Design and Simulation of Two Stroke Engines

Design and Simulation of Two-Stroke Engines
P2
T2
P2
C2
A2
Pr2
-Pi2
Fig. 2.76 Outflow from a cylinder or plenum to a pipe.
The solution of the gas dynamics of the flow must include separate treatments for subsonic
outflow and sonic outflow. The first presentation of the solution for this type of flow
was by Wallace and Nassif [2.5] and their basic theory was used in a computer-oriented
presentation by Blair and Cahoon [2.6]. Probably the earliest and most detailed exposition of
the derivation of the equations involved is that by McConnell [2.7]. However, while all of
these presentations declared that the flow was analyzed non-isentropically, a subtle error was
introduced within the analysis that negated that assumption. Moreover, all of the earlier solutions,
including that by Bingham [2.19], used fixed values of the cylinder properties throughout
and solved the equations with either the properties of air (y = 1.4 and R = 287 J/kgK) or
exhaust gas (y = 1.35 and R = 300 J/kgK). The arithmetic solution was stored in tabular form
and indexed during the course of a computation. Today, that solution approach is inadequate,
for the precise equations in fully non-isentropic form must be solved at each instant of a
computation for the properties of the gas which exists at that location at that juncture.
Since a more complex solution, i.e., that for restricted pipes in Sect. 2.12, has already
been presented, the complete solution for outflow from a cylinder or plenum in an unsteady
gas-dynamic regime will not pose any new theoretical difficulties.
The case of subsonic particle flow will be presented first and that for sonic flow is given
in Sec. 2.16.1.
In Fig. 2.16 the expanding flow from the throat to the downstream superposition point 2
is seen to leave turbulent vortices in the corners of that section. That the streamlines of the
flow give rise to particle flow separation implies a gain of entropy from the throat to area
section 2. On the other hand, the flow from the cylinder to the throat is contracting and can be
considered to be isentropic in the same fashion as the contractions debated in Sees. 2.11 and
2.12. This is summarized on the temperature-entropy diagram in Fig. 2.17 where the gain of
entropy for the flow rising from pressure pt to pressure pS2 is clearly visible. The isentropic
nature of the flow from pi to pt, a vertical line on Fig. 2.17, can also be observed.
The properties and composition of the gas particles are those of the gas at the exit of the
cylinder to the pipe. The word "exit" is used most precisely. For most cylinders and plenums
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