Improvement of engine performance with high compression ratio based on knock suppression using Miller cycle with boost pressure and split injection

Abstract

In theory, high compression ratio has the potential to improve the thermal efficiency and promote the power output of the SI engine. However, the application of high compression ratio is substantially limited by the knock in practical working process. The objective of this work is to comprehensively investigate the application of high compression ratio on a gasoline engine based on the Miller cycle with boost pressure and split injection. In this work, the specific optimum strategies for CR10 and CR12 were experimentally investigated respectively on a single cylinder DISI engine. It was found that a high level of Miller cycle with a higher boost pressure could be used in CR12 to achieve an effective compression ratio similar to CR10, which could eliminate the knock limits at a high compression ratio and high load. To verify the advantages of the high compression ratio, the fuel economy and power performance of CR10 and CR12 were compared at full and partial loads. The result revealed that, compared with CR10, a similar power performance and a reduced fuel consumption of CR12 at full load could be achieved by using the strong Miller cycle and split injection. At partial load, the conditions of CR12 had very superior fuel economy and power performance compared to those of CR10.

Keywords

high compression ratio / knock / Miller cycle / split injection / engine performance

Introduction

As the global warming and energy crisis get serious, more and more stringent regulations on CO₂ emission have been mandated in many countries, placing heavy burden on automotive industry and academia. Studies on improving the thermal efficiency and reducing the fuel consumption of the SI engine have been intensified worldwide [¹–³]. The downsized SI engine with boost pressure and a high compression ratio (CR) has been proven to have a significant potential in improving thermal efficiency and enhancing power output. However, a stronger knock tendency appears as the compression ratio and intake pressure increase, especially at a high load, which can severely damage the engine and restrict the improvement of thermal efficiency [⁴,⁵]. Therefore, searching for effective methods for suppressing engine knock has become a research hotspot. Plentiful investigations have been conducted to evaluate the effects of various strategies on knock resistance and engine performance. Among them, low compression ratio, retarding ignition timing (IT) [⁶–⁸], enriching the mixture [⁸,⁹] and exhaust gas recirculation (EGR) [¹⁰–¹²] are commonly applied in production engines. With these methods, the knock can be suppressed significantly; however, the thermal efficiency is deteriorated simultaneously. Stratified mixture based on the split injection strategy helps to suppress knock by a local cooling effect and accelerating flame propagation [¹³–¹⁵], but it has to be carefully designed to avoid soot emission and the deterioration of fuel economy. According to Refs. [⁴,¹⁶–¹⁹], Miller cycle has good performances in both suppressing knock and improving thermal efficiency. Therefore, it has received a lot of attention.

Miller cycle, realized by either early or late intake valve closing (EIVC or LIVC), has the advantages in alleviating knock, improving fuel economy, and reducing NO_x emission. First, the capability of knock suppression of Miller cycle comes from the lower pressure and temperature at the end of compression stroke owing to reduced effective compression ratio [⁴]. Hence, a higher geometric compression ratio can be used by applying Miller cycle. Compared with that via EIVC, the Miller cycle via LIVC has a better knock resistance due to the lower in-cylinder temperature cooled by the fresh air flowing back to the intake manifolds [¹⁶]. Next, Miller cycle improves fuel economy because of a higher thermal efficiency over the Otto cycle. Li et al. [¹⁶] experimentally investigated the effects of EIVC and LIVC on the fuel economy of a boosted DI gasoline with a compression ratio of 12 (CR12). Compared with the original production engine with CR 9.3, the brake specific fuel consumption (BSFC) was improved by 4.7% with CR12 and LIVC at high load, while the effect of EIVC was negligibly small. The results were consistent with the thermodynamic calculations conducted by Zheng et al. [¹⁷], which revealed that the use of Miller cycle improved the fuel economy for both the partial and full load operations by reducing the pumping loss and optimizing the combustion phasing, although the improvement by LIVC was superior to that by EIVC at full load due to more optimized combustion phasing. Finally, the Miller cycle can also reduce NO_x emission by decreasing intake charge quantity and combustion temperature. A minimum reduction of NO_x emission rate of 8% with an engine-power-loss of 1% was achieved by Wang et al. [²⁰,²¹]. In spite of the advantages presented above, the inherent drawback of the substantially decreased torque at low speed impedes the employment of the Miller cycle at low speed and high load. The most common technique of compensating the torque penalty is to boost the pressure [²²,²³]. Gonca et al. [²³] achieved an effective power increase of 5.1% with an efficiency increase of 6.3% by applying the Miller cycle with boost pressure in a diesel engine. However, the knock tendency increases with boost pressure. To decrease the knock tendency, the Miller cycle with boost pressure is always coupled with another strategy like EGR [²⁴–²⁶]. The investigation conducted by Martins and Lanzanova [²⁶] demonstrated that in a Miller cycle spark-ignited engine running on hydrous ethanol with boost pressure, the addition of EGR could be beneficial to reducing knock and improving the thermodynamic properties of the charge. Nevertheless, the torque of an engine equipped with EGR declines due to the diminished fresh air and injection quantity. Among the knock suppression strategies mentioned above, the split injection shows a potential to mitigate knock problem [²⁷], improve thermal efficiency, and promote engine power [¹⁵] by enhancing the turbulence and inducing proper fuel stratification in the combustion chamber [²⁸–³⁰]. Intensified turbulence increases the flame speed through increasing the flame surface area, affecting the flame strain and curvature and enhancing the molecular diffusivity and thermal conduction [³¹,³²]. Proper fuel stratification induced by split injection with rich mixture near the spark plug and lean mixture in the end-gas facilitates the spark-induced flame propagation and inhibits the end-gas auto-ignition [²⁹]. Li et al. [³³] found that late split injections could overcome the issue of low combustion speed with EIVC, thereby improving the engine power. Therefore, combining the split injection to the Miller cycle with boost pressure is of great potential to suppress knock and improve engine performance.

As is known to all, EGR, low CR, transforming the combustion chamber shape, alternative fuels, and delaying IT to suppress knock could reduce the thermal efficiency in general. Therefore, it was found in Ref. [⁵] that using the Miller cycle with boost pressure has the possibility to suppress knock and simultaneously promote the engine torque. However, compared with the Miller cycle without boost pressure, the knock tendency with boost pressure becomes higher. In this respect, coupling with split injection could make further improvement in knock resistance and engine power by facilitating the turbulence and decreasing the in-cylinder temperature. In theory, increasing compression ratio could further improve the engine performance, but the very high propensity of knock limits the application of high compression ratio in SI engine. Hence, the best performance of gasoline engine at a high compression ratio is not completely understood. In addition, still limited information has been known about the performance of the Miller cycle with boost pressure and split injection under high compression ratio conditions.

Therefore, the objective of the present work is to comprehensively optimize the proposed strategy under the condition of high compression ratio (CR12) and thus to not only solve the limitation of knock but also improve the engine performances involving output torque, fuel economy and COV, simultaneously. For this purpose, in the present work, the strategy of miller cycle with boost pressure and split injection is optimized under the conditions of CR10 and CR12, respectively. Besides, it is found that more retarded intake valve closing timing and higher boost pressure can be applied under the condition of CR12 to achieve the optimal engine performances in contrast with CR10. Moreover, the engine performances of CR12 at full and partial loads are estimated by comparing those of CR10 with the optimal strategy. Since the high geometric compression ratio has become a main trend of SI engine for its inherent advantage in thermal efficiency, investigations in this work may have some guiding significance to practical application.

Experimental apparatus and conditions

The study was conducted on a 4-stroke, direct injection, single-cylinder SI engine (Ricardo E6) as shown in Fig. 1. The specifications of the engine are listed in Table 1. The engine combustion chamber consists of a flat-top piston and a pent-roof cylinder head with spray-guided design. The compression ratio of this engine can be easily changed by adjusting the height of cylinder head through a mechanical gear system. Readers may refer to Ref. [¹²] for the details of the schematic process of changing the compression ratio. A BMW piezoelectric injector was used to achieve split injection and the injection pressure was fixed at 12.5 MPa for all measurements. The injection timings and start of spark were controlled by MOTEC M400 ECU. To achieve the Miller cycle, a highly flexible electrohydraulic valve train was applied. For the baseline case without Miller cycle, the intake valve closing timing was 130 CAD BTDC. The intake air was supplied by a compressor and metered with sonic nozzles to produce the desired intake pressures. The air/fuel equivalence ratio was measured by a lambda sensor with an accuracy of ±0.1%, and was kept stoichiometric throughout the tests. The engine was equipped with a direct current dynamometer for speed control and torque measurement. The engine speed was maintained at 1600 r/min for all cases. The intake boost pressure adopted in the experiment can be attained by a turbocharger in an actual engine. Considering that a turbocharger cannot be driven by a single cylinder engine, an external air-compressor was used to provide the required intake pressures. Therefore, as a fundamental study, the effect of intake boost pressure operation on engine performance is not considered in this work.

In this work, the pressure data acquisition system was consisted with a Kistler 6118B pressure transducer, a Kistler 5011 charge amplifier, and a National Instruments PC-612 data acquisition card. Pressure sampling was triggered using a photoelectric encoder coupled to the crankshaft with a resolution of 0.1 CAD. To reduce the errors, 200 consecutive cycles were recorded for each case, so that an average could be taken. All the temperatures were measured with K-type thermocouples. The intake temperature was controlled by calescence instrument. The coolant temperature was maintained at 80±3°C. Commercial gasoline (RON 92) was delivered, and the accuracy of the fuel consumption meter was ± 0.5%. The resolutions and uncertainties of the measurement equipment are listed in Table 2. Each test condition was repeated for three times except for the condition with extensive knock, and the standard deviations of the results were presented as error bars to illustrate uncertainties [³⁴].

Baseline cases

To provide a reference for comparison with other cases using different methods, a baseline case for each compression ratio (CR10 and CR12) was conducted first. As is seen from Table 3 that, the baseline cases used single injection at 240 CAD BTDC. The intake valve closing timing was 130 CAD BTDC in the baseline cases. Natural aspiration was used for both cases. Herein, the baseline cases for two compression ratios are called CR10-baseline case and CR12-baseline case, respectively. Several ignition timings were swept until continual knock happened to achieve the best output for each case. The baseline cases were conducted at full load with wide open throttle (WOT).

Figure 2 is a comparison of the fuel economy and power performance of CR10 and CR12. The error bars of both cases are lower than 0.3% of the experimental data, except for CR10 at the ignition timing of 4 CAD BTDC (IT4), which indicates the cases are stable. Increasing the compression ratio from 10:1 to 12:1 substantially decreases the maximum output torque and retards the ignition timing. With a higher compression ratio, a higher in-cylinder temperature at the end of the compression stroke is prone to shorten the ignition delay of the end gas, consequently raising knock tendency. To achieve the best engine output, the combustion phasing should be maintained at a specific crank angle range [¹²]. However, it is hard to achieve the optimum combustion phasing for CR12, ascribed to retarded ignition timing limited by severe knock tendency. The minimum BSFC of CR12-baseline case is nearly equal to that of CR10-baseline case. It is the improvement of the thermal efficiency as the compression ratio increases that compensates for the negative effect of deteriorated combustion phasing. A conclusion can be drawn that the engine torque output under full load is deteriorated due to knock limitation as the compression ratio increases from 10:1 to 12:1, which goes against the common wish to improve efficiency and promote engine power by increasing the compression ratio. To address this issue, the most urgent work is to suppress engine knock. As has been thoroughly discussed in Ref. [⁵], the strategy of the Miller cycle with boost pressure and split injection can effectively reduce the propensity of knock and promote power output. Therefore, the detailed optimal strategies at full load for CR10 and CR12 will be expounded and a comparison of the optimized fuel economy and power performance between CR10 and CR12 be performed.

Results and discussion

Optimal strategy for CR10

To investigate the effect of different levels of Miller cycle with boost pressure on engine performance and to obtain an optimum strategy for CR10, several experimental cases were conducted. The intake pressures of 1.2 bar, 1.4 bar, and 1.6 bar were chosen in this work. To ensure a consistent intake charge quantity with the baseline for each case, the intake valve closing timing was swept to determine the corresponding LIVC for each boost pressure. Consequently, the corresponding delayed intake valve closing timings for the chosen intake pressure were 45 CAD, 60 CAD, and 70 CAD, respectively, which are named by LIVC45+ 1.2 bar, LIVC60+ 1.4 bar, and LIVC70+ 1.6 bar. In addition, another case with a LIVC of 45 CAD and an intake pressure of 1 bar called LIVC45 was also included as a reference case. Last of all, split injection was taken into account to further improve the engine performance. Therefore, a case named LIVC60+ 1.4 bar+ dual 100 CAD BTDC, which indicates that a secondary injection of 20% of the total fuel at 100 CAD BTDC was combined with the case LIVC60+ 1.4 bar, was also performed. The split injection strategy used here has been validated to be the best under the condition of CR10 in Ref. [⁵].

The anti-knock performances of different strategies are revealed from Fig. 3. For the Miller cycle case and the Miller cycle with boost pressure cases, CA50 is retarded substantially, and P_max and the percentage of knock cycles decrease compared with those of the baseline case, indicating a prominent knock suppression capability of the Miller cycle. Note that CA50 is defined by a specific crank angle where 50% of the total fuel energy is released. With respect to a certain operation condition, an optimal CA50 to achieve the maximum BMEP and brake thermal efficiency can be determined by adjusting the ignition timing. It is commonly suggested that the optimal CA50 for a conventional SI engine is around 10 CAD ATDC [³⁵,³⁶]. However, some recent studies [³⁷,³⁸] proposed that the optimal CA50 varies from 5 to 11 CAD ATDC depending on the design and operating variables. According to the analysis of the experimental data, the optimal CA50 for the present study falls in the range of 10 to 15 CAD ATDC, which is slightly retarded compared with the common value due to a relatively high compression ratio and heat transfer for the engine used under the present operating conditions [³⁸]. In the present study, P_max is the average value of the maximum in-cylinder pressures of the 200 cycles. MAPO is defined as the largest absolute amplitude of the band pass filtered pressure oscillation within a crank angle. A cycle is considered to bea knock cycle when MAPO exceeds 0.1 MPa [³⁹]. It can be observed that the knock tendency increases when the pressure is boosted based on the Miller cycle with the same LIVC. The percentage of knock cycles of LIVC45+ 1.2 bar at IT22 is 16% higher than that of LIVC45. Further retarding the intake valve closure and boosting the intake pressure can improve the knock resistance. The percentages of knock cycles of LIVC60+ 1.4 bar and LIVC70+ 1.6 bar are both lower than that of LIVC45. Note that the method of LIVC60+ 1.4 bar has a higher maximum pressure compared to that of LIVC70+ 1.6 bar, which will lead to a higher torque to be discussed later. According to Fig. 4, the average temperature and peak pressure in the cylinder decline with the retarded intake valve closure, which accounts for the decreasing knock tendency. As the Miller cycle is intensified, the intake valve closure is retarded. As a consequence, more fresh air is pushed out of the cylinder, taking away more heat, so that the average temperature and cylinder wall temperature decrease with the intensified Miller cycle. Therefore, the problem of the increasing knock propensity caused by boosting pressure can be well resolved by enhancing the intensity of the Miller cycle. It is noteworthy that there still exist a small number of knock cycles under the condition of LIVC60+ 1.4 bar, so further improvement on knock resistance can be achieved by combining the split injection with LIVC60+ 1.4 bar. It is observed that the knock cycle vanishes with an advanced CA50 and slightly elevated P_max under the condition of LIVC60+ 1.4 bar+ dual 100 CAD BTDC. As is supported by the CFD simulations in Refs. [²⁸,²⁹], the split injection forms the fuel stratification with rich mixture around the spark plug and lean mixture near the wall, and enhances the in-cylinder turbulence, thus accelerating the propagation of spark-induced flame, which accounts for the improvements in knock resistance and combustion phasing. Besides, as can be observed from Fig. 4(a), the in-cylinder temperature decreases when the split injection is applied, which also contributes to a higher knock resistance. It is intuitively observed from the pressure profiles, as demonstrated in Figs. 5(a)–5(c), that the pressure oscillation retards and attenuates prominently via applying the strategies of the Miller cycle with boost pressure and split injection. The heat release in the baseline case is much more drastic with a large amplitude of oscillation than that in the other two cases, indicating that earlier auto ignition occurred in the baseline case.

The engine performance parameters including BSFC, torque, CA50, and IMEP-COV for CR10 in different cases are depicted in Fig. 6. In general, the cases of the Miller cycle with boost pressure have superior fuel economy and power performances than the baseline case. Compared with the baseline case, BSFCs drop by about 5.6%, 7.9%, and 7.2% for LIVC45+ 1.2 bar, LIVC60+ 1.4 bar and LIVC70+ 1.6 bar, respectively. The improved fuel economy can be explained as follows. First of all, the thermal efficiency is directly determined by the combustion process. It can be observed from Fig. 6(b) that a more advanced CA50 can be achieved for the Miller cycle with boost pressure compared with the baseline case, thanks to superior knock resistance. A higher thermal efficiency is consequently received due to improved combustion phasing. Secondly, the thermal efficiency is related to the thermal loss. The baseline case owns a higher in-cylinder temperature than the Miller cycle with boost pressure case, inducing more heat transfer to the ambient through the cylinder wall, and thus resulting in a lower thermal efficiency. As exhibited in Fig. 4(a), the in-cylinder temperature decreases with the intensified Miller cycler, thereby reducing the heat loss from heat transfer. The third reason for the higher thermal efficiency of the Miller cycle is the lower exhaust loss owing to lower exhaust temperatures. As the Miller cycle is intensified, the exhaust loss decreases. In addition, as can be observed in Fig. 4(b), the input work needed in the compression stroke of the Miller cycle is less than that in the baseline case. Compared with the Miller cycle, the baseline case has a longer compression stroke, demanding more compression work. Besides, the in-cylinder pressure of the Miller cycle is lower than that of the baseline case, so the compression work is less due to the smaller resistance force during compression stroke. Lastly, the pumping loss of the Miller cycles with boost pressures is still smaller than that of the baseline case. The pumping work is negative in the case without boost pressure. As the intake pressure rises, the pumping work increases until it turns to positive, namely, the pumping loss becomes negative (see the P-V curves of LIVC60+ 1.4 bar and LIVC70+ 1.6 bar in Fig. 4(b)). In spite of the prominent advantages of the Miller cycle and boost pressure presented above, the relationship between the Miller cycle and the thermal efficiency is nonlinear. The too intensive Miller cycle can diminish the engine efficiency due to the significantly deteriorated constant volume heat release level. It can be observed that the effective thermal efficiency of LIVC60 is the highest of different intensities of the Miller cycle with the same ignition timing. Further retarding the intake valve closing timing will substantially reduce the in-cylinder temperature and pressure at the end of compression stroke, thereby prolonging the combustion duration and consequently resulting in a lower constant volume heat release degree or even incomplete combustion. Furthermore, the intake charge of the next cycle is heated by the backflow from the cylinder when the piston moves upward before the intake valve closes. As the Miller cycle is intensified, the temperature of intake air increases, which relatively increases the heat transfer loss. BSFC is calculated from the output power and fuel consumption rate. Applying the Miller cycle can reduce the fuel consumption rate but deteriorate the power output, while boosting pressure will compensate for the power output but will increase the fuel consumption rate. Therefore, BSFC depends on the competition between these two factors. For the experimental conditions in this work, the best BSFC occurs in LIVC60+ 1.4 bar. In this respect, a split injection was conducted to further improve the performance. Finally, the best BSFC of 224.59 g·(kW·h)^–1 and effective thermal efficiency of 36.57% were achieved under the condition of LIVC60+ 1.4 bar+ dual 100 CAD BTDC.

As illustrated in Fig. 6(c), the maximum torque of the Miller cycle with boost pressure cases is higher than that of the baseline case. The growths are approximately 3%, 5.8%, and 5.4% for LIVC45+ 1.2 bar, LIVC60+ 1.4 bar, and LIVC70+ 1.6 bar, respectively. The improvement is a comprehensive result of the Miller cycle and boost pressure. As has been discussed above, the thermal efficiency of the Miller cycle with boost pressure cases is higher than that of the baseline case, so the output power of the Miller cycle with boost pressure cases is correspondingly higher on the condition that the intake charge is kept constant throughout the tests. Besides, the torque output is also related to the mechanical loss, a large portion of which is the friction loss. Compared with the Miller cycle with boost pressure cases, the baseline case produced more friction loss due to the higher average and maximum pressures in the cylinder. It can be observed that the best torque output exists in LIVC60+ 1.4 bar. The torque decreases when the Miller cycle is further enhanced and the pressure is boosted, which indicates that boost pressure can hardly compensate for the torque loss caused by the Miller cycle when the intake valve closing timing delays too much. Based on the LIVC60+ 1.4 bar, a torque increase of 0.5% was achieved by combining the split injection strategy. Note that the error bars of all cases are lower than 0.15 N·m, nearly 0.3% of the experimental data. In addition, it can be observed from Fig. 6(d) that the IMEP-COV of all cases are lower than 5%, except for CR10-Baseline case at IT22, which has a value slightly greater than 5%. The small values of error bar and IMEP-COV indicate that the combustion of all cases is stable. From the above, the optimal strategy for CR10 is LIVC60+ 1.4 bar+ dual 100 CAD BTDC. Compared with the baseline case, the torque is 6.3% higher and BSFC decreases by 7.7% after optimization.

Application of high compression ratio with Miller cycle and split injection

To further improve the engine performance, the compression ratio was increased to 12:1. However, the torque output at full load is actually deteriorated as the compression ratio rises as expected. In this section, the engine performance for CR12 at full load is to be optimized using the proposed methodology of the Miller cycle with boost pressure and split injection. First, the knock resistances, fuel economy, and power performance of different split injection strategies are to be discussed to find an optimal split injection strategy for CR12 especially. Then, comparisons between engine performances with different levels of Miller cycle with boost pressure are to be performed subsequently. Finally, an optimal strategy for CR12 will be obtained.

The thermodynamic condition of engine with CR12 is quite different from that of the engine with CR10. The in-cylinder temperature and pressure near top dead center are much higher for CR12. Split injection helps to lower down the in-cylinder temperature, the effect of which varies with the secondary injection quantities and injection timings. To determine the optimal split injection strategy for CR12, secondary injection timings from 60 to 180 CAD BTDC with an increase of 40 CAD were swept for each secondary injection percentage of 20%, 40%, and 60%. Two additional cases with a secondary injection percentage of 80% and secondary injection timings of 100 and 140 CAD BTDC were performed to observe the optimum torque. The case with a secondary injection timing of 60 CAD BTDC is called dual 60 CAD BTDC, and similarly, dual 100 CAD BTDC, dual 140 CAD BTDC, and dual 180 CAD BTDC for the other three injection timings were carried out. The first injection timing was fixed at 240 CAD BTDC under all conditions.

In the baseline case of CR12, continuous knock cycles occurred at IT10, so the knock resistance performances of different split injection strategies are compared at IT10. The results are presented in Fig. 7. The frequency of knock occurrence of all injection percentages is lower than that of the baseline case when the secondary injection timing is 60 or 100 CAD BTDC. Of the four secondary injection timings, dual 60 CAD BTDC exhibits the best knock resistance. With respect to the injection mass, the most effective secondary injection percentage for knock suppressing is 80%. The results of Refs. [²⁹,³⁰] indicate that the split injection forms fuel stratification with rich mixture around the spark plug and lean mixture near the wall. As the secondary injection percentage increases, the fuel/air equivalence ratio near the wall becomes smaller, which prolongs the ignition delay of the end gas, thus reducing the knock propensity. It is of interest to note that the relationship between knock propensity and secondary injection timing is non-monotonic. When the secondary injection percentage is 60%, the knock percentage increases first and then decreases when the secondary injection timing is retarded on the basis of 240 CAD BTDC. The result is attributed to the competition between the effects of fuel stratification and thermal stratification induced by split injection. When the secondary injection timing is retarded, the fuel concentration in the near wall region gets leaner but the local temperature gets higher due to the attenuated cooling effect of fuel evaporation. The lean mixture inhibits the end-gas auto-ignition while the low temperature has the opposite effect. With the retarded secondary injection timing, the effect of temperature prevails over that of fuel concentration first and then attenuates until the effect of lean mixtures plays a dominant role in suppressing the end-gas auto-ignition.

In GDI engine, the injection strategy has a strong influence on fuel distribution in the cylinder, thus affecting BSFC and the thermal efficiency. Figure 8 compares the fuel economy and power performance of different split injection strategies. As can be seen, the lowest BSFC and the highest output torque occur in dual 140 CAD BTDC with an injection percentage of 60%. However, the knock tendency of this strategy is substantially high, which is only second to that of dual 180 CAD BTDC with the injection percentage of 20%. The case with a secondary injection percentage of 20% at 60 CAD BTDC has good fuel economy and power performances, only next to those of dual 140 CAD BTDC. However, the IMEP-COV of this case is as high as 8.13%, which indicates an unstable combustion due to the too retarded secondary injection timing. Therefore, the case dual 100 CAD BTDC with a secondary injection percentage of 20%, which performs well in all the aspects of knock suppression, fuel economy, torque output and combustion stability, is chosen as the optimal split injection strategy for CR12. It is called dual 100 CAD BTDC later for simplicity.

Now that the optimal split injection strategy for CR12 has been proposed, the next work is to find the optimum Miller cycle with boost pressure, and finally to get the optimum torque output for CR12 at full load. In this section, the optimum Miller cycle with boost pressure for CR10, i.e. CR10-LIVC60+ 1.4 bar, is used as a comparative case. The level of Miller cycle and boost pressure is increased on this basis. The boost pressures adopted in CR12 are 1.4 bar, 1.6 bar and 1.8 bar, with the corresponding Miller cycles of LIVC65, LIVC75, and LIVC85, respectively. They are named as LIVC65+ 1.4 bar, LIVC75+ 1.6 bar, and LIVC85+ 1.8 bar. The corresponding intake valve closing timing is slightly changed because the compression ratio affects the intake charge quantity. The largest boost pressure is 1.8 bar, and the corresponding intake valve closing timing is 45 CAD BTDC. The most advanced ignition timing under this condition is 22 CAD BTDC. Further retarded intake valve closing timing will lead to the unreasonable condition under which the ignition occurs before the intake valve closure, so a higher boost pressure than 1.8 bar is not allowed. Note that, the high boost pressure of 1.8 bar used in this work is only to validate the effect of the Miller cycle with boost pressure on the engine performance. The optimum strategy of the Miller cycle with boost pressure was obtained by comparing the fuel economy and the power performance. Finally, the split injection of dual 100 CAD BTDC was added to further improve the torque output.

The BSFCs and CA50 of different cases for CR12 and CR10-LIVC60+ 1.4 bar are shown in Fig. 9. With the same boost pressure of 1.4 bar, the BSFC of CR12 are inferior to that of CR10 due to the limitation of high knock propensity. It is hard to achieve the optimal combustion phasing for CR12 under the condition of LIVC65+ 1.4 bar. It can be seen from Fig. 9(b) that the CA50 of CR12-LIVC65+ 1.4 bar is not located in the optimal region of CA50 for SI engine. Therefore, the high level of the Miller cycle has to be applied to improve the knock resistance. The BSFC and effective thermal efficiency are improved with the intensified Miller cycle and boosted pressure. When the boost pressure increases to 1.8 bar, the BSFC of CR12 is obviously lower than that of CR10-LIVC+ 1.4 bar. The LIVC85+ 1.8 bar+ dual 100 CAD BTDC was conducted by coupling split injection with a secondary injection percentage of 20% at 100 CAD BTDC to the optimal Miller cycle with boost pressure, but there was no obvious improvement observed. In the condition of CR10, however, split injection can further improve the fuel economy on the basis of the Miller cycle with boost pressure. The reason for this is that the split injection can further reduce the in-cylinder temperature, and subsequently lower down knock tendency and improve combustion phasing. However, for CR12, the in-cylinder temperature can hardly be further reduced by split injection since it has already been reduced significantly by a high intensity of the Miller cycle.

The profiles of torques with error bar and IMEP-COV versus injection timings are plotted in Fig. 10. The error bars of all cases are below 0.2 N·m, and the IMEP-COV of most cases are within 5%, which indicates that all the cases undergo stable combustion. As can be observed, the maximum torque of CR12 is well below that of CR10 with an identical boost pressure of 1.4 bar. The limitation lies in the significantly high knock tendency of CR12, which prevents it from achieving an optimal combustion phasing. As the Miller cycle is intensified, the knock resistance is improved, so that an optimal combustion phasing can be achieved for CR12 by advancing the ignition timing. An optimum torque output of 47.66 N·m is obtained in the condition of LIVC85+ 1.8 bar with a CA50 of nearly 15 CAD ATDC. Coupling with split injection on this basis, the maximum torque can be elevated to 47.73 N·m. To sum up, the optimal strategy for CR12 is LIVC85+ 1.8 bar+ dual 100 CAD BTDC. After optimization, the BSFC was reduced by 8.7%, and the torque was increased by 10.1% compared with the CR12-baseline case.

Comparison of performances of different compression ratios

As has been mentioned above, baseline cases of CR10 and CR12 without using optimization strategies have been compared at the beginning of this work. It is found that the engine torque is deteriorated seriously when the compression ratio is raised from 10:1 to12:1 due to increasing knock tendency. The maximum torque of CR10-baseline case is 45.16 N·m, and that of CR12-baseline case is 43.35 N·m. To alleviate the knock propensity and improve the engine torque, the strategy of the Miller cycle with boost pressure and split injection was applied to CR10 and CR12 respectively. Now that the optimal strategies for CR10 and CR12 have been obtained, the BSFC and power performance at full load are to be compared in this section. Besides, the engine performances of CR10 and CR12 under 75% and 50% loads will also be compared as the representatives of partial load performance.

According to the tests of CR10, it can be found that the engine torque increases first and then decreases as the Miller cycle and boost pressure are enhanced. The reason for this is that the deteriorated engine torque induced by the Miller cycle cannot be compensated for by boosting pressure when the intake valve closing timing is delayed too much. In terms of CR12, the geometric compression ratio is larger than that of CR10, so a higher level of the Miller cycle can be applied to achieve an effective compression ratio similar to that of CR10-LIVC60+ 1.4 bar. As a consequence, the increasing knock propensity due to the higher compression ratio can be further reduced by a stronger Miller cycle. Therefore, an optimal combustion phasing for CR12 can be achieved. The optimal strategies of CR10 and CR12 are LIVC60+ 1.4 bar+ dual 100 CAD BTDC and LIVC85+ 1.8 bar+ dual 100 CAD BTDC, respectively.

The fuel economy and power performance of CR10 and CR12 at full load by optimizing methodologies are compared in Fig. 11. The maximum torque of CR12 after optimization was nearly equal to that of CR10 with a slight drop of 0.27 N·m. This can be explained by the fact that more fresh air was pushed out from the cylinder due to a much more delayed intake valve closing timing used in CR12, thus reducing the in-cylinder temperature and suppressing knock. Therefore, more advanced ignition timing can be applied to achieve the optimal combustion phasing, resulting in more power output. In addition, the optimal boost pressures for CR10 and CR12 are 1.4 bar and 1.8 bar, respectively. The optimal case of CR12 received a higher input work from the increasing pumping work due to the higher boost pressure. It can be observed from Fig. 11 that the fuel economy of CR12 after optimization is superior to that of CR10. However, similar BSFCs for CR10 and CR12 were discovered from the comparison of the baseline cases before optimization. The minimum BSFC of CR12 decreases by about 2% compared with that of CR10. This improvement indicates that the advantage of high compression ratio in improving thermal efficiency shows up through inhibiting knock. In conclusion, a similar power performance and a superior fuel economy of CR12 at full load without knock combustion can be achieved by using a strong Miller cycle with a high boost pressure when compared with those of CR10.

As has been discussed, the thermal efficiency and engine torque are limited by the severely increasing knock tendency under the conditions of full load. Therefore, further comparisons were simply conducted at partial load. In this work, the engine performances of CR10 and CR12 at 75% and 50% loads will be compared as the representatives of partial load performance. The intake charge rate was 14.5 kg/h with a throttle opening percentage of 20%, which was 75% of that with WOT, named load 75%. When the throttle opening percentage was 15%, the intake charge was 9.5 kg/h, which was 50% of that with WOT, named load 50%.

Figure 12 shows the BSFC, CA50, torque and IMEP-COV of CR12 and CR10 at load 50% and load 75%. The small values of error bar and IMEP-COV below 5% indicate that the combustion in all cases is stable. The fuel economy of CR12 at both loads is superior to those of CR10. The minimum BSFC of CR12 is 3.1% and 1.1% lower than those of CR10 at the load of 75% and 50% respectively. High compression ratio has the advantage of improving thermal efficiency according to the thermodynamic calculation of \eta =\mathrm{1}-{\displaystyle \frac{\mathrm{1}}{{\epsilon }^{k-\mathrm{1}}}} , where \eta is the theoretical thermal efficiency of the Otto cycle, \epsilon is the compression ratio, and k is the specific heat ratio of fresh air. Therefore, at partial load when the knock propensity is low, the advantages of high compression ratio should show up according to theoretical calculation. The torques of CR12 at both load 50% and load 75% are higher than those of CR10. As the compression ratio increases, the in-cylinder peak pressure rises, producing a higher power output. The torque increases first until it reaches a maximum value and then decreases with advanced ignition timing. Under the condition of load 75%, the peak torque of CR12 appears at IT20 with a value of 34.1 N·m, which is 1.9% higher than that of CR10. Further advanced ignition timing will lead to knock cycle, thereby deteriorating the torque output. The peak torque of CR12-load 50% is 24.6 N·m, which appears at IT 24 CAD BTDC with an optimal CA50 of about 12.5 CAD ATDC. The result is consistent with the knowledge that the optimal advanced ignition timing increases as the engine load decreases when the engine speed is kept constant. The reason for this is that the ignition delay becomes longer due to the lower in-cylinder pressure at low load. In summary, CR12 has an absolutely superior fuel economy and power performance compared with CR10 due to a higher thermal efficiency at partial load.

Conclusions

In this work, the objective is to investigate the performance of high compression ratio on a DISI engine. For this purpose, a strategy of the Miller cycle coupling with boost pressure and split injection was employed at full load to suppress knock and promote engine performance. Optimal strategies for CR10 and CR12 were experimentally conducted. In addition, the fuel economy and power performance of CR10 and CR12 at full and partial loads after optimization were comprehensively and systematically compared. The main conclusions are summarized as follows:

The strategy of the Miller cycle coupling with boost pressure and split injection can improve the knock resistance of engine and maintain the torque output at the same time. The optimal strategy of LIVC60+ 1.4 bar+ dual 100 CAD BTDC for CR10 is obtained, with the maximum output torque equaling 48 N·m and the effective thermal efficiency corresponding to 36.57%. The torque decreases when the intensity of the Miller cycle is further enhanced and the pressure is boosted, which indicates that the boost pressure cannot compensate for the torque loss caused by the Miller cycle when the intake valve closing timing delays too much.

The optimal strategy for CR12 is LIVC85+ 1.8 bar+ dual 100 CAD BTDC in the present work. After the optimization, the best torque of 47.73 N·m, and an effective thermal efficiency of 36.9% are achieved, with an increase of 10.1% in the torque and a decrease of 8.7% in BSFC in contrast to the CR12-baseline case.

A similar power performance and a superior fuel economy of CR12 at full load can be achieved by using a strong Miller cycle with boost pressure when compared with those of CR10. The maximum torque of CR12 after optimization was nearly equal to that of CR10 with only a slight drop of 0.27 N·m. The minimum BSFC of CR12 decreases by about 2% compared with that of CR10. Overall, the entire performance using present methodologies for CR12 is better than that for CR10. At the loads of 50% and 75%, on the other hand, the effective thermal efficiencies and toques of CR12 are obviously superior to those of CR10. As the compression ratio increases, the theoretical thermal efficiency can be improved according to the thermodynamic calculation of the Otto cycle. In addition, the peak pressure in the cylinder is higher for CR12, resulting in a higher power output.

In conclusion, the increasing knock propensity of a high compression ratio engine can be suppressed by a strong Miller cycle, based on which, coupling with high boost pressure and split injection can compensate for the deteriorated torque caused by the Miller cycle. Compared with CR10, a similar power performance and a better fuel economy of CR12 at full load can be achieved by using the proposed method. Therefore, the present work provides a potential method to apply high CR on various working process at both high load and partial load. However, more input work is needed to produce a higher boost pressure for CR12. At partial load, the advantages of a high compression ratio obviously show up with superior fuel economy and power performance.

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