVC timings. As retarding the IVC timing, IMEP shows a trend of decreasing, which correlates with the trend of maximum PRR. As discussed, retarding the IVC timing will decrease the effective compression ratio, which consequently deteriorates the thermal efficiency of the engine. Therefore, the IMEP is reduced with the delayed IVC timing. However, it should be noted that the condition with IVC timing of −126 °ATDC shows an IMEP of 9.7 bar with an acceptable maximum PRR, which is still higher than that of the B20 case discussed in Section 3.2.4. With the IVC timing of −134 • ATDC, high-temperature combustion regions already appear at −5 • ATDC. At the TDC, the temperature reaches more than 1000 K at all locations in the cylinder. As for the IVC timing of −118 • ATDC, the high-temperature combustion regions only appear around the TDC. Meanwhile, the temperature at the bowl region is always lower than that with IVC timing of −134 • ATDC. This phenomenon is consistent with the results for in-cylinder pressure and HRR, mainly because the IVC timing of −118 • ATDC has a low effective compression ratio, which is not beneficial for high-temperature combustion. Figure 18 compares the IMEP for various IVC timings. As retarding the IVC timing, IMEP shows a trend of decreasing, which correlates with the trend of maximum PRR. As discussed, retarding the IVC timing will decrease the effective compression ratio, which consequently deteriorates the thermal efficiency of the engine. Therefore, the IMEP is reduced with the delayed IVC timing. However, it should be noted that the condition with IVC timing of −126 • ATDC shows an IMEP of 9.7 bar with an acceptable maximum PRR, which is still higher than that of the B20 case discussed in Section 3.2.4.   Figure 19 compares the NOx and CO emissions with different IVC timings. It is found that with the delay of IVC timing, NOx emission is significantly reduced. This is because retarding IVC timing will lead to a decrease in the combustion temperature, as discussed in Section 3.3.3. At the same time, the duration of high-temperature combustion is also reduced with the delayed IVC timing. As a result, less NOx is formed.   Figure 19 compares the NOx and CO emissions with different IVC timings. It is found that with the delay of IVC timing, NOx emission is significantly reduced. This is because retarding IVC timing will lead to a decrease in the combustion temperature, as discussed in Section 3.3.3. At the same time, the duration of high-temperature combustion is also reduced with the delayed IVC timing. As a result, less NOx is formed.  Figure 19 compares the NOx and CO emissions with different IVC timings. It is found that with the delay of IVC timing, NOx emission is significantly reduced. This is because retarding IVC timing will lead to a decrease in the combustion temperature, as discussed in Section 3.3.3. At the same time, the duration of high-temperature combustion is also reduced with the delayed IVC timing. As a result, less NOx is formed. A different trend is observed for CO emission. When retarding the IVC timing, the CO emission shows a trend of increasing, which demonstrates a negative correlation with the maximum PRR and IMEP. Figure 20 demonstrates the spatial distribution of CO under conditions with IVC timings of −134° and −118° ATDC. As can be seen from the figure, when the IVC timing is −118 °ATDC, a large amount of CO is formed in the bowl region of the combustion chamber and the CO near the centerline of the combustion chamber is not completely oxidized after generation. This is mainly because the temperature in the region near the centerline of the cylinder is low, as illustrated in Figure 17. As a result, the generated CO cannot be fully oxidized. In comparison, in the condition with IVC timing of −134 °ATDC, the CO generated in the bowl region is generally able to be oxidized.  A different trend is observed for CO emission. When retarding the IVC timing, the CO emission shows a trend of increasing, which demonstrates a negative correlation with the maximum PRR and IMEP. Figure 20 demonstrates the spatial distribution of CO under conditions with IVC timings of −134 • and −118 • ATDC. As can be seen from the figure, when the IVC timing is −118 • ATDC, a large amount of CO is formed in the bowl region of the combustion chamber and the CO near the centerline of the combustion chamber is not completely oxidized after generation. This is mainly because the temperature in the region near the centerline of the cylinder is low, as illustrated in Figure 17. As a result, the generated CO cannot be fully oxidized. In comparison, in the condition with IVC timing of −134 • ATDC, the CO generated in the bowl region is generally able to be oxidized. A different trend is observed for CO emission. When retarding the IVC timing, the CO emission shows a trend of increasing, which demonstrates a negative correlation with the maximum PRR and IMEP. Figure 20 demonstrates the spatial distribution of CO under conditions with IVC timings of −134° and −118° ATDC. As can be seen from the figure, when the IVC timing is −118 °ATDC, a large amount of CO is formed in the bowl region of the combustion chamber and the CO near the centerline of the combustion chamber is not completely oxidized after generation. This is mainly because the temperature in the region near the centerline of the cylinder is low, as illustrated in Figure 17. As a result, the generated CO cannot be fully oxidized. In comparison, in the condition with IVC timing of −134 °ATDC, the CO generated in the bowl region is generally able to be oxidized.