Design and Simulation of Two Stroke Engines

Design and Simulation of Two-Stroke Engines
It will be seen that the density is reduced in the more ratified expansion wave. The pipe
area is identical as the diameter is unchanged, i.e., Aj = 0.000491 m 2 . The mass rate of flow is
in the opposite direction to the wave propagation as:
mj = pjAjCj = 1.0272 x 0.000491 x (-53.87) = -0.0272 kg/s
2.1.5 Distortion of the wave profile
It is clear from the foregoing that the value of propagation velocity is a function of the
wave pressure and wave temperature at any point on that pressure wave. It should also be
evident that, as all of the points on a wave are propagating at different velocities, the wave
must change its shape in its passage along any duct. To illustrate this the calculations conducted
in the previous section are displayed in Fig. 2.2. In Fig. 2.2(a) it can be seen that both
the front and tail of the wave travel at the reference acoustic velocity, ao, which is 53 m/s
slower than the peak wave velocity. In their travel along the pipe, the front and the tail will
keep station with each other in both time and distance. However, at the front of the wave, all
of the pressure points between it and the peak are traveling faster and will inevitably catch up
with it. Whether that will actually happen before some other event intrudes (for instance, the
wave front could reach the end of the pipe) will depend on the length of the pipe and the time
interval between the peak and the wave front. Nevertheless, there will always be the tendency
for the wave peak to get closer to the wave front and further away from the wave tail. This is
known as "steep-fronting." The wave peak could, in theory, try to pass the wave front, which
is what happens to a water wave in the ocean when it "crests." In gas flow, "cresting" is
impossible and the reality is that a shock wave would be formed. This can be analyzed theoretically
and Bannister [2.2] gives an excellent account of the mathematical solution for the
particle velocity and the propagation velocity, ocsh, of a shock wave of pressure ratio, Psh,
propagating into an undisturbed gas medium at reference pressure, po, and acoustic velocity,
ao. The derivation of the equations set out below is presented in Appendix A2.2. The theoretically
derived expressions for propagation velocity, ash, and particle velocity, csh, of a compression
shock front are:
p . Pe
Po
y+1 y-1
a sh =a0lrr— p sh +
c sh =
= a oV G 67 p sh + G 17
Y + l ^
a sh
a shy
(2.1.24)
a0(Psh ~ 1) (2-1-25)
YVG67Psh + G17
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