PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Characterization of centrifugal fan noise generated in residential
HVAC systems using in-duct measurements
Sarah VAN TRICHT1; Pieterjan BROOS1; Hervé DENAYER2; Maarten VANIERSCHOT1; Wim DE
ROECK1
1

KU Leuven, Mechanical Engineering Technology Cluster TC, Group T Leuven campus, Belgium
2

KU Leuven, DMMS lab Flanders Make, Belgium

ABSTRACTThe acoustic characterization of a centrifugal fan in a residential HVAC system is carried out through thedetermination of the total source spectrum of the sound generated by the fan under varying operating
conditions. The most commonly used characterization technique, described by ISO 5136, requires ananechoic termination and the possibility to insert a microphone in the duct. To avoid the large dependence on
the efficiency of the anechoic termination, an active one-port characterization using flush mounted
microphones is adopted in this research. One of the major advantages of this approach is the fact that thecharacterization is carried out independent of downstream reflections, thus not requiring the construction ofan anechoic termination. At first, the passive property of the fan, i.e. the reflection coefficient of the
propagating waves at the inlet of the fan, is determined. Subsequently, the downstream reflection componentof the test rig is characterized. Finally, both passive models are combined to compute the active source
spectrum describing all noise generation and dissipation phenomena of the fan. The acoustic characterizationis compared to existing scaling laws, such as described e.g. in VDI 2081.
Keywords: Fan noise, Scaling laws

1. INTRODUCTION
Noise pollution due to ventilation systems is an important concern, as the most frequently reported
issues with HVAC systems are linked to excessive noise emissions. The noise nuisance often resultsin the misuse of ventilation systems, causing poor indoor air quality and a loss in energy efficiency(1). Through an accurate prediction of the acoustic field generated by HVAC systems, noise pollution
can be avoided and innovative noise mitigation approaches can be assessed.
To allow the calculation or prediction of the acoustic field generated by residential ventilation
systems, knowledge of the total source spectrum of the sound generated by a centrifugal fan is of great
importance. Centrifugal fans are commonly used in residential ventilation systems C (onlymechanically discharges used indoor air) and systems D (mechanically supplies fresh outdoor air anddischarges used indoor air). Using the source spectrum, the sound generating mechanisms of acentrifugal fan can be investigated in further detail and efficient sound attenuation devices can be
designed (2).
General guidelines and reference spectra for the sound generated by fans can be found in e.g. VDI
2081 (3). According to these guidelines, the emitted sound power level of a fan is determined from a
constant value, the specific sound power level that depends on the assembly type of the fan, and theoperational point of the fan, determined by the volumetric flow rate through the fan and the totalpressure drop across the fan. The source spectrum of a fan can thus be related to the flow rate andpressure drop across the fan by a scaling law. The octave sound power spectrum of a fan is estimatedwith a standard octave sound power spectrum, through superimposing the sound power level output
1

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Corresponding author, sarah.vantricht@kuleuven.beof a fan with a discrete spectrum whose strength depends on the type of fan. However, the available
data on residential centrifugal fans is limited, as most reference spectra and guidelines concern more
powerful fans of different assembly types. Current guidelines on the acoustic characterization of fan sstated in e.g. ISO 5136 (4) describe characterization techniques for fans with duct diameters between
0,15 and 2 meters. These techniques are difficult to apply on smaller residential centrifugal fans andrequire the use of an anechoic termination.
Centrifugal fans have at least one inlet and one outlet. In residential ventilation systems C, theinlet is connected to the extraction grilles in the building. Consequently, only the sound generated inand transported through the inlet ducts is of interest, and the acoustic load of the fan is only relevantat the inlet of the fan. If the inlet and the outlet of the fan are acoustically uncoupled from each other,
the source can be considered as a one-port source for a plane wave, linear and time-invariant system(2). The acoustic characterization of a centrifugal fan can now be carried out through the determinationof the passive property of the fan, i.e. the reflection coefficien t of the propagating waves at the inletof the fan. Subsequently, the downstream reflection component of the test rig is characterized. Bothpassive models are combined to compute the active source spectrum describing all noise generationand dissipation phenomena of the fan, eliminating the need for an anechoic termination. The proposed
active one-port characterization is therefore an improved and better suited characterization techniquefor residential centrifugal fans.
Through the measurement of the total source spectrum of a fan under varying operating conditions,scaling laws that relate the operating conditions to the sound generated by the fan can be determined.
These scaling laws can be used to predict the source spectra of fans for a large range of operating
conditions. The experimentally determined scaling laws are compared to already existing scaling laws.
This paper describes two different types of centrifugal fans. Subsequently, the active one-port
characterization method is discussed, followed by a description of the measurement set-up used.
Thereafter, the determined source spectra of the sound generated by centrifugal fans are discussed.
Finally, a scaling law that relates the operational point of the fan to the sound generated by thecentrifugal fan is proposed and compared to existing scaling laws.

2. DESCRIPTION OF THE FANS
Two types of centrifugal fans are acoustically characterized, a constant pressure fan and a constant
power fan, both depicted in figure 1. When changing the aerodynamic load of the pipin g system, theconstant pressure fan tries to keep the pressure across the fan constant. The pressure can only be
adjusted by changing the settings of the fan, adjusting the rotational speed of the fan. The constant
power fan aims to keep the active power constant when the aerodynamic load of the system changes.
Both fans are aerodynamically characterized through the determined fan curves that relate the pressure
increase across the fan to the volumetric flow rate through the fan, shown in figure 1. These curves
are determined for all possible settings of the fans. When the flow rate through the fan is known, theoperational point of the fan can be determined using the fan curves. The diameter of the ducts
connected to the centrifugal fans is 0.125 meter. Figure 1 shows that all inlet du cts are connected to amanifold, from which the air enters into the centrifugal fan.

Figure 1 – The constant pressure centrifugal fan (above), the constant power centrifugal fan (below) and
fan curves showing a possible operational point of a centrifugal fan (right)

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3. THE MEASUREMENT METHOD
3.1 Passive one-port characterization
Previous measurements, where the centrifugal fan was considered a two -port source, determinedthat the transmission of sound between the inlet and outlet of the fan can be neglected. The inlet andoutlet of the centrifugal fan are thus acoustically uncoupled from each other. As only the soundgenerated at the inlet of the fan is of interest in a ventilation system C, the centrifugal fan is consideredan acoustic one-port source. An acoustic one-port source, as depicted in figure 2, can be described byequations relating the upstream and downstream propagating waves. Only plane waves are considered,constricting the frequency range to below the cut-off frequency of the first transversal mode. Whenextending the characterization to higher frequencies, a multi-port model is needed. In a duct with adiameter of 0,125 meter, the cut-off frequency of the first transversal mode is 1607 Hz.
The acoustic field in the inlet duct of the fan can now be described by two variables, the complex
amplitudes ‫݌‬௜ା and ‫݌‬௜ି of the upstream and downstream propagating pressure waves in the duct, asshown in figure 2. These amplitudes can’t be measured directly and are computed from a measurable
physical quantity, the acoustic pressure fluctuations ‫݌‬௜ᇱ due to an external excitation. Thesefluctuations are measured at four distinct axial positions in the duct. The decomposition method is
explained in detail by Munjal (5). The iterative plane wave decomposition method used starts with amultiple microphone decomposition method (MMM). The MMM is executed with the measurementsfrom four flush mounted microphones in the inlet duct, resulting in an overdetermined system of
equations. The equations used in this characterization method are reformulated in terms of transfer
functions with a reference signal correlated to the excitation signal, to suppress both the influence ofmeasurement errors and the influence of pressure fluctuations uncorrelated to the excitation signal.
With the initial values of the complex wave amplitudes calculated with the MMM, the final
microphone spacing is obtained, the mean flow velocity and speed of sound are updated and afrequency dependent attenuation coefficient is computed. This procedure is repeated until all theseparameters converge. This method is described by Denayer et al. (6).

‫݌‬௜ᇱ
ܴ௜
‫ݑ‬଴

‫݌‬௜ା
‫݌‬௜ି

‫݌‬௦ି

ܴା

FAN
Figure 2 – Schematic overview of the experimental configuration for the characterization of an acoustic
one-port source
The passive one-port model uses a reflection coefficient of the fan ܴ ା to describe the acoustic
behavior of the fan in frequency-domain. This coefficient relates upstream and downstream
propagating pressure waves in the inlet of the duct, and describes all linear sound attenuation andamplification mechanisms:‫݌‬௜ି  ൌ  ܴ ା ή ‫݌‬௜ା .
(1)
The reflection coefficient is determined for various operating conditions of the fan, to determine
if the reflection coefficient depends on the working point of the fan. The upstream termination of thetest rig can also be represented by a reflection coefficient ܴ௜ , as there are no noise sources present at
the termination of the measurement setup:‫݌‬௜ା ൌ  ܴ௜ ή ‫݌‬௜ି .
(2)Both reflection coefficients are determined with at least two independent measurements with adifferent flow rate, using a dominant excitation upstream of the microphone array in the inlet duct.
The dominant excitation source is uncorrelated to the sound generated by the fan, allowing to neglect
the source spectrum of the fan when determining the reflection coefficients. The passive one-port

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characterization is reformulated in terms of transfer functions with the excitation signal to ensure thatthe determination is free from aerodynamic contamination.
3.2 Active one-port characterization
The passive characterization does not consider the aerodynamic noise generation inside the fan.
The source term ‫݌‬௦ି represents the non-linear noise generation and dissipation phenomena due to thefan. The passive one-port model stated in equation (1) can now be extended to:‫݌‬௜ି  ൌ  ܴ ା ή ‫݌‬௜ା ൅ ‫݌‬௦ି Ǥ
(3)
The active source vector can now be computed by applying the plane wave decomposition method(5) to the acoustic pressure measured without external excitation and with:(4)
However, a reference signal correlated with the source spectrum of the fan is not available. Since
no external excitation is used, the active one-port model can’t be reformulated in terms of transfer
functions. However, by inserting equation (2) for the reflection coefficient of the termination of thetest rig in equation (4), both passive models are combined and the active source spectrum can be
expressed in terms of the upstream propagating waves:‫݌‬௦ି ൌ ሺͳ െ ܴା ή ܴ௜ ሻ ή ‫݌‬௜ି Ǥ
(5)This greatly simplifies the analysis and additionally simplifies the plane wave decomposition fromthe measured pressure spectra. As a result, the influence of measurement errors is minimalized. As
centrifugal fans generate broadband noise, the source spectrum is determined in a statisticaldescription, the cross-spectral source term ‫ܩ‬௦ defined as:‫ܩ‬௦ ൌ ‫݌‬௦ି ή ‫݌‬௦ି‫ כ‬Ǥ
(6)This characterization method enables the characterization of the sound generated by a centrifugal
fan independent of downstream reflections, thus not requiring the construction of an anechoic
termination at the inlet duct of the fan.
‫݌‬௦ି  ൌ  ‫݌‬௜ି െ  ܴ ା ή ‫݌‬௜ା Ǥ

4. MEASUREMENT SET-UP
The acoustic characterization of a centrifugal fan is executed in a semi-anechoic room to eliminate
possible noise disturbances. The aerodynamic load of the piping system is changed by changing theposition of a butterfly valve. This valve is situated in the outlet duct of the fan. To measure the velocityof the air flow through the fan, an L-type pitot tube from Sensing Precision is mounted on the outlet
duct of the fan. The flow velocity is measured with an accuracy of ±2.5% of the reading.
BUTTERFLY VALVE

FAN
0,9 m

6 cm

.
Figure 3 – Picture and overview of the measurement setup for the characterization of a centrifugal fan
The pressure spectra inside the inlet duct is measured using four flush-mounted ¼” microphones(type PCB 378C10), with a distance of 6 cm, 8 cm and 6 cm between two microphones. The distance
between the fan and the closest microphone is 0,9 meter. During the passive characterization, theexternal excitation signal, a stepped sine signal, is sent to a loudspeaker array after amplification. The
frequency range of this signal is 200-1600 Hz, with a frequency step of 50 Hz. No external excitation
is used during the active characterization. The output of the microphones, as well as the excitation
signal as reference signal, are sent to a Supervisory Control And Data Acquisition System (SCADAS)
via coax cables. The results are exported using Siemens LMS Test.Lab 17 and processed with
MATLAB.

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5. RESULTS
5.1 Passive characterization
The reflection coefficient of the propagating waves at the inlet of a centrifugal fan is determinedfor different settings of the fan, for different rotational speeds of the fan and for the two different
types of fans. Results are shown in figure 4.

Figure 4 - The reflection coefficient ܴ ା of the propagating waves at the inlet of a constant pressure
centrifugal fan (left) and a constant power centrifugal fan (right)
The reflection coefficient of a centrifugal fan is hence independent of the setting and the rotational
speed of the fan, as the coefficient remains constant when the operating conditions of the fan change.
The reflection coefficient is frequency dependent, as the collector manifold directly coupled to the
fan can cause resonances dependent on the shape of the cavity. Subsequently, the downstream
reflection component of the test rig or the reflection coefficient of the termination of the inlet duct, isdetermined. The reflection coefficient of the termination of the inlet duct has the same tren d as thereflection coefficient of an unflanged finite duct (7). At the termination of the duct, the loudspeakerarray causes a discontinuity in the diameter of the duct. The reduction in area results in a reflectionof the incoming waves.
5.2 Active characterization
The active source spectra of the sound generated by two different types of centrifugal fans undervarying operating conditions are determined. To be able to determine the narrowband source spectrum,
the reflection coefficients computed in the passive characterization are interpolated over the frequency
domain with a frequency step of one hertz. The operating conditions of the fans are altered by bothchanging the aerodynamic load of the piping system and by changing the setting or conditions of the
fan itself. The characterization results in a narrowband source spectrum on a linear frequency scale,that describes the broadband sound generated by centrifugal fans in detail, as shown in figure 5 andfigure 6.

Figure 5 – The measured total source spectrum (re 20 μPa) of the sound generated by a constant pressure
centrifugal fan under varying operating conditions

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Figure 6 – The measured total source spectrum (re 20 μPa) of the sound generated by a constant power
centrifugal fan under varying operating conditions
The sound generated by the fans has a global broadband character. The shape of the source spectra
agree with source spectra of fans determined in previous studies, as there is a steep decay in themagnitude of the spectra at low frequencies, and a slow decay at higher frequencies. The soundgenerated by centrifugal fans is strongly influenced by various installation effects, e.g. the mechanicaldesign of the fan and the design of the ventilation system. These installation effects result in peaks inthe source spectrum at certain frequencies. When the operating conditions of the fan change, theposition of the peaks caused by these installation effects remain constant. The installation effects are
not taken into account in guidelines and reference spectra. The source data is sensitive to the operating
conditions and the inlet flow conditions of the fan, as the source spectrum of a fan shifts when theconditions are changed. The blade frequency of the fan is not present in the source spectra, as there isno peak in the source spectrum of which the frequency changes when the rotational speed of the fanchanges. The tonal peaks present on the source spectra are hence not related to the rotational speed of
the fan.

6. SCALING LAWS
6.1 Existing scaling laws
Beranek (8) states that the overall sound power output ‫ܮ‬ௐ  of a fan can be calculated with equation(7), where ܸሶ is the volume rate of the flow, ‫ ݌‬is the total pressure increase and ‫ܮ‬ௐௌெ is the specificsound power level of the fan. The value of ‫ܮ‬ௐௌெ is constant, and depends on the assembly type of thefan. For a centrifugal fan this is equal to 34 dB according to the VDI (3).
(7)‫ܮ‬ௐ ൌ ‫ܮ‬ௐௌெ ൅ ͳͲ ଵ଴ ܸሶ ൅ ʹͲ ଵ଴ ‫ ݌‬
The overall scaled sound power level can thus be calculated with equation (8), this scaling
is not proportional to the aerodynamic power of the fan and is shown in figure 7. The crossspectral source term is converted to the sound power level with equation (9).
‫ܮ‬ௐௌெ ൌ ‫ܮ‬ௐǡ௘௫௣ െ ͳͲ ଵ଴ ܸሶ െ ʹͲ ଵ଴ ‫ ݌‬(8)(9)
The VDI estimates the noise spectrum of a fan by superimposing the overall sound power level on
a discrete spectrum ο‫ܮ‬ௐǡை௞௧ whose strength depends on the type of fan. This predicted trend of thesound spectrum generated by a fan is also shown in figure 7.
with ‫ܮ‬ௐǡ௘௫௣ ൌ ͳͲ ଵ଴ ‫ܩ‬௦௦ െ ͵ ݀‫ ܤ‬൅ ͳͲ ଵ଴ ‫ܣ‬

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Figure 7 – The scaled total source spectrum according to Beranek of a constant pressure centrifugal fan(left) and a constant power centrifugal fan (right)
The relation between the generated sound spectrum and the operating conditions of the fan isaccurately predicted by the VDI. However, the ‫ܮ‬ௐௌெ determined for centrifugal fans seems to be a grossoverestimation. To compare the overall sound power level generated by a fan to the estimated value by the
VDI, measurements of the entire frequency scale of the source spectrum should be conducted. The estimatedtrend of the frequency spectrum of the sound generated by centrifugal fans is accurate, but does not include
the influence of installation effect on the spectrum. These can however not be neglected.
6.2 Improved scaling law
As previously stated, the shape of the source spectra of centrifugal fans does not depend on therotational speed of the fan as there are no blade frequency peaks present in the source spectra. However,
the magnitude of the frequency spectrum does depend on the pressure increase across the fan and thevolumetric flow rate through the fan. Therefore scaling laws can be determined that relate themagnitude of the spectrum to the operational point of the fan. Different existing scaling laws statedin literature, e.g. the scaling laws determined by Bies et al. (9), are applied on the measurements ofthe source spectra under varying operational conditions. It is determined that the sound generated bya centrifugal fan relates to the aerodynamic power delivered by the fan, as applying the scaling law
stated in equation (10) aligns the source spectra with the least deviation. The source spectra scaled tothe pressure across the fan ‫ ݌‬and the flow velocity through the fan ‫ ݑ‬with formula (10) are shown infigure 8 and 9. The scaling law determined is also related to the flow velocity and the horsepower
needed to drive the fan as stated in equation (11).
ଷ(10)‫ܮ‬ௐௌெǡ௜௠௣௥௢௩௘ௗ ൌ ‫ܮ‬ௐǡ௘௫௣ െ ͳͲ ଵ଴ ‫ݑ‬ଷ െ ͳͲ ଵ଴ ‫݌‬ଶ   (11)
If the ‫ܮ‬ௐௌெǡ௜௠௣௥௢௩௘ௗ  of a fan is known, the source spectrum generated by the fan can be predictedunder all possible working conditions. This prediction can be used to design silencers with the sourceload interaction taken into account (2).
‫ܮ‬ௐௌெǡ௜௠௣௥௢௩௘ௗ ൎ ͳͲ ଵ଴ ‫ ଺ݑ‬ൎ ʹͲ ଵ଴ ݄‫݌‬

Figure 8 – The scaled total source spectrum of the sound generated by a constant pressure centrifugal fan

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Figure 9 – The scaled total source spectrum of the sound generated by a constant power centrifugal fan
CONCLUSIONS
Two types of centrifugal fans are acoustically characterized by determining the source spectrum of
the fans under varying operating conditions. The measurement method consists of two steps. First, thereflection coefficient of the incoming waves at the inlet of the fan is determined using an external
excitation. Additionally, the downstream reflection component of the termination of the inlet duct ischaracterized. This eliminates the need for an anechoic termination to characterize the fan. Secondly,
both passive models are combined to compute the active source spectrum describing all noise
generation and dissipation phenomena of the fan, as well as the installation effect due to themechanical design of the fan. The sound generated by a centrifugal fan largely depends on the working
point of the fan. The source spectra shifts proportionally to the aerodynamic power generated by thefan. The measured source spectra of the fans are scaled to the pressure increase across the fan and theflow rate through the fan. The scaling to ‫ݑ‬ଷ and ‫݌‬ଷȀଶ aligns the source spectra measured under varying
operational conditions and results in a more accurate specific sound power level of the fan compared
to existing scaling laws.

ACKNOWLEDGEMENTS
The authors gratefully acknowledge the financial support of this research by the VLAIO throughthe TETRA project number 170036 (SilenceVent).

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