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PHASED ARRAY MICROPHONE MEASUREMENT OF AN
AXIAL FLOW FAN
by
Bence Mihály TÓTH
/AGMES4/
Submitted to the
Department of Fluid Mechanics of the
Budapest University of Technology and Economics
in partial fulfilment of the requirements for the degree of
Master of Science in Mechanical Engineering Modelling
on the 16th May 2014
Project Report
Final Project /BMEGEÁTMWD2/
Supervisor:
Tamás BENEDEK, PhD student
Evaluation Team Members, advisors:
Dr János VAD, associate professor
Csaba HORVÁTH, assistant research fellow
Department of Fluid Mechanics
Faculty of Mechanical Engineering
Budapest University of Technology and Economics
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DECLARATION
Full Name (as in ID): Bence Mihály TÓTH
Neptun Code: AGMES4
University: Budapest University of Technology and Economics
Faculty: Faculty of Mechanical Engineering
Department: Department of Fluid Mechanics
Major/Minor: MSc in Mechanical Engineering Modelling
Fluid Mechanics major / Solid Mechanics minor
Project Report Title: Phased Array Microphone Measurement
of an Axial Flow Fan
Academic year of submission: 2013 / 2014 - II.
I, the undersigned, hereby declare that the Project Report submitted for
assessment and defence, exclusively contains the results of my own work assisted by
my supervisor. Further to it, it is also stated that all other results taken from the
technical literature or other sources are clearly identified and referred to according to
copyright (footnotes/references are chapter and verse, and placed appropriately).
I accept that the scientific results presented in my Project Report can be utilised by
the Department of the supervisor for further research or teaching purposes.
Budapest, 16th May, 2014
__________________________________
(Signature)
FOR YOUR INFORMATION
The submitted Project Report in written and in electronic format can be found
in the Library of the Department of Fluid Mechanics at the Budapest University of
Technology and Economics. Address: H-1111 Budapest, Bertalan L. 4-6. „Ae”
building of the BME.
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ACKNOWLEDGEMENTS
I would like to thank Mr Tamás BENEDEK, Dr János VAD and Mr Csaba
HORVÁTH for their help in the measurement process and the data analysis. I am
grateful to Ms Orsolya IGAZ for her cooperation in carrying out the velocity
measurements and to Mr Zsolt VÁRHEGYI for his help with the MATLAB
algorithm.
Köszönöm családom és barátaim segítségét, akik végig támogattak egyetemi
éveim alatt.
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ABSTRACT
A method based on [1] is used to relate the radial distribution of aerodynamic
losses to the generated noise in case of an axial fan.
Aerodynamic characteristics are estimated based on geometry and inlet velocity
profile measurements. The blade sweep is accounted for in the calculations. Two
parameters are investigated: loss coefficient and Lieblein diffusion factor [2].
Both parameters were written in a level form.
Noise distribution was measured using a Phased Array Microphone (PAM).
Radially averaged plots were created for the third octave bands from 2000 Hz to
6300 Hz and a linear fit using the least squares method was carried out to find
parameters that best approximate the noise as a function of either or both on
suction and pressure sides. On the suction side the -dependent function seems
appropriate in the 2000 Hz – 3150 Hz range and the full band, too. The
approximation based on fails to reproduce the noise distribution. On the
pressure side the situation is similar, but the -dependent function preforms
better in the low frequency range. The full band estimation is acceptable in both
cases for both trial functions. Some measurement points do not support the
original assumption that increasing aerodynamic losses would lead to increasing
noise.
The ROSI [3] method was used to generate source maps of the fan from a co-
rotating coordinate system. The results show a significant noise source in the
vicinity of the leading edge tip, while on the pressure side the leading edge mid-
chord area generates more noise. In general, the pressure side is louder.
Further measurements are necessary to investigate the trial functions behaviour
as well as to determine the generation mechanism of the noise sources.
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KIVONAT
A dolgozatban egy axiális ventilátor aerodinamikai veszteségeinek sugár menti
eloszlását hasonlítom össze a keletkezett zajjal [1] alapján.
Az aerodinamikai veszteségek becslése geometriai adatok és a belépő
sebességprofil mérése alapján történt. A számítások során figyelembe vettem a
lapátferdítés hatását. Két változót vizsgáltam: az veszteségi számot, illetve a
Lieblein diffúziós tényezőt [2]. Mindkét paramétert szintes írásmódban
használtam.
A zaj eloszlását mikrofontömb segítségével mértem. A mérési adatokat a
ventilátor forgása mentén átlagoltam, majd a sugár mentén forráserősség-eloszlási
diagramokat készítettem. Ezt mind a szívó, mind a nyomó oldalon elvégeztem a
2000 Hz-től 6300 Hz-ig terjedő tercsávokban. Ezekre a diagramokra mind , mind
felhasználásával hatványkitevős alakban írt próbafüggvényeket illesztettem. A
próbafüggvények paramétereit a legkisebb négyzetek módszerével határoztam
meg. Az eredmények alapján a szívó oldalon az -függő megoldás teljesít jobban
a 2000 Hz-3150 Hz tartományban illetve a teljes sávban is, míg a alapú közelítés
nem tudja visszaadni a függvények menetét. A nyomó oldalon hasonló a helyzet,
viszont a -függő megoldás is elfogadhatóan teljesít a mély tartományban. A teljes
sávban mindkét közelítés elfogadható. Néhány mérési pontban azonban a
közelítés eredménye ellentmond az eredeti feltevésnek, miszerint az
aerodinamikai veszteségek növekedése a zaj növekedésével járna együtt.
A ROSI [3] algoritmus segítségével zajtérképeket készítettem a ventilátorról
együttforgó koordináta-rendszerben. Az eredmények alapján a szívó oldalon a
belépőél csúcsa a legjelentősebb zajforrás, míg a nyomó oldalon a belépőél
középső része az. Általánosságban a nyomó oldalon keletkezik több zaj.
További mérések szükségesek az illesztett függvények viselkedésének
vizsgálata illetve a zajtérképeken látható források eredetének magyarázása
érdekében.
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CONTENTS
1. INTRODUCTION 5
2. AXIAL FANS, LOSSES AND NOISE 6
2.1. Fans 6 2.2. Fan types 6 2.3. Losses 7 2.4. Fan noise 8
3. PHASED ARRAY MICROPHONES 10
3.1. Time-domain beamforming 10 3.2. Frequency-domain beamforming 11 3.3. ROSI method [3] 13 3.4. Spatial resolution 15
4. GEOMETRY MEASUREMENT 16
4.1. Measured data 16 4.2. Calculated data 18 4.3. Uncertainties 19
5. AERODYNAMIC PROPERTIES 20
5.1. Inlet velocity measurement 20 5.2. Outlet velocity measurements 21 5.3. Calculations for unswept blades 21 5.4. Sweep correction 24 5.5. Uncertainties 25 5.6. Results 25
6. ACOUSTIC PROPERTIES 27
6.1. Equipment 27 6.2. Procedure 27 6.3. Delay-and-Sum results 29 6.4. Radial noise distribution 32 6.5. Source distribution on blades 38
7. SUMMARY 47
8. FURTHER AIMS 48
9. BIBLIOGRAPHY 49
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
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NOMENCLATURE
LATIN LETTERS
a speed of sound [m/s]
A, B function fitting coefficients [-]
AR aspect ratio [-]
d diameter [mm]
c chord [mm]
D diffusion factor [-]
e steering vector [-]
f blade curvature [mm]
fs sampling frequency [Hz]
Fourier operator
g tip clearance [mm]
h vector of signal spectra [Pa]
i unit vector in x direction [m]
j imaginary unit, √
L radial SPL distribution [dB]
M number of microphones
Ma Mach number [-]
n rotational speed [1/s]
N number of blades
p pressure [Pa]
P power [W]
q monopole intensity [kg/s2]
Q freq. domain monopole intensity
[kg/Hz2]
r radius [mm]
R outer radius [mm]
Rc camber radius [mm]
Rp pipe radius [mm]
R matrix of cross spectra [Pa2/Hz2]
s spacing [mm]
S auto spectrum [Pa2/Hz2]
t time [s]
u tangential velocity [m/s]
U tip tangential velocity [m/s]
v absolute velocity [m/s]
w relative velocity [m/s]
W weighting matrix
x observer location [m]
y source location [m]
z averaged PAM output [Pa]
Z freq. domain PAM output [Pa]
GREEK LETTERS
flow angle relative to blade [°]
sweep angle [°]
Dirac-delta function
difference
noise [Pa]
local flow number [-]
efficiency [-]
stagger angle [°]
wavelength [m]
PAM spatial resolution [m]
camber angle [°]
pressure number [-]
density [kg/m3]
retarded time [s]
circular frequency [rad/s]
SUBSCRIPTS / SUPERSCRIPTS
* complex conjugate K conjugate transposed
0 ambient conditions
1 suction side
2 pressure side
ax axial
is isentropic
m microphone index
mid medium value
re real
sw sweep corrected
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
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LIST OF FIGURES
Figure 2.1. Axial (left) and radial (right) fan schematics 6
Figure 4.1. The investigated fan [1] 16
Figure 4.2. Fan geometry 17
Figure 5.1. Nondimensional axial velocity profile 20
Figure 5.2. Characteristic curve of the investigated fan [12] 21
Figure 5.3. The relative deflection ε/ε* versus (i-i*)/ε* recreated from [13] 23
Figure 5.4. Aerodynamic properties along radius 26
Figure 6.1. The measurement setup 27
Figure 6.2. Comparison of source maps acquired with 30 s (left) and 20 s (right) averaging 28
Figure 6.3. DS source map at 2000 Hz mid-frequency 29
Figure 6.4. DS source map at 2500 Hz mid-frequency 30
Figure 6.5. DS source map at 3150 Hz mid-frequency 30
Figure 6.6. DS source map at 4000 Hz mid-frequency 30
Figure 6.7. DS source map at 5000 Hz mid-frequency 31
Figure 6.8. DS source map at 6300 Hz mid-frequency 31
Figure 6.9. DS source map at full band 31
Figure 6.10. A-weighting spectrum 33
Figure 6.11. SPL versus radius at 2 kHz on suction side 33
Figure 6.12. SPL versus radius at 2500 Hz on suction side 34
Figure 6.13. SPL versus radius at 3150 Hz on suction side 34
Figure 6.14. SPL versus radius at 4 kHz on suction side 34
Figure 6.15. SPL versus radius at 5 kHz on suction side 34
Figure 6.16. SPL versus radius at 6300 Hz on suction side 35
Figure 6.17. SPL versus radius at full band on suction side 35
Figure 6.18. SPL versus radius at 2000 Hz on pressure side 36
Figure 6.19. SPL versus radius at 2500 Hz on pressure side 36
Figure 6.20. SPL versus radius at 3150 Hz on pressure side 37
Figure 6.21. SPL versus radius at 4000 Hz on pressure side 37
Figure 6.22. SPL versus radius at 5000 Hz on pressure side 37
Figure 6.23. SPL versus radius at 6300 Hz on pressure side 38
Figure 6.24. SPL versus radius at full band on pressure side 38
Figure 6.25. Suction side source location at 0.5 m distance 39
Figure 6.26. Pressure side source location at 1 m distance 39
Figure 6.27. Synthetic algorithm source map 40
Figure 6.28. Suction side source map at 2000 Hz 41
Figure 6.29. Suction side source map at 2500 Hz 42
Figure 6.30. Suction side source map at 3150 Hz 42
Figure 6.31. Suction side source map at 4000 Hz 42
Figure 6.32. Suction side source map at 5000 Hz 43
Figure 6.33. Suction side source map at 6300 Hz 43
Figure 6.34. Suction side source map at full band 43
Figure 6.35. Pressure side source map at 2000 Hz 44
Figure 6.36. Pressure side source map at 2500 Hz 44
Figure 6.37. Pressure side source map at 3150 Hz 44
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
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Figure 6.38. Pressure side source map at 4000 Hz 45
Figure 6.39. Pressure side source map at 5000 Hz 45
Figure 6.40. Pressure side source map at 6300 Hz 45
Figure 6.41. Pressure side source map at full band 46
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
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LIST OF TABLES
Table 4.1. Geometric data along radius 17
Table 4.2. Interpolated 18
Table 4.3. Calculated data 19
Table 4.4. Dimensional uncertainties 19
Table 5.1: Uncertainties 25
Table 5.2: Calculated efficiencies, pressure numbers and diffusion factors 26
Table 6.1. Suction side function fit parameters 32
Table 6.2. Pressure side function fit parameters 36
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1. INTRODUCTION
Noise of turbomachinery is a growing concern. These pieces of equipment are
widely used in urban areas, buildings and offices; therefore reducing their noise is
of great importance.
The connection between aerodynamic losses and generated noise is investigated
in case of a short-ducted industrial fan following the methods described in [1].
Aerodynamic characteristics are estimated based on geometry and inlet velocity
profile measurements. The blade sweep is accounted for in the calculations. Two
parameters are investigated: loss coefficient and Lieblein diffusion factor [2].
Both parameters are written in a level-like, i.e. logarithmic form.
Noise distribution is measured using a Phased Array Microphone (PAM).
Radially averaged plots are created for the third octave bands from 2000 Hz to 6300
Hz and a linear fit using the least squares method is carried out to find parameters
that best approximate the noise as a function of either or both on suction and
pressure sides. The correctness of these approximations is investigated through the
R2 value as well as their behaviour.
The ROSI [3] method is used to generate source maps of the fan from a co-
rotating coordinate system. These maps are analysed to find the most important
noise sources. An attempt is made to explain their origin.
Finally, recommendations for further work are given.
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
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2. AXIAL FANS, LOSSES AND NOISE
Turbomachinery are pieces of equipment that transfer energy between a rotor
and a fluid [4]. This can happen in two ways: either energy is transported from the
fluid to the rotor (turbines) or from the rotor to the fluid. Machines realising the
latter method can be divided into three groups. In increasing order of pressure
ratio, these machines are: fans, blowers and compressors.
2.1. FANS
Fans are devices whose operation is based on Euler’s turbine equation [5]. They
are used to transport gases by generating a pressure ratio of
or lower. In
this case, because of the low pressure increase, fluid density and temperature can be
regarded as constant.
2.2. FAN TYPES
Fans are characterised by the direction of the flow and the rotational axis. The
two most common types are axial and radial fans, shown on Figure 2.1.
Figure 2.1. Axial (left) and radial (right) fan schematics
In the present thesis an axial fan transporting air from an open space to another
open space are investigated. In such a scenario, the total static pressure rise is 0,
since the static pressure on both sides is p0, the ambient pressure. The total pressure
rise is
(
)
(2.1)
Axial fans are capable of producing less total pressure rise than radial ones;
therefore their transported volume flow rate per unit power is larger.
Axial fans may come in several configurations: with flat plate blades or airfoil
profile blades, with our without nose cones and hub diffusers, with direct or
indirect drive etc. The investigated fan had flat plate blades. This has the advantage
of easier construction, but has aerodynamic drawbacks. Profiled blades are more
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
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apt since in that case the separation point can move on the leading edge under off-
design operating conditions, thus the efficiency in these cases is higher.
2.3. LOSSES
The different losses of axial fans are described here based on [5].
2.3.1. Friction loss
Due to friction, the air on the suction side of the blades loses some of its velocity.
The boundary layer thickens and the losses grow. This loss can be minimised by
choosing a blade profile with the highest lift-to-drag ratio.
2.3.2. Secondary loss
The term “secondary loss” refers to the losses that occur because of the real flow
being different from the ideal designed one, inside the region enclosed by two
blades, the hub and the duct. In modern fan design the whole flow is considered as
one 3D phenomenon, so that such distinctions are not used anymore.
2.3.3. Annulus loss
Pressure loss caused by friction on the hub surface and the casing surface is
called annulus loss.
2.3.4. Tip clearance loss
The name refers to the pressure loss that occurs because of unwanted tip
clearance flow. This is the most important source of loss and has a significant
contribution to noise, too.
2.3.5. Guide vane loss
The presence of guide vanes causes two types of losses: friction and secondary
loss. But since the relative velocity is lower, the losses are lower too, than that of the
rotor.
2.3.6. Swirl loss
This loss occurs when guide vanes are not applied, or when the fan in operated
in an off-design point. The rotational loss equals to the kinetic energy of the rotating
jet per unit time. It can be avoided by a contra-rotating arrangement, but that is an
expensive and very noisy solution.
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
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2.3.7. Diffuser loss
Diffuser loss occurs in two cases. Firstly, in case of a ducted fan, the flow
between the hub and the duct is decelerating, which may cause separations and
pressure losses to occur. This can be avoided by using a hub diffuser that extends
into the pipe and helps to slowly increase the cross section, thus avoids separation.
Secondly, when the air enters free space: in this case the outlet velocity should be
chosen as low as possible, so that the Borda-Carnot loss is minimised.
2.4. FAN NOISE
Fans are responsible for the most noise in ventilation systems. There are several
noise generation mechanisms that are detailed here based on [6].
2.4.1. Mechanical noise
Mechanical noise originates mainly from two sources: bearing noise and the
noise of unbalanced rotating parts.
In most cases ball bearings are used to support the shaft. Ball rotation causes
vibration in the structure that is radiated from the housing as noise. This is the case
for unbalanced rotors. too. Usually mechanical noise is only important at slowly
rotating fans because at higher speeds aerodynamic noise increases significantly. In
the domain below 25 [m/s] however, mechanical noise is an important source
especially because of the high frequency and presence of tonal components that
make it more annoying than broadband low frequency aerodynamic noise.
2.4.2. Vortex noise
Behind a bluff body submerged in a flow a separation bubble might appear that
causes the formation of vortices. When the Reynolds number is high, viscosity
cannot dissipate these and vortex shedding occurs behind the body. This causes a
fluctuating force that is a source of dipole noise. The noise power is found to be
proportional to the sixth power of velocity.
(2.2)
Already in a non-separated flow the turbulent boundary layer (BL) on the blades
acts as a noise source. This is a dipole source too, since the fluctuating pressure
acting on the blade surface generates a fluctuating force, therefore the power is
again proportional to the sixth power of the velocity.
(2.3)
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The incoming turbulent flow serves as a noise source too, since the velocity
fluctuations perpendicular to the mean velocity direction create a time-varying
fluctuation and a dipole source, too. The power is again proportional to the sixth
power of the velocity.
(2.4)
The most important contribution is usually from the vortices shed behind the
blade trailing edge. These vortices are formed as the interaction of different
pressure and suction side flow velocities. The trailing edge noise power scales with
velocity6, too.
(2.5)
2.4.3. Rotational noise
The periodic motion of the rotor causes a pressure fluctuation that is the cause of
rotational noise. The intensity and frequency dependence of this contributor
depends heavily on the tip clear size between the rotor and the casing. Rotational
noise is however not important in the velocity range in which axial fans usually
operate as it only becomes significant at about 100 [m/s] of tangential velocity.
2.4.4. Turbulent noise
The turbulent flow itself can be a significant noise source. Its intensity is
proportional to the eighth power of velocity [7] since it is described as a
quadrupole. As such it only becomes important at fairly high velocities (above 50
[m/s]). It is important to note that the spectrum shape is velocity-dependent too: a
two-fold increase in velocity means a six-fold frequency increase.
(2.6)
2.4.5. Rotor-stator interaction noise
The rotor wake impinging on a nearby object creates the rotor-stator interaction
noise. This can be a very significant noise source, especially if the number of the
stators (engine supports etc.) equals to the number of blades. The generated noise is
tonal, therefore it is very annoying. Rotor-stator interaction can be avoided by
placing the supports far from the rotor or if that is not possible, the rotor and stator
number should be chosen to be relative primes to each other.
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
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3. PHASED ARRAY MICROPHONES
For a long time, acoustic experiments were limited to the measurement of overall
noise. With the rapid development of computers however, the identification of and
spatial differentiation between noise sources has become possible. This process is
carried out by Phased Array Microphones (PAM). In most cases, the delay-and-sum
(DS) technique is used, either in time or in frequency domain to provide data about
the positions of the most important noise sources.
Beamforming consists of recording several microphone signals, then
decomposing the spatial domain into focus points, calculating the time delays for
each of them and calculating the output value by assuming a source at the actual
focus point. If the value of the output is large, it means that the source was at the
focus point, if it is small then there was no source at the focus point. Using this
method it is possible to reconstruct the spatial distribution of sound sources.
3.1. TIME-DOMAIN BEAMFORMING
The operation of time-domain beamforming is described here based on [8].
A sound field of a monopole source at y0 is described by the following equation:
( ) ( ) (3.1)
where p is the pressure, is the speed of sound, q is the monopole intensity, t is
the temporal, x is the spatial coordinate and δ is the Dirac-delta function. The
solution in the free field is the well-known Green function:
( )
( | |
)
| | (3.2)
This expression means that the emitted signal arrives to the observation point
after a time delay or retarded time | |
and its magnitude is multiplied by a factor
of
| | accounting for the decrease in intensity as the cross section area grows in
case of spherical wave propagation.
Time-domain beamforming uses a set of M microphones placed at locations xm
that record the pressure fluctuations. The retarded time
| |
(3.3)
is the time when the signal reaching the microphone m=1…M was emitted by the
source. Assuming a source at the yf focus position, time difference is
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
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| |
(3.4)
The recorded pressure fluctuations are compensated for this time difference and
the microphone signals are summed, with amplitude correction taking the different
source―microphone distances into account. The output z is then
( )
∑
| |
| |
( ) (3.5)
The expression means that the output signal z for an assumed source can be
given as a function of time by averaging the contributions of each microphone. Each
contribution consists of q source output taken at . This is to assure
that signals from the same phase are summed even though the sound waves have
to travel different paths towards each microphone. Then the amplitude is corrected
by a factor corresponding to the distance of the microphone and the source to
balance the effects of decreasing amplitude over propagation length.
If the focus position coincides with the source position , ( ) ( ) is
obtained, otherwise the signal in different phases should result in an average of a
lower value.
3.2. FREQUENCY-DOMAIN BEAMFORMING
The previously discussed DS technique can also be applied in the frequency
domain as described in [8] for a stationary source.
The discrete Fourier transform of the time-domain signal recorded by
microphone m=1…M at location xm using sampling frequency fs is given as
( ) ∑ ( )
(3.6)
where
(3.7)
are the discrete frequencies at which the transformation is done, N is the number
of samples, n is the current sample index and j is the imaginary unit.
After transforming equation (2.6) the following is obtained:
( )
∑
| |
| |
( )
( ) (3.8)
As usual, the distance was chosen as the weighting factor in order to cancel the
amplitude reduction due to the intensity change. In the expression above, Q is the
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
12
frequency-domain monopole source intensity, yf is the focus location, y0 is the
source location, is the time delay between microphone m and the source,
while is the time delay between microphone m and the focus point.
Z variable then gives the frequency-domain output at a chosen focus point as
a function of discrete frequencies as a sum over each microphone. The summed
contribution of each microphone is the Q source intensity at the frequency in
question normalized by the distances of the microphone to the focus and the source
to account for the decreasing intensity because of the spherical wave propagation.
The exponential part modifies the phase. This is important because the sound
waves have to travel different paths to each microphone that would modify the
result. By this method, we can assure that the summation is carried out with the
same emitted signal phase.
It is still true that the expression has a maximum when the source is at the
investigated focus point:
( )
∑ ( )
( ) (3.9)
The array output in (3.8) is reformulated using a matrix notation:
( ) (3.10)
where ( ) denotes the conjugate transposed of a vector or matrix. In the vector h
the Fourier transformed microphone signals m=1…M are collected:
( ) (
( ) ( )
( )
) (3.11)
e is called the steering vector, a phasor with exponents chosen to cancel the phase
shifts due to wave propagation:
(
) (3.12)
The microphone weights are summarized in the diagonal matrix W:
(
( ) ( ) ( )
) (3.13)
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
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In practical applications the signal and therefore the results in Z are very noisy.
To reduce the noise, the output is averaged over a certain K number of windows. It
can be shown that as the number of averages goes to infinity, the average Z goes to
zero. The auto spectrum is calculated as
( )
∑
( ) ( )
(3.14)
where the asterisk denotes the complex conjugate and ( ) is the array output
for the ith window. This can be summarised as
( ) (3.15)
where ( ) is the matrix of cross spectrum density estimates:
( )
∑
( ) ( )
(3.16)
In the expression above, W is a correction factor that takes into account the
energy loss caused by the window function and ( ) is the ith sample recorded
by microphone m. These values are arranged into matrix R in the following way:
(
( )
( ) ( )
( )
( ) ( )
( ) ( )
( ))
(3.17)
In some cases the signal-to-noise ratio (SNR) may still be low. This can be
increased by removing the main diagonal from matrix R, since the values there
contain auto cross spectra [9]. These spectra are more vulnerable to external noise
since they are computed from one microphone signal only. The SNR can then be
increased by applying a modified matrix R’:
(
( )
( )
( )
( )
( ) ( ) )
(3.18)
3.3. ROSI METHOD [3]
The previously discussed beamforming method is only applicable to stationary
sources. The theory and, based on that, a computer program called ROSI was
developed that can handle moving sources too [3]. In the current investigation
about fans, the emphasis is of course on rotary motions.
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
14
First, the equation for the sound pressure field of a moving monopole is given
using the notation of Equation (3.1):
( ) ( ( )) (3.19)
In the current case, the source position y is a function of time. The convective
derivative is defined as
(3.20)
where Ma is the Mach number of the flow. Using that and the results of Dowling
and Ffowcs Williams [10] the T(x, y(τe), t, τe) transfer function between the moving
source and the receiver at x is written as
( ( ) )
( ( ( ) )) (3.21)
In the expression above, the emission time τe is defined using the x direction unit
vector i in the following way:
| ( ) ( ) | (3.22)
while Q is the inner product
( ( ) ) ( ( ) ( ) ) (3.23)
Using transfer function T, the pm signal recorded by microphone m can be written
as
( ) ( ( ) ) ( ) ( ) (3.24)
where ( ) is the noise and the contribution from other sources. This can be
written briefly as
( ) ( ) ( ) ( ) (3.25)
using the different tm receiver times for different microphones from (3.22).
A reconstructed array output signal ( ) can be found using the DS procedure:
( )
∑ ( )
(3.26)
where the reconstructed source signal is
( )
( )
( ) (3.27)
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
15
The frequency spectrum is calculated as the discrete Fourier transform of the
source signal:
( )
∑ ( )
(3.28)
The auto power spectrum is then
| ( )|
|∑ ( )
|
∑ ∑ ( )
( )
(3.29)
The theory and the ROSI computer programme were tested on a rotating whistle,
a model-scale helicopter and a wind turbine rotor and it proved its value in the
identification of noise sources on rotating objects.
3.4. SPATIAL RESOLUTION
The spatial resolution of a phased array microphone is [11]
(3.30)
where is the target distance from the PAM, is the wavelength
corresponding to the mid-frequency of interest and is the characteristic
dimension of the PAM.
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
16
4. GEOMETRY MEASUREMENT
In order to be able to calculate aerodynamic properties along the blade radius of
the assigned fan, geometrical measurements had to be taken at several points.
Measured were the chord c, the curvature f, the stagger angle γ, and the sweep
angle at each point. Additional measurements were also taken to help calculate
the necessary quantities. These are listed below. Measurement uncertainties were
estimated as well.
Figure 4.1. The investigated fan [1]
4.1. MEASURED DATA
The following data were measured. Duct diameter Dp=315 [mm] corresponding
to a duct radius Rp=157.5 [mm]. Fan diameter Df=300 [mm], therefore the fan radius
is R=150 [mm]. Hub diameter dh=94 [mm], therefore hub radius rh=47 [mm]. The tip
clearance was g=7.5 [mm], constant along the circumference. Number of blades is
N=5. Figure 4.2 shows the interpretation of geometric data.
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
17
Figure 4.2. Fan geometry
Table 4.1 contains the chord c, curvature f, stagger angle γ and axis-normal
sweep angle β’ values at five radii nondimensionalised with Rp hub radius.
r/Rp=0.30 is the hub radius, r/Rp=0.63 is the midspan radius and r/Rp=0.95 is the
outermost blade radius (tip). As seen above, β’ is measured in the plane normal to
the axis of rotation.
Table 4.1. Geometric data along radius
r/Rp [-] r [mm] c [mm] f [mm] γ [°] β’ [°]
0.30 47 88 12 35 0
0.46 73 97 9 33 23
0.63 99 108 9 31 31
0.79 124 118 8 29 39
0.95 150 130 8 27 44
The data were measured using a ruler, a calliper and a Leica Racer 100 electric
angle measurement device.
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
18
In order to provide a smoother distribution of the dimensions and account for
measurement error the data – with the exception of f – were fitted with second-
order polynomials and the interpolated values were used in the following. In
addition to that, the value of β’ was modified to obtain β, the angle in the plane of
the blade (rotated by the stagger angle). This was done based on Equation (4.1).
(4.1)
Table 4.2 contains the interpolated values.
Table 4.2. Interpolated geometric data
r/RP [-] r [mm] c [mm] f [mm] γ [°] β [°]
0.30 47 87.93 12 35.00 1.81
0.46 73 97.45 9 33.00 23.19
0.63 99 107.77 9 30.98 37.04
0.79 124 118.46 8 29.03 44.52
0.95 150 130.38 8 26.99 47.06
4.2. CALCULATED DATA
Knowledge of the geometric data made possible the calculation of the spacing s,
the solidity c/s, the camber radius Rc and the camber angle θ. The formulae are the
following.
(4.2)
(4.3)
( ) (4.4)
Inlet and outlet flow angles are:
(4.5)
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
19
(4.6)
Table 4.3 contains these values along the radius.
Table 4.3. Calculated data
r/RP [-] s [mm] c/s [-] Rc [mm] θ [°] α1’ [°] α2’ [°]
0.30 59.06 1.49 86.54 61.07 85.53 24.46
0.46 91.73 1.06 136.38 41.86 77.93 36.07
0.63 124.41 0.87 165.81 37.93 77.98 40.05
0.79 155.82 0.76 223.27 30.77 76.35 45.58
0.95 188.50 0.69 269.60 27.99 77.00 49.01
4.3. UNCERTAINTIES
Measurement uncertainties were estimated by measuring each dimension ten
times. The uncertainties are listed in Table 4.4.
Table 4.4. Dimensional uncertainties
c [mm] f [mm] γ [°] β [°]
±2 ±1 ±0.2 ±1
In each case except for the blade angle, the interpolated values were found to be
inside of the uncertainty region.
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
20
5. AERODYNAMIC PROPERTIES
Aerodynamic properties of the fan were evaluated along the radius to be
comparable with phased array microphone noise measurements. The inlet velocity
profile was measured, and then the characteristic variables, such as the Ψ pressure
number, the η efficiency and the D diffusion factor were calculated. The data were
corrected to account for the skewed blades based on literature.
5.1. INLET VELOCITY MEASUREMENT
The inlet velocity was recorded at several points to allow the calculation of the
aerodynamic properties of the fan. These measurements were carried out using a
“Mini-Air” Dostmann P670 turbine anemometer. In total, four radii were examined
and the velocity profiles were found to be in good agreement with each other.
Then tangential velocity of the fan u was determined:
(5.1)
where n=23.29 [1/s] is the rotational speed measured by a stroboscope.
The local flow number is calculated as the measured axial velocity divided by the
tip tangential velocity:
(5.2)
The average profile is shown on Figure 5.1 versus the nondimensional radius
along with a second order polynomial fit. The error bars indicate 5% error, which is
a characteristic value of Mini-Air measurements in this velocity range.
Figure 5.1. Nondimensional axial velocity profile
0.10
0.20
0.30
0.40
0.50
0.00 0.25 0.50 0.75 1.00
φ [
-]
r/Rp [-]
♦ measured
▬ fitted
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
21
The volume flow rate calculated based on the velocity measurements is 1948
[m3/h], which is in good agreement with the findings of a previous report [12].
Figure 5.2 shows the characteristic curve of the investigated fan.
Figure 5.2. Characteristic curve of the investigated fan [12]
5.2. OUTLET VELOCITY MEASUREMENTS
The outlet velocity was measured along four radii using the same Mini-Air
probe. The results were however found to be erroneous. This is because of the large
separation bubble behind the fan hub that causes backflow. The Mini-Air is not able
to differentiate between directions when measuring velocity, thus the data could
not be used. Velocity measurements would have been possible using Laser Doppler
Anemometry (LDA), but this technique was not available.
5.3. CALCULATIONS FOR UNSWEPT BLADES
In order to calculate efficiency and pressure number distribution along the radius
r the following calculations were carried out.
The real inlet angle was determined on the basis of the velocity magnitudes
assuming :
(5.3)
The angle difference i can then be determined as the difference of the two angles:
(5.4)
Assuming nominal operating conditions, α1=α1*. The nominal outlet angle α2* is
calculated as follows [13]:
0
10
20
30
40
50
60
500 750 1000 1250 1500
Δp
[Pa]
Q [m3/h]
♦ measured
▬ fitted
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
22
(
) (5.5)
The value of m is:
(5.6)
assuming circular blade profiles. With this, δ* is:
(
)
(5.7)
The angle α2’* is then
(5.8)
while α1’* is
(5.9)
The nominal angle of incidence i* is defined as the following:
(5.10)
while
(5.11)
and
(5.12)
Values of flow deflection can be read from Figure 5.3 taken from [13] as a
function of the dimensionless parameter group
.
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
23
Figure 5.3. The relative deflection ε/ε* versus (i-i*)/ε* recreated from [13]
Using this figure to calculate ε, α2 is given as:
(5.13)
The outlet axial velocity is assumed to be identical to the inlet velocity:
(5.14)
Thus the relative outlet velocity is
(5.15)
The tangential component of the outlet velocity is
(5.16)
It was assumed that the air exits at the same radius where it entered the fan. The
total isentropic pressure rise is then calculated from Euler’s turbine equation
(5.17)
While the total real pressure rise in case of a fan blowing from free space to free
space is
(
) (5.18)
The efficiency is defined as the real-to-isentropic pressure rise ratio:
(5.19)
The pressure numbers are defined as the pressure rise at the given radius
divided by the dynamic pressure calculated at the outermost radius, that is:
0.2
0.4
0.6
0.8
1.0
1.2
1.4
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
ε/ε*
[-]
(i-i*)/ε* [-]
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
24
(5.20)
where
(5.21)
5.4. SWEEP CORRECTION
The results of the previous calculations have to be corrected in case of swept
blade fans. This is done based on [14].
First, the angle λ is calculated
(
) (5.22)
Then, using the midspan value of the M parameter is calculated as
(5.23)
The blade aspect ratio AR is
(5.24)
where cmid is the chord value at midspan. Using these, A=0.5 can be found from
[14] so that
(5.25)
Using CF, the isentropic pressure number after sweep correction is
(5.26)
The tangential component of the absolute outlet velocity after sweep correction is
(5.27)
The real pressure number after sweep correction is
(5.28)
The outlet angle after sweep correction
(5.29)
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
25
The D diffusion factor is calculated to take the losses attributed to the widening
blade channels and the adverse pressure gradient into account
( ) (5.30)
The diffusion factor after sweep correction is
( ) (5.31)
The efficiency after sweep correction
(5.32)
5.5. UNCERTAINTIES
Since the estimation of uncertainties would have been very difficult, a simplified,
strongly conservative approach was used. First, all measured variables were set to
their measured values minus the measurement uncertainty and the calculated
values were recorded. Then the measured variables were set to their measured
values plus the uncertainty and the calculated values were recorded again. The
difference of the two values was regarded as the uncertainty. These are given in
Table 5.1 below.
Table 5.1: Uncertainties
η
[-]
Ψis
[-]
Ψre
[-]
D
[-]
ηsw
[-]
Ψis,sw
[-]
Ψre,sw
[-]
Dsw
[-]
0.06 0.02 0.01 0.04 0.07 0.01 0.01 0.04
5.6. RESULTS
The results of the aerodynamic calculations are given below in Table 5.2.
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
26
Table 5.2: Calculated efficiencies, pressure numbers and diffusion factors
r/Rp
[-]
η
[-]
Ψis
[-]
Ψre
[-]
D
[-]
ηsw
[-]
Ψis,sw
[-]
Ψre,sw
[-]
Dsw
[-]
0.30 0.84 0.08 0.07 0.01 0.36 0.85 0.08 0.07
0.46 0.57 0.17 0.10 0.07 0.42 0.58 0.17 0.10
0.63 0.50 0.25 0.13 0.12 0.38 0.51 0.24 0.12
0.79 0.50 0.31 0.15 0.16 0.33 0.50 0.30 0.15
0.95 0.47 0.46 0.21 0.24 0.35 0.47 0.45 0.21
The spanwise distribution of these values along the radius is demonstrated on
Figure 5.4.
Figure 5.4. Aerodynamic properties along radius
One may observe that the sweep correction hardly modifies the efficiencies and
the diffusion factors. The efficiency is highest at the innermost radius and decreases
as the coordinate tends towards the blade tip. The diffusion factors have a smaller
variation along the radius, starting from low, reaching a plateau and the slightly
decreasing again. The pressure numbers are increasing along the radius, which is
understandable given the increasing tangential velocity. There is a significant
difference between the real and the isentropic pressure numbers, and the difference
grows with the radius.
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.25 0.5 0.75 1
η [
-]
ψis
, ψ
v ,
ω, D
, φ
[-]
r/Rp [-]
x η x ηsw
● ψis ● ψis,sw
♦ ω ♦ ωsw
■ D ■ Dsw
▲ψv ▲ψv,sw
+ φ
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
27
6. ACOUSTIC PROPERTIES
The acoustic properties of the fan were measured using a phased array
microphone. The acoustic investigation had two aims. Firstly, to acquire the
averaged radial noise distribution of the fan in order to compare with the radial
distribution of aerodynamic properties as described above. Secondly, to create noise
maps of the fan in a co-rotating system of coordinates. This would allow the
identification of noise sources on the fan blade geometry.
6.1. EQUIPMENT
The measurement setup is shown on Figure 6.1. The measurement setup The
noise signals were recorded using a 24-channel phased array microphone (PAM).
The PAM was attached to amplifier and to a device responsible for sampling and
digitizing the microphone data (ADC). The digital data was fed into a personal
computer (PC) that saved the measurement files. In order to measure rotation
speed, an optical tachometer (TACH) was attached to the fan (FAN), whose output
was connected to the sampler in the place of one of the microphones.
Figure 6.1. The measurement setup
FAN denotes the investigated fan, TACH is the optical tachometer, ADC is the sampler and
analogue-to-digital converter, PC is the computer used to gather the data.
6.2. PROCEDURE
Radial noise distribution was recorded using the phased array measurement
technique. 30 [s] long noise samples were recorded at a sampling frequency of 44.1
[kHz]. When measuring the suction side, the microphone array was placed at a
distance of 0.5 [m] from the fan in order to achieve good spatial resolution. On the
pressure side however, this distance was not applicable as the aerodynamic
pressure fluctuations caused the overload of the amplifier, therefore the distance
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
28
had to be increased to 1 [m]. An optical tachometer was attached to the fan to
record the instantaneous angular velocity.
The effect of sample length was evaluated as seen on Figure 6.2. It was
concluded that no significant difference can be seen between a 20 [s] and a 30 [s]
long sample, as seen on the figures.
Figure 6.2. Comparison of source maps acquired with 30 s (left) and 20 s (right) averaging.
The two images were taken with the same colour bar settings.
The samples were processed using the Acubeam software programmed by Péter
TÓTH and the results were then averaged along concentric circles in Tecplot using
100 nodes in both radial and circumferential directions.
From here, a procedure described in [1] was applied. The spanwise noise
pressure distribution was assumed to be a monotonically increasing function of
aerodynamic loss. Two quantities were considered to describe this loss: the loss
coefficient and the D diffusion factor. The two test functions were written in a
power form as follows:
(6.1)
(6.2)
Since the measured quantity is sound pressure level (SPL), it is convenient to
write the above equations in a level-form, taking their base-10 logarithm and
multiplying them by 20. This gives the following expressions for the sound pressure
levels depending on the loss coefficient ( ) and the diffusion factor ( ):
( ) (6.3)
( ) (6.4)
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
29
Introducing the “loss level”
(6.5)
and the “diffusion level”
(6.6)
the equations can be written in the following form:
(6.7)
(6.8)
The new parameters and were found by applying a least-
squares fit onto the measured radial SPL distribution at the five known values of
and calculated above.
6.3. DELAY-AND-SUM RESULTS
DS results were obtained using the ImageJ program and its special plugins for
each third-octave band at both pressure and suction sides.
Figure 6.3. DS source map on suction side (left) and pressure side (right)
at 2000 Hz mid-frequency
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
30
Figure 6.4. DS source map on suction side (left) and pressure side (right)
at 2500 Hz mid-frequency
Figure 6.5. DS source map on suction side (left) and pressure side (right)
at 3150 Hz mid-frequency
Figure 6.6. DS source map on suction side (left) and pressure side (right)
at 4000 Hz mid-frequency
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
31
Figure 6.7. DS source map on suction side (left) and pressure side (right)
at 5000 Hz mid-frequency
Figure 6.8. DS source map on suction side (left) and pressure side (right)
at 6300 Hz mid-frequency
Figure 6.9. DS source map on suction side (left) and pressure side (right)
at full band
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
32
As seen on the figures, the DS method is not able to handle rotating sources. The
output is such a case is a smoothed, radially almost symmetric map that is due to
the rotating fan. It can still be used to illustrate some radiation characteristics of the
fan though. It is clearly visible that the outer radius of the fan is the dominant noise
source, which is expected because of the increasing tangential velocity. This can
only be observed on the suction side maps however, as on the pressure side the
larger target distance causes the decreases of PAM spatial resolution. The DS
method is able to give an estimate of the source strengths as well.
6.4. RADIAL NOISE DISTRIBUTION
6.4.1. Suction side results
Table 6.1 shows the parameters and the R2 values of the function fit for the
different third octave frequency bands on the suction side.
Table 6.1. Suction side function fit parameters
fmid [Hz] A2,ω B2,ω R2ω A2,D B2,D R2D
2000 68.18 3.21 0.94 60.59 -9.17 0.05
2500 65.04 1.06 0.47 64.34 1.01 0.00
3150 61.89 3.87 0.93 51.77 -13.21 0.07
4000 52.32 1.59 0.21 36.08 -32.43 0.60
5000 47.66 -0.69 0.06 48.44 0.04 0.00
6300 44.60 -2.24 0.26 47.55 1.14 0.00
full band 75.97 1.98 0.95 70.55 -7.31 0.09
The results show agreeable R2 values for the loss coefficient (ω) dependency in
the low frequency range. This is a welcomed result, since from the viewpoint of
human comfort, the 2000-3150 Hz frequency range is the most important regime.
This can be seen from the large positive weighting in the dB(A) scale in this
frequency range show on Figure 6.10. The fan also radiates with a much higher
intensity in this deep range that causes the full band data to fit well onto the ω
dependent trial function but worse on the diffusion factor dependent one.
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
33
Figure 6.10. A-weighting spectrum
It is important to note that the negative coefficients occurring for the loss
coefficient dependent approximations at 5 kHz and 6.3 kHz, and for the diffusion
factor dependent approximations at 2 kHz, 3150 Hz, 5 kHz and the full band mean
that increasing aerodynamic loss leads to decreasing noise. These measurement
points do not support the original theory that noise is an asymptotically increasing
function of aerodynamic loss.
On the figures below, LM is the source intensity distribution acquired with
diagonal removal on, while LM’ is without diagonal removal.
Figure 6.11. SPL versus radius at 2 kHz on suction side
-25
-20
-15
-10
-5
0
5
20 200 2000 20000
A [
dB(A
)]
f [Hz]
60
62
64
66
68
0.25 0.50 0.75 1.00
LP [
dB]
r/Rp
fmid=2 kHz
─ LM
─ LM' ■ LPω
▲LPD
62
64
66
68
0.25 0.50 0.75 1.00
LP [
dB]
r/Rp
fmid=2.5 kHz
─ LM
─ LM' ■ LPω
▲LPD
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
34
Figure 6.12. SPL versus radius at 2500 Hz on suction side
Figure 6.13. SPL versus radius at 3150 Hz on suction side
Figure 6.14. SPL versus radius at 4 kHz on suction side
Figure 6.15. SPL versus radius at 5 kHz on suction side
52
54
56
58
60
62
64
0.25 0.50 0.75 1.00
LP [
dB]
r/Rp
fmid=3150 Hz
─ LM
─ LM' ■ LPω
▲LPD
48
50
52
54
56
58
60
0.25 0.50 0.75 1.00
LP [
dB]
r/Rp
fmid=4 kHz
─ LM
─ LM' ■ LPω
▲LPD
44
46
48
50
52
54
56
58
0.25 0.50 0.75 1.00
LP [
dB]
r/Rp
fmid=5 kHz
─ LM
─ LM' ■ LPω
▲LPD
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
35
Figure 6.16. SPL versus radius at 6300 Hz on suction side
Figure 6.17. SPL versus radius at full band on suction side
Figure 6.11 through Figure 6.17 show the estimated SPL distributions and the
actual measured one versus the radius. The estimations are agreeable at 2000, 2500
and 3150 Hz mid-frequencies, but above that they fail to follow the trends in the
SPL function. The full band estimation is good due to the fact that most of the
intensity is radiated in the low frequency domain, where the estimations work
relatively well.
6.4.2. Pressure side results
Table 6.2 shows the parameters of the fitted functions on the pressure side.
42
44
46
48
50
52
54
56
0.25 0.50 0.75 1.00
LP [
dB]
r/Rp
fmid=6.3 kHz
─ LM
─ LM' ■ LPω
▲LPD
70
72
74
76
78
0.25 0.50 0.75 1.00
LP [
dB]
r/Rp
full band
─ LM
─ LM' ■ LPω
▲LPD
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
36
Table 6.2. Pressure side function fit parameters
fmid [Hz] A2,ω B2,ω R2ω A2,D B2,D R2D
2000 65.86 -1.60 0.72 73.53 13.26 0.33
2500 65.05 -0.63 0.50 68.63 6.47 0.36
3150 62.79 0.82 0.68 61.40 -1.11 0.01
4000 59.29 0.20 0.03 61.77 6.02 0.16
5000 55.17 1.46 0.44 55.90 5.17 0.04
6300 48.71 0.18 0.01 57.34 19.70 0.44
full band 76.69 -0.46 0.20 80.61 7.66 0.39
On the pressure side the R2 values are generally lower than on the suction side. It
is again important to highlight the frequency bands with negative coefficients, such
as 2 kHz and 2.5 kHz for the loss coefficient dependent approximation and 3150 Hz
for the diffusion factor dependent approximation. In these cases, increasing
aerodynamic loss leads to decreasing noise. This is against our initial assumption
stating that there should be a monotonically increasing relationship between the
losses and noise.
Figure 6.18. SPL versus radius at 2000 Hz on pressure side
Figure 6.19. SPL versus radius at 2500 Hz on pressure side
66
67
68
69
70
0.25 0.50 0.75 1.00
LP [
dB]
r/Rp
fmid=2 kHz
─ LM
─ LM' ■ LPω
▲LPD
64
65
66
67
68
0.25 0.50 0.75 1.00
LP [
dB]
r/Rp
fmid=2.5 kHz
─ LM
─ LM' ■ LPω
▲LPD
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
37
Figure 6.20. SPL versus radius at 3150 Hz on pressure side
Figure 6.21. SPL versus radius at 4000 Hz on pressure side
Figure 6.22. SPL versus radius at 5000 Hz on pressure side
60
61
62
63
64
65
0.25 0.50 0.75 1.00
LP [
dB]
r/Rp
fmid=3150 Hz
─ LM
─ LM' ■ LPω
▲LPD
58
59
60
61
62
0.25 0.50 0.75 1.00
LP [
dB]
r/Rp
fmid=4 kHz
─ LM
─ LM' ■ LPω
▲LPD
50
52
54
56
58
60
0.25 0.50 0.75 1.00
LP [
dB]
r/Rp
fmid=5 kHz
─ LM
─ LM' ■ LPω
▲LPD
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
38
Figure 6.23. SPL versus radius at 6300 Hz on pressure side
Figure 6.24. SPL versus radius at full band on pressure side
Figure 6.18 through Figure 6.24 show the calculated and the measured radial SPL
distribution. Both approximations, but especially the diffusion factor dependent
one, seem to give acceptable results in the low frequency range. Besides that the
agreement is quite poor. Again, because of the high relative intensity in the low
range, the full band approximation is acceptable.
Effects of diagonal removal can also be deduced from the figure. The method
decreases the signal amplitude but increases its dynamic range. Besides that, it
barely modifies the shape of the functions; therefore it can be used well to obtain
information about source distribution.
6.5. SOURCE DISTRIBUTION ON BLADES
The Acubeam ROSI algorithm was used to create blade source maps in the co-
rotating system. This allows the identification of significant noise sources on the
blade.
46
48
50
52
54
56
58
0.25 0.50 0.75 1.00
LP [
dB]
r/Rp
fmid=6.3 kHz
─ LM
─ LM' ■ LPω
▲LPD
76
77
78
79
80
0.25 0.50 0.75 1.00
LP [
dB]
r/Rp
full band
─ LM
─ LM' ■ LPω
▲LPD
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
39
6.5.1. ROSI rotation tests
Before taking any actual measurements, it had to be examined where the
Acubeam algorithm places the sources on the circumference of their rotation path,
i.e. what is the phase difference between the phase used to display the sources and
the phase when the tach signal arrives.
To achieve this, test measurements were taken with a localized source. The test
source was placed on the same radial line as the reflective dot used for the optical
tachometer. This allowed the determination of the phase difference between the
tach signal and the rotated source on the output image. Several setups were
analysed: multiple distances and both the pressure and the suction side was
investigated. Source maps of very low dynamic range were created and the rotation
angle was then obtained. Several results were analysed to establish a reliable value
with uncertainties.
The results show that the algorithm rotates the source map by about the
following amounts:
on the pressure side at a distance of 1 m, by -13.30°±2.15°
on the suction side at a distance of 0.5 m, by 6.15°±1.35°.
These pictures of the localised source are shown on Figure 6.25 and Figure 6.26.
The dot indicates the midpoint axis of the PAM, the small circle is the theoretical
location of the source and the colourful area is the measured source location. The
dashed circle indicates the source path, while the arrow shows the direction of
rotation.
Figure 6.25. Suction side source location
at 0.5 m distance
Figure 6.26. Pressure side source location
at 1 m distance
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
40
6.5.2. Synthetic source
In order to further investigate the rotation effects of Acubeam, an algorithm was
developed in MATLAB that generates the noise recorded by each microphone in
the presence of a monopole source rotating at a given radius with a given angular
velocity in a plane parallel to the PAM plane. This solution allows the investigation
of several variables, like angular velocity, direction of rotation, distance from the
PAM etc. in a controlled manner. The algorithm can generate signals of different
sampling rates and accounts for the variable distances and reception phases during
the monopole movement. It also incorporates the Doppler effect.
The output noise from this algorithm was fed into the Acubeam software and
source maps similar to the previous ones were created. These source maps show the
synthetic source exactly at its place at the start time, at 0 rotational phase, on the
horizontal axis. This suggests that the Acubeam algorithm places the sources
exactly to the place where it assumed it at the time of the tach signal. Such a source
map is shown on Figure 6.27.
Figure 6.27. Synthetic algorithm source map
In this case, the angle differences found above have to be explained in some way,
since according to this result all measured sample noise sources should lay on the
horizontal axis. A possible explanation is that the swirling flow coming from the fan
is able to modify the path of the sound waves. This effect together with the fact that
the sample source is not a geometrical point but has a finite size and with the
PAM’s finite spatial resolution may account for the experienced rotation angles.
Since the main aim is to correctly evaluate the experimental results, in the
following the rotation angles obtained using the sample noise source are used, i.e.
those listed in Section 6.5.1.
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
41
6.5.3. Source maps
Source maps were created for the fan from suction and pressure side as well. The
position of the fan blades is marked along with 3° uncertainty (dotted lines).
The black dot indicates the position of the index signal while the arrow the
direction of rotation. The left image was obtained with diagonal removal switched
on, while the right without it. Diagonal removal is expected to reduce the
amplitude and increase the dynamic range, therefore the two diagrams have
different scale settings. This allows the comparison of the shapes on the two figures.
The maps were created using 5 dB dynamic range below which the data was
cropped (white areas). The straight line on the source maps shows the theoretical
spatial resolution of the PAM.
DS source strengths obtained with ImageJ and with the ROSI method should not
be compared directly, because the two softwares have different calibration settings.
This is not a problem though, since our main interest is in describing the relative
importance of the source regions.
Suction side
Figure 6.28. Suction side source map at 2000 Hz with (left) and without (right) diagonal removal
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
42
Figure 6.29. Suction side source map at 2500 Hz with (left) and without (right) diagonal removal
Figure 6.30. Suction side source map at 3150 Hz with (left) and without (right) diagonal removal
Figure 6.31. Suction side source map at 4000 Hz with (left) and without (right) diagonal removal
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
43
Figure 6.32. Suction side source map at 5000 Hz with (left) and without (right) diagonal removal
Figure 6.33. Suction side source map at 6300 Hz with (left) and without (right) diagonal removal
Figure 6.34. Suction side source map at full band with (left) and without (right) diagonal removal
The source maps indicate significant noise peaks in the vicinity of the leading
edge tips. Two possible explanations exist for this. One of them is that the outer
radius has the highest velocity and the leading edge tip has a geometric
discontinuity. These factors together could make this region the loudest noise
source. It may also be the effect of a vortex separating from one blade and
impinging on the leading edge of the other. Another possible explanation is that the
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
44
noise sources are in fact the vortices separating behind the plane of the fan and they
are visible because of the bad z-direction resolution of the PAM.
Pressure side
Figure 6.35. Pressure side source map at 2000 Hz with (left) and without (right) diagonal removal
Figure 6.36. Pressure side source map at 2500 Hz with (left) and without (right) diagonal removal
Figure 6.37. Pressure side source map at 3150 Hz with (left) and without (right) diagonal removal
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
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Figure 6.38. Pressure side source map at 4000 Hz with (left) and without (right) diagonal removal
Figure 6.39. Pressure side source map at 5000 Hz with (left) and without (right) diagonal removal
Figure 6.40. Pressure side source map at 6300 Hz with (left) and without (right) diagonal removal
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
46
Figure 6.41. Pressure side source map at full band with (left) and without (right) diagonal removal
On the pressure side, the maximum SPL is about 2 dB higher than on the
pressure side. The source maps generally have a higher spatial resolution due to the
fact that measurements had to be taken from a larger distance. Blade periodicity can
still be observed on the maps except for the lowest frequencies. On the pressure
side the most significant source regions are the leading edges. This is probably
because of the wake from the previous blade impinging on the next leading edge.
6.5.4. Effects of diagonal removal
The maps with and without removal show similar geometric noise level
distributions, so the removal is a reliable method that does not neglect any useful
data. As expected, the method reduces the maximum amplitudes and increases the
dynamic range of the source maps. As such, it is a very useful tool in creating maps
that are easier to understand and contain the necessary information without the
noise effects coming from the autospectra in the main diagonal.
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
47
7. SUMMARY
A method based on [1] is used to relate the radial distribution of aerodynamic
losses and generated noise in case of an axial fan.
Aerodynamic characteristics are estimated based on geometry and inlet velocity
profile measurements. The blade sweep is accounted for in the calculations. Two
parameters are investigated: loss coefficient and diffusion factor. Both
parameters were written in a level-like form.
Noise distribution was measured using a Phased Array Microphone (PAM).
Radially averaged plots were created for the third octave bands from 2000 Hz to
6300 Hz and a linear fit using the least squares method was carried out to find
parameters that best approximate the noise as a function of either or both on
suction and pressure sides. On the suction side both functions seem appropriate in
the 2000 Hz – 3150 Hz range and the full band, too. Above that the agreement is
quite poor. On the pressure side, the dependent function preforms better and
gives good results in the low frequency range, but again, at higher frequencies both
functions fail to reproduce the chordwise distribution of noise. The full band
estimation is acceptable in both cases for both trial functions due to the fact that
most of the noise is radiated in the low frequency range, where the intensity
approximation is quite good. It is important to note however, that some
measurement points show negative function fit coefficients that do not support the
original theory that states that increasing aerodynamic losses would lead to
increasing noise generation.
The ROSI method was used to generate source maps of the fan from a co-rotating
coordinate system. The results show a significant noise source in the vicinity of the
leading edge tip, while on the pressure side the leading edge mid-chord area
generates more noise. In general, the pressure side is louder.
The results show that the phased array measurement technique can effectively be
applied to study the noise of turbomachinery.
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
48
8. FURTHER AIMS
Measurements of another, unswept fan have been carried out in a similar
manner. Those shall be evaluated in order to gain more insight into the noise
generation mechanisms present in axial fans.
It should be determined whether the noise sources in the blade tip region result
from the tip vortices or from the geometric discrepancy. Some preliminary
measurements were taken with a decreased tip clearance but their results were not
conclusive and they should be repeated. These measurements with a reduced tip
clearance will be carried out in order to determine its effects on the source intensity
and thus show the origin of noise.
A code generating a synthetic noise from an orbiting monopole source was
designed to test the ROSI algorithm and allow the more exact determination of the
angle by which ROSI rotates the source map. This could easily be enhanced to be
able to simulate a source of a given spectrum. With some further work, it could be
enabled to simulate several sources rotating together, each having different
spectrum.
A program based on the genetic algorithm (evolution strategy) was proposed
that would be able to calculate the most efficient blade geometry for an axial fan of
given pressure rise and volume flow rate. This code shall be completed. If the
results regarding the connection of aerodynamic losses and noise show agreement,
that could be used to design axial fans taking both efficiency and noise level into
account.
PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN
49
9. BIBLIOGRAPHY
[1] T. Benedek and J. Vad, “Concerted Aerodynamic and Acoustic
Diagnostics of an Axial Flow Industrial Fan, Involving the Phased Array
Microphone Technique (Draft),” in ASME Turbo Expo 2014, Düsseldorf,
2014.
[2] S. Lieblein, F. C. Schwenk and R. L. Broderick, “Diffusion Factor for
Estimating Losses and Limiting Blade Loadings in Axial-Flow-Compressor
Blade Elements,” National Advisory Comittee for Aeronautics,
Washington, 1953.
[3] P. Sijtsma, S. Oerlemans and H. Holthusen, “Location of rotating sources
by phased array measurements,” in 7th AIAA/CEAS Aeroacoustics
Conference, Maastricht, 2001.
[4] “Turbomachinery,” [Online]. Available:
http://en.wikipedia.org/wiki/Turbomachinery.
[5] J. Vad, “Ipari légtechnika”.
[6] J. Gruber, Ventilátorok, Budapest: Műszaki Könyvkiadó, 1974.
[7] M. J. Lighthill, “On Sound Generated Aerodynamically. I. General
Theory,” Proceedings of the Royal Society of London. Series A, vol. 211, no.
1107, pp. 564-587, 1952.
[8] L. Koop, “Beam forming methods in microphone array measurements.
Theory, practice and limitations,” in von Kármán Institute Lecture Series,
Rhode Saint Genèse, 2007.
[9] P. Tóth, “Mikrofontömbös méréstechnika,” 2012.
[10] J. E. Ffowcs Williams and A. P. Dowling, Sound and Sources of Sound,
Wiley, 1983.
[11] J. Hald, “Combined NAH and Beamforming Using the Same Array,”
Brüel & Kjær Technical Note, 2005-1.
[12] “Comparative Measurements on Axial Flow Fans,” Department of Fluid
Mechanics, BME, Budapest, 2012.
[13] S. L. Dixon, Fluid Mechanics and Thermodynamics of Turbomachinery,
Butterworth-Heinemann, 1998.
[14] P. V. Ramakrishna and M. Govardhan, “On loading corrections and loss
distributions in low-speed forward swept axial compressor rotors,”
Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power
and Energy, vol. 225, no. 1, pp. 120-130, 2011.
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