Design and Simulation of Two Stroke Engines

Design and Simulation of Two-Stroke Engines
column labeled "E or C" describes whether the flow encountered was at an expansion (E) or
a contraction (C) in pipe area.
Table 2.12.3 Output data from the calculations using the more complex theory
No.
1
2
3
4
5
6
Pn
0.8850
0.9036
1.1227
1.1292
1.1371
1.0174
Pf2
1.0785
1.0746
1.3118
1.2886
1.2595
1.0487
mg/s
46.38
43.91
48.70
44.69
39.77
27.98
T02K
294.5
296.2
293.0
295.2
298.1
306.7
Theory
Sec. 2.10
Sec. 2.12
Sec. 2.11
Sec. 2.12
Sec. 2.12
Sec. 2.12
For simple expansions, in test data sets 1 and 2, the constant pressure theory works remarkably
well with an almost negligible error, i.e., less than 3% in mass flow rate terms. If the
expansion has a realistic coefficient of discharge of 0.85 applied to it then that error on mass
flow rate rises slightly from 2.65 to 2.8%. The magnitudes of the reflected pressure waves
compare quite favorably in most circumstances.
At a simple sudden contraction in test data sets 3 and 4, even with a coefficient discharge
of 1.0 the mass flow rate error is significant at 8.2%, rising to 17.9% error when the quite
logical Cd value of 0.7 is applied to the sudden contraction. The magnitudes of the reflected
pressure waves are significantly different when emanating from the simple and the complex
theories.
When any form of restriction is placed in the pipe, i.e., in test data sets 5 and 6 for an
expansion and a contraction, respectively, the constant pressure theory is simply not capable
of providing any relevant information either for the magnitude of the reflected wave or for the
mass flow rates. The error is greater for expansions than contractions, which is the opposite
of the situation when restrictions in the pipe are not present. Note the significant entropy
gains in tests 4-6.
The constant pressure theory is seen to be reasonably accurate only for flow which encounters
sudden expansions in the ducting.
2.13 An introduction to reflections of pressure waves at branches in a pipe
The simple theoretical treatment for this situation was also suggested by Benson [2.4]
and in precisely the same form as for the sudden area changes found in the previous section.
A sketch of a typical branch is shown in Fig. 2.13. The sign convention for all of the branch
theory presented here is that inward propagation of a pressure wave toward the branch will be
regarded as "positive." Benson [2.4] postulates that the superposition pressure at the junction,
at any instant of wave incidence and reflection, can be regarded as a constant. This is a
straightforward extension of his thinking for the expansion and contractions given in Sec. 2.9.
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