The Atkinson cycle and the Miller cycle have something in common in that they are high expansion cycles that lengthen the expansion stroke compared to the compression stroke. However, these two cycles differ in mechanical methods implemented as real engine cycles. The Atkinson cycle, devised by Atkinson in 1882, is more thermally efficient because it has a larger expansion ratio than diesel cycles with the same compression ratio. However, as the structural complexity increases to structurally increase the expansion, durability problems arise. The Miller cycle was devised to compensate for this problem. The Miller cycle implements a high expansion cycle with a long expansion period compared to the compression period by adjusting the opening and closing periods of the intake valve during the suction process of the intake air from the atmosphere. The Miller cycle, which is a low-compression and high-expansion cycle, has a longer expansion ratio than the compression ratio and has a more effective expansion work, which improves performance. Additionally, a low compression pressure from a low compression ratio can reduce the combustion temperature to improve the nitrogen oxides. This technology is mainly applied to four-stroke engines.

Gonca et al. mentioned that the application of Miller cycles through simulation and experimentation to a four-stroke organization resulted in theoretical improvements in specific fuel consumption (SFC) and NO, with an improvement of approximately 2.5% power loss [1]. In other studies, Gonca et al. reported simultaneous reductions in CO₂ and reductions in NO, HC, and CO in combination with a four-stroke diesel engine and a Miller cycle applied with turbo charging [2]. Lee et al. reported the effectiveness of applying Miller cycles with high efficiency T/C to a marine two-stroke diesel engine [3][4].

The system has scavenging ports, the start of compression, and the end of expansion is determined by the closing and opening of the exhaust valve. The low-pressure and high-expansion cycles of a marine two-stroke engine can be implemented by adjusting the closing timing of the exhaust valve. Figure 1 presents a conceptual diagram of the Miller cycle of a two-stroke engine using the uniflow-scavenging method. Because the two-stroke engine of the uniflow scavenging system has an exhaust valve on the top of the cylinder cover, the start of compression occurs when the exhaust valve is closed. In the figure, for diesel cycles, compression can be achieved from the time the piston passes through the port. In the case of the Miller cycle, the piston passes through the port, and the exhaust valve closes during the upward stroke to initiate compression. To realize high expansion, reducing the compression ratio by delaying the closing of the exhaust valve will reduce the maximum explosive pressure because the effective compression period will be shortened. To compensate for this, a Miller cycle must be applied simultaneously with a high-boost turbocharger.

Figure 1: 
Miller cycle for two-stroke marine engine[1]

The marine 2-stroke engine is designed to be longer than the on-shore diesel engine to increase the propulsion efficiency, and the exhaust gas energy is lower than that of the 4-stroke engine, as the intake through the port pushes out the exhaust during the desired period. This means that the energy flowing into the turbocharger was low. Therefore, a high-efficiency turbocharger is required to apply a high-expansion cycle to two-stroke engines. The T/C system is a common application in diesel engines, and several research papers have been published to reduce emissions through T/C [4]-[7]. In this study, we theoretically examine the feasibility and effectiveness of the high expansion cycle by applying a two-stage turbocharger to marine 2-stroke engines.

Figures 7 and 8 show the low compression – high expansion of the Miller cycle applied with a two-stage turbo charge of different T/C efficiencies (η_T/C) from the diesel cycle, which achieved a scavenge air pressure of 2 bar by applying a single-stage turbo charge. Figure 7 shows an enlarged area with low pressure to help understand when compression occurs and where exhaust heat escapes. The ideal cycle of the blue dotted line is a diesel cycle that can be achieved by a single-stage turbo charge. In the figure, Miller cycles 1, 2, and 3 represent the Miller cycles achieved by applying a two-stage overcharge, as shown in Figure 4. The greater the difference between Pch and Pti in the Miller cycle, the more efficient is the turbocharger. As the efficiency of the turbocharger increases from the exhaust conditions of the diesel cycle, the achievable compression ratio decreases. This means that the achievable Miller angle increases. A decrease in the compression ratio decreases T_max, resulting in a decrease in NO_x.

Figure 7: 
P-V diagram of the scavenge and exhaust part of high expansion cycle adopting two-stage T/C

Figure 8: 
P-V diagram of the maximum pressure part of high expansion cycle adopting two-stage T/C

Figure 8 shows an enlarged display of high pressure in the cases shown in Figure 7, indicating that P_max also increases as the supercharger efficiency increases. The high expansion cycle, miller cycle through high-efficiency turbo-charging maintains or increases the output owing to an increase in P_max compared to a diesel cycle, resulting in a decrease in T_max, resulting in two effects: improved power and reduced NO_x.

Table 1 summarizes the results of Figures 7 and 8. The figures for pressure and temperature for the diesel and Miller cycles are compared. Note that diesel cycles with one-stage T/C have a charging pressure of 2.2 bar and Miller cycles 1, 2, and 3 with two-stage T/C are higher at 5.3, 5.7, and 6.3 bar, respectively. Pmax can also be approximately 30 bar higher when a two-stage T/C is applied, which increases the output. In contrast, Tmax shows that the diesel cycle is the highest at 1938 K, and the Miller cycle is lower than that of the diesel cycle. This is the result of reduced compression ratios in the Miller cycle, resulting in a lower compression pressure. A comparison with the Miller cycle shows that P_max and T_max increase as the T/C efficiency increases. Furthermore, the higher the T/C efficiency, the greater the rate of expansion (ε_e/ε_c). This means that the efficiency of the T/C is extremely important to achieve good performance and reduction in combustion temperature, which are the effects of the high-expansion Miller cycle.

To increase engine performance, the heat generated by combustion must be sufficiently used in the cycle to increase the efficiency of the cycle. Because the engine cycle is connected to the turbine cycle of the T/C, the optimal performance is determined by matching the engine cycle with the T/C cycle. The marine low-speed two-stroke diesel engine has not yet introduced a two-stage turbo-charging system. However, improving global warming and marine air pollution requires continuous performance improvement of engines, which are mostly used by merchant ships. Therefore, in this study, we examine the possibility of improving performance and reducing nitrogen oxides through theoretical studies of high-expansion cycles with two-stage T/C applied to 2-stroke marine diesel engines.

This study examined the possibility of performance improvement by simultaneously applying high expansion cycles and two-stage T/C to improve the performance of diesel engines. It was confirmed that the same calorific input into the cycle increased the Pmax and improved the performance. However, the feasibility of two-stage turbo charge and high-expansion cycles under various loads is challenging in this work because the waste gates of low-pressure and high-pressure turbines required for two-stage system configurations are not considered. Therefore, we believe that further research is needed on system configurations that can realize optimal performance through the application of waste gates.

The calculation of nitrogen oxides can be calculated using mechanisms in the chemical reactions of fuel and air molecules composed of oxygen and nitrogen. The Zeldovich mechanism, prompt mechanism, N₂O mechanism, and NNH mechanism were used in the calculation of nitrogen oxides [9]. Because the reaction of the Zeldovich mechanism to NO is determined by the combustion temperature and reaction rate at chemical non-equilibrium states, this study did not reflect the direct calculation of NOx and considered the possibility of reducing NOx by calculating the combustion temperature at each state. However, this study calculates only the highest combustion temperatures according to different specific heat and cut-off ratios of the diesel cycle; therefore, direct connections are difficult because the chemical reaction mechanisms for equilibrium and non-equilibrium are not considered at all. It is reported in various literature that NO_x is produced by strongly reacting at temperatures above 1600℃ [10][11], so it is possible to reduce NO_x by reducing combustion temperature.

In this study, we derive the results of a review of the theoretical application of a two-stage turbocharged Miller cycle while simultaneously implementing a high expansion cycle by reducing the compression ratio from the ideal cycle of a marine two-stroke diesel engine to increase the relative expansion ratio. The result is the theoretical maximum pressure and distribution of pressure ratios that can be reached through a two-stage turbo-charged system compared to the input calories, and the effect that can be achieved when applied to the high expansion theory cycle. In summary, the results are as follows:

The maximum pressure that can be achieved in a 2-stage turbo-charging system increases as the cut-off ratio increases, which means that the size of the calories put into the cycle increases.

• 1) The maximum pressure in 2-stage turbo-charging system can be achieved when the pressure ratio of the low-and high-pressure compressors is the same.
• 2) A high expansion cycle can be realized by reducing the compression ratio in the diesel cycle, which can reduce the highest temperature of the combustion chamber, which is expected to reduce NOx.
• 3) Because the scavenging pressure can be further increased through the application of the 2-stage T/C, even if the compression ratio is lowered in the high expansion cycle, the maximum combustion pressure can be further increased.
• 4) High efficiency of T/C is important to achieve the high expansion cycle.