Aeroacoustics of a Low-Speed Free Tip Fan With a Complex Clearance
GeometryAEROACOUSTICS OF A LOW-SPEED FREE TIP FAN WITH A COMPLEX
CLEARANCE GEOMETRY
Dominic Lallier-Daniels Department of Mechanical Engineering
Université de Sherbrooke Sherbrooke, Québec, Canada
Email:
[email protected]
Sherbrooke, Québec, Canada Email:
[email protected]
Email:
[email protected]
ABSTRACT The influence of tip leakage flow on the performance of
tur-
bomachinery, both from an aerodynamic and acoustic point of view,
has been demonstrated by several authors. However, most studies
present in the literature are focused on the effects of tip leakage
from an aerodynamic point of view and often forgo the mechanisms
associated with the acoustics effect. The effect of different tip
geometries is also still ill understood.
The current advancement of a numerical study delving into tip
leakage flow noise in low-speed turbomachinery applications is
presented in this paper. The study as a whole aims to inves- tigate
the mechanisms associated with tip leakage flow noise on different
axial fans with varying tip configurations. The study is carried
out using lattice-Boltzmann simulations that allow to obtain the
aerodynamic and aeroacoustic field simultaneously.
As a first step in this investigation of tip flow noise, this paper
focuses on a free-tip axial flow fan with a complex tip geometry.
The global aerodynamic and acoustic performance of the fan is
evaluated numerically and compared to available experimental
results. An investigation of the simulated flowfield with regards
to the observed acoustics is then carried out.
NOMENCLATURE Fi External forces (N) Q Flowrate (m3/s) S Strain
tensor
−→c Particle velocity (m/s) f Frequency (Hz) f = f (−→x ,−→c , t)
Particle distribution function f eq Maxwell-Boltzmann distribution
m Molecular weight (g/mol) p Pressure (Pa) p Differential pressure
rise (Pa) r Radius (m) t Time (s) −→u Macroscopic fluid velocity
(m/s) −→x Spatial coordinates Vorticity tensor λi ith eigenvalue of
the pressure Hessian ρ Macroscopic fluid density (kg/m3) τ
Relaxation time
INTRODUCTION Understanding and controlling the performance of
turboma-
chinery systems is a very complex problematic even in ideal
configurations, with many phenomena degrading both aerody- namic
and aeroacoustic performance. One such phenomenon, tip leakage
flow, is unavoidable in turbomachine applications and can
potentially lead to drastic performances losses and increased
noise.
Experimental studies have shown the effect of tip leakage flow on
overall noise in axial fans [1–7] to different degrees, with
Proceedings of the ASME 2014 International Mechanical Engineering
Congress and Exposition IMECE2014
November 14-20, 2014, Montreal, Quebec, Canada
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1 Copyright © 2014 by ASME
leakage flow generating an inherently unsteady flow in the tip re-
gion of the blades and affecting broadband as well as tonal noise
levels. A detailed experimental study on a stationary airfoil per-
formed by Grilliat [8] also showed that the noise sources due to
tip leakage flow can be related to the diffraction of turbulent
eddies formed by the tip leakage jet-like structures. More re-
cently, simulations on a ring-shrouded fan geometry used in au-
tomotive cooling were carried out using several unsteady meth- ods
by Magne et al. [9–12], including URANS and the lattice- Boltzmann
method (LBM); analysis showed that sub-harmonic humps observed in
the acoustic spectra were caused by large coherent structures
forming in the tip gap and that the frequen- cies above 1 kHz were
dominated by tip noise. More recently, a numerical study by Zhu et
al. [13] studied the contribution of tip leakage flow in a free-tip
tube-axial fan using the lattice- Boltzmann method and showed it
had an important influence on overall noise levels.
Several authors have also explored methods to try and con- trol tip
leakage flow. Three dimensional blade design (skew, sweep) was
shown to have an effect on the performance of tur- bomachines with
regards to stall and efficiency by reducing the spanwise flows and
tip leakage flowrate [14, 15]. Others [1, 16] also studied the
effect of adding a ring-shroud at the tip of ax- ial fan blades to
eliminate leakage flow over the blade tip sur- face, which was
shown to increase the efficiency and stall char- acteristics of the
fan as well as leading to lowered noise lev- els. This, however,
does not eliminate the tip leakage flow com- pletely and leads to a
fairly complex flow topology in the tip region [17]. Several casing
modifications aiming to control this tip flow can be identified in
industrial patents on low speed ax- ial fans [18–21]. However, the
tip leakage control methods cited here mostly focus on increasing
the aerodynamic characteristics (pressure rise, efficiency, stall)
of the studied fans, with little em- phasis on the mechanisms
responsible for the lowered aeroacous- tic noise and no analysis on
the effect of the tip geometry.
The current study presents the current advancement of a nu- merical
investigation into the aerodynamic and aeroacoustic per- formance
of low-speed axial fans aimed at studying the contribu- tion of tip
leakage flow to overall fan noise. The research seeks to bridge the
gap seen in literature by analyzing and quantifying the
contribution of tip flow noise for different tip configurations
using numerical simulation, which would allow for an extensive
investigation of the flowfield. In order to perform this analysis,
a lattice-Boltzmann method flow solver is being used, allowing for
direct acoustic simulation taking into account the aerodynamic
phenomena and the environmental geometry for the propagation of
sound.
This is opposed to the more widely used indirect acous- tic
evaluation methods using for example the Ffowcs Williams Hawkings
(FWH) analogy [22], where a solid or porous surface on which the
unsteady flowfield is recorded is used to calculate and propagate
the resulting acoustic field in a simplified environ-
ment, coupled with unsteady flow solvers to circumvent the use of
large meshes and unreasonable computing times. Examples of FWH
usage to evaluate turbomachinery noise can be found in [9, 11, 23,
24]. It is to be noted that the FWH analogy can still be used in
LBM calculations, as is shown in the paper.
The simulation subject presented in this paper is an axial au-
tomotive cooling fan with a free-tip configuration, highly swept
blades and a converging static shroud geometry. The fan has been
subjected to experimentation campaigns to quantify its aerody-
namic and aeroacoustic performance. Thus, comparison of the
aerodynamic performance of the fan predicted by the simula- tions
is first presented. The acoustic performance of the fan is then
also compared with the available experimental results and an
analysis of the noise sources in the flow are investigated. This is
the first step in a larger frame of study of tip noise, which has
elected to study three fans with different tip configurations; the
second fan that will be studied is a ring-shrouded fan for which
LBM calculations have already been carried out [9, 12, 25] as well
as a tube-axial free-tip fan [26, 27]. Research is ongoing and this
paper presents the current advancement of the numerical
investigation campaign using LBM aiming at taking advantage of the
method’s ability to resolve the aerodynamic and aeroacoustic fields
concurrently for low-speed fan applications.
LATTICE-BOLTZMANN METHOD The lattice-Boltzmann method has been used
in this paper
to carry out the flow simulations using the CFD software Pow-
erFlow 4.4. The method is based on the kinetic theory devel- oped
by Boltzmann in 1872 and thus is based on a mesoscopic approach to
calculate the flowfield and derive the macroscopic quantities. The
continuous Boltzmann equation can be written as in Eq. 1
∂ f ∂ t
) coll
(1)
with f = f (−→x ,−→c , t) the particle distribution function at
spa- tial coordinates−→x and time t possessing a speed−→c while Fi
cor- responds to external forces and m is the molecular weight of
the gas considered. The term
( ∂ f ∂ t
) coll
is dubbed the collision term and regulates the interaction of the
particles with each other. The collision operator currently used in
PowerFlow is the Bhatnagar- Gross-Krook operator, or BGK [28],
which is of the form seen in Eq. 2.
( ∂ f ∂ t
2 Copyright © 2014 by ASME
with f eq the thermodynamic equilibrium function also called the
Maxwell-Boltzmann distribution and τ is the relaxation time. Using
this collision operator and a Chapman-Enskog develop- ment [], Eq.1
recoups the Navier-Stokes equations.
Resolution of the continuous Boltzmann equation, however, is no
easier than direct resolution of the Navier-Stokes equations. Thus
the equation is further discretized by constraining the num- ber of
velocities that a given particle can possess, thus yielding a
discretized velocity form of the Boltzmann equation (DVBE). The
adoption of the discrete velocity model limits the validity of the
LBM to relatively low Mach numbers (Mach 0.4-0.5 is cited as the
maximum in literature) but makes it suitable for low-speed
applications.
For applications with moving parts, specifically turboma- chine
applications, a local reference frame approach is imple- mented to
the LBM calculations [29, 30].
A modified relaxation time τ → τturb derived from a renor-
malization group k− ε transport equations [31, 32] is also used to
model the unresolved small scale flow features.
The LBM possesses some key advantages over traditional CFD methods.
First off, the LBM is inherently an unsteady and compressible
method. This is of importance when trying to study fundamentally
transient phenomena such as turbomachinery ap- plications. Also,
while the LBM is of global 2nd order, it shows acoustic dissipation
properties equivalent to 6th order centered Navier-Stokes schemes
and dispersion equivalent 2nd or 3rd or- der Navier-Stokes schemes
[33–35]. This is of prime importance as it potentially allows for
direct acoustic simulation.
The LBM equation is also explicit in nature, with the calcu- lation
of a step being split into a collision and convection process,
allowing for massive parallelization of the algorithm and the pos-
sibility to perform simulations of complex/large geometries with a
reasonable return time in exchange for the use of massively
parallel computer resources.
LBM Case Studies In recent years, a series of studies using the LBM
have been
published, of which we present here a sample. Brès et al. [36]
performed calculations on a tandem cylinder
configuration used as a benchmark for the evaluation of land- ing
gear noise which were compared to experimental data gath- ered by
NASA. Comparison of streamlines, velocity field and turbulent
kinetic energy contours is favorable and the fluctuat- ing pressure
spectra at the surface of the cylinders is accurately reproduced by
the LBM.
Sanjosé et al. [37] also used LBM simulations to study the
self-noise of a Controlled Diffusion (CD) airfoil for which there
exists an extensive collection of experimental data. The study
shows a good agreement with the experiments with regards to the
mean flow characteristics on the airfoil (pressure coefficient and
boundary layer profile) as well as the unsteady pressure
fluc-
(a) (b)
FIGURE 1. ILLUSTRATION OF THE GEOMETRY OF THE AU- TOMOTIVE COOLING
FAN (A) FAN ROTOR, (B) AXIS CUT OF THE SHROUD.
tuations and radiated noise levels in the farfield. The LBM was
also shown to be able to accurately reproduce
the behavior of complex low-speed fan geometries. Pérot et al. and
Magne et al. [9, 25] simulated a low-speed
ring-shrouded axial fan intended for automotive engine cooling
applications and showed that the simulation was able to repro- duce
the global aerodynamic performance of the fan as predicted by
experimental data. Recent work by Magne et al. [12] also showed
what the far-field acoustics of the fan could be very ac- curately
reproduced by LBM simulations given a proper repre- sentation of
the installation.
Other work by Pérot et al. on an axial free-tip tube-axial test fan
[26] showed similar results with regards to the capture of the
aerodynamic performance of the fan.
TESTED FAN AND EXPERIMENTAL DATA Tested Fan Geometry
The fan studied in the current paper is designed for the pur- pose
of automotive engine cooling. The fan itself is an axial 5- bladed
fan with an outer radius of 16 cm and a 6 cm radius hub. The fan
blades are highly skewed and have a variable profile and angle of
attack along the span of the blades.
The tip of the blades is free, as opposed to often seen ring-
shroud configurations in similar fans, and is shown to have a
variable radius along the chord in conjunction with a convergent
static shroud. The tip clearance is constant at 3 mm along the
chord normal to the blade tip surface. The fan and shroud ge-
ometries are illustrated in Fig. 1.
During normal operation, the fan rotates at 2630 RPM and its design
flowrate is 0.43 m3/s.
Available Data Experimental data was made available for this fan
and in-
cluded both aerodynamic and aeroacoustic data. However, aero-
3 Copyright © 2014 by ASME
FIGURE 2. SCHEMATIC OF THE AMCA TEST CHAMBER
dynamic and aeroacoustic data were collected on separate test
rigs.
Aerodynamic Setup The first rig was used to col- lect aerodynamic
performance data conforming with the ANSI/AMCA 230-12 standards. A
schematic of the AMCA flow chamber is presented in Fig. 2. In the
setup, the fan/shroud as- sembly was inserted into a 700 mm
diameter duct with an intake bellmouth and terminated by a
perforated plate with a 20 cm (8 in) diameter circular
aperture.
The performance curve of the fan (pressure rise as a function of
flowrate) was measured on this setup through the use of two series
of 4 static pressure wall taps located at 90o from each other
located respectively 25 mm upstream and 35 mm downstream of the fan
to measure the pressure differential across the fan plane. The
pressure difference was measured using a Baratron 220CD
differential capacitance manometer with a 0.15% accuracy. The
torque applied to the fan was also measured using a Himmelstein
& co. MCRT 3-08TLS torquemeter with a 0.01356 Nm accuracy.
Additionally, a 5-hole probe was used to measure the spanwise
time-averaged velocity profiles 30 mm behind the trailing edge of
the fan blades for the 0.53 m3/s flowrate case.
Acoustic Setup A second experiment was setup to eval- uate the
acoustic performance of the fan in an anechoic en- vironment. An
assembly composed of a duct containing the fan/shroud similar to
the AMCA setup was suspended and cen- tered in an anechoic room
with a length of 4.8 m, a width of 3.5 m and a height of 2.6 m to
the end of the acoustic lining of the chamber. The flowrate through
the fan was controlled through the use of a damper plate . A
schematic of the test rig is pre- sented in Fig. 3.
In the experiment, acoustic pressure was recorded at 81 lo- cations
located upstream of the fan, as illustrated in Fig 4. The data was
recorded using a sampling rate of 24 kHz over 20 s for the 0.53
m3/s flowrate. The microphones used were BSWA Tech model MPA201 1/2
inch microphones.
Differences in Experimental Setups The main dif- ferences in the
described experimental setups mainly pertains to
FIGURE 3. SCHEMATIC OF THE ANECHOIC TEST CHAMBER
FIGURE 4. MICROPHONE ARRAY FOR ACOUSTIC MEASURE- MENTS
the acoustic properties of the test environment. The AMCA ex-
perimental setup was used as a means to investigate the aerody-
namic performance of the fan and was thus not placed in ane- choic
conditions, whereas the anechoic chamber setup was con- cerned with
obtaining the acoustic pressure upstream of the fan using an array
of microphones, as illustrated in Fig. 4.
However, there are some geometric differences in the two se- tups.
First of all, the test duct termination was different between the
two cases; the AMCA experiment used a simple perforated plate, as
the flowrate through the fan was driven through the use
4 Copyright © 2014 by ASME
TABLE 1. DIMENSIONS OF THE TEST DUCT ASSEMBLY IN THE EXPERIMENTAL
SETUPS
Case D1 D2 L1 L2 L3
(mm) (mm) (mm) (mm) (mm)
AMCA 1167 700 560 870 1050
Anechoic 1167 700 560 650 1050
of an auxiliary fan whereas in the acoustic setup, flowrate had to
be controlled through a sliding plate used to set the system
resistance.
The length of the test ducts were also a little different be- tween
the two cases, as highlighted in Tab. 1; the dimensions to those
present in Figs. 2 and 3.
SIMULATION SETUP In order to try and reproduce the experimental
conditions
used for both the aerodynamic and acoustic data measurement
campaigns as faithfully as possible, simulations were run on two
different cases.
Aerodynamic Setup For the AMCA case, the scope of the simulations
was restrained to the bellmouth/duct geometry, and did not include
the fairly complex flow chamber topology, including the diverse
flow straighteners. Thus, the fan rig was placed inside a large
prismatic domain (33 m across) reminiscent of a semi-anechoic
chamber, with solid wall boundary conditions being imposed on all
but two of the surfaces. On these last two surfaces atmospheric
pressure is imposed. The flowrate through the fan is varied in the
simulations through the modification of the radius of the hole in
the diaphragm downstream of the fan and is not imposed artificially
through boundary conditions, but rather resolved given the physics
of the flow.
In the simulation, two circular arrays of 24 measurement points
located 25 mm upstream and 35 mm downstream of the fan on the duct
wall are used to mimic the pressure taps used in the experiment to
evaluate the pressure rise across the fan. A series of spanwise
probes was also used to measure the veloc- ity profiles 30 mm
behind the fan trailing edge to compare with the experimental
5-hole probe data gathered on the 0.53 m3/s flowrate case.
The simulations were achieved with a maximum resolution of 0.5 mm
in close proximity to the fan, with the resolution in the outer
layers of the simulation decreasing to 1024 mm. This resulted in
25M voxels and 37M surfels total for the simulation mesh. The
timestep was 1.914*10−6 s to achieve unity CFL. A
series of coarser simulations with a resolution of 1 mm were also
run, and we will hereafter refer to these simulations as ’Aero
Coarse/Fine’. The resolutions used here are similar to those used
in previous axial fan studies using PowerFLOW [25–27].
Acoustic Setup In the case of the simulations reproduc- ing the
anechoic chamber setup, the simulation was made to in- clude the
complete geometry of the fan test rig (duct with bell- mouth and
damper plate assembly). The rig was then placed in a simulation
volume with dimensions coinciding with those of the anechoic
chamber used for gathering the experimental data to the inside of
the acoustic lining of the chamber walls. A porous medium that was
used to mimic the effect of the acousticly ab- sorbant liner used
in the experiment. Solid walls boundary con- ditions are imposed on
the outer limits of the simulation volume.
Besides the probes described for the AMCA simulation, ad- ditional
probes were used to collect acoustic pressure upstream of the duct
bellmouth according to the microphone locations used in the
experimental anechoic setup. The probes resolve the pres- sure
fluctuations up to 2080 Hz.
As with the AMCA configuration, a maximum resolution of 0.5 mm was
used in proximity to the fan with the resolution in the outer
layers of the simulation decreasing to 128 mm. This resulted in a
mesh with 24 M voxels and 36 M surfels in total. The timestep was
the same as the AMCA case. Similarly, a series of simulations with
a coarser 1 mm resolution were run, and we will hereby refer to the
acoustic numerical cases as ’Acoustic Coarse/Fine’.
As a visual aid, the mesh in close proximity to the duct of the
anechoic simulation setup is shown in Fig. 5. The voxel regions
(VRs) are identified along with the voxel size associated. It is to
be noted that the grid in close proximity to the fan, VR 11 (0.5 mm
elements), is set in a volume created from the offset of the fan
surfaces and is difficult to vizualise in a plane.
RESULTS Aerodynamic Results
As a first step of the investigation into the performance of the
simulations, the aerodynamic properties of the fan obtained
numerically were compared with the available experimental data
collected on the AMCA setup, namely the Q-P performance curve as
well as spanwise velocity profiles behind the fan.
The data presented here is based on the simulations realized with
the model mimicking the AMCA rig unless otherwise men-
tioned.
Global Fan Performance With regards to global fan performance,
available data included the pressure rise as well as the torque
applied to the fan for a series of flowrates. The char- acteristic
performance curve of the fan can be observed in Fig. 6.
5 Copyright © 2014 by ASME
(a)
(b)
(c)
FIGURE 5. ILLUSTRATION OF THE MESH AROUND THE FINE ANECHOIC
SIMULATION SETUP (A) VIEW OF THE GRID AROUND THE DUCT (B) VIEW OF
THE GRID AROUND THE FAN (C) VIEW OF THE GRID NEAR THE TIP OF THE
FAN.
FIGURE 6. PRESSURE CHARACTERISTIC OF THE TESTED FAN.
Present on Fig. 6 are the predictions for the pressure rise across
the fan as predicted by the AMCA and anechoic simulations for the
coarse and fine resolutions. Overall, it can be seen that the
simulations underpredict the experimental levels by a maximum of 20
%. However, from the series of coarse simulations on both setups,
it appears that the slope of the fan characteristic is repro- duced
by the simulations, level discrepancies not withstanding.
As was mentioned before, since the flowrate was not im- posed
through the use of boundary conditions, the main aim of the coarse
simulations was to be able to adjust the simulations to obtain the
nominal 0.53 m3/s flowrate for the fine simulations for both the
AMCA and anechoic cases. However, there is a small discrepancy of
approximately 3% in the flowrates, with the fine simulations
exhibiting a lower flowrate than the expected 0.53 m3/s.
The torque applied to the fan is also presented in Fig. 7. A trend
similar to the pressure characteristic can be observed for the
torque curve, where the simulation underpredicts the exper- imental
values by approximately 20% but seems to be able to evaluate the
experimental slope as a function of flowrate.
From these results, it would appear that additional mesh con-
vergence is required in order to correctly simulate the character-
istics of the tested fan, as it seems to be a configuration that is
very sensitive to the quality of the grid, especially when consid-
ering the acoustics that are presented in a subsequent
section.
Spanwise Velocity Profiles As mentioned before, time-averaged
spanwise velocity profiles were also measured ex- perimentally via
the use of a 5-hole probe located 3 cm behind the trailing edge of
the fan on the AMCA experimental setup. This included the
measurement of axial, tangential and radial ve-
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FIGURE 7. TORQUE APPLIED TO THE FAN AS A FUNCTION OF
FLOWRATE.
FIGURE 8. COMPARISON OF TIME-AVERAGED AXIAL VE- LOCITY 3 CM BEHIND
THE TRAILING EDGE OF THE TESTED FAN ON THE AMCA SETUP
locity. The axial velocity profile is presented in Fig. 8 and
com-
pared to the aforementioned 5-hole probe data.There is a good
correlation between the experiment and simulation, with a small
discrepancy in the flowrate (approximately 3-4 %) probably ex-
plaining most of the differences seen for the fine case whereas the
coarse case was very close to the 0.53 m3/s nominal flowrate. This
also confirms the proper prediction of the flowrate.
Similarly, the spanwise azimuthal velocity profile is shown in Fig.
9. Overall, the shape and velocity levels from the experi-
FIGURE 9. COMPARISON OF TIME-AVERAGED AZIMUTHAL VELOCITY 3 CM
BEHIND THE TRAILING EDGE OF THE TESTED FAN ON THE AMCA SETUP
ment are correctly reproduced in the simulation. However, there are
still some important discrepancies. First off, the experimental
data shows the appearance of a large spike in azimuthal velocity at
r
rtip,T E = 0.4, which corresponds to the hub radius. There is
however a smaller amplitude spike in the numerical results. The
experimental value here seems rather high for that particular po-
sition as it exceeds by 66 % the value near the tip of the
blade
r rtip,T E
= 1.
Near the tip of the blade, the velocity distribution is also a bit
different between the simulation and the experiment, with the
experimental curve showing a sharp drop in azimuthal velocity over
a r
rtip,T E value of 1 whilst the simulation shows a kind of
forked profile in the tip region; the velocity levels are however
very similar in that area for the fine case and the experiment. It
can be seen that the velocity values near the tip were overes-
timated by the coarse case, with the finer mesh allowing for a
better resolution of the tip flow.
In the mid-span region, a similar shape in the azimuthal ve- locity
profile is predicted by both the simulation and experiment, with a
0.5 to 1 m/s difference being observable however between the
two.
Except for the tip region, the differences in the azimuthal
velocity profile predicted by the coarse and fine simulations are
virtually identical.
Radial velocity profiles are not presented here, as the level of
uncertainty in the experimental data was high regarding the levels
of velocity due to the unsteady nature of the flow.
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FIGURE 10. PSD MEASURED ON THE MICROPHONE LO- CATED ON THE ENTRANCE
PLANE OF THE BELLMOUTH ON THE ROTATION AXIS OF THE FAN
Aeroacoustic Results With the aerodynamic results having proven
relatively sat-
isfactory, the current study then shifted towards the main point,
which is concerned with the acoustics of the fan and the related
mechanisms. As previously stated, the available acoustic data
consists of acoustic pressure measurements collected on an array of
81 microphones upstream of the fan for the 0.53 m3/s
flowrate.
Microphone Array As a first step, the acoustic pressure predicted
by the simulations was compared with the experimen- tal data made
available on the aforementioned microphone array. Figure 10 shows
the power spectral density (PSD) predicted by the simulation for
the coarse and fine meshes at the microphone located on the fan
axis in the bellmouth plane and the correspond- ing experimental
data. The blade passing frequency (BPF) har- monics are highlighted
up to 4th.
On the graph, the spectral resolution of all presented spectra was
set up to be 4 Hz. The rather coarse resolution is due to the fact
that there was only 0.5 s of converged time usable in the fine
simulation to evaluate the aeroacoustics; additional calculation
time is being put into the simulation in order to alleviate this
problem.
However, from the preliminary results, several observations can be
made. First off, it can be see that the fine simulation seems to be
able to capture peaks associated with the first, second and third
harmonics of the BPF while they are not clearly captured on the
coarse mesh. The levels, however, are not yet in accordance with
the experimental results, as the simulation underestimates the
first and third BPF by 8 and 15 dB respectively whereas the second
BPF is overestimated by 15 dB. This suggests that noise
FIGURE 11. ACOUSTIC PRESSURE STILL SHOWING THE AP- PEARANCE OF A
ROTATING (2,0) MODE IN THE 243-275 HZ BAND IN THE DOWNSTREAM
CHAMBER OF THE ANECHOIC SIMULATION
predictions for this particular fan geometry are very sensible to
the mesh resolution near the fan. More refined models of the setup
will be run incessantly to try and reach grid independance.
The fine simulation also predicts the appearance of strong peaks in
the frequency range between the BPF harmonics that, while
coinciding with minor peaks in the experimental spectrum, seem
exacerbated. These particular frequency bands were ana- lyzed in
more depth and are presented in the next section.
Acoustic Pressure in the Test Duct The acoustic pressure field was
analyzed on an axial cut of the duct for the inter-BPF high-level
frequency bands identified on the spectra in Fig. 10. The
occurrence of strong rotating duct modes was observed in the
downstream portion of the duct.
For example, the 243-275 Hz band thus shows the appear- ance of a
standing rotating (2,0) duct mode, as illustrated in Fig. 11. The
acoustic field in the downstream portion then drives the acoustic
waves propagation along the duct wall in the up- stream portion as
a (2,0) mode. Figure 11 shows a longitudinal cut of the duct in the
upper left corner, while the other parts of the image show
crosscuts of the duct whose locations are marked on the
longitudinal cut.
In a similar visualization, a (3,0) rotating duct mode is seen to
appear in the downstream chamber in the 279-303 Hz band, as
illustrated in Fig. 12.
At higher frequencies, strong resonance is still observed in the
downstream chamber, but the modes are not clearly identi- fiable
using qualitative vizualisations of the acoustic pressure,
8 Copyright © 2014 by ASME
FIGURE 12. ACOUSTIC PRESSURE STILL SHOWING THE AP- PEARANCE OF A
ROTATING (3,0) MODE IN THE 279-303 HZ BAND IN THE DOWNSTREAM
CHAMBER OF THE ANECHOIC SIMULATION
whereas propagation upstream forms higher radial modes. These
preliminary results show that the damper plate ter-
mination seems to facilitate the appearance of standing rotat- ing
modes in the simulation by creating an almost closed cav- ity.
However, with the available data it is undetermined if these modes
are as dominant in the experiment as they appear to be in the
simulations.
Ffowcs-Williams and Hawkings analysis Using the fan surface as a
source, the Ffowcs-Williams Hawkings (FWH) analogy with free-field
propagation was also employed to com- pare with the direct acoustic
results of the simulation. The result is shown in Fig. 13. The
reader should keep in mind that that some of the differences in
level between the FWH and the direct acoustic evaluation are
attributable to the directivity effects of the duct and the absence
of some sources in the FWH evaluation.
However, from the comparison of the direct acoustics and the FWH
analogy, it can be observed that both the BPF harmon- ics and the
inter-BPF peaks at 175 Hz, in the 332-405 Hz band and at 565 Hz
that are present in the direct acoustic evaluation are also
represented in the FWH spectra, which identifies the fan as the
source of these frequency peaks. These inter-BPF peaks do coincide
with peaks in the experimental spectra, albeit with exacerbated
levels in the simulation.
It is however seen that the 243-275 Hz and 279-303 Hz peaks are
absent in the FWH spectra, encouraging the interpreta- tion of
these specific frequency peaks as being due to installation effects
(strong duct modes).
FIGURE 13. PSD AT THE MICROPHONE LOCATION LOCATED ON THE ENTRANCE
PLANE OF THE BELLMOUTH ON THE RO- TATION AXIS OF THE FAN AS
MEASURED DIRECTLY IN THE SIMULATION AND THROUGH A FWH FREE-FIELD
PROPAGA- TION USING THE FAN AS A SOURCE.
Surface PSD The pressure fluctuations on the fan blades
corresponding to the different frequency bands where high-level
peaks were present also analyzed.
Figures 14 to 17 present the PSD levels of the filtered pres- sure
fluctuations on the surface of the fan, with the suction side shown
in the left part and the pressure side shown on the right and a
view of the tip surface in the middle for four different fre-
quency bands, namely the 165-185 Hz, 210-230 Hz (1st BPF), 325-405
Hz and 485-605 Hz bands.
For the 165-185 Hz band in Fig. 14, it is possible to see that the
pressure side presents the most elevated PSD levels, with a
concentation being apparent in the tip region of the blade along
the leading edge. There is also a high PSD level on the suction
side along the leading edge in the tip region and along the tip
edge.
Figure 15 presents the PSD levels of the filtered pressure
fluctuations around 1st BPF, with the suction side shown on the
left, the pressure side on the right and a view of the tip surface
in the middle. From the suction side view, it can be seen that
there is a high level of pressure fluctuations near the leading
edge in the tip region of the blade. The same occurrence can be
observed on the pressure side, but the elevated PSD region covers
approxi- mately a third of the blade chord instead of only the
leading edge area. A similar pattern can be observed in the 325-405
Hz band in Fig. 16.
For the higher 485-605 Hz in Fig. 17 band, it can be seen that the
tip region is the main zone of high levels of pressure
fluctuations., with hotspots once again apparent near the
leading
9 Copyright © 2014 by ASME
FIGURE 14. PSD LEVELS OF THE PRESSURE FLUCTUATIONS ON THE FAN
BLADES FOR THE 165-185 HZ FREQUENCY BAND.
FIGURE 15. PSD LEVELS OF THE PRESSURE FLUCTUATIONS ON THE FAN
BLADES FOR THE 210-230 HZ FREQUENCY BAND (1ST BPF).
FIGURE 16. PSD LEVELS OF THE PRESSURE FLUCTUATIONS ON THE FAN
BLADES FOR THE 325-405 HZ FREQUENCY BAND.
edge of the blade and along the tip edge on the pressure side.
These vizualisations highlights that the tip region of the
blade seems be subjected to intense pressure fluctuations. This is
thought to be due to the influence of the vortices coming from the
preceding blades’ tip gap flow.
Vortices can be identified using the λ2 criterion proposed by Jeong
and Hussain [38]. The criterion is based on taking the gradient of
the steady, incompressible and inviscid Navier-Stokes equations,
which yields
FIGURE 17. PSD LEVELS OF THE PRESSURE FLUCTUATIONS ON THE FAN
BLADES FOR THE 485-605 HZ FREQUENCY BAND.
S2 + 2 =− 1
ρ ∇(∇p) (3)
where S and are the symmetric and antisymmetric parts of ∇u and
represent the strain and vorticity tensors, or
Si j = 1 2
∂xi
) (5)
and ∇(∇p) is the pressure Hessian. The criterion is made to take
the eigenvalues λ1 ≥ λ2 ≥ λ3 of the matrix S2+
2 to deter- mine the existence of a local minima in the pressure
distribution due to vortical motion when S2 +
2 has two negative eigenval- ues, which ensures an ’excess’ of
vorticity when compared to the strain in an eigenplane, thus
defining a vortex core.
Using this criterion, a large vortex structure is seen forming in
Fig. 18 on the suction side edge of the tip surface and is con-
vected towards the following blade’s pressure surface, passing near
the leading edge. These vortical structures are inherently unsteady
and would produce high pressure fluctuations as they pass near the
blade surface, impacting both the aerodynamic and acoustic
performance of the fan. They could also be construed to be the main
reason behind the appearance of BPF tones as they created
distortions in what would otherwise be a clean inflow where the BPF
tones would not be able to appear.
The tip surface is also presented in the middle of Figs. 15 to 17;
it can be seen that there are important pressure fluctuations on
the tip surface as well, which can be attributed to the high-speed
jet-like flows associated with tip leakage flow [8, 39].
10 Copyright © 2014 by ASME
FIGURE 18. ISOSURFACES OF λ2 OF VALUE -0.5 SHOWING THE DEVELOPMENT
OF VORTICAL STRUCTURES IN THE TIP GAP OF THE TESTED FAN
CONCLUSION In this paper, preliminary simulation results covering
both
the aerodynamics and aeroacoustics of a low speed axial fan were
presented.
It was shown from a comparison of the global performance
characteristics of the fan that the simulations tended to
underesti- mate the fan pressure rise. However the pressure
characteristic’s slope was well represented. A similar trend is
observed for the torque characteristic. This was surprising as good
results were achieved on a ring-shrouded fan also used in
automotive cooling applications in previous studies [12,25] with
similar mesh resolu- tions. Further investigation is underway to
verify that the current numerical setup correctly reflects the
experimental conditions.
A good agreement was found between simulation and exper- iment for
the axial velocity profiles behind the fan. Looking at the
azimuthal velocity however, while the overall level and shape of
the profiles were well reproduced by the fine simulation, dis-
crepancies still exist near the hub and tip of the blade between
the numerical results the experiment. An improvement in the
prediction of the azimuthal velocity levels in the tip region with
the refinement of the mesh was however observed.
Regarding the acoustics of the fan, it was first seen that the
coarse anechoic simulation did not allow to properly cap- ture the
BPF harmonics seen in the experiment, whereas the fine case
captured the three first harmonics, albeit with differences in the
levels observed. The fine acoustic simulation also produced high
peaks in the inter-BPF frequency bands that, while coincid- ing
with minor peaks in the experimental spectra, seem exacer- bated in
level. These seem to be due to strong resonance effects in the
downstream chamber and the formation of duct modes. However, a
free-field FWH analysis using the fan surface as a source also
highlighted the fact that some of the inter-BPF bands, namely the
175 Hz, 330-400 Hz and 565 Hz peaks, can be related to surface
pressure fluctuations on the blades.
An analysis of the filtered pressure fluctuations on the fan blades
also highlighted the presence of high levels of fluctuations
associated with the tip region in the frequency bands associated
with peaks in the numerical spectra. Elevated levels of pressure
fluctuations near the leading edge on the suction side as well as
hotspots present on the pressure side of the blades near the tip
are throught to be due to the influence of vortical structures gen-
erated by tip leakage flow from the preceeding blades. Impor- tant
fluctuations were also observed on the tip surface of the fan
blades, which could be attributed to the jet-like flows associated
with tip leakage. This tends to point to tip leakage flow as a
potentially important contributor to the fan noise and provides a
possible explanation of the strong BPF tones observed in this fan
configuration. This could also explain the acoustic sensitivity of
the configuration to the resolution of the mesh in the tip gap, as
the fine mesh appears to resolve the tip flow better according to
the spanwise velocity profiles.
However, the model still needs refinement, as it was ob- served
that the acoustics of the fan in particular were very sensi- tive
to grid refinement and that in this respect grid independance was
almost surely not reached so far. Further simulations on this
impeller are being run in order to ascertain these claims.
ACKNOWLEDGMENT This research was financed in part thanks to a
scholarship
from NSERC-CREATE. A sincere thanks to Robert Bosch LLC for their
financial and
technical support. Computations using PowerFLOW were made possible
due
to an academic license agreement and technical support from the EXA
Corporation and were performed on the supercomputer Mammouth-MP2
from Université de Sherbrooke, managed by Calcul Québec and Compute
Canada. The operation of this su- percomputer is funded by the
Canada Foundation for Innova- tion (CFI), NanoQuébec, RMGA and the
Fonds de recherche du Québec - Nature et technologies
(FRQ-NT).
11 Copyright © 2014 by ASME
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