Design and Simulation of Two Stroke Engines

Design and Simulation of Two-Stroke Engines
From Eq. 8.5.2, this means at frequencies of
a0 2a0 3a0 4a0 5a0
> » > » ? CIO.
2L b 2Lb 2Lb 2Lb 2Lb
At these frequencies the silencer will provide a transmission loss of zero, i.e., no silencing
effect at all, and such frequencies are known as the "pass-bands." It is also possible for the
silencer to resonate in the transverse direction through the diametral dimension, db, and provide
further pass-band frequencies at what would normally be a rather high frequency level.
There are many empirical equations in existence for the transmission loss of such a silencer,
but Kato and Ishikawa [8.18] state that the theoretical solution of Fukuda [8.9] is
found to be useful. The relationship of Fukuda [8.9] is as follows for the transmission loss of
a diffusing silencer, |3tr, in dB units:
where
and
Ptr=101og10(Ar2F(K,L)) 2 dB (8.5.3)
=
sin(KLb)xsin(KLt)
COS(KLJ) x COS(KL2)
K =
27tf
Not surprisingly, in such empirical relationships there are many correcting factors offered
for the modification of the basic relationship to cope with the effects of gas particle velocity,
end correction effects for pipes which are re-entrant or flush with the box walls, boxes which
are lined with absorbent material but not sufficiently dense as to be called an absorption
silencer, etc. I leave it to you to pursue these myriad formulae, should you be so inclined,
which can be found in the references.
To assist you with the use of the basic equations for design purposes, a simple computer
program is included in the Appendix Listing of Computer Programs as Prog.8.1, DIFFUSING
SILENCER. The attenuation equations programmed are those seen above from Fukuda, Eqs.
8.5.3-8.5.5.
To determine if such a design program is useful in a practical sense, an analysis of SYS­
TEM 2 and SYSTEM 3, emanating from Coates [8.3], is attempted and the results shown in
Figs. 8.12 and 8.13. They show the computer screen output from Prog.8.1, which are plots of
the attenuation in dB as a function of noise frequency up to a maximum of 4 kHz, beyond
which frequency most experts agree the diffusing silencer will have little silencing effect.
The theory would continue to predict some attenuation to the highest frequency levels, indeed
beyond the upper threshold of hearing. Also displayed on the computer screen are the input
data for the geometry of that diffusing silencer according to the symbolism presented in Fig.
a 0
558
(8.5.4)
(8.5.5)