Design and Simulation of Two Stroke Engines

Design and Simulation of Two-Stroke Engines
It is obvious that exhaust pulses resulting from cylinder blowdown come under the heading
of compression waves, and expansion waves are generated by the rapidly falling crankcase
pressure during induction in the case of the two-stroke engine, or cylinder pressure for a
four-stroke cycle unit. However, as in most technologies, other expressions are used in the
literature as jargon to describe compression and expansion waves. Compression waves are
variously called "exhaust pulses," "compression pulses" or "ramming waves." Expansion
waves are often described as "suction pulses," "sub-atmospheric pulses" or "intake pulses."
However, as will be seen from the following sections, expansion and compression waves do
appear in both inlet and exhaust systems.
2.1.2 Propagation velocities of acoustic pressure waves
As already pointed out, acoustic pressure waves are pressure waves where the pressure
amplitudes are small. Let dp be the pressure difference from atmospheric pressure, i.e., (pe - po)
or (po - pi), for the compression or expansion wave, respectively. The value of dp for Fred's
"boo" would be on the order of 0.2 Pa. The pressure ratio, P, for any pressure wave is defined
as the pressure, p, at any point on the wave under consideration divided by the undisturbed
pressure, po- The undisturbed pressure is more commonly called the reference pressure. Here,
the value for Fred's "boo" would be:
P = JL = 101 ' 325 - 2 = 1.000002
PO 101,325
For the loudest of acoustic sounds, say a rifle shot at about 0.2 m away from the human
ear, dp could be 2000 Pa and the pressure ratio would be 1.02. That such very loud sounds are
still small in pressure wave terms can be gauged from the fact that a typical exhaust pulse in
an engine exhaust pipe has a pressure ratio of about 1.5.
According to Earnshaw [2.1], the velocity of a sound wave in air is given by ao, where:
a0 = VYRIb (2.1.1)
The value denoted by y is the ratio of specific heats for air. In the above equations, TQ is
the reference temperature and po is the reference density, which are related to the reference
pressure, po, by the state equation:
po = PoRT0
(2.1.3)
For sound waves in air, po, TQ and po are the values of the atmospheric pressure, temperature
and density, respectively, and R is the gas constant for the particular gas involved.
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