8.9 PLENUM CHAMBERS

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A plenum chamber is similar to a dissipative silencer, but it is also similar

to a small room with a noise source in one wall. The dimensions of the

plenum chamber are usually larger than the wavelength of the sound being

attenuated. In addition, the inlet and outlet of the plenum chamber are

usually not placed on the same axis, which is often the case for dissipative

silencers.

One of the applications for plenum chambers is to smooth out flow

fluctuations and poor velocity distribution after a fan or blower in an air

distribution system, in addition to attenuation of the noise generated by the

fan or blower.

The results of experimental measurements of plenum chamber acoustic

performance are available in the literature (Wells, 1958; Benade, 1968). The

following analysis yields expressions that predict acoustic performance in

good agreement with experimental data for wavelengths smaller than the

dimensions of the chamber. At low frequencies (wavelengths much larger

than the chamber dimensions), the calculated transmission loss may be

5–10 dB smaller than experimental data, i.e., the calculations are ‘‘conservative’’

as far as the noise control situation is concerned. When the ‘‘room

Silencer Design 391

FIGURE 8-20 Schematic of a silencer for automotive applications.

Copyright © 2003 Marcel Dekker, Inc.

constant’’ for the plenum is very large (or the surface absorption coefficient

for the lining approaches unity), the transmission loss for the plenum is

determined primarily by the direct acoustic energy from the inlet to the

outlet.

Let us consider the plenum chamber shown in Fig. 8-22. The acoustic

intensity associated with the inlet energy Win that is radiated directly from

the inlet (area SoЮ to the outlet is given by the following expression:

ID ј

QWin

4_d2 (8-184)

The directivity factor Q ј 2, if the inlet opening is located near the center of

the inlet side of the plenum chamber. If the inlet opening is located near the

top or bottom edge of the inlet side of the plenum chamber, Q ј 4. The

quantity d is the slant distance between the center of the inlet and center of

the outlet opening of the plenum chamber. For the plenum chamber shown

in Fig. 8-22, the distance d is given by the following expression:

d ј ЅрL_hЮ2 юH2_1=2 (8-185)

392 Chapter 8

FIGURE 8-21 Baffle-type or panel-type silencers: (a) in-line panels and (b) staggered

panels with heat-recovery water-filled tubes.

Copyright © 2003 Marcel Dekker, Inc.

The quantity L is the vertical dimension of the plenum chamber (if the

openings are located in the vertical sides of the chamber),H is the horizontal

distance between the inlet and outlet openings, and h is the height (or

diameter, if circular) of the openings.

An alternative arrangement for the inlet and outlet openings for a

plenum chamber is shown in Fig. 8-23. For this case, the angle _ is given

by the following expression:

cos_ ј L1=d (8-186)

The dimension L1 is the distance between the center of the inlet opening and

the chamber side in which the outlet opening is located, and d is the slant

distance between the two openings.

The acoustic energyWout;D associated with the direct sound field at the

outlet is found by multiplying the intensity by the area of the outlet opening

projected in the direction of the inlet opening:

Wout;D ј

QWinSo cos _

4_d2 (8-187)

The angle _ is defined in Fig. 8-22, and is given by the following expression:

cos_ ј H=d (8-188)

The acoustic energy density associated with the reverberant sound field

in the plenum chamber may be determined from Eq. (7-12):

DR ј

4Win

cR

(8-189)

Silencer Design 393

FIGURE 8-22 Configuration for a plenum chamber.

Copyright © 2003 Marcel Dekker, Inc.

The quantity R is the room constant for the plenum chamber:

R ј

S__

1 _ __

(8-190)

The surface area S is the total surface area of the chamber, including the

lined surface area SL and the area of each opening So:

S ј SL ю 2So (8-191)

The average surface absorption coefficient __ may be determined from the

following expression, assuming that the absorption coefficient for the openings

is unity:

__ ј

__LSL ю 2So

S

(8-192)

The sound power at the outlet opening associated with the reverberant

sound field is given by Eq. (7-10):

Wout;R ј 1

4DRcSo ј WinSo=R (8-193)

The total energy leaving the plenum chamber is the sum of the direct

and reverberant components from Eqs (8-187) and (8-193):

Wout ј WinSo

Qcos _

4_d2 ю

1

R

_ _

(8-194)

394 Chapter 8

FIGURE 8-23 Plenum chamber with an alternative location for the outlet.

Copyright © 2003 Marcel Dekker, Inc.

The sound pressure transmission coefficient may be determined from Eq.

(8-194):

at ј

Wout

Win ј

SoQcos _

4_d2 ю

So

R

(8-195)

The transmission loss for the chamber is given by the following expression:

TL ј 10log10р1=atЮ (8-196)

The first term in Eq. (8-194) represents the energy transmitted directly from

the inlet to the outlet opening of the plenum chamber. The second term

represents the energy from the reverberant field within the chamber.

A double-chamber plenum, as shown in Fig. 8-24, may be used to

reduce the effect of the direct sound transmission. If we denote the first or

inlet section by subscript 1 and the second or outlet section by subscript 2,

the sound power transmission coefficient for the double-chamber plenum

may be estimated from Eq. (7-69) with the transmission coefficient of the

opening between the two chambers taken as unity and Sw ј S01:

at ј

Wout

Win ј

So1

R1

So2 Q2 cos _2

4_d2

2 ю

4So2

R2

_ _

(8-197)

The quantities So1 and So2 are the outlet areas for each chamber and R1 and

R2 are the room constants for each chamber, given by Eq. (8-190).

Example 8-12. A plenum chamber has dimensions of 0.800m р31:5inЮ _ 0:800m_1:600m (63.0 in) long. The inlet and outlet ducts have a height of

h ј 300mm (11.8in) and a width of 400mm (15.75in). The inlet and outlet

duct openings are located along the edge of the plenumрQ ј 4Ю, as shown in

Fig. 8-22. The plenum chamber is lined with 1-in thick acoustic foam, the

Silencer Design 395

FIGURE 8-24 Double-chamber plenum.

Copyright © 2003 Marcel Dekker, Inc.

properties of which are given in Appendix D. Determine the transmission

loss for the plenum chamber.

The slant distance between the inlet and outlet openings is as follows:

d2 ј рL_hЮ2 юH2 ј р0:800_0:300Ю2 ю1:6002 ј 2:810m2

d ј 1:676m р5:50ftЮ

The cosine of the angle between the slant distance and the normal to the

outlet opening is as follows:

cos_ ј

H

d ј

1:600

1:676 ј 0:9545 or _ ј 17:358

The areas of the openings and the lined portion of the chamber are as

follows:

So ј р0:300Юр0:400Ю ј 0:120m2 р1:292 ft2Ю

SL ј р2Юр0:800ю0:800Юр1:600Ю ю р2Юр0:800Юр0:800Ю _ р2Юр0:120Ю

SL ј 6:160m2 р66:31ft2Ю

Let us work out the transmission loss for the octave band with a center

frequency of 500 Hz. The surface absorption coefficient for the acoustic

foam at 500Hz is 0.51. The average surface absorption coefficient in the

500Hz octave band for the plenum is found using Eq. (8-192):

__ ј р6:160Юр0:51Ю ю р2Юр0:120Ю

р6:400Ю ј 0:5284

The room constant for the plenum is found from Eq. (8-190):

R ј р6:400Юр0:5284Ю

1_0:5284 ј 7:170m2

The sound power transmission coefficient for the 500Hz octave band

is determined from Eq. (8-195):

at ј р0:120Ю

р7:170Ю ю р4Юр0:9545Юр0:120Ю

р4_Юр1:676Ю2 ј 0:01674ю0:01297 ј 0:02971

The transmission loss for the plenum in the 500Hz octave band is as

follows:

TL ј 10log10р1=0:02971Ю ј 15:3 dB

The calculations may be repeated for the other octave bands. The

results are summarized in Table 8-5.

396 Chapter 8

Copyright © 2003 Marcel Dekker, Inc.

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