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REEVALUATING NOISE SOURCES APPEARING ON
THE AXIS FOR BEAMFORM MAPS OF ROTATING
SOURCES
Csaba HORVÁTH1, Bence TÓTH1, Péter TÓTH2,
Tamás BENEDEK1, János VAD1
1 Budapest University of Technology and Economics,
Faculty of Mechanical Engineering,
Department of Fluid Mechanics,
1111 Budapest, Bertalan Lajos utca 4-6, Hungary
2 CFD.HU Ltd., 1027 Budapest, Medve utca 24, Hungary
SUMMARY
This paper presents a beamforming investigation that focuses on the noise source appearing on
the axis of turbomachinery. Until now these noise sources were often disregarded during
beamforming investigations, as they were associated with motor noise. With the help of the Mach
radius concept, it is shown that the noise source is not only resulting from motor noise, but also
from other noise sources which are located at other radial positions. This shows the importance
of understanding these noise sources in order to accurately evaluate beamforming results of
rotating noise sources. The results of the investigation also provide the basis of a new
beamforming method designed specifically for rotating coherent noise sources.
INTRODUCTION
As legislations and regulations have become more stringent along with the expectations of customers,
the amount of research in the field of turbomachinery aeroacoustics has progressively increased. As
a result of this, turbomachinery design requirements are continuously evolving, often pushing the
limits of design practices. The drive to further increase efficiency and reduce noise levels is also
pushing technology to develop at a fast pace. Design, simulation, and measurement technologies are
therefore being refined and even radically reformed in the process. With regard to acoustic
measurement technology, microphone technology has been improved, measurement techniques have
been developed, and a combination of the two has helped us gain more information from the recorded
acoustic data than ever before possible.
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Traditionally, microphones have been set up and recorded individually, with the spectrum of the
individual microphone signals providing a vast amount of information regarding the radiated noise
field of the investigated phenomena. The development of phased array microphone beamforming
technology has made it possible to extend these capabilities, simultaneously recording multiple
microphone signals and then processing the results in order to learn more about the noise sources
which are being investigated. Beamforming processes developed specifically for rotating sources
have provided a nonintrusive means by which the noise sources of turbomachinery can be localized.
Utilizing phased array microphones and these advanced beamforming algorithms we are able to
collect data for identifying turbomachinery noise sources, which is becoming a common practice [1-
4]. On the other hand, the results are not so easily understood. Most beamforming algorithms assume
that the noise is generated by compact incoherent noise sources, in most cases resulting in beamform
maps which localize the noise sources to their true locations. If the investigated noise sources are
coherent, the beamforming algorithms often have a hard time distinguishing one source from the
other, resulting in the noise sources incorrectly being located on the map. With regard to rotating
coherent noise sources, the publications of Horváth et al. have shown that the noise sources are
pinpointed to their respective Mach radii rather than their true noise source locations [5].
In this investigation, beamform maps for a synthetic axial flow fan test case are investigated from the
axial direction. The focus of the investigation is the noise source appearing on the axis of the fan. In
many similar investigations, noise sources located on the axis have been associated with motor noise
[1, 4]. Taking into account what is now known about rotating coherent noise sources appearing at
their respective Mach radii, it is shown here that the noise sources appearing on the hub can, in some
cases, be resulting from noise sources located on the rotors or even on the guide vanes, depending on
how the results are processed. An explanation is provided as to why these noise sources appear on
the axis, and information is given as to their true noise source locations. This investigation is
motivated by a desire to better understand this phenomenon, which is necessary in order to accurately
process beamforming results of rotating coherent as well as incoherent noise sources, and which
provides the basis of a new beamforming investigation method designed specifically for the
investigation of rotating coherent noise sources.
TURBOMACHINERY NOISE SOURCES
In categorizing turbomachinery noise sources, they can be split into two main groups, tonal and
broadband noise sources. Tonal noise sources are characterized by a discrete frequency, and are
associated with the regular cyclic motion of the rotor blades with respect to a stationary observer and
with the interaction of the rotors with adjacent structures [6]. These are referred to as Blade Passing
Frequency (BPF) tones and interaction tones, respectively. Broadband noise sources are characterized
by a wide frequency range, and are associated with the turbulent flow in the inlet stream, boundary
layer, and wake [6]. With respect to the present investigation, the coherence of the noise sources also
needs to be taken into consideration. Coherent noise sources are characterized by a time invariant
phase relationship. While by definition broadband noise cannot be coherent, many tonal
turbomachinery noise sources often are.
AXIAL FLOW FAN TEST CASE
In this investigation a synthetic axial flow fan test case is presented. The synthetic fan is used instead
of a real fan in order to provide a means by which multiple noise sources can individually be
investigated. The left side of Figure 1 provides a schematic of the fan test case which is synthesized
herein. An axial flow fan having 15 rotor blades (only 5 are pictured in order to make the figure clear)
and 1 downstream guide vane is investigated by a microphone phased array located 0.3 m in the
upstream axial direction. The diameter of the phased array is 1m. The fan has a diameter of 0.4 m and
is rotated at -12000 RPM (-200 rev/s). In this way the investigated frequency is maximized while
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keeping the blade tip velocity subsonic. It is evident that this is not a common fan test case, but is
used in order to provide representative data which can easily be created and processed with the
available technology.
Figure 1: Schematic of the fan test case which is synthesized in the investigation (left) and the synthetic fan test case,
with monopole noise sources replacing the rotors, guide vane and motor (right)
The following three components of turbomachinery noise are investigated: motor noise, guide vane
noise radiating from the guide vanes as they interact with the rotors, and rotor noise radiating from
the rotors as they interact with the guide vanes. The motor is represented by 1 stationary monopole
noise source located on the axis. The guide vane is represented by 1 stationary monopole noise source
located at the blade tip, and the rotors are represented by 15 coherent rotating monopole noise sources
located at the blade tips. The right side of Figure 1 shows a schematic of the monopole noise sources
which replace the true noise sources. They are represented by small spheres in the figure, and out of
the 15, only 5 rotor noise sources are shown, in order to improve the clarity of the figure.
In order to account for the limited resolution of the finite aperture array, the investigated frequency
is chosen as 3000 Hz. The parameters of the synthetic axial flow fan test case are set accordingly, and
therefore the results provide beamform maps which clearly depict the investigated noise sources. The
stationary monopole noise source located on the axis and representing the motor radiates at 3000 Hz,
and should be considered as a harmonic of the motor noise. The stationary monopole noise source
representing the guide vane also radiates at 3000 Hz, as the potential field and/or the viscous wake of
the 15 rotor blades rotating at -12000 RPM interact with the guide vane. The 15 coherent rotating
monopole noise sources located at the blade tips and representing the rotors radiate at 3000 Hz, which
is the 15th harmonic of the potential field and/or viscous wake of the guide vane interacting with the
rotor blades. The magnitude of each noise source was taken as equal for demonstration purposes.
MEASUREMENT SETUP
The synthetic measurement test case (referred to as measurement) is produced by two monopole noise
sources. One is located on the axis and radiates at a frequency of 3000 Hz. This noise source
represents the motor and is stationary in both the absolute as well as the rotating reference frame. The
other is located at a radius of 0.2 m and radiates at a frequency of 3000 Hz. It represents the guide
vane and is stationary in the absolute reference frame, while rotating around the axis at 12000 RPM
in the rotating reference frame. The measurement setup can be seen in Figure 2.
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Figure 2: Synthetic measurement test case
SIMULATION SETUP
The synthetic simulation test case (referred to as simulation) is produced by three types of noise
sources. The first is located on the axis and radiates at a frequency of 3000 Hz. As in the case of the
measurement, this noise source represents the motor and is stationary in both the absolute as well as
the rotating reference frame. The second noise source is located at a radius of 0.2 m and radiates at a
frequency of 3000 Hz. It represents the single downstream guide vane and is stationary in the absolute
reference frame, while rotating around the axis at 12000 RPM in the rotating reference frame. The
third consists of 15 coherent noise sources which are evenly distributed around the axis at a radius of
0.2 m. These noise sources represent the 15 rotor blades and are radiating at a frequency of 3000 Hz
while rotating at -12000 RPM in the absolute reference frame. In the rotating reference frame these
noise sources are stationary. A schematic of the simulation test case can be seen on the right side of
Figure 1. Note that the figure does not show all 15 rotor noise sources, in order to make the figure
easier to understand.
BEAMFORMING
The acoustical measurements are performed using the Optinav Inc. Array 24: Microphone Phased
Array System. The microphones of the system are arranged along a logarithmic spiral and mounted
on an aluminum plate. This system provides the hardware for carrying out the measurements, with
the phase difference measured between the microphone signals providing the information which is
needed for localizing the noise sources with beamforming algorithms [7]. For the simulation, in-house
virtual noise source generation and propagation software is used for creating the virtual microphone
signals at the same 24 microphone positions. The in-house code is able to produce noise sources
which are moving at subsonic speeds, while taking into account the Doppler Effect. Both the
measurement and the simulation data is processed by versatile in-house beamforming software. Two
types of algorithms are used: the classical frequency-domain based Delay & Sum (DS) method [7],
which can localize stationary sources in an absolute reference frame, and the Rotating Source
Identifier (ROSI) method [1], which can localize the sources which are stationary in a rotating
reference frame. The results provide beamform maps, which display the magnitudes and the positions
of the strongest sources located in the investigated plane for a given frequency range. Using these
two algorithms, the sound sources originating from both the stationary and rotating elements of the
fan can be localized.
Beamforming, in essence, utilizes the phase differences measured between the microphone signals to
determine the direction of arrival of the wave fronts. By adjusting the phase shifts (time delays) of
the microphone signals relative to each other, a maximum correlation can be obtained between them.
The corresponding phase shifts give information as to the direction of arrival of the wave fronts and
hence the locations of the noise sources. This forms the basis of the DS beamforming method [7].
The method can be considered as forming a sensitivity curve, called mainlobe that is directed toward
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possible compact monopole noise source positions by phase adjustments. These possible source
positions are defined by the user, providing focus points for the beamforming methodology, and the
beamform maps display the strengths of the investigated sources.
The ROSI beamforming method is an extension of the DS method for rotating source models [1]. The
main difference between the two methods is that the ROSI method applies a so called
deDopplerization step in order to place the rotating noise sources into a rotating reference frame and
hence make them stationary. The positions and velocities of the possible noise sources are accounted
for by correcting the time difference and amplitude data with regard to each receiver position. The
corrected source signals are then processed with a beamforming method that corresponds with the
DS method. For a more detailed description of the ROSI method, see reference [1]. A more detailed
description of the phased array microphone system and of the beamforming algorithms applied in the
in-house code is available in [4].
In general, beamforming methods developed for rotating noise sources, such as the ROSI method [1]
and the Rotating Beamforming method [2] are very useful for investigating rotating incoherent noise
sources. In examining the test cases that are provided in [1-2], it can be seen that the investigators
took this into account and investigated rotating broadband noise sources and rotating incoherent tonal
noise sources. On the other hand, if one wants to look at cases where both coherent and incoherent
noise sources are present, the effect of the coherent noise sources need to accounted for.
MACH RADIUS
Coherent noise sources often give misleading beamforming results. The interaction patterns of the
wave fronts make it hard to distinguish one noise source from another by most beamforming methods.
The interaction patterns of rotating coherent noise sources also give misleading results, as the
apparent sources do not show where the actual noise sources are located, but rather point to the Mach
radius [5]. The name “Mach radius” or “sonic radius” refers to the mode phase speed, the speed at
which the lobes of the given mode rotate around the axis, having a Mach number of 1 at the Mach
radius (
*
z
, a normalized radius, where
1
*z
refers to the blade tip) when examined from the
viewpoint of the observer [8]. For turbomachinery applications, the Mach radius is calculated using
Equation 1, with
n
being the harmonic index,
B
being the blade count or guide vane count,
t
M
being the blade tip Mach number,
x
M
being the flow Mach number, and
being the angle of the
viewer with regard to the axis (upstream direction referring to
0
), with subscripts 1 and 2 referring
to the rotor or guide vane of the acoustic harmonic and loading harmonic, respectively. The equation
is formulated for a turbomachinery system consisting of two rotors or one rotor and one guide vane
which are moving relative to one another. Acoustic harmonic refers to the rotor or guide vane which
is radiating noise while being loaded by the potential field and/or the viscous wake of the other, which
is referred to as the loading harmonic. Both rows of rotors or guide vanes need to be considered as
acoustic as well as loading harmonics in order to receive a complete and accurate sound field, since
each blade row loads the other blade row and also radiates sound simultaneously [8].
sin
cos1
222111
2211
*x
tt
M
MBnMBn
BnBn
z
(1)
Examining the Mach radius equation for the case presented in this study leads to some interesting
conclusions. The first thing that can be noticed is that examining the system from the axial direction
leads to
0sin
. This would be true in an idealized case, if only a single microphone were used,
but since 24 microphones are used, none of which are located exactly on the axis,
0
. A value of
1
was used for the calculation of the Mach radius with regard to an angle representative of the
center of the array, as was done in [5].
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The next point of interest is with regard to those interaction tones that result in a Mach radius that is
equal to zero, or in other words, when the noise source aligns with the axis of rotation. For cases of
subsonic flow, this can occur when
0
2211 BnBn
, as can be seen in Equation 1. In the test case
presented here, this will happen when the 1st harmonic of the 15 blade rotor and the 15th harmonic of
the single guide vane are investigated at their interaction frequency of 3000 Hz. The azimuthal mode
number (
m
) provides some physical meaning as to what a Mach radius of zero means (see Equation
2) [9-10]. The azimuthal mode number gives the number of pressure lobes that are rotating
azimuthally around the axis as a result of the rotating potential field and viscous wake of the blades
and their interactions with adjacent structures [9-10]. For the case of
0m
there are no azimuthal
lobes rotating around the axis, and similarly to duct acoustics, this results in axial modes that produce
plane waves which propagate in the axial direction [11].
2211 BnBnm
(2)
PLANE WAVES
Though the mode pertaining to
0m
produces plane waves, it is known from the literature that plane
waves that behave as prescribed by their model equations can only be produced in cylindrical ducts
at low frequencies [12]. The literature also states that plane waves can be considered as behaving as
spherical waves that are examined at a large distance from their source, or as spherical waves which
are examined in a space of small extent as compared to the distance from the source [12]. In the fan
test case, the plane waves are produced by a finite number of coherent sources which are evenly
distributed around the circumference of the unducted synthetic axial flow fan test case. The wave
front should therefore only be considered as a plane wave if investigating the circumferentially
distributed coherent noise sources from a small distance with a phased array that has a smaller
diameter than the noise source, or if investigating the wave front from a large distance. In our case,
the array is located relatively close to the source, but the diameter of the array is relatively large as
compared to the noise source. The wave fronts are therefore not expected to behave as planar waves.
In order to visualize what would happen if truly planar waves, the wave fronts of which are parallel
to the plane of the array, were investigated with the applied beamforming methods, a simulated
synthetic plane wave test case is examined here with the DS method. In general, the DS method
assumes that compact monopole noise sources are being investigated, and therefore should not be
able to localize noise sources in planes that are very close to it. The plane waves are produced by the
same in-house code used to create the simulation case of the axial fan test case. The results can be
seen in Figure 3. The DS method is used to try and localize noise sources in multiple planes located
at various distances from the phased array as a function of array diameter. These are 0.5 array
diameters (left side of Figure 3), 1 array diameter (middle of Figure 3), and 10 array diameters (right
side of Figure 3). Assuming that the source is located at a close distance (such as 0.5 array diameters),
the beamform maps show only sidelobes, artificial noise sources resulting from the beamforming
process, while assuming that the noise sources are located farther away, the beamform maps localize
the noise source to the middle of the investigated plane. As discussed above, beamforming is akin to
determining the normal to the wave front at the microphone positions and tracing those back to their
origin. Therefore, for a plane wave that is investigated by a beamforming method that is looking for
monopole noise sources located far away from the phased array, the beamform map should locate the
noise source to the center of the investigated plane.
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Figure 3: Investigation of plane waves using the Delay & Sum beamforming algorithm, assuming that the source is
located at different distances: 0.5 D (left), D (middle), 10 D (right)
RESULTS
As stated in the introduction, the focus of this investigation is the noise source appearing on the axis
of the fan. These noise sources are often neglected during the investigations, as they are associated
with motor noise, as seen in [4] and [1]. Mach radius calculations show that these noise sources are
not necessarily related to motor noise, suggesting that they should be further investigated. The
measurement and simulation test cases investigated here are designed to prove this point by providing
an opportunity for investigating each noise source separately. Each noise source is investigated in an
absolute as well as rotating reference frame with the help of the DS and ROSI methods.
The first noise source to be presented is that of motor noise in the absolute reference frame. Figure 4
presents both the measurement (left side) and simulation (right side) beamform maps of the narrow
band frequency range pertaining to 3000 Hz. The measurement results are realized by the DS method
and the simulation results are realized by the ROSI method, since the simulation was created in the
rotating reference frame while the measurement was executed in the absolute reference frame. The
application of the DS or ROSI methods, as a result of differing reference frames, does not cause any
significant discrepancies in the results, as can be seen here. As would be expected from the results,
the noise sources are localized to their true noise source locations. It should be noted that the
measurement and simulation tests are independent of one another and the levels are therefore not
expected to agree.
Figure 4: Absolute reference frame beamform maps of the motor noise source: Measurement case (left) and Simulation
case (right)
In the absolute reference frame a single guide vane also radiates sound at a frequency of 3000 Hz as
it is loaded by 15 rotor blades rotating at 12000 RPM (200 rev/s). Figure 5 presents both the
measurement (left side) and simulation (right side) beamform maps for this case. The measurement
results are realized by the DS method and the simulation results are realized by the ROSI method.
The results show that the stationary noise sources are once again localized to their true noise source
locations. As seen in Figures 1 and 2, the guide vanes in the two cases are located in different
locations. The guide vane in the measurement is located at coordinate [0, 0.2], while in the simulation
it is located at approximately [-0.16, -0.12]. The position of the guide vane in the simulation results
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depends on what position the ROSI method rotated all the results to during the beamforming process.
Starting the processing of the results at an earlier or later time step would rotate the noise source to a
different position along the circumference.
Figure 5: Absolute reference frame beamform maps of the guide vane noise source: Measurement case (left) and
Simulation case (right)
When the 15 rotor blades pass the guide vane, they are loaded by the guide vane at a frequency of
200 Hz. The 15th harmonic of this loading also radiates at 3000 Hz. The reason for investigating the
15th harmonic is that it is the harmonic which will produce an interaction tone that is located on the
axis according to the Mach radius calculations. The left side of Figure 6 presents the beamform map
of these rotating noise sources when investigated in the absolute reference frame by the ROSI method.
Only simulation results are shown, since no measurement data is available for this case. Contrary to
what would be expected if the Mach radius calculations are not taken into consideration, there is only
a single noise source located on the axis of rotation. Taking into consideration what we know about
Mach radius, the noise source is correctly located on the axis since the 15 coherent noise sources
produce sound waves that add up constructively or destructively producing a wave front similar to a
plane wave within the extent of the noise source. When investigated with a relatively large array that
is located at a relatively large distance, the wave front will be comprehended by the beamforming
process as coming from a monopole noise source located on the axis.
Figure 6: Beamform maps of the simulation case of the rotor noise sources: Absolute reference frame (left), Rotating
reference frame (right)
The same noise sources will now be investigated in a rotating reference frame in order to remove the
rotation from the rotors, as is customary in turbomachinery investigations. The beamform map for
the 15th harmonic of the 15 stationary rotor blades can be seen on the right side of Figure 6. This
beamform map is produced by the DS method. After removing the rotation of the noise sources, we
are left with 15 stationary coherent noise sources which are evenly distributed around the
circumference. The beamform map once again localizes the noise source to a point on the axis, as
well as producing many sidelobes in the investigated plane. The 15 coherent noise sources do not
appear on the beamform map at their true locations.
While the rotating reference frame removes the already existing rotation from the rotors, it also puts
all objects into rotation which would otherwise be stationary. The guide vane is one such object.
Figure 7 shows the rotating reference frame beamform maps for the measurement (left side) and
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simulation (right side) of the guide vane noise source. The measurement data is processed using the
ROSI method, and the simulation data is processed using the DS method. Looking at the results for
3000 Hz, it can be seen that a noise source appears on the axis, as is expected according to the Mach
radius calculations. Though the noise source is a single rotating noise source that is radiating at 3000
Hz, rotating it at 12000 RPM (200 rev/s) it becomes coherent with itself, producing 15 sections of
high and low pressure along the circumference. For each rotation, the pattern is repeated in the same
locations. In the measurement results a ring shaped sidelobe can be seen at a radial position halfway
between the axis and the rotating guide vane noise source. The simulation results show sidelobe
characteristics similar to those seen in Figure 6 for the simulated rotor noise sources also investigated
with the DS method.
Figure 7: Rotating reference frame beamform maps of the guide vane noise source: Measurement case (left) and
Simulation case (right)
Rotating reference frame beamform maps for the measurement (left side) and simulation (right side)
of the motor noise, which is stationary in both the absolute as well as rotating reference frame, can
be seen in Figure 8. The results are very similar to the results seen in the absolute reference frame,
though some slight differences can be seen in the levels.
Figure 8: Rotating reference frame beamform maps of the motor noise source: Measurement case (left) and Simulation
case (right)
The above results present the beamform maps produced by the individual noise sources. In reality
these noise sources occur simultaneously. The following sets of figures will compare instances when
only the motor, the motor and the guide vane, or the motor, guide vane, and the rotors are
simultaneously investigated with beamforming methods.
An investigation of the absolute reference frame simulation results with the ROSI method is looked
at in Figure 9. The left side of Figure 9 presents the simulation results for the 15 rotating rotor noise
sources. The middle section of Figure 9 presents the simulation results for the 15 rotating rotor noise
sources and the stationary guide vane noise source. The right side of Figure 9 presents the simulation
results for the 15 rotating rotor noise sources, the stationary guide vane noise source, and the
stationary motor noise source. The results show how the levels of the 15 rotating rotor noise sources
and the motor noise source add together when they are investigated simultaneously. If only seeing
the results for all three of the noise sources radiating simultaneously (right side of Figure 9) and not
taking into account the Mach radius concept, one gets the impression that only the motor and the
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guide vane are radiating noise, and the motor is the dominant noise source in the investigation.
Reemphasizing that all of the monopole noise sources included in the simulation have the same level,
this investigation shows that in reality the 15 rotating rotor noise sources made the largest contribution
to the noise sources appearing on the beamform maps. The possible noise source and the Mach radius
concept cannot be neglected in processing the results.
Figure 9: Absolute reference frame beamform maps of the simulation case investigated with the ROSI method: Rotor
noise sources (left), rotor noise sources and guide vane noise source (middle), and rotor noise sources, guide vane
noise source, and motor noise source (right)
Investigating the same three noise sources in the rotating reference frame is also interesting. Figure
10 presents the simulation results in the rotating reference frame which are investigated by the DS
method. The left side of Figure 10 presents the simulation results for the 15 stationary rotor noise
sources. The middle section of Figure 10 presents the simulation results for the 15 stationary rotor
noise sources and the rotating guide vane noise source. The right side of Figure 10 presents the
simulation results for the 15 stationary rotor noise sources, the rotating guide vane noise source, and
the stationary motor noise source. Though the sidelobes appearing in these beamform maps dominate
the peak values, it can once again be seen that the levels of the three noise sources, all appearing on
the axis, add together. The noise sources of the 15 stationary rotor blades and of the guide vane cannot
be seen at their true radial positions. If one would not take into account what is known about the Mach
radius concept, the results would suggest that the only noise source appearing in the results is the
motor. This is especially emphasized since the sidelobes are located at a larger radius than the rotor
blade tip, and would therefore be excluded from the investigation. It is once again shown that the
Mach radius concept needs to be taken into account when investigating rotating coherent noise
sources from the axial direction, regardless of the reference frame in which they are being looked at.
Figure 10: Rotating reference frame beamform maps of the simulation case investigated with the DS method: Rotor
noise sources (left), rotor noise sources and guide vane noise source (middle), and rotor noise sources, guide vane
noise source, and motor noise source (right)
CONCLUSIONS
The investigation looked at a synthetic axial flow fan test case in order to learn more about the noise
sources appearing on the axis. Until now these noise sources were associated with motor noise, but
these results show that this is not necessarily the case. The Mach radius concept provides information
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regarding the origin of these noise sources, and the beamform maps presented in the investigation
results confirm that rotating coherent noise sources can produce noise sources that are located on the
axis. This information is necessary in order to accurately process beamforming results of rotating
coherent as well as incoherent noise sources, and provides the basis of a new beamforming
investigation method designed specifically for the investigation of rotating coherent noise sources.
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