Sufei Wang and Fujun Zhang

（School of Mechanical Engineering, Beijing Institute of Engineering, Beijing 100081, China）

Abstract: Exhaust resonance effect on the 2-stroke engine aspiration is investigated via one-dimensional simulation on GT-Power. Result shows that exhaust resonance is established when the number of oscillation periods per engine cycle derived from the engine speed and exhaust length is an integer. Exhaust resonance may raise or lower the trapping ratio, and the specific effect depends on the value of the number of oscillation periods per engine cycle. There is a liner regression relationship between the trapping ratio and average after back pressure. The primary way to improve the trapping ratio with the exhaust resonance is to increase the average after back pressure. The optimum exhaust resonance state is the one that suits the port timings so that the peak of exhaust pressure lies within the after charging period, raising the average after back pressure. For the case where the exhaust duration is 184°CA and the scavenge duration is 111°CA, the optimum number of oscillation periods per engine cycle is 3.

Key words: 2-stroke engine；exhaust resonance；trapping ratio；pressure fluctuation

Loop- and cross-flow 2-stroke engine generally use scavenge and exhaust ports for aspiration. In order to allow for free exhausting, exhaust port opening is usually significantly earlier than scavenge port. For piston-controlled ports,opening and closing angle is symmetric, which means closing of exhaust port is later than scavenge port. For this reason, exhaust state in the exhaust manifold has a significant effect on the charge state at the end of gas-exchange. If exhaust pressure is lower than in-cylinder pressure,charged gas could leak into exhaust, lowering charge coefficient, reducing engine performance and hindering fuel efficiency and exhaust performance for gasoline engines. If an exhaust resonance state is established so that exhaust pressure is significantly higher than average between scavenge port close and exhaust port close,charge leak could be reduced, promoting engine performance. Zhang et al.[1]proposed a mathematical model of the exhaust system of 2-stroke engines and gave out the condition required for exhaust resonance to occur in single-cylinder engines. Xie[2]introduced the effect of diffuser-taper exhaust pipe on aspiration of 2-stroke engines and proposed the law of optimum pipe length.Xu et al.[3]analyzed the effect of exhaust manifold length and resonance chamber volume on exhaust pressure resonance and engine performance via simulation and conducted some kind of optimization. Sammut et al.[4]concluded that the primary effect of exhaust resonance on 4-stroke engine is to reduce residue gas in cylinder by onedimensional simulation. Blair et al.[5]proposed the criteria of resonance in a uniform and diffuser-taper exhaust pipe for 4-stroke engines. A few other researchers[6-11]studied the effect of intake and exhaust dynamics. As a whole, researches on exhaust dynamics primarily focus on diffuser-taper exhaust pipe, while little is done on uniform pipes. In this study, resonance criteria of uniform exhaust pipe is studied via GT-Power one-dimensional simulation. It is proved that the optimum exhaust resonance state improves the trapping ratio by raising the average after exhaust pressure. The criteria of optimum resonance state is given.

1 Principal of Exhaust Resonance

At the opening of exhaust port, exhaust gas in the cylinder rush into the exhaust pipe and produce an original pressure wave that propagates toward the end of exhaust pipe, which reflexes it, producing a reflexed pressure wave that propagates towards the exhaust port. The pressure fluctuation at the exhaust port is formed by the superposition of original and reflexed pressure waves. According to the law of wave superposition, if the phase of reflexed pressure wave is identical to that of original pressure wave, the pressure fluctuation at exhaust port will reach its maximum, and an exhaust resonance state is reached. If the end of the exhaust pipe is connected to the atmosphere or a large chamber, as in most cases, the phase of the reflexed pressure wave will be the opposite of the original pressure wave. In order to achieve exhaust resonance, the phase of the original pressure wave should also be opposite to its starting phase at the time when the reflexed pressure wave first reaches exhaust port. In other words, the time it takes for the pressure wave to travel back and forth for one time, t, should be half of the period of oscillation

where n is the crankshaft speed, m is the number of oscillation periods per engine cycle, and T is the timespan of an engine cycle. Considering that

where u is the velocity of pressure wave propagation and l is the length of exhaust pipe. It could be derived that

Exhaust resonance is achieved when the value of l makes m an integer.

2 Setup of the Simulation Model

In order to validate the proposed principal of exhaust resonance and study the effect of exhaust resonance on the aspiration of 2-stroke engines, the simulation model of a small 2-stroke engine is established in GT-Power, as in Fig.1.The parameters of the engine are listed in Tab.1.

Exhaust pressure during the period from scavenge port close to exhaust port close have a direct effect on charge pressure and density,which in turn affect the engine performance.Thus, exhaust pressure fluctuation during this period and its effect on engine aspiration and performance is studied. Define the period between the scavenge port close and the exhaust port close as the after aspiration period. Define the average exhaust pressure during the after aspiration period as the average after exhaust pressure.

where peais the average after exhaust pressure,EPC is exhaust port close, SPC is scavenge port close, peis exhaust pressure, θ is crank angle.

Amplitude of exhaust pressure fluctuation at exhaust port(referred to as Δp hereinafter), average after exhaust pressure and trapping ratio(referred to as TR hereinafter) are obtained through simulations.

3 Results and Explanation

3.1 Effect of speed and number of oscillation periods per engine cycle on state of exhaust resonance

Fig.1 GT-Power simulation model of a 2-stroke engine

Tab. 1 Parameters of the 2-stroke engine

As described in Section 1, the amplitude of exhaust pressure fluctuation at exhaust port reaches its maximum when exhaust resonance is obtained. Thus, exhaust resonance could be identified by speculating the change of the amplitude of exhaust pressure fluctuation. Fig.2 shows the change due to change in speed and exhaust length. It is observed that when the number of oscillation periods per engine cycle m is an integer, especially when m=2, 3, Δp is significantly larger than the one in other cases, implying that exhaust resonance is established. Δp does not stay unchanged for the same m. At a high engine speed, Δp is generally larger than that of lower engine speed.

3.2 Effect of exhaust resonance on aspiration

Fig.2 Change in amplitude of exhaust pressure fluctuation due to change in speed and exhaust length

Fig.3 Change in average after exhaust pressure due to change in speed and exhaust length

Fig.3 shows the change in average after exhaust pressure due to change in speed and exhaust length. Both speed and exhaust length has a significant effect on average after exhaust pressure. Average after exhaust pressure is strongly related to exhaust resonance. Similar number of oscillation periods per engine cycle m produces similar average after exhaust pressure, but the average after exhaust pressure is not linear related to oscillation periods per engine cycle or amplitude of exhaust pressure fluctuation at exhaust port. At m=2 and m=3, exhaust resonance is obtained, the exhaust pressure fluctuation at exhaust port reaches its maximum, but the average after exhaust pressure reaches its minimum and maximum respectively.

Fig.4 shows the change in the trapping ratio due to change in speed and exhaust length. The trend is mostly identical to that of the average after exhaust pressure, the primary difference being that higher speed increases the variation range of trapping ratio.

In order to analyze quantitatively the relationship between the trapping ratio and average after exhaust pressure, a regressive analysis is conducted with data from various engine speeds and exhaust lengths. Fig.5 is the result of regressive analysis. Results show that there is a linear regressive relationship between the trapping ratio and average after exhaust pressure. The trapping ratio rise along with the rise of average after the exhaust pressure. The regressive equation is y = 0.37x + 0.22 with R2=0.87, where y is trapping ratio and x is the average after exhaust pressure in 105Pa. Thus the concluded that exhaust pressure fluctuation affects trapping ratio by affecting average after exhaust pressure. The key to improve trapping ratio by organizing exhaust resonance is to increase average after exhaust pressure.

3.3 Relationship between exhaust resonance and port timing

Fig.4 Change in trapping ratio due to change in speed and exhaust length

Fig.5 Regressive analysis of trapping ratio and average after exhaust pressure

Fig.6 Exhaust pressure fluctuation pattern of three resonance state at n=6 500 r/min

To further investigate the effect of exhaust resonance on the trapping ratio, the pattern of exhaust pressure during one engine cycle at n=6 500 r/min and l=250, 350 and 550 mm, where the exhaust resonance are present for all three cases, is compared in Fig.6. At the given port timing, the exhaust pressure is at its maximum during the after aspiration period when m=3, at its minimum when m=2 and not far from its average value when m=4. Results listed in Tab.2 show that the trapping ratio and engine torque at m=3 are significantly higher than those at m=2 or 4, which means that m=3 is the desired resonance state. It can be concluded that by increasing the average after exhaust pressure, exhaust resonance could raise the trapping ratio and in turn improve engine aspiration and performance. In order to improve engine aspiration,not only should the exhaust system reach a resonance state, but also the number of oscillation periods per engine cycle should suit the port timing so that exhaust pressure reaches its maximum during the after aspiration period. Only in this way could the average after exhaust pres-sure be raised and the trapping ratio increased.

Tab. 2 Comparison of three resonance state at n=6 500 r/min

4 Conclusions

② Exhaust resonance has a significant effect on the average after exhaust pressure and trapping ratio. A similar number of oscillation periods per engine cycle m produces a similar average after exhaust pressure, but the average after exhaust pressure is not linear related to oscillation periods per engine cycle or amplitude of exhaust pressure fluctuation at the exhaust port.There is a linear regressive relationship between the trapping ratio and average after exhaust pressure. The trapping ratio rise along with the rise of average after exhaust pressure. The regressive equation is y = 0.37x + 0.22, where y is the trapping ratio and x is the average after exhaust pressure in 105Pa.

③ In order to improve engine aspiration, not only should the exhaust system reach a resonance state, but also the number of oscillation periods per engine cycle should suit the port timing so that the exhaust pressure reaches its maximum during the after aspiration period, raising the after exhaust pressure and trapping ratio.For the case where the exhaust duration is 184°CA and scavenge duration is 111°CA, the number of oscillation periods per engine cycle m=3 produces the highest trapping ratio.