Introduction to Acoustics

Static efficiency normalized to its maximum value
1.00
0.80
0.60
0.40
0.20
0
0
0.020
0.040
0.060 0.080 0.100
Volume flow rate (m 3 /s)
Fig. 23.16 Illustration of air-moving device static efficiency
for a constant input power
large devices. In the design of small ventilating systems,
the system resistance is often not known accurately, and
optimal design may be difficult to achieve. However,
an operating point to the left of the point of maximum
static efficiency is usually undesirable, both from the
viewpoint of flow instability and increased noise.
The choice of a type of air-moving device is usually
dictated by the desired specific speed Ns defined as
Ns = NQ1/2
P3/4 , (23.36)
where N is the rotational speed of the air moving device,
and P and Q are defined above. Axial flow devices are
generally used at low pressures and high-volume flow
rates (high specific speed), and centrifugal devices are
usually used at relatively high pressures and low-volume
flow rates (low specific speed).
For noise radiation from large air-moving devices,
it is often useful to use a sound law first proposed by
Madison [23.78]. Its validity depends on the point of rating
for a homologous series of air-moving devices. For
such a series, it is useful to define dimensionless parameters,
the pressure coefficient ψ and the flow coefficient
φ as:
2P
ψ = , (23.37)
2 ρ (π DN)
φ = Q
π D3 , (23.38)
N
where D is a characteristic dimension (diameter), and
N is the rotational speed of the device. Then, the performance
curve for any device in the series can be expressed
Noise 23.2 Noise Sources 985
as a single curve of ψ versus φ and the operating point
discussed above becomes the point of rating for the
series.
The sound law is then
W = Ws × P2 Q
P2 0 Q0
, (23.39)
where Ws is the specific sound power, and W is the
radiated sound power of the device P0 and Q0 are 1 Pa
and 1 m 3 /s, respectively.
No frequency dependence was given in (23.39), but
values of Ws are often published in octave bands. It must
be emphasized that (23.39) is valid only at a given point
of rating. If the operating point goes from shutoff (P = 0)
to free discharge (Q = 0), the point of rating is changing,
and the radiated sound power does not go to zero at these
extremes; in fact, it generally increases, as illustrated in
Fig. 23.17. The above sound law is most useful in the
design of large systems when the system resistance is
known and the air-moving device operates near its point
of maximum static efficiency. Using (23.37), (23.38),
and (23.39), it can be shown that at a given point-ofrating,
the sound power is proportional to the fifth power
of the speed of the device.
For small air-moving devices, it is most meaningful
to obtain sound power level data on the device itself,
usually as a function of speed, operating point, or both.
An apparatus for determination of sound power of small
devices has been standardized both nationally and internationally
[23.79,80]andisshowninFig.23.18 [23.81].
The AMD is mounted on a flexible membrane for airborne
noise tests. Small fans mounted on lightweight
structures are known to transmit energy into the structure,
which can then be radiated as sound. The same test
apparatus can also be used for evaluation of the structureborne
vibration of small AMDs if the membrane is
replaced by a specially designed plate [23.82].
Relative A-weighted sound power level (dB)
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0
0.020
0.040
0.060
0.080 0.100 0.120
Flow rate (m 3 /s)
Fig. 23.17 An illustration of relative sound power level as
a function of flow for a small air-moving device
Part G 23.2