42.5 Attenuation of Lined Ducts

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42.5.1 Computation of Attenuation in a Lined Duct

A lined duct is an air passage with one or more of

the interior surfaces covered with an acoustical

material such as a glass or mineral fiber blanket.

The parallel baffles are merely a series of side-byside

ducts that generally have a rectangular or

round cross section. If the walls are covered with

absorptive material, attenuation will occur because

of the viscous motion of the air in and out of the

porous of blanket.

Figure 42.7 shows an isometric illustration of a

lined duct. The attenuation of sound for a lined

duct is dependent primarily on the duct length, le;

the thickness of the lining, b; the density of the

lining, r; the width of the air passage, l; and

the wavelength of sound, l: At low frequencies

ðl=l , 0:1Þ; the attenuation of sound in a lined

duct may be calculated from the following

empirical formula:

ATT ¼ KlP=S ð42:24Þ

where

Kl ¼ the coefficient, which is determined

from the random incidence absorption coefficient

of lined material, given in the chart of

Figure 42.8

P ¼ acoustically lined perimeter of duct (m)

S ¼ cross-sectional open area of duct (m2)

If the absorbing material is lined in the

rectangular cross section as shown in Figure 42.9

to Figure 42.11, the attenuation can be estimated

using the formulas given in Table 42.3 [5].

42.5.2 Attenuation in a Lined Bend

A lined bend duct is shown in Figure 42.12.

The insertion loss, IL, of a lined bend results from

two mechanisms: the reflection of sound back

toward the source side, and the scattering of sound

energy into the high-frequency region is rapidly

attenuated by the lining beyond the bend. Higherfrequency

modes will be attenuated by even an

unlined duct for frequencies below the ratio of the

air passage between the linings to the wavelength

of sound equal to 0.5. At frequencies well above

this ratio, the insertion loss of a lined bend is

expected to be comparable to the reverberant-field

FIGURE 42.7 Illustration of a lined duct.

2

1

0

0 0.5 1

Kl

a

FIGURE 42.8 Kl value for sound-absorption coefficient

by reverberation room method.

42-10 Vibration and Shock Handbook

© 2005 by Taylor & Francis Group, LLC

end correction derived for the duct. The insertion loss of a lined bend may be obtained as following

equation [6]:

IL ¼

KlP

S þ ðl1 þ l2Þ þ F ð42:25Þ

where F is obtained from Figure 42.13.

FIGURE 42.9 Duct-liner configurations corresponding to Table 42.3.

120

110

100

90

80

70

60

50

40

30

20

10

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

1

2

3

4

5

6

7

8

9

10

11

12

Absorption Coefficient a

n

n

FIGURE 42.10 Relationship between absorption coefficient and stationary wave factor, n:

Design of Absorption 42-11

© 2005 by Taylor & Francis Group, LLC

The total insertion loss for a lined bend is given

in Figure 42.13 along with the attenuation of the

lining beyond the bend.

42.5.3 Attenuation in Splitter

Lined Duct

The use of parallel or zigzag baffle-type separators

(splitters) to increase the perimeter – area ratio

results in more compact attenuators. In rock-wool

blankets, the attenuation of a parallel type splitter

duct may be obtained directly from Figure 42.14.

The peak value of the attenuation is related to

wavelength of sound and the splitter interval. With

the zigzag arrangement of acoustic blankets, the attenuation of high frequencies is improved over that of

the parallel splitter [7].

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