42.8 Practical Example of Dissipative Muffler

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An example is given on the design of a dissipative

muffler for noise reduction in an axial-flow fan for

a ventilation system.

1. Specification of the axial-flow fan

* Volume flow rate: Q ¼ 125 m3/min

* Wind pressure: p ¼ 80 mm Aq

* Rotor blade number: Z ¼ 10

* Stationary blade number: Zs ¼ 5

* Rotational speed: N ¼ 2580 rpm

* Shaft horsepower: P ¼ 3.75 kW

2. The desired values of attenuation and head

loss with the muffler installation follow. The

noise of the fan propagates both intake and

discharge sides. A performance level (noise

reduction) of about 37.5 dB is required, when specific sound level Ks is obtained on the basis of the

axial-flow fan specification given by

Ks ¼ LA 2 10 log10ðp2QÞ ð42:31Þ

3. Figure 42.19 gives the noise spectrum for the axial-flow fan. The blade passing frequency, BPF, is a

fundamental component of the velocity fluctuation as the flow passes the blades. It is seen in the

noise spectrum in Figure 42.19 at 430 Hz ðQ £ Z ¼ ð2580=60Þ £ 10Þ: By adding the background

noise spectrum to this spectrum, it is seen that a muffler that provides an attenuation over 20 dB

near 430 Hz, and about 15 dB in the frequency range of 800 to 1000 Hz is necessary.

The head loss value of the muffler is to be maintained within 4 mm Aq.

FIGURE 42.18 Degradation of the absorption coefficient

by water content.

FIGURE 42.19 Noise spectrum of the axial flow fan of a factory ventilation system.

Design of Absorption 42-17

© 2005 by Taylor & Francis Group, LLC

4. The structure of the dissipative muffler is shown in Figure 42.20. The maximum value of outer

diameter of the muffler is 750 mm, and the length chosen to optimize the performance.

5. The packing density of glass wool is chosen as 65 kg/m3. The surface treatment of glass wool uses

perforated metal with 1 mm thickness, 36% open area with 6 mm hole diameter. A sound

absorption body of 200 mm diameter is supported in the center part, and it is welded to the outside

cylinder by three props in the flow direction, and two in the circumferential direction.

6. The attenuation characteristics of the dissipative muffler may be calculated using Equation 42.27

TL ¼ 10 log10 1 þ

1

2

agmkle

􀀘 􀀙2 􀀒 􀀓

The proportion of the volume of glass wool filled into the muffler is approximately

(0.752 2 0.552 þ 0.22)/0.752 ¼ 0.53. For a packing density of 100 kg/m3, we have 0.53 £ 65/

100 ¼ 0.347. The value of ag < 0.6 is obtained from Table 42.2.

The required expansion ratio, m; length, le; and wave number, k; are given by

m ¼ ð750=500Þ2 ¼ 2:25; le ¼ 1:2 m; k ¼ 2pf =c

The speed of sound c depends on the environmental temperature. For a temperature of 258C, we get

346.5 m/sec (¼ 331.5 þ 0.6 £ 25). The TL values at 100 to 1000 Hz are calculated. We have

f ¼ 100 Hz; TL ¼ 5:0 dB

f ¼ 430 Hz; TL ¼ 16:1 dB

f ¼ 1000 Hz; TL ¼ 23:4 dB

The flow velocity satisfies desired value of head loss ploss (in mm Aq), and is calculated by following

empirical equation [12]:

ploss ¼ 0:142m20:1

f

le

d1

􀀏 􀀐3=4 dm

d1

􀀏 􀀐21=3

( )

u2

g ð42:32Þ

Use the numerical values as follows:

* mf ¼ (550/500)2 ¼ 1.21, ratio of cross-sectional area between air passage and muffler.

* d1 ¼ 500 mm, diameter of inlet.

* le ¼ 1.2 m, length of muffler.

* dm ¼ 200 mm, diameter of absorption body.

* u ¼ 10 m/sec or less, flow velocity at inlet.

* g ¼ 9.8 m/sec2, acceleration of gravity force.

FIGURE 42.20 Half cross-sectional view of dissipative muffler for the axial flow fan.

42-18 Vibration and Shock Handbook

© 2005 by Taylor & Francis Group, LLC

The corresponding head loss is 3.25 mm Aq, which corresponds to JIS B 833, and nearly agrees with

the predicted value. Specifically, the condition of 4 mm Aq or less of the designed value is satisfied.

The connection of axial-flow fan and the muffler uses vibration isolation, using the thick synthetic

rubber.

7. The result of the attenuation realized from the spectrum after the muffler installation is shown in

Figure 42.21. It is proven that the attenuation characteristics almost parallel the designed value. The

frequency range where the approximation is valid is given by

f , c=d ¼ 346:5=0:175 ¼ 1980 Hz

For frequencies below 250 Hz, the estimated result of the attenuation becomes slightly

overestimated.

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