Design and Simulation of Two Stroke Engines

Design and Simulation of Two-Stroke Engines
Table 2.14.5 Further output data regarding errors on mass flow
Test no.
1
2
3
4
rtV| err%
2.49
1.01
0.32
4.85
rh2 err%
13.29
11.70
4.13
16.67
rh3 err%
6.73
3.79
0.27
20.0
iterations
It can be seen in test number 1 that the constant pressure theory takes no account of the
branch angle, nor of the non-isentropic nature of the flow, and this induces mass flow differences
of up to 13.3% by comparison with the more complex theory. The actual values of the
reflected pressure waves are quite close for both theories, but the ensuing mass flow error is
significant and is an important argument for the inclusion of the more complex theory in any
engine simulation method requiring accuracy. In test number 2 the results are closer, i.e., the
mass flow errors are smaller, an effect induced by virtue of the fact that the larger diameter of
pipe 3 at 35 mm reduces the particle velocity into pipe 2. As the pressure loss around the
intersection into pipe 2, which is angled back from pipe 1 at 30°, is seen from Eq. 2.14.1 to be
a function of the square of the superposition velocity c^2> men that decreases the pressure loss
error within the computation and in reality. This effect is exaggerated in test number 3 where,
even though the pipe diameters are equal, the suction wave incident at pipe 3 also reduces the
gas particle velocity entering pipe 2; the errors on mass flow are here reduced to a maximum
of only 4.1%. The opposite effect is shown in test number 4 where an opposing compression
wave incident at the branch in pipe 3 forces more gas into pipe 2; the mass flow errors now
rise to a maximum value of 20%.
In all of the tests the amplitudes of the reflected pressure waves are quite close from the
application of the two theories but the compounding effect of the pressure error on the density,
and the non-isentropic nature of the flow derived by the more complex theory, gives rise
to the more serious errors in the computation of the mass flow rate by the "constant pressure"
theory.
2.15 Reflection of pressure waves in tapered pipes
The presence of tapered pipes in the ducts of an engine is commonplace. The action of the
tapered pipe in providing pressure wave reflections is often used as a tuning element to significantly
enhance the performance of engines. The fundamental reason for this effect is that
the tapered pipe acts as either a nozzle or as a diffuser, in other words as a more gradual
process for the reflection of pressure waves at sudden expansions and contractions previously
debated in Sees. 2.10 and 2.11. Almost by definition the process is not only more gradual but
more efficient as a reflector of wave energy in that the process is more efficient and spread out
in terms of both length and time. As a consequence, any ensuing tuning effect on the engine is
not only more pronounced but is effective over a wider speed range.
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2
2
2
2