3) The peak combustion pressures are lower in the equivalent two-stroke cycle engine, so the noise spectrum induced by that lesser combustion pressure is reduced
8.4.1 The theoretical work of Coates(8.3)
In those publications, a theoretical solution is produced(8.3) which shows that the sound pressure level at any point in space beyond the termination of an exhaust system into the atmosphere is, not empirically, but directly capable of being calculated. The amplitude of the nth frequency component of the sound pressure, Pn, is shown to be primarily a complex function of: (a) the instantaneous mass flow rate leaving the end of the pipe system, q, and (b) the location of the measuring microphone in both distance and directivity from the pipe end, together with other parameters of some lesser significance.
For any sinusoidal variation, the mean square sound pressure level, Prms, of that nth frequency component is given by:
Prmsn2 =Pn2/2
From this the rms sound pressure level, Lpn, of the nth frequency component is found from:
Lpn=10*log,0[Prmsn2/4*1010] dB
The theoretical analysis hinges on being able to calculate the instantaneous mass flux-time history, q, at the termination of the pipe system to the atmosphere and to conduct a Fourier analysis(8.20) of it over a complete cycle. From this Fourier
analysis it becomes possible to establish the component harmonics of the mass flow rate, qn, and hence the corresponding pressure amplitudes, Pn.
It will be recalled from Chapter 2, that the unsteady gas flow calculation by the method of characteristics involves tracking Riemann variables by a mesh method of calculation along an entire pipe system, including in this case the presence of silencer components installed within it. Assuming that the mesh location at the termination of the pipe to atmosphere is denoted by z, then the instantaneous mass flow rate is given by q, where D is density, F is area, CG is superposition particle velocity and g is the ratio of specific heats:
q=Dz*CGz*Fz
=[Do*Xz<2/(e-")]*[(2/(g-l))*Ao*(Xz-l)]*Fz
=[Do*((3z+Bz)/2),2/|8-1»]*[Ao*Oz-6z)/(g-l)]*Fz
This relationship for mass flow rate is the same as that deduced in Eq. 2.4.10. It will be observed that the accuracy of the solution depends on the ability of the theoretical calculation to trace the Riemann variables, d and 6, to the very end of the most complex pipe and silencer system. How successful that can be may be judged from some of the results presented by Coates(8.3).
8.4.2 The experimental work of Coates(8.3)
The experimental rig used by Coates is described clearly in that technical paper(8.3), but a summary here will aid the discussion of the experimental results and their correlation with the theoretical calculations. The exhaust system is simulated by a rotary valve which allows realistic exhaust pressure pulses of cold air to be blov, n down into a pipe system at any desired cyclic speed for those exhaust pressure pulsations. The various pipe systems attached to the exhaust simulator are shown in Fig. 8.2, and are defined as SYSTEMS 1-4. Briefly, they are as follows:
SYSTEM 1 is a plain, straight pipe of 28.6 mm diameter, 1.83 m long and completely unsilenced.
SYSTEM 2 has a 1.83m plain pipe of 28.6 mm diameter culminating in what is termed adiffusing silencer which is 305 mm long and 76 mm diameter. The tail pipe, of equal size to the entering pipe, is 152 mm long.
SYSTEM 3 is almost identical to SYSTEM 2 but has the entry and exit pipes reentering into the diffusing silencer so that they are 102 mm apart within the chamber.
SYSTEM 4 has what is defined as a side-resonant silencer placed in the middle of the 1.83 m pipe, and the 28.6 mm diameter through-pipe has 40 holes drilled into it of 3.18 mm diameter.
More formalized sketches of diffusing, side resonant and absorption silencers are to be found in Figs. 8.7-8.9. Further discussion of their silencing effect, based on an acoustic analysis, will be found in Sect. 8.5. It is sufficient to remark at this juncture that:
(a) The intent of a diffusing silencer is to absorb all noise at frequencies other than those at which the box will resonate. Those frequencies which are not absorbed are called the pass-bands.
SYSTEM 1
L, 1830
| 028.6
SYSTEM 2
1830
| 028.f
305
V
52
•*—•
y A
l0 7 6 028.6
SYSTEM 3
1780 076
| 028.I
SYSTEM 4
50 53
305 52 028.6
*• • * - * •
254
1830
028.6 perforated section of
5 rows of 8 holes / each hole 03.18 equispaced '
305
f
ooooo
076 0 52 -*—>-
.
28.6
Fig. 8.2 Various exhaust systems and silencers used by Coates and Blair(8.3).
(b) The intent of a side-resonant silencer is to completely absorb noise of a specific frequency, such as the fundamental exhaust pulse frequency of an engine.
(c) The intent of an absorption silencer is to behave as a diffusing silencer, but to have the packing absorb the resonating noise at the pass-band frequencies.
The pressure-time histories within these various systems, and the one-third octave noise spectrograms emanating from these systems, were recorded. Of interest are the noise spectra and these are shown for SYSTEMS 1-4 in Figs. 8.3- 8.6, respectively. The noise spectra are presented in the units of overall sound
Chapter 8 - Reduction of Noise Emission from Two-Stroke Engines pressure level, dBlin, as a function of frequency. There are four spectrograms on any given figure: the one at the top is where the measuring microphone is placed directly in line with the pipe end and the directivity angle is declared as zero, and the others are at angles of 30,60 and 90s. The solid line on any diagram is the measured noise spectra and the dashed line is that emanating from the theoretical solution outlined in Sect. 8.4.1. It can be seen that there is a very good degree of correlation between the calculated and measured noise spectra, particularly at frequency levels below 2000 Hz.
Of interest is the prediction of the mass flow spectrum at the termination of SYSTEM 1, which is shown in Fig. 8.10. It is predicted by the insertion of the appropriate data for the geometry and cylinder conditions of SYSTEM 1 into a slightly modified version of Prog.2.1, where the graphic output is altered to demonstrate the instantaneous mass flow rate at the termination to the atmosphere of a plain straight pipe. In other words, Eq. 2.4.10 is programmed as output data rather than the familiar pressure diagrams shown in Chapter 2. If one examines Fig.
8.10, the mass flow rate leaving the pipe end of SYSTEM 1 at a simulator rotor valve speed of 1000 rpm, i.e., a cycling rate of 2000 exhaust pulses created per minute as explained by Coates(8.3), one can see that there are four basic oscillations of the mass flow rate during one complete cycle. Thus, a Fourier analysis of this spectrum would reveal a fundamental frequency of 4*2000/60, or 133.3 Hz. If the theoretical postulations of Coates(8.3) have any validity, then this should show up clearly as the noisiest frequency in the measured noise spectra for that same rotor speed, as illustrated in Fig. 8.3. In that diagram, the fundamental, and noisiest frequency is visibly at 133 Hz. The theoretical solution of Coates, as would be expected from the above discussion because his calculation is also conducted by the method of
6-0* I0O0 RPM
25 IOO I00O H i — 10,000 25 100 IOOO Hi 10,000
Fig. 8.3 One-third noise spectrogram from SYSTEM 1.
The Basic Design of Two-Stroke Engines
e-0* i ooo
RPM25 „ IOO IOOO H i — IO.OOO e-9d"
I 2 0 | i i i i •—i—i—i r i i—i i i i i i i i i i—i i i ' i i
Fig. 8.4 One-third noise spectrogram from SYSTEM 2.
characteristics, also agrees with the prediction of 133 Hz as the noisiest frequency.
Perhaps the most important conclusion to be drawn from this result is that the designer of silencing systems, having the muffling of the noisiest frequency as afirst priority, can use the unsteady gas-dynamic modelling programs as a means of prediction of the mass flow rate at the pipe termination to atmosphere, be it the inlet
Chapter 8 - Reduction of Noise Emission from Two-Stroke Engines
* * i i 1 1 • 1 1 — • t • 1 1 1
IOOO Hi- 10,000
Fig. 8.5 One-third noise spectrogram from SYSTEM 3.
or the exhaust system, and from that mass flow rate calculation over a complete cycle determine the fundamental noisiest frequency to be tackled by the silencer.
Of direct interest is the silencing effect of the various silencer elements attached
to the exhaust pipe by Coates, SYSTEMS 2-4, the noise spectra for which are shown
2 5 IOO IOOO H i — IO.OOO Fig. 8.6 One-third noise spectrogram from SYSTEM 4.
in Figs. 8.4-8.6. The SYSTEM 2, a simple diffusing silencer without reentrant pipes, can be seen to reduce the noise level of the fundamental frequency at 133 Hz from 116 dB to 104 dB, an attenuation of 12 dB. From the discussion in Sect. 8.1.2, an attenuation of 12 dB is a considerable level of noise reduction. It will also be observed that a large "hole," or strong attenuation, has been created in the noise
Chapter 8 - Reduction of Noise Emission from Two-Stroke Engines
LB
J 1
S1
•
L1
SB
i L
1
L2
Q^T
S2J
LT „
Fig. 8.7 Significant dimensions of a diffusing silencer element.
1.
SB
• r
SH / NH
LB
m L H *
o o o o o o c o o o o o o c o o o o o o c /
i r
J L
TH
j
S3
1 L
r W-
Fig. 8.8 Significant dimensions of a side-resonant silencer element.
spectra of SYSTEM 2 at a frequency of 400 Hz. In Sect. 8.5.1 this will be a source of further comment when an empirical frequency analysis is attempted for this particular design.
The noise spectra for SYSTEM 3, a diffusing silencer with reentrant pipes, is shown in Fig. 8.5. The noise level of the fundamental frequency of 133 Hz has been reduced further to 98 dB. The "hole" of high attenuation is now at 300 Hz and deeper than that recorded by SYSTEM 2.
LB
-SOUND ABSORPTION PACKING MATERIAL
o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o
o o o o o o o o o o o o o o o o o
S3S H // NH
Fig. 8.9 Significant dimensions of an absorption silencer.
EXHAUST SIMULATOR ROTOR SPEED=1000 rpm
3605
Fig. 8.10 Mass flow rate at the termination of pipe SYSTEM 1 to atmosphere.
The noise spectra for SYSTEM 4 is shown in Fig. 8.6. This is a side-resonant silencer. The noise level of the fundamental frequency of 133 Hz is nearly as quiet as SYSTEM 2, but a new attenuation hole has appeared at a higher frequency, about 500 Hz. This, too, will be commented on in Sect. 8.5.2 when an empirical acoustic analysis is presented for this type of silencer. It can also be seen that the noise level at higher frequencies, i.e., above 1000 Hz, is reduced considerably from the unsilenced SYSTEM 1.
The most important conclusion from this work by Coates is that the noise propagation into space from a pipe system, with or without silencing elements, could be predicted by a theoretical calculation based on the motion of finite
Chapter 8 - Reduction of Noise Emission from Two-Stroke Engines amplitude waves propagating within the pipe system to the pipe termination to the atmosphere. In other words, there did not have to be a reliance by designers on empirically based acoustic equations for the design of silencers, be they for the intake or the exhaust system, for internal combustion engines.