Design and Simulation of Two Stroke Engines

Chapter 2 - Gas Flow through Two-Stroke Engines
As in (c), the sudden contraction behaves like a partially closed end, sending back a
partial "echo" of the incident pulse. The onward transmitted pressure wave is also one of
expansion, but it should be noted that it has an increased expansion pressure ratio of 0.741.
The theoretical presentation here, due to Benson [2.4], is clearly too simple to be completely
accurate in all circumstances. It is, however, a very good guide as to the magnitude of
pressure wave reflection and transmission. The major objections to its use where accuracy is
required are that the assumption of "constant pressure" at the discontinuity in pipe area cannot
possibly be tenable over all flow situations and that the thermodynamic assumption is of
isentropic flow in all circumstances. A more complete theoretical approach is examined in
more detail in the following sections. A full discussion of the accuracy of such a simple
assumption is illustrated by numeric examples in Sec. 2.12.2.
2.10 Reflection of pressure waves at an expansion in pipe area
This section contains the non-isentropic analysis of unsteady gas flow at an expansion in
pipe area. The sketch in Fig. 2.8(a) details the nomenclature for the flow regime, in precisely
the same manner as in Sec. 2.9. However, to analyze the flow completely, the further information
contained in sketch format in Figs. 2.9(a) and 2.10(a) must also be considered.
In Fig. 2.10(a) the expanding flow is seen to leave turbulent vortices in the corners of the
larger section. That the streamlines of the flow give rise to particle flow separation implies a
gain of entropy from area section 1 to area section 2. This is summarized on the temperatureentropy
diagram in Fig. 2.9(a) where the gain of entropy for the flow falling from pressure psi
to pressure pS2 is clearly visible.
As usual, the analysis of flow in this quasi-steady and non-isentropic context uses, where
appropriate, the equations of continuity, the First Law of Thermodynamics and the momen-
Tl
T2
T0
ISENTROP CLINE
* ^
1
^y^
^^-
> 1
J
/
\yy j
2 y
(a) non-isentropic expansion (b) isentropic contraction
yPs1
/p p r
r >
ENTROPY
Fig. 2.9 Temperature entropy characteristics for simple expansions and contractions.
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