Design and Simulation of Two Stroke Engines

Design and Simulation of Two-Stroke Engines
ear, it is possible to physically measure the pressure level caused by sound and to assign an
experimental number to that value. This number will not detail whether the sound is "wanted"
or "unwanted." As already pointed out, to some it will always be described as noise.
8.1.1 Transmission of sound
As discussed in Sec. 2.1.2, sound propagates in three dimensions from a source through
the air (or a gas) as the medium of its transmission. The fundamental theory for this propagation
is in Sec. 2.1.2. The speed of the propagation of a wave of acoustic amplitude is given by
ao, where:
a0=V^Tb=J— (8.1.1)
V Po
As shown in Sec. 2.1.6, the value for the ratio of specific heats, y, is 1.4 for air and 1.375
for exhaust gas when both are at a temperature around 25 °C, and for exhaust gas emanating
from a stoichiometric combustion. At such room temperature conditions, the value of the gas
constant, R, is 287 J/kgK for air and 291 J/kgK for the exhaust gas. Treating exhaust gas as air
in calculations for sound wave attenuation in silencers produces errors of no real significance.
For example, if the temperature is raised to 500 K, where y and R for air and exhaust
gas are taken from Sec. 2.1.6 and Table 2.1.3,
aair = Vl.373 x 287 x 500 = 444 m/s
a exhaust = Vl.35 x 290.8 x 500 = 443 m/s
As exhaust gas in a two-stroke engine contains a significant proportion of air which is
short-circuited during the scavenge process, this reduces the already negligible error even
further.
8.1.2 Intensity and loudness of sound
The propagation of pressure waves is already covered thoroughly in Sec. 2.1, so it is not
necessary to repeat it here. Sound waves are but small pressure waves. However, the propagation
of these small pressure pulses in air, following one after the other, varying in both spacing
and amplitude, gives rise to the human perception of the pitch and of the amplitude of the
sound. The frequency of the pressure pulsations produces the pitch and their amplitude denotes
the loudness. The human ear can detect frequencies ranging from 20 Hz to 20 kHz,
although as one becomes older that spectrum shortens to a maximum of about 12 kHz. For an
alternative introductory view of this topic, consult the books by Annand and Roe [1.8] and by
Taylor [8.11].
More particularly, the intensity, I, is used to denote the physical energy of a sound, and
loudness, (3, is defined in this book as the human perception of that intensity in terms of sound
pressure level. I am well aware that the term "loudness" is often defined differently in other
542