Design and Simulation of Two Stroke Engines

Chapter 2 - Gas Flow through Two-Stroke Engines
direction of propagation. This means that an exhaust pulse arriving at an open end is sending
suction reflections back toward the engine which will help to extract exhaust gas particles
further down the pipe and away from the engine cylinder. Clearly this is a reflection to be
used by the designer so as to aid the scavenging, i.e., emptying, of the cylinder of its exhaust
gas. The numerical data below emphasize this point.
To get a basic understanding of the results of employing this theory for the calculation of
reflection of compression waves at the atmospheric end of a pipe, consider an example using
the compression pressure wave, pe, previously used in Sec. 2.1.4.
Recall that the wave pe is a compression wave of pressure ratio 1.2. In the nomenclature
of this section it becomes the incident pressure wave pj at the open end. This pressure ratio is
shown to give a pressure amplitude ratio, Xj, of 1.02639. Using Eq. 2.8.1, the reflected pressure
amplitude ratio, Xr, is given by:
Xr = 2 - Xj = 2 - 1.02639 = 0.9736
or pr = Xp 7 = 0.9736 7 = 0.8293
That the reflection of a compression wave at the open end is a rarefaction wave is now
evident numerically.
2.8.2 Reflection of an expansion wave at a bellmouth open end in a pipe
This reflection process is connected with inflow and therefore it is necessary to consider
the fluid mechanics of the flow into a pipe. Inflow of air in an intake system, which is the
normal place to find expansion waves, is usually conducted through a bellmouth-ended pipe
of the type illustrated in Fig. 2.7. This form of pipe end will be discussed in the first instance.
The analysis of gas flow to and from a thermodynamic system, which may also be experiencing
heat transfer and work transfer processes, is analyzed by the First Law of Thermodynamics.
The theoretical approach is to be found in any standard textbook on thermodynamics
[5.11]. In general this is expressed as:
A(heat transfer) + A(energy entering) = A(system energy) +
A(energy leaving) + A(work transfer)
The First Law of Thermodynamics for an open system flow from the atmosphere to the
superposition station at the full pipe area in Fig. 2.7(d) is as follows:
6 Am h 5E Am h
Qsystem + 0 0 + ~f" = system + s s + ^ + SWsystem (2.8.4)
V
2 < c^
7
V
2 J
If the flow at the instant in question can be presumed to be quasi-steady and steady-state
flow without heat transfer, and also to be isentropic, then AQ, AW, and AE are all zero. The
93