Acoustic impedance effects

An alternative and/or parallel explanation for some of the differ­ences in sound level which have been noted, is the acoustic im­pedance of the ductwork configuration. Until recently, there were severe practical difficulties in making impedance mea­surements but these have been reduced with recent advances in digital frequency analysis and correlation techniques.

Whereas it was previously necessary to investigate the stand­ing wave patterns by a microphone traverse along the duct for each discrete frequency of interest, it is now possible to use phase-matched condenser microphones for simultaneous measurement of sound pressure levels at a known separation. The signals may then be processed through a Fast Fourier Transform (FFT) twin channel frequency analyzer to derive im­pedances from the cross-spectral density function (see Bibliog­raphy, Section 14.15) or by a transfer function method.

The specific acoustic impedance i may be defined as the ratio of acoustic pressure p to acoustic particle velocity u and in air is equal to pC.

In a duct, however, this is not a particularly helpful concept and the acoustic impedance I is used, defined as the ratio of acous­tic pressure p to the acoustic volume velocity q.

With plane wave propagation along a duct of cross-sectional area A and with no reflected waves, then

| = — = — = — Equ 14.24

Q Au A

Where reflected waves are present, the pressure and volume velocities are the sum of incident and reflected pressures and the difference between forward and reflected velocities respec­tively so that the ratio of — is generally complex. Knowing the u

Impedance at a point together with either the acoustic pressure or volume velocity, it is possible to calculate the unknown pa­rameters.

Whilst the main applications of these acoustic impedance con­cepts have been in reactive silencer design, an impedance model of a ducted fan as been given by Baade where it is con­sidered as a dipole source of noise with internal impedance lF.

Acoustic loads of impedance ILj and IL0 are coupled to the end of straight inlet and outlet ducting respectively. Acoustic imped­ances seen by the fan impeller are li and l0. The volume veloci­ties qi and q0 are equal in magnitude but of opposite sign and are related to the dipole source strength by equation:

-q0

P2R

W„ =

1 + j Li tan kM

Inlet

Frequency — Hz Outlet Figure 14.19 Mixed flow fan noise at inlet and outlet under various test config­urations

Ap

Equ 14.25

By manipulation of these terms and noting that the acoustic power flowW0 =q02R|l0|

Ap2R0

O+If + ‘o)2 Baade deduced that:

Lo + jtan k

1 + jlotan kl0

But with vary distribution of the resistance on the fan inlet and outlet.

For any meaningful comparisons to be made between noise tests and fans in a homologous range, and also to compare sound power levels of fans of different types, it must be accu­rate and repeatable. They must provide information that can be used by a system designer for noise management and, where necessary, attenuation. To do this, it is necessary that they are conducted under a similar ducting configuration and if at all possible, under a similar distribution of inlet to outlet ducting re­sistance.

To repeat, the ducting acts as an acoustical impedance. The noise output at inlet and outlet not only varies according to the point on the fan characteristic. It also varies according to how it is ducted and the distribution of this ducting. We thus have at least eight different noise levels (four installation categories to be measured for inlet and outlet noise). If we add to these the “breakout” noise levels, then a further four levels can be expected.

Frequency Hz	Mixed flow	Mixed flow	In-line Radial	Bifurcated Axial	Axial	Backward Curved Centrifugal
Duct configuration
Type D	Type B — Type C	Type B — Type C	Type B — Type C	Type B — Type C	Type B — Type C
DBW	DBW	DBW	DBW	DBW	DBW
50	5.0	17.0	-1.9	7.1	-0.4	-4.0
63	8.5	9.9	-2.1	1.9	1.8	0.8
80	6.0	12.3	-2.9	-5.3	-1.1	2.1
100	8.0	5.2	-7.8	-5.2	-1.7	4.4
125	9.5	8.0	-10.7	-9.3	-11.3	4.7
160	9.0	16.3	-1.6	-16.2	-10.7	4.1
200	5.5	5.3	-4.8	-4.0	-3.4	-2.7
250	4.0	4.8	-4.2	0.7	-2.0	0.5
315	6.5	6.6	-4.2	-6.1	-0.5	3.9
400	7.0	9.6	0.1	-5.0	-0.2	3.0
500	7.0	8.4	3.5	-3.3	0	5.1
630	5.5	3.1	4.8	-2.6	-2.1	5.0
800	5.0	1.5	1.5	-1.8	-2.2	4.9
1000	2.5	-0.7	-0.7	-3.2	-1.8	5.3
1250	-2.5	-3.7	-0.6	-4.3	-2.3	3.6
1600	1.0	2.4	-0.8	-3.3	-2.5	3.3
2000	2.0	4.7	-1.7	-3.7	-2.7	3.0
2500	0	3.0	-2.6	-3.7	-3.0	1.8
3150	-4.5	1.2	-3.3	-4.7	-3.7	2.2
4000	-2.5	3.2	-3.6	-5.7	-3.4	2.5
Total	4.6	6.8	-2.1	-2.9	-3.7	-0.9

Table 14.5 Difference between outlet and inlet sound power levels for various fan types each at their design flowrate expressed as (outlet — inlet) in sound power level re 10-12 watts

Some representative differences for different fan types are shown in Table 14.5. And still our misery is not ended! The ac­tual type of microphone head used can affect the results (un­less correction factors are included in the measurement code) see Figure 14.21.

ISO 5136 gives these correction factors, for the different types of shield identified, according to the flow velocity and modal ef­fects. The turbulence screen is recommended for the highest velocities, but a foam ball is adequate for the velocities experi­enced in normal HVAC applications.

INLET

OUTLET

81^.78.7 75.7 S S 8 8 8 R-[2] 04 FREQUENCY Hz

ALL DOWNSTREAM 120 5 110 CЫ — ri 100

Ui A Cc Ui 5

UPSTREAM ^20 5 110

100. 90 80 70 60

	120* 110′ 100* 90′ 80′ 70­ 60-
90-5 KA flftA
FREQUENCY Hz
120r 110 100­90′ 80­70­60-
84.5 86.4 87.4

50

To o © * * * c 2S8gggg3 •- ci *T si FREQUENCY Hz

120r 110­ 1004*’ 90 80 70′ 60

3,8 84.8 07 6 87.8 86.0

Q Z 3 O 05 50

60′

8 § § 8 FREQUENCY Hz

83 9 85.6 86.4 87.3

77.7 74.6……………….. . .-—,70.0

60-

* * C 8 8 8 113

FREQUENCY Hz

84.6 85.2 86.0

Va upstream Ґ* DOWNSTREAM 120­$ 110′ CD. TJ -j 100′ LU. § 90′ A: I 80; Cl 70

%UPSTREAM V4 DOWNSTREAM 120′ 5 110— *o -j 100-

O 2 D O w 50

LOCOif»OgiЈ^^ CM in ^ ci FREQUENCY Hz

120 110 100-1Ј 90­ 80′ 70′ 60

85.6 88.0 88.2 86.7

© * * * ic c 8 8 8 8 8 3

I

C N s 8 § 8 § 3 Ci 00 FREQUENCY Hz

FREQUENCY Hz

Figure 14.20 Variations in sound power levels for 610 mm bifurcated axial flow fan

31 63 125 2S0500 1K 2K 4K 8K

60

100

CD X»

90

80

70

CC LU O CL O 2 3 O CO

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