Design and Simulation of Two Stroke Engines

Design and Simulation of Two-Stroke Engines
At 7 and 8 are the valves or ports into the cylinder where, depending on the valve or port
opening schedule, acts as everything from a partially closed or open end to a cylinder at
varying pressures, to a complete "echo" situation when these valves or ports are closed. At 9
are bends in the ducting where the pressure wave is reflected from the deflection process in
major or minor part depending on the severity of the radius of the bend. At 10 in the exhaust
ducting are sudden expansion and contractions in the pipe. At 11 is a tapered exhaust pipe
which will act as a diffuser or a nozzle depending on the direction of the particle flow; wave
reflections ensue in both cases. At 12 is a restriction in the form of a catalyst, little different
from an air filter other than that chemical reactions are taking place at the same time; this
sentence is easily written but the theoretical calculations to predict the wave motion and the
thermodynamics of the reaction are somewhat more complex. At 13 is a re-entrant pipe to a
chamber which is a very common element in any silencer design. At 14 is an absorption
silencer element, a length of perforated pipe surrounded by packing, which acts as both diffuser
and the trimmer of sharp peaks on exhaust pulses; by definition it provides wave reflections.
At 15 is a plain-ended exhaust pipe entering the atmosphere and here too pressure wave
reflections take place.
The above tour of the pressure wave routes in and out of an engine is far from a complete
description of the processes but it is meant to illustrate both the complexity of the events and
to postulate that, without a complete understanding of every and all possibilities for wave
reflection in and through an internal-combustion engine, none can seriously declaim to be a
designer of engines.
The resulting pressure-time history is complicated and beyond the memory-tracking capability
of the human mind. Computers are the type of methodical calculation tool ideal for
this pedantic exercise, and you will be introduced to their use for this purpose. Before that
juncture, it is essential to comprehend the basic effect of each of these reflection mechanisms,
as the mathematics of their behavior must be programmed in order to track the progress of all
incident and reflected waves.
The next sections of this text analyze virtually all of the above possibilities for wave
reflection due to changes in pipe or duct geometry and analyze the reflection and transmission
process which takes place at each juncture.
2.6.1 Notation for reflection and transmission of pressure waves in pipes
A wave arriving at a position where it can be reflected is called the incident wave. In the
paragraphs that follow, all incident pressure waves, whether they be compression or expansion
waves, will be designated by the subscript "i," i.e., pressure pj, pressure ratio Pj, pressure
amplitude ratio Xj, particle velocity q, density pj, acoustic velocity aj, and propagation velocity
CCJ. All reflections will be designated by the subscript "r," i.e., pressure pr, pressure ratio
Pr, pressure amplitude ratio Xr, particle velocity cr, density pr, acoustic velocity ar, and propagation
velocity ccr. All superposition characteristics will be designated by the subscript "s,"
i.e., pressure ps, pressure ratio Ps, pressure amplitude ratio Xs, particle velocity cs, density ps,
acoustic velocity as, and propagation velocity ccs.
Where a gas particle flow regime is taking place, it is always considered to flow from gas
in regime subscripted with a "1" and flowing to gas in a regime subscripted by a "2." Thus the
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