Design and Simulation of Two Stroke Engines

Design and Simulation of Two-Stroke Engines
HI
DC
CO
CO
LU
CC
Q.
1.3
1.1
1.0
MEASURED
0.9
TIME, seconds
0.8
0.00 0.01 0.02 0.03 0.04 0.05 0.06
Fig. 2.30 Measured and calculated pressures at station 2.
port to influence the cylinder emptying process, so this is more of a tribute to the accuracy of
the cylinder to pipe boundary conditions of Sec. 2.16, rather than any comment on the GPB
finite system modeling of the wave action in the pipe system!
The main event is the creation of the exhaust pulse as a wave of compression, the peak of
which is passing station 1 at 0.00384 second. It reflects at the open end as an expansion wave
and the peak returns to station 1 at 0.0382 second. The basic theory of the motion of finite
amplitude waves is discussed in Sec. 2.1.4 and of reflections of compression waves at a plain
open end in Sec. 2.8.1. As the reference acoustic velocity in air at 20°C is 343 m/s, which is
estimated to be the average propagation velocity on the simplistic grounds that the expansion
wave travels as much below sonic velocity as the compression wave is supersonic above it,
the expected return point in time by a very simple computation is:
time t = 0.00384 + 2 ( 5901 ~ 317 ) = 0.0364 second
1000 x 343
This approximate calculation can be seen to give an answer which is close to reality.
In Figs. 2.28 to 2.30 the individual waves can be seen clearly. The creation of the exhaust
pulse is accurate as can be seen in Figs. 2.28 and 2.29. Later it passes station 2 after 0.01
second. Steep-fronting of the compression wave has occurred as discussed in Sec. 2.1.5. In
Fig. 2.30 the steep-fronted compression wave reflects at the plain open end as an expansion
wave. The profile has changed little by the time it passes station 2 going leftward, but upon
returning to station 2 it has steepened at the rear of the expansion wave, again as discussed in
Sec. 2.1.5. It will be seen that a shock did not develop on the wave at any time even though the
long pipe runs provided the waves with the space and time to so comply.
Although the size and scale of the diagrams make it difficult to observe, nevertheless it
can be seen that the pressure at 0.01 second in Fig. 2.28 and at 0.02 second in Fig. 2.29 is
slightly above atmospheric. It can be seen that the pressure at 0.04 second in Fig. 2.30 is
slightly below atmospheric. These arise due to the main compression wave, and the expansion
wave reflection of it, sending their continual reflections due to friction in the opposite
direction to their propagation. As this is an important topic, a separate graph is presented in
174