2.3.1. Effects with Miller Cycle Application
This paper will elaborate the effects with the Miller cycle application in three aspects, which are pumping loss, combustion and friction loss.
To express without ambiguity, in this paper, the increase or decrease rate of a parameter in the following analysis (such as BSFC, thermal efficiency, etc.) is defined as |A-Abaseline|/Abaseline.
• Pumping Loss
EWG position directly affects intake pressure before intercooler. Since the test shows that EWG position and intake pressure before intercooler relative to intake advance angle changes similarly under various points of operation, for the sake of simplicity, the point of operation at 3000 rpm and 10 bar is illustrated in detail. This is shown in graphical form in
Figure 4 at the point of operation at 3000 rpm and 10 bar.
As shown in
Figure 4, intake pressure before intercooler rises dramatically as EWG opening drops. When the intake advance angle is increased from 0 (baseline engine) to 25 °CA, EWG opening is reduced from 91.6% to 29%, and the corresponding intake pressure before intercooler is increased from 112.1 to 129.9 kPa, which can guarantee the required load of Miller cycle engines.
On the one hand, since the exhaust gas still contains high energy, the further intervention of the turbocharger is beneficial to the utilization of exhaust energy, thereby improving the thermal efficiency of the engine; on the other hand, the application of turbocharger causes an increase in exhaust backpressure, which, to some extent, mitigates the pumping loss improvement due to the larger throttle angle. In general, attributed to a turbocharger, the output power under the deep Miller cycle is not worse than that of the baseline engine under medium and high load at 3000 rpm, and making good use of the exhaust gas has a certain improvement on the thermal efficiency of Miller cycle engines.
Pumping mean effective pressure (PMEP) is a common parameter that characterizes the pumping loss in the engine’s working cycle [
17].
Figure 5 shows PMEP relative to intake advance angle under baseline EVC, and PMEP relative to exhaust retardation angle under the Miller cycle at different points of operation during the test.
Figure 6 illustrates intake pressure after intercooler versus intake advance angle and exhaust retardation angle.
As can be seen in
Figure 5, due to larger throttle opening, PMEP is increased from −0.44 to −0.29 bar when intake advance angle changes from 0 (baseline engine) to 25 °CA at the point of operation at 3000 rpm and 5 bar, which conspicuously reduces pumping loss in the engine’s working cycle; while under medium- and high-load conditions, the drop of the EWG opening adversely affects the exhaust backpressure due to the increase of turbocharging effect, which weakens the improvement of the throttle opening on pumping loss. As a result, PMEP under medium- and high-load conditions only slightly improved relative to the baseline engine during the Miller cycle deepening process.
The change of exhaust retardation angle also had certain effects on pumping loss under the load characteristics of 3000 rpm. At the point of operation at 3000 rpm and 5 bar, as the exhaust retardation angle decreases, the throttle opening angle can be further enlarged. Consequently, when the baseline exhaust retardation angle is reduced from 25 to 0 °CA, PMEP follows from −0.29 to −0.26 bar, which mitigates pumping loss. Under medium- and high-load conditions, due to the faster gas flow in the cylinder, the excessive exhaust retardation angle of the baseline engine causes the exhaust back pressure to affect PMEP during the intake process for a longer time. As a result, when the exhaust retardation angle is advanced, the pumping loss of the Miller cycle intake process is greatly improved. For the high-load condition of 3000 rpm with the most obvious improvement, PMEP is improved from −0.28 to 0.06 bar after the baseline exhaust retardation angle 30 °CA is adjusted to 5 °CA. According to the test, the improved exhaust retardation angle even has a positive effect on the pumping process. Compared with the results above, the influence of the throttle opening and the EWG opening on the Miller cycle pumping loss under medium- and large-load conditions is relatively insignificant.
As shown in
Figure 6, the intake pressure after intercooler remains low at the point of operation at 3000 rpm and 5 bar; under medium and high load, the intake pressure after intercooler rises quickly when the Miller cycle becomes deeper, which guarantees the sufficient air supply. Meanwhile, the intake pressure after intercooler keeps increasing with the decrease of the exhaust retardation angle.
• Combustion
Figure 7 shows the logP versus logV diagram relative to intake advance angle under baseline EVC at different points of operation. It should be noted that, due to the fluctuation of the test value, the curve was smoothed to a certain extent without decreasing the accuracy.
As shown in
Figure 7, an obvious effect of over expansion occurs when the baseline engine is adjusted to the extreme Miller condition at different points of operation, which confirms that the application of the Miller cycle by VVT adjustment is effective. On this basis, a further analysis on combustion can be performed properly.
The change of intake advance angle has a significant influence on the combustion phase.
Figure 8 shows the optimal ignition timing, CA50 and CA10-90 relative to intake advance angle under baseline EVC.
Figure 8 first shows the control principle of CA50 during the test: When CA50 is around 8 °CA, the ignition timing is considered to be the best. (If knock occurs when CA50 is greater than 8 °CA, the minimum ignition timing is set at the knock limitation point). Subsequently, as shown in
Figure 8, the optimal ignition timing is conspicuously affected by the intake advance angle. As the intake advance angle increases, the effective compression ratio of the Miller cycle decreases, so the knock tendency is suppressed, which could further advance the ignition timing. The load of the engine also has a great influence on the optimal ignition timing: When the intake advance angle is 25 °CA, the optimum ignition timings at 3000 rpm and 5 bar, 3000 rpm and 10 bar, and 3000 rpm and 15 bar are at 27.75, 19.5 and 14.25 °CA BTDC (Before Top Dead Center), respectively. This is because, as the load rises, more fuel is injected in one working cycle, which augments the possibility of knock. Therefore, as the load rises, the ignition timing must be delayed to suppress the tendency of knock.
The change of CA10-90 relative to intake advance angle indicates the influence of the Miller cycle on combustion duration. It can be found from
Figure 8 that, at the point of operation at 3000 rpm and 15 bar, due to the ignition timing advance caused by the Miller cycle, combustion duration is remarkably reduced; the combustion duration under medium load conditions also decreases slightly (about 3.2%) with the increase of intake advance angle. The shortening of the combustion duration also indicates the optimization effect of the Miller cycle on in-cylinder combustion. For low-load conditions, the Miller cycle has not been found to improve CA10-90 during combustion.
Additionally, the test found that the variation of exhaust retardation angle under medium and low load conditions had only little effects on the combustion phase. However, after applying the Miller cycle, the change in in-cylinder maximum combustion temperature deserves further attention. In this paper, the in-cylinder temperature is calculated as follows. Firstly a calculation of the air density is completed with the help of in-cylinder pressure, specific gas constant and the intake temperature:
Then the temperature in the cylinder by the thermal equation of state is calculated:
In this formula, V0 represents the displacement of the cylinder while veff represents the volumetric efficiency. The value 0.9 is a suggested value for the volumetric efficiency which will automatically be corrected by the formula with the help of the calculated intake pressure.
Figure 9 illustrates maximum combustion temperature relative to intake advance angle under baseline EVC, and maximum combustion temperature relative to exhaust retardation angle under the Miller cycle at different points of operation during the test.
It can be seen from
Figure 9 that the in-cylinder maximum combustion temperature relative to intake advance angle varies from loads at 3000 rpm: At the point of operation at 3000 rpm and 5 bar, the in-cylinder maximum combustion temperature shows a slight downward trend while the in-cylinder maximum combustion temperature shows an opposite trend under medium- and high-load conditions. On the other hand, the in-cylinder maximum combustion temperature relative to exhaust retardation angle under different loads at 3000 rpm shows a much more obvious change: As the exhaust retardation angle decreases, the in-cylinder maximum combustion temperature drops remarkably. The dramatic drop occurs under the high load condition at 3000 rpm, and a deep Miller cycle combined with a smaller exhaust retardation angle can reduce the maximum combustion temperature even below the baseline engine under all three test conditions. The reason for this phenomenon is that when the exhaust retardation angle is reduced, less high-temperature exhaust gas in the intake stroke is returned to the cylinder, so the temperature of the cylinder gas at the end of the intake stroke is lower, which is beneficial to the combustion process.
According to the above analysis, it can be concluded that deep Miller cycle with the appropriate valve overlap angle can effectively reduce in-cylinder maximum combustion temperature at 3000 rpm: For the most commonly used 3000 rpm and 10 bar condition, the in-cylinder maximum combustion temperature of the baseline engine reaches approximately 2260 °C. After applying deep Miller cycle combined with the smaller exhaust retardation angle (30 °CA for the intake advance angle and 5 °CA for the exhaust retardation angle), the in-cylinder maximum combustion temperature drops to approximately 2240 °C, and further reducing the exhaust retardation angle can even lower the maximum combustion temperature to below 2200 °C.
The reduction of in-cylinder maximum combustion temperature is a manifestation of the improvement in combustion conditions because a higher in-cylinder maximum combustion temperature produces a higher thermal load, which causes the thermal efficiency deterioration of the engine; at the same time, a higher in-cylinder maximum combustion temperature does harm to the lubrication and the durability of the components; besides, a higher in-cylinder maximum combustion temperature increases the generation of NOx, which adversely influences the engine emission characteristics.
• Friction loss
The energy lost in one cycle to overcome the friction also has a significant impact on the fuel economy. Friction mean effective pressure (FMEP) is a common parameter to characterize the friction loss in the engine working cycle. The main influencing factor of FMEP is the average speed of the piston during the working cycle and in-cylinder peak pressure. Since the engine speed is always maintained at 3000 rpm during the test, the average piston speed does not affect the FMEP. Consequently, only the in-cylinder peak pressure determines the value of FMEP.
Figure 10 and
Figure 11 show in-cylinder peak pressure and FMEP relative to intake advance angle under baseline EVC, and in-cylinder peak pressure relative to exhaust retardation angle under the Miller cycle at different points of operation during the test.
As shown in
Figure 10, the in-cylinder peak pressure is remarkably affected by the load: The in-cylinder peak pressure increases as the load rises, which, as a result, magnifies the friction loss. As can be seen in
Figure 11, the fluctuation of FMEP at 3000 rpm and 10 bar seems to be abnormal, but generally speaking, the trends at different loads are consistent with the relationship between the peak pressure and intake advance angle or exhaust retardation angle.
Under high-load conditions, as the Miller cycle is deepened, the in-cylinder peak pressure changes oppositely from the medium and low load. This is because when the Miller cycle is deepened, the CA50 is greatly decreased due to the advance of the ignition timing. Moreover, the in-cylinder combustion rate is accelerated, which causes the in-cylinder peak pressure and FMEP to rise, so that the friction loss becomes correspondingly larger. Contrary to the intake advance angle characteristic, under the high load condition, as the exhaust retardation angle decreases, the in-cylinder peak pressure decreases remarkably. When the exhaust retardation angle decreases from 30 to 5 °CA, the in-cylinder peak pressure drops from 77.32 to 67.11 bar, which is a drop of about 13%. This is followed by a drop in FMEP, which dramatically reduces the in-cylinder friction loss, which indicates that a deep Miller cycle matching a smaller exhaust retardation angle under the high load condition can achieve an equivalent FMEP to the baseline engine. Meanwhile, the baseline engine is further improved in terms of pumping loss and combustion after the Miller cycle application.
2.3.2. Performance Increase of the Miller Cycle
After the Miller cycle application, the above effects directly affect the BSFC under different loads.
Figure 12 shows BSFC relative to intake advance angle under baseline EVC, and BSFC relative to exhaust retardation angle under the Miller cycle at different points of operation during the test.
It can be seen from
Figure 12 that, as the intake advance angle increases, the continuous deepening of the Miller cycle has a significant influence on BSFC. At the point of operation at 3000 rpm and 5 bar, the BSFC is reduced from 265.1 g/kW·h of the baseline engine to 258.9 g/kW·h, with an improvement of about 2.3%. For low-load conditions, the reduction in BSFC is mainly due to the significant improvement in PMEP as the Miller cycle is deepened, which is beneficial to the fuel economy. For medium load conditions, when the Miller cycle is deepened, the influence of PMEP is negligible, while the combustion and FMEP are slightly improved. As a result, when the intake advance angle is adjusted from baseline VVT to Miller cycle VVT, BSFC drops from 236.3 to 233.1 g/kW·h.
In addition, it can be inferred from
Figure 12 that the engine load also determines BSFC considerably. The rise of engine load can accelerate the in-cylinder air flow speed and the speed of flame front, which is beneficial to reduce the BSFC. However, as the engine load rises, the gas flow in the cylinder is strengthened and the heat transfer loss is also increased. Therefore, the optimal BSFC is achieved within the range from medium to high load at 3000 rpm (the above two effects are balanced at medium and high load). The exhaust retardation angle also has a certain impact on BSFC. Under low load conditions, since the pumping loss, combustion and friction loss vary slightly with the change of exhaust retardation angle, the BSFC change is also insignificant. BSFC reaches 257.9 g/kW·h when the exhaust retardation angle is 5 °CA at 3000 rpm and 5 bar, which is slightly lower than the IVC optimization result by 1g/kW·h. At the point of operation of 3000 rpm and 10 bar, the change of exhaust retardation angle still has a potential for the BSFC reduction. The reason is that the pumping loss and combustion are improved to some extent with the advance of the exhaust retardation angle. Therefore, compared with the IVC optimization results, when the exhaust retardation angle is 5 °CA, the BSFC can reach 230.5 g/kW·h, which is about 2.4% lower than the BSFC of the baseline engine.
At the point of operation at 3000 rpm and 15 bar, the BSFC has an obvious minimum value in
Figure 10. To explain it clearly,
Figure 13 shows BSFC and related effects relative to the intake advance angle under baseline EVC, and BSFC and related effects relative to the exhaust retardation angle under the Miller cycle at the point of operation 3000 rpm and 10 bar.
At the point of operation at 3000 rpm and 15 bar, as Miller cycle is deepened, the PMEP variation range is relatively small, and the optimal intake advance angle is about 10 to 15 °CA; the ignition timing and CA50 are significantly advanced, which results in a large improvement in combustion. However, due to the rise of in-cylinder peak pressure, the deteriorated friction loss offsets some of the improvement due to the benefit in combustion. As can be seen in
Figure 6, the intake pressure after intercooler is also the maximum at the intake advance angle of 15 °CA. The relationship between the above three achieves the best overall effect when the intake advance angle is 15 °CA. Compared to 237.0 g/kW·h BSFC of the baseline engine, the deep Miller cycle can be used to reduce it to 230.9/kW·h, which is about 2.6%.
Similarly, the optimal BSFC at 15 °CA exhaust retardation angle is the consequence of the integrated effects of pumping loss, combustion and friction loss. As the exhaust retardation angle decreases, friction loss is well improved. At the same time, due to the knock limit, the CA50 deteriorates remarkably, and besides, when the exhaust retardation angle continues to decrease from 15 °CA, the in-cylinder maximum combustion temperature (not shown) also drops by only a small amount. Due to poor combustion, when the exhaust retardation angle is adjusted excessively, the BSFC saved by pumping loss and friction loss improvement is insufficient to overcome the loss caused by combustion deterioration, resulting in degradation of engine fuel economy. Therefore, the optimal exhaust retardation angle is set to 15 °CA, and the BSFC at this time is 229.2 g/kW·h.
By calculating the brake thermal efficiency, the improvement of the brake thermal efficiency after the application of the Miller cycle can be obtained. When the brake thermal efficiency is calculated, 44000 J/kg is used as the low calorific value of gasoline.
Figure 14 shows the comparison of brake thermal efficiency among the baseline engine and different Miller cycle optimization stages at different points of operation. The Miller cycle optimization is defined as the settings of IVC optimization and EVC optimization.
The brake thermal efficiency reaches 31.7%, 35.5%, and 35.7%, which has a 2.8%, 2.5%, and 2.6% improvement compared to the baseline engine, respectively, at three points of operation. Therefore, regardless of the load at 3000 rpm, the brake thermal efficiency is prominently improved after the Miller cycle application. The test shows that under the condition of 3000 rpm and 5 bar, due to slower airflow velocity and the higher pumping loss caused by smaller throttle opening, the brake thermal efficiency at low load is about 4% inferior to that at medium and high load, which can indicate that the optimal brake thermal efficiency of Miller cycle engine is achieved in the relatively high-load working range at 3000 rpm.