Aerodynamic Sound from Centrifugal-Fan Rotors

Aerodynamic Sound from Centrifugal-Fan Rotors

R. C. C••v•

Research Division, American Radiator and Standard Sanitary Corporation, New Brunswick, New Jersey (Received 25 February 1965)

The sound powers of small uncased centrifugal-fan rotors were measured at low-tip Mach numbers. Cor- relation of the data by use of a similarity relationship derived from theory has shown that the broad-band rotor sound is a result of randomly oriented dipole sources caused by fluctuations in fluid momentum. Deviations of the dependence of sound power on speed from that theoretically predicted were found. Speed dependences less than that predicted can be explained as a nearfield effect; the lack of agreement between theory and the fan law for sound can be explained on the same basis. Observed speed dependences greater than that predicted appear to result from having fixed frequency limits on the measurement system. A sharp wedge placed near the rotor periphery was found to generate discrete-frequency dipole sound. Quadrupole sound appeared to be negligible.

INTRODUCTION

THE em. pirical "fan law" for sound, developed from experiments over a period of years, shows how

the sound power of a homologous series of centrifugal fans depends on the various quantities that describe fan operationJ Recent experimental evidence indicates that the fan law is not strictly applicable to all sizes of centrifugal fans. 2-5

The general theoretical development of aerodynamic- noise mechanisms 6-8 has helped to provide a meaningful basis for predicting the dependence of the sound power of monopole-, dipole-, and quadrupole-sound sources on certain aerodynamic variables. When these dependences are derived in terms of variables related to centri-

fugal fans, there is no agreement with the fan law. It was one intention of this study to determine the

nature of the two most prominent sound sources in a fan, i.e., the broad-band rotor sound and the cutoff tone, in order to find the relevant theoretical sound-power relationship. A second intention was to determine a reason for the lack of agreement between theory and experiment and between various experiments.

1 R. Jorgensen, Fan Engineering (Buffalo Forge Co., Buffalo, N.Y., 1961), p. 225.

•' H. C. Hardy, ASHRAE J. 5, 95-100 (1963). a G. C. Maling, Jr., J. Acoust. Soc. Am. 35, 1556-1564 (1963). 4 G. H. Huebner, ASHRAE J. 5, 87-94 (1963). 5 F. S. Howes and R. R. Real, J. Acoust. Soc. Am. 30, 714-720

(1958). 6 M. J. Lighthill, Proc. Roy. Soc. (London) 1211, 564-587

(1952). 7 N. Curie, Proc. Roy. Soc. (London) A231, 505-514 (1955). 8 A. Powell, J. Acoust. Soc. Am. 32, 982-990 (1960).

Accordingly, sound-power relationships for the various orders of source were derived and are presented herein. Measurements were then made of the sound

generated by small uncased centrifugal-fan rotors with forward-curved blades when these rotors were turning alone in an anechoic chamber and when they were turning with a fixed wedge placed near the rotor periphery to simulate a cutoff. Figure 1 shows a sketch of the experimental equipment, together with some details of the rotor geometry. The measurements are compared, in the succeeding Figures, on the basis of both the fan

.083D

0 ONE

._BLADE DETAI•

WEDGE INLET (SIMULATED CUTOFF) DUCT

Fro. 1. An uncased centrifugal-fan rotor could be rotated in an anechoic chamber with or without an inlet duct or wedge. The rotors had forward-curved blades with a shape as shown in the detail.

969

Copyright ¸ 1965 by the Acoustical Society of America.

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08:35:46

970 R. C. C H A N A U D

law and the theoretical relationships. The comparisons are analyzed in Sec. IV.

I. PREVIOUS INVESTIGATIONS

The fan law for sound is expressed by Jorgensen • in the form P o: p2NSD7, where the sound power P is de- pendent on the fluid density p, the fan-rotation rate N, and the fan-rotor diameter D. This relationship was meant to apply only for geometrically similar centrifugal fans operated at the same point of rating on the static-pressure versus capacity curve and for relatively low Mach numbers. It appears that the relationship is applicable to large-size commercial fans ø but not to smaller ones. 3,•ø It has been noted that the speed dependence is adhered to more closely than the size dependence? • Measurements of the sound power of uncased rotors and rotorlike elements have shown that

significant deviations from the fan law for sound can occur. For example, Huebner, 4 in one case, observed for uncased centrifugal-fan rotors that P • N. 6'5

Dimensional analysis has been used to show that the sound power of a centrifugal fan depends on the follow- ing dynamical parameters3,•2:

Mach number M= U/c,

Reynolds number R-- UD/•, Strouhal number S= fD/ U= f /•-N, Flow coefficient •= Q/UD •,

where D is the rotor diameter, N is the rotor revolution rate, Q is the volumetric flow rate, U is the rotor-tip speed, c is the sound speed, f is the sound frequency, and • is the fluid kinematic viscosity.

The relevance of the Mach number was established

early while the importance of the Strouhal number has been demonstrated only recently? ,3 The influence of the Reynolds number, although recognized, appears to be negligible relative to other parameters. a,• The flow coefficient, which relates the radial component of velocity at the rotor periphery to the tangential component, appears also to play a minor role in sound production?

One theoretical development of aerodynamic-noise mechanisms, originated by Lighthill 6 and later gen- eralized by others, 7'8 has shown that the acoustic- pressure field generated by a time-varying flow can be a result of either mass-flux, momentum, or momentum- flux fluctuations. In a free flow, no net mass-flux or momentum fluctuations can occur; the remaining momentum-flux variations can be interpreted as giving rise

9 R. D. Madison and J. B. Graham, Heating, Piping Air Con- ditioning 30, 207-214 (1958).

•0 R. B. Goldman and G. C. Maling, Jr., Noise Control 1, No. 6, 26-29 (1955).

n C. M. Harris, Handbook of Noise Control (McGraw-Hill Book Co., Inc., New York, 1957), Chap. 25.

•2 G. Riollet, Congr. Intern. Mecan. Appl., 9th, Bruxelles 2, 448-457 (1959).

to acoustic quadrupole sources distributed throughout the flow. • When bounding surfaces, immersed in the flow, are present, net fluctuations in mass flux and momentum may occur and give rise, respectivdy, to surface distributions of acoustic monopoles and dipoles. Dipole sources only are found to occur if the bounding surface is rigid and totally immersed in a low-Mach- number flow. Two important examples of this are the aeolian tone • and the edgetone? 4 The fluctuations in fluid momentum were found to be describable in terms

of the fluctuating force exerted at the surface.

II. SIMILARITY CONSIDERATIONS

With the increased understanding of noise mechanisms provided by the theory, it is possible to use dimensional analysis to show the explicit dependence of the sound power of a source in a fan on the two most important parameters, the Strouhal number and Mach number.

PowelP • developed an expression for the sound power radiated from a volume V of quadrupole sources in the form

.uVvV/c (2)

Here u and f represent typical velocities and frequencies within a correlation volume v. Similar expressions can be obtained for the sound power radiated from an area A of monopole or dipole sources and are

Pm o: pu•2aA/c and Pd cr pu4ffaA/c a. (3)

Here, u and f represent typical velocities and frequencies within a correlation area a.

When the sound frequency is determined by an outside agency, e.g., the blade-passage tone, the Strouhal number becomes an independent variable. Substituting the net fluctuating volumetric flow rate at this Strouhal number qs into the monopole expression and similarly the net fluctuating force Fs into the dipole expression, the above relationships become for this case.

Pm cr pUaD•[qs/ UD•]•S•.M,

Pd cr pUaD2[Fs/pUaaaa3, (4)

When the sound frequency is determined by the fluid motion, e.g., the broad-band rotor sound, it seems reasonable to assume f o: U/D. Assuming that similarity holds, the bracketed terms in the expressions immedi- ately above can be set equal to a constant so that the relationships reduce to

Pm cr pUaD2M cr pN4D 6, (5)

Pd cr pUaD•M a or pN•D 8, (6)

pq cr oUaD•M5oc NaD •o, (7)

• O. M. Phillips, J. Fluid Mech. 1, 607-624 (1956). •4 A. Powell, J. Acoust. Soc. Am. 33, 395-409 (1961). •5 A. Powell, J. Acoust. Soc. Am. 31, 812-813 (1959).


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CENTRIFUGAL-FAN ROTORS 971

where the rotor rotation rate N has replaced the rotor- tip speed U. The constants of proportionality in Eqs. (5)-(7) are, in reality, functions of the Reynolds number and flow coefficient, but the evidence suggests that the functional relationship is not a strong one. a.øa" The above expressions can be compared with a modified form of the fan law for sound,

p o: pU3D2M 2 • pN•D 7. (8)

None of Eqs. (5)-(7) agrees with Eq. (8). Hardy, 2 having derived expressions similar to Eqs. (5)-(7), chose the dipole one as being relevant to centrifugal fans, but did not explain the discrepancy between theory and experiment. Huebner 4 has also suggested that the dipole is the important source of centrifugal-fan sound. Sound from the related axial-flow fan appears also to be of dipole nature) 6

The above comparison of theory with experiment suggests, at least, that quadrupole radiation is relatively unimportant in centrifugal fans operating at low tip Mach numbers. The continuing difficulties with jet noise, •7 where quadrupole radiation is predominant, suggests that there would be little immediate hope for significant reductions in fan noise if quadrupole sources were important in fans.

100

90

a. 60

z

c)

50

40

30

-UNCASED SIROCCO ROTOR I I I I ,

I L/D =3'33 I I I

STROUHAL NUMBER ß • • - , • ••-'A

0.40 o m • I 0 • •i•/ II

. • I%•z,4•,,o, zo,4o,•o I :, 'Z I I II III

5 20 30 40 50 60708090100

ROT• TIP SPEED, U-F•SEC '

Fro. 2. The over-all sound pressure (20_<f_<20 000) of an uncased Sirocco rotor follows the speed dependence predicted by the fan law for sound while the sound pressures of the high-frequency components follow the dependence predicted by theory.

III. EXPERIMENTAL INVESTIGATION

In order to determine with assurance which of the

deduced sound-power relationships is relevant, experiments were conducted on uncased Sirocco rotors turning alone or turning near a fixed wedge placed near the rotor periphery. (See Fig. 1.) These experiments were a result of considering that the broad-band sound from the rotor and the discrete-frequency tone generated near the wedge are the major sources of noise in a fan and that information of importance could be obtained without the presence of a casing. The influence of changes in throughflow (•) on sound production was examined by placement of a variable-flow-resistance duct at the rotor inlet as shown in Fig. 1.

A shaft, covered with a damped metal housing and driven by a remote variable-speed drive, was rigidly supported within a 1000-ft 3 anechoic room so that the shaft termination was near the room center. The revolu-

tion rate of the shaft was detected by a magnetic pickup fixed near a 6-pronged sprocket wheel on the shaft. The electrical signal was fed to a Computer Measurements Company frequency counter where the revolutions per minute could be read directly.

A Brtiel and Kjaer type 4133 microphone was attached to a polar traverse system as shown in Fig. 1; the signal was fed to a type 2107 frequency analyzer and to a type 2105 level recorder. In addition, a high-pass filter,

16 E. J. Richards and I. J. Shadand, Paper L12 in Proceedings of the Fourth International Congress on Acoustics, Copenhagen, 1962 (Organization Committee of the 4th ICA and Harlang & Toksvig, Copenhagen, 1962).

17 M. J. Lighthill, AIAA J. 1, 1507-1517 (1963).

which reduced signals below 100 cps at 60 dB/oct, could be inserted. Measurement of the over-all sound- pressure level could include components either from 20 to 20 000 cps or 100 to 20 000 cps. The sound pressure and sound power were related, respectively, to 0.0002 dyn/cm 2 and 10 -•2 W.

Four American-Standard rotors, with 32 forward- curved blades, were used to obtain data. Their diam- eters D were 4.5, 6.0, 7.5, and 9.0 in. The blades on each rotor were 0.54D in length and 0.083D in radial dimension (see Fig. 1). The rotors were not precisely similar; all pieces except the hubs were made of xJ-•-in.- thick aluminum.

A. Rotor without Edge

The directionality of the sound field generated by the rotor was measured at various rotor speeds and was found to be quite uniform. Measurements, made at certain frequencies representative of the various octave bands with the 6% bandwidth selectivity of the analyzer, indicated that directionality became important only at frequencies higher than 10 kc/sec. It was considered, then, that pressure measurements made at one position could be used to calculate closely the sound power of the source. The results presented here were derived from data obtained at the microphone position L=2.5 ft, 0= 75 ø (see Fig. 1).

The over-all sound-pressure level, in the band 20- 20 000 cps, was measured as a function of rotor-tip speed. In addition, sound-pressure-level readings were obtained in narrow bands (6% bandwidth) at certain


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972 R. C. CHANAUD

-15

-20 -25

TiP MACH NUMBER, M 0.02 0.04 0.06 0.08 0.10 0.12

UNCASED SIROCCO ROTORS O- 6.o A-7.5 o-9.0

o •7 o

A ß - ooo--o-o o I

-30 20 $0 40 50 60 80 I00 150

ROTOR TIP SPEED, U- FT/SEC '

Fro. 3. Correlation of the over-all sound-power data (20_<f •_ 20 000) by use of the fan law requires that the law be modified as shown.

-4O UI•CASED SIl•OCCO ROTORS D I SYMBOL

ø. o 4.5 •: "' I M= 0.070 6 o -o .... o-

:• I x ". I 7.5 --•'--•'-- • [•' '•_ '-..._2%•.-. I 90 ..... - 50 -- _ •-•.. I

• -60 • o ,

-70 O. S I S 0 30 I O0

STROUHAL NUMBER, • D•

Fro. 5. The dimensionless sound powers in narrow frequency bands (6• bandwidth) of various diameter rotors display similarity over a limited range of Strouhal numbers. Deviations at low S appear to be a nearfield effect; deviations at high S cannot be completely explained on the basis of directionality changes.

Strouhal numbers within the spectrum range. A typical result is shown in Fig. 2. The data shown with symbols are approximate since fluctuations in level of at least 4-3 dB were present. For comparsion purposes, S-0.32 at the rotor-revolution frequency and S= 10.2 at the blade-passage frequency. The over-all sound pressure followed the speed dependence predicted by the fan law, Eq. (8), except at low speeds where the background noise was predominant. The sound pressure at the lower Strouhal numbers approximately followed the same dependence at the over-all sound-pressure level, while the sound pressure at the higher Strouhal numbers more closely followed the dipole dependence of Eq. (6). A heavy cardboard cylinder was then inserted into the rotor at the inner periphery of the blades and the data were retaken. The low S components were reduced to background levels while the components with S> 2 were unchanged. As a result, changes in the flow coefficient must be expected to mainly influence the lower Strouhal-number part of the spectrum.

The over-all sound powers for the various diameter rotors were calculated and were compared on the basis of the fan law, Eq. (8). The result is shown in Fig. 3; the expanded vertical scale should be noted. Each data point represents an average of five observations. The speed dependence predicted by the fan law was adhered to closely. The best correlation with size was obtained by multiplying Eq. (8) by the rotor diameter; the new

-25

-$0

-35 o

-40 20

UNCASED SIROCCO ROTORS

•o o•

$0 40 50 60 80 I00

ROTOR TIP SPEED, U-- F•SEC '

I D

• - 45 INCHES 0-60

A-75 o 90--

c •AA ._• •

•50

Fro. 4. Correlation of the over-all sound-power data (100_-<f _< 20 000) by use of the theory is good when the lowest frequencies are excluded from the measurement.

relationship was made dimensionless by use of the microphone distance L. Over-all sound powers, in the narrower band 100-20 000 cps, were calculated from data taken at the same time and were compared with the dipole relationship of Eq. (6). The result, shown in Fig. 4, shows an important change in observed dependence caused by filtering out the very lowest frequencies; the theoretical prediction is followed fairly closely. A possible cause for the slightly greater dependence on speed over that predicted is given in Sec. IV.

To show that the Strouhal number is a useful param- eter for correlating spectra, the spectrum of each rotor was analyzed (6øfo bandwidth) and compared; a typical result for constant U is shown in Fig. 5. The sound power in any narrow Strouhal-number band was considered to be approximately correct when calculated from the mean square of the fluctuating pressure as shown on the meter dial. Spectral similarity is achieved only over a limited range of Strouhal numbers. Devia- tion from similarity at the high Strouhal numbers might be expected to be a result of directionality effects, but, based on the directionality data obtained, the amount of deviation observed could not be accounted for on this

basis alone. Powell, •a in studying edge noise generated by a turbulent flow over a flat plate whose dimensions were large with respect to a typical wavelength, predicted that the dipole sound power would vary like U 5 in lieu of U ø. His argument would help to explain the present results, even though here the blade dimensions were of the same order as the wavelength of interest. Deviation from similarity at low Strouhal numbers is related to the different speed dependences found by selective filtration of the low-frequency components; both results can be explained as a nearfield effect, and this is discussed further in Sec. IV.

A duct was placed at the rotor inlet as shown in Fig. 1. The inlet flow, restricted by various diameter-orifice plates, came from outside the anechoic room. Data, similar to those already presented, were obtained when the flow coefficient q• varied in six steps from 0 to 0.25. No significant changes in sound production were found

zs A. Powell, J. Acoust. Soc. Am. 31, 1649-1653 (1959).


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CENTRIFUGAL-FAN ROTORS 973

to occur; this was not the case for small complete fans20

B. Rotor with Edge

The major source of discrete frequency sound in a centrifugal fan is that produced by passage of rotor blades past a fixed cutoff. It was considered that an equivalent situation would occur if a fixed rigid wedge were placed near the outer periphery of an uncased rotor. Considering both theory and experiment, it was anticipated that dipole sound would be produced at the edge and, since it would be at a discrete frequency, the usual dipole directionality was expected. Directionality measurements did confirm the dipole nature of the source; a typical result is shown in Fig. 6 for various rotor-tip speeds.

With the edge -• in. from the smallest rotor and at geometrically similar distances from the larger rotors, the sound power of the edgetone was calculated from pressure measurements at the position L= 2.5 ft, 0= 75 ø. The results were compared on the basis of the dipole relationship in Eq. (4) and are shown in Fig. 7. The ordinate represents a measure of the dimensionless fluctuating force shown in Eq. (4), and this force was approximately constant up to a certain tip speed, different for each rotor, and then decreased slightly with further speed increase. The decrease in dimensionless force commenced when strong modulation of the edgetone started and was found to be related to excessive vibration of the rotor.

IV. DISCUSSION

Both theoretical considerations and experiment sug- gest that the broad-band sound from a fan rotor can be likened to a collection of randomly oriented dipole sources. In addition, considerations of rotor geometry and Mach-number range of the present experiments would seem to require exclusion of monopole and quadrupole sources as the cause of the sound. The relevance of the dipole relationship, expressed in either of Eqs. (4) or (6), has been established by the measurements

9O

FIO. 6. The sound • ' '•. -/,•.U.•2•5• l

.e,d b, ,ow i,o about a wedge placed near the rotor periphery is almost that of a

point dipole whose axis • 60 '••.•/4 "X• .• is perpendicular to the

plane of the wedge, • 1%• //•, •

-45

-60 15

UNCA•ED SIRGCCO •tOTO•RS v_Ia•.5iNCHES CUTOFF TONE [ o-- 6

S-- 10.2 I d-- 7.5

ß • 0•0 • o oc •o oo o o

20 :50 40 50 60 80 I00 150 FT.

ROTOR TIP SPEED, U- •- '-'":•SEC.

Fro. 7. The dimensionless fluctuating force on the wedge, repre- sented by the ordinate, is relatively constant. Decreases at high U appear to be related to rotor vibration.

of the sound from an edge near the rotor. It is necessary then to determine why the dipole relationship does not always apply to the rotor sound.

One must consider that pressure measurements made at frequencies near 20 cps are of nearfield pressures. If these low-frequency components contribute most to the over-all sound pressure, then any deductions of sound intensity, by use of the usual farfield relationship between pressure and radial velocity, must be incorrect. It is possible to show, using similarity, what kind of sound-power relationships might be experimentally obtained if correction for the nearfield effect of a dipole is not made. They are, for various wavenumbers k,

pcr pUaDSM (D/L)S cr pN4DO(D/L)S,

pcr pU•D2MS(D/L ) cr pNSD 7 (D/L),

kL<<l,

kœ• •. (9)

The hydrodynamic-field relationship in the first expression does not apply here but serves to show how the speed exponent can change with changes in microphone distance. Equation (9) applies strictly only for a small range of values around kL= 1, but the correlation shown in Fig. 3 through use of this expression suggests that it may have some relevance. When frequencies below 100 cps (kL < 1.4) were filtered out, the observed sound-power relationship was altered (see Fig. 4) to one more like that predicted for the true sound power. This observation and that of deviations from spectral similarity can both be explained in terms of a nearfield effect.

pUSD2M 3

•A• FIXED S RANGE OF SOUND •-••'

STROuHAL NUMBER, S = •/Tr N

FIXED -• RANGE FOR • MEASUREMENT

INCREASING

N

Fro. 8. Limitations on the range of frequencies measured can cause a deviation of the speed dependence of the sound power from that[predicted by theory. For the situation shown above, P cr N% where n ;>6.


08:35:46

974 R. C. C H A N A U D

The close similarity of Eq. (9) to the fan law for sound, Eq. (8), suggests that this explanation may also be applicable to measurements made on large commercial fans. It has been recommended as a standard practice for sound-power measurements of fans that the microphone be located between 5 and 10 ft from the fan? Published sound-power spectra n show that the major contributions to the total power are at the lowest frequencies (commonly 20 cps), so there is further reason for considering the fan law to be result of measurements made in the near field of a dipole source.

On the other hand, it has been found that the sound power of a fan rotor can depend on a higher exponent of U than the sixth predicted by Eq. (6). An example in the present experiments is the data presented in Fig. 4. A possible explanation for this is as follows. The evidence suggests that a given series of geometrically similar rotors will generate sound between two limiting Strouhal numbers; measurement systems are generally restricted to fixed frequency limits. The effect of this difference can be shown with the aid of Fig. 8 in which are shown three hypothetical sound spectra and their relationship to the limits of the measurement system. Considering that even small centrifugal-fan rotors generate significant pressure fluctuations at frequencies as low as 20 cps, the relative position of the frequency limits shown in the Figure appears to represent a typical case. When N is increased, the frequency limits move to the left so that more sound sources are available for meas-

urement. Then, for the total sound power, P/pU3D•M a • N% where n is greater than, equal to, or less than one, respectively, for the spectra marked A, B, and C. Spectrum B most closely corresponds to the present experiments, and a 3-dB increase of ln[-P/pU3D•M•-] for a doubling of N would be expected. The results, shown in Figure 4, show approximately this dependence. Spec- trum C appears to correspond to spectra of centrifugal-

Air Moving & Conditioning Assoc. Bull. 300 (Feb. 1962).

fan rotors obtained by Huebner. 4 He observed for these rotors that P c• N0.5 or n-0.5, which would be expected from the above considerations.

Combinations, other than that shown in Fig. 8, may occur in practice. Together with the nearfield effect, this might be expected to result in a rather broad range for the experimentally determined exponent of the speed in the sound-power expression.

V. CONCLUSION

The broad-band aerodynamic sound from an uncased centrifugal-fan rotor can be interpreted to be a result of radiation from randomly oriented dipole sources within the flow. These sources arise, according to theory, from fluctuations in fluid momentum and result in a net

fluctuating force on the rotor. (An important implica- tion of this finding is that the force, which might nor- mally be measured through complex instrumentation on the rotor itself, can be deduced directly from a sound- pressure measurement.) Equation (6) is a useful expression for showing how the sound power of a rotor depends on its size and speed. Modifications of this expression are required (1) when the microphone is in the near field of frequency components that contribute strongly to the over-all power and (2) when the frequency limits of the measurement system are not sufficiently broad to include all components of the sound spectrum at all speeds. The modifications result in variations in the exponent of revolution rate N; the size factor remains D s. The discrete frequency sound from a wedge placed near the rotor periphery is dipole in nature and can be described best by use of Eq. (4).

The dependence of sound power on density, according to theory, should be linear. There does not appear to be a satisfactory explanation for the appearance of the square of the density in the fan law for sound. The dependence of sound power on flow coefficient and Reynolds number appears to be very weak in these experiments.


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Aerodynamic Sound from Centrifugal-Fan Rotors