Application of a hybrid Computational Aeroacoustics method to an automotive blower

mustardarchaeologistMechanics

Feb 22, 2014 (3 years and 7 months ago)

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Application of a hybrid Computational
Aeroacoustics method to an automotive
blower

M PIELLARD and B COUTTY
Delphi Thermal, Customer Technology Center Luxembourg, Luxembourg







ABSTRACT

A hybrid method of aeroacoustic noise computation based on Lighthill’s Acoustic
Analogy is applied to investigate the noise radiated by an automotive blower. The two-
steps hybrid simulation method relies on Lighthill’s acoustic analogy. To account in the
frequency domain for aeroacoustic sources linked to the fan rotation, a porous surface
enclosing the fan is defined, allowing specifying surface source terms. In order to
validate the simulation results, the experimental setup is reproduced in the numerical
model. Therefore it is possible to draw a fair results’ comparison in terms of
aerodynamic mean flow quantities as well as acoustic power levels.
1 INTRODUCTION
In an industrial context, the development of an efficient hybrid noise computation
method has to consider its applicability and the computing time necessary to reach a
relevant solution. A previous study [1] was focused on a ducted diaphragm geometry,
for which a fair agreement between simulation and reference results could be reached.
This study showed in particular the importance of using an integration technique to
interpolate source terms from the fluid mesh to the acoustic mesh. In this work, a level
of complexity in the simulation process is added since a centrifugal fan with its scroll is
involved. Indeed, the presence of the fan means a much more complex geometry, a
different handling of the fluid simulation with a sliding mesh, and additional Lighthill’s
surface sources.
After introducing the simulation method with theoretical developments, its practical
implementation is explained. Then the experimental setup is detailed, and details about
fluid and acoustic simulations are given. The compared analysis of simulation and
experimental results allows understanding the method’s relevancy. Finally, conclusions
are drawn and some prospects are proposed.
2 SIMULATION METHOD
The simulation method is a two step hybrid approach relying on Lighthill's acoustic
analogy [2], assuming the decoupling of noise generation and propagation. The first step
consists of an incompressible Large Eddy Simulation of the turbulent flow field, during
which source terms are transiently recorded. In the second step, a variational
formulation of Lighthill's Acoustic Analogy discretized by a finite element discretization
is solved in the Fourier space, leading to the radiated noise up to the free field thanks to
the use of infinite elements [3].
2.1 Theory: Lighthill’s Acoustic Analogy
The implementation of Lighthill's acoustic analogy was firstly derived by Oberai et al
[4], refer also to Actran User's Guide [3] and Caro et al [5] for instance. The starting
point is Lighthill's equation:
( )
( )
ji
ij
ii
xx
T
xx
c
t ∂∂

=−
∂∂

−−


2
0
2
2
00
2
2
ρρρρ
(1)
with Lighthill's tensor
ij
T defined as
(
)
(
)
(
)
ijijjiij
cppuuT
τρρδρ
−−−−+=
0
2
00
(2)
where
ρ
is the density and
0
ρ
its reference value in a medium at rest,
0
c is the
reference sound velocity,
i
u are the fluid velocity components,
p
is the pressure and
ij
τ
is the viscous stress tensor.
The variational formulation of Lighthill's analogy is then obtained after writing the
strong variational statement associated with equation (1), and integrating by parts along
spatial derivatives following Green's theorem. This formulation is actually an equation
on the acoustic density fluctuations
0
ρ
ρ
ρ

=
a
, which reads:
δρδρ
δρρδρ
δρ
ρ
∀Γ

Σ∂
+




−=












+


∫∫∫
ΓΩΩ
)(
2
0
2
2
xxx dn
x
d
xx
T
d
xx
c
t
i
j
ij
ij
ij
ii
aa
(3)
where
δρ
is a test function,
Ω
designates the computational domain, with the total
stress
ij
Σ
defined as
(
)
ijijjiij
ppuu
τ
δ
ρ


+
=
Σ
0
(4)
Two source terms can be distinguished: a volume and a surface contribution. Recalling
the momentum equation, we can write
( )( )
( )
iiijijji
j
i
j
ij
i
u
t
nppuu
x
n
x
n
ρτδρ


−=−−+


=

Σ

0
(5)


As a result, if the surface
Γ
is fixed or vibrates in its own plane, expression (5) reduces
to zero. However, in the case of a rotating machine where the rotating part is enclosed in
a fixed volume, a control surface, also called porous surface, can be defined, and the
source term
jij
x

Σ

accounts for the effect of the flow enclosed inside the control
surface on noise generation. In the acoustic simulation, the surface
Γ
will be a boundary
condition of the problem, while it represents the interface between the rotating and fixed
domains in the fluid simulation.
2.2 Practical application of the method
The method consists of coupling a CFD code with a finite element acoustic software
where the variational formulation of Lighthill's acoustic analogy is implemented. The
main steps of a practical computation, provided that an unsteady solution of the flow
field has already been obtained, are as follows:
• An analysis of the flow field allows determining in which region(s) of the flow
volume source terms will be considered; an acoustic mesh is built on the whole
region of interest for acoustics, with possibly smaller elements in source terms
regions; the surface which will support surface source terms is also carefully
meshed at the interface of the sliding mesh.
• The time history of velocity components, density and pressure is stored on the
CFD mesh during the fluid simulation within Ansys Fluent 12.1 [6].
• Source terms, computed on the CFD mesh for better accuracy, are integrated on
the acoustic mesh.
• Unsteady source terms are transformed from time to spectral domain.
• The acoustic computation is performed with Actran 11 [3], taking into account
the spectral volume and surface source terms.
3 APPLICATION TO AN AUTOMOTIVE CENTRIFUGAL BLOWER
3.1 Experimental setup
3.1.1 Test set-up
Acoustic tests are performed following ISO 10302 set-up [7]. ISO 10302 defines an
experimental method for sound power measurement of an airborne noise by air-moving
devices. The air-moving device used in this study is an automotive blower. The blower
is connected to a Mylar plenum which outlet size varies, allowing choosing the blower
operating point. The Mylar plenum sides are made of an acoustically transparent
material. The plenum design follows ISO 10302 design at scale 1:1. It was validated in
terms of insertion loss according to ISO 10302 method.
10 microphones are installed on a 2 meters radius half sphere centred on the connection
between blower duct and Mylar plenum according to ISO 10302. Sound pressure levels
are evaluated at each microphone.
3.1.2 Part under test
The tested blower is directly cut from a production HVAC module. It consists of a 39
forward skewed blades centrifugal fan, an electrical motor, a plastic scroll and cover and
an outlet duct. The motor is installed in the cover through rubbers as per production.
The outlet of the scroll is connected to the Mylar plenum through a straight 20 cm duct.
In order to avoid sound transmission through the walls or from connections between
plastic parts, which will not be modelled in the simulation, the scroll, cover and ducts
were covered by a layer of foam and heavy material, see Figure 1. Chosen operating
point of the blower is 3000 rpm, 438 m
3
/h for 562 Pa (ρ=1.2 kg/m
3
).


Figure 1. Left: Experimental setup with Mylar box; right: blower under test.

3.2 Simulation setup
3.2.1 CFD simulation
The CFD simulation setup is representative of the experimental setup, see the scheme
on Figure 2. The fan, scroll and duct are completely modelled; a half sphere is added at
the inlet of the fan to simulate a free field inlet; the motor is not considered in the
geometry, since a close dome is used; finally the Mylar box is entirely represented, with
its actual opening of diamond shape. Actually the size of the outlet drives the operating
point of the simulation as in the experiment. A tetrahedral mesh is built on this
geometry, composed of a total of 4 million cells. As shown on Figure 2, the mesh size is
quite large in the Mylar box (around 20mm), but the fan, scroll and duct are quite
refined with cells of size 1.5mm, 3mm and 7mm. A box is also created in the jet area to
keep a constant cell size of 7mm, see Figure 2. No boundary layers are used.
Ansys Fluent 12.1 is used for the CFD simulation. An atmospheric pressure condition is
set at both inlet and outlet boundary conditions to simulate free field conditions. A first
steady-state k-epsilon Reynolds Averaged Navier-Stokes (RANS) simulation is run to
initialize the flow field, using a moving reference frame model to account for the fan
rotation at 3000rpm. Then a Detached Eddy Simulation (DES), blending Large Eddy
Simulation with a Spalart-Allmaras RANS model, is chosen for the transient run; here
the fan rotation is performed using a sliding mesh model, allowing the fan walls to
physically rotate. Central differencing is used for spatial discretization of momentum
and turbulent viscosity equations, and a second order scheme is used for pressure. A
second order transient formulation is chosen, with a time step of 5×10
-5
s. The


simulation is first run until the stabilization of the flow (14 cycles), and then transient
aerodynamic quantities are recorded during 4.25 cycles of the fan.



Figure 2. Left: CFD model and boundary conditions; right: overview of the mesh and
zoom in the blower scroll area.

Instantaneous pictures of the flow field are presented on Figure 3. Vorticity contours
exhibit the main features of the flow: a complex flow field inside the scroll around the
fan, and a jet originating from the duct inside the Mylar box. Organized turbulence
structures are created in the boundary layers. The velocity magnitude contours in an x-
plane cutting the fan and scroll particularly show the complex flow behaviour in this
region. This complexity justifies the choice of the aeroacoustic model, where all flow
details occurring in the rotating region are discarded, since only flow features on the
porous surface are accounted for. It is also quite clear that the flow discretization is not
very fine in the jet area. This choice was made to decrease the simulation time and the
database size.


Figure 3. Left: vorticity magnitude in an X-plane cut; right: velocity magnitude in the
fan/scroll area.

3.2.2 Acoustic simulation
A quadratic acoustic mesh of 308,000 nodes and 217,000 tetrahedral elements is built
based on the geometry presented on Figure 4; it is composed of the scroll and duct
interior domains, without the fan, the porous surface which will support Lighthill’s
Mylar box
outlet
inlet
fan

refinement box in
the jet area
surface source term and is a boundary condition, the upstream wall of Mylar box (its
material in the experiment can be modelled as a wall), the ground which is a wall, and
the infinite elements placed on a half sphere above the setup. Lighthill’s volume
sources, which exist only in the CFD domain, are accounted for in the scroll and duct
domain, in the half sphere at blower inlet, and in the lower part of Mylar box where the
jet takes place.
Infinite
Elements
Ground
(perfectly
reflecting wall)
Porous surface
(yellow)
Upstream wall
of Mylar box
Microphone #1

Figure 4. Acoustic simulation model and boundary conditions.

Maps of volume and surface source terms are presented on Figure 5. While the location
of the volume source terms is quite easy to understand in the scroll, duct and jet regions,
there are quite heavy sources appearing in the Mylar box near the end of the domain.
This is actually related to the representation of the source terms; as they are integrated
onto the acoustic mesh, their level is dependant on the original source level, as well as
on the acoustic mesh size. This explains the presence of very high level sources in the
second part of Mylar box. Moreover, the use of quadratic elements for the acoustic mesh
also changes the representation of the sources by breaking their continuity (only in the
representation). In order to make sure that no sources are cut at the domain outlet, which
could cause spurious noise, a spatial filter of cosine type is defined to damp out the
sources at the boundaries; a representation of the filter is shown on Figure 6. The map of
surface source term magnitude integrated onto the porous surface shows that most
surface source terms are located at the fan basement, which is also the most loaded
region in terms of airflow.


Figure 5. Left: instantaneous magnitude of
jij
xT


(volume sources) integrated onto
the acoustic mesh; right: instantaneous magnitude of
jij
x

Σ

(surface sources)
integrated onto the porous surface mesh.




Figure 6. Spatial filter used to damp source terms, in side and top view from left to
right; red=1: no damping is applied, blue=0: sources are reduced to zero.

3.3 Comparison between simulation and experimental results
In both the simulation and the experiment, a comparison of Sound Pressure Level (SPL)
is performed on Microphone #1, whose location is shown in Figure 4. Those spectra are
displayed on Figure 7. Due to the length of the simulation signal, no averaging could be
performed; this explains the number and amplitude of the peaks present in the
simulation spectrum. It has been verified on the experimental signal that performing no
average can lead to variations of ±5dB(A) amplitude. The sharp peak present on the
experimental spectrum at 550Hz corresponds to the number of spokes on the fan hub;
these spokes are not modelled in the simulation since the hub is closed (simulating the
spokes, and thus opening the hub would lead to a great complexity since the motor
geometry would have to be modelled). Therefore this sharp peak cannot be found on the
simulation spectrum. The overall shape of the simulation spectrum suggests that the
broadband noise is correctly caught, but some wide peaks seem to have no physical
origin: at 300Hz, 500Hz, 700Hz and 850Hz. The acoustic propagation model has first
been suspected of being responsible for these peaks. However, a previous simplified
simulation using the same CFD data showed a similar behaviour; a spectrum from this
simulation is also displayed in Figure 7. In this simplified acoustic setup, the ground and
the upstream Mylar wall were not modelled.
To explain the differences between the simulation and experimental signals, it has also
to be mentioned that it was not possible to reproduce exactly the mean airflow
conditions. Indeed in the experiment it was measured 438m
3
/h and 562Pa, while the
simulation provided 442m
3
/h and 480Pa in the Mylar box.

Figure 7. Sound Pressure Levels radiated at microphone #1. Black: experimental
signal; blue: signal from the described simulation; red: signal obtained from the
simplified simulation.

A refined CFD simulation was performed to check if it could improve the results after
propagation. First spectrum, in Figure 8, is already showing an improvement since the
300Hz, 700Hz and 850Hz peaks are greatly reduced. The fluid simulation will thus
definitely be carefully worked to provide more accurate results.

Figure 8. Sound Pressure Levels radiated at microphone #1. Black: experimental
signal; blue: signal from the simulation with new CFD results.


4 CONCLUSIONS
A hybrid Computational Aeroacoustics method based on Lighthill’s acoustic analogy
was applied to an automotive blower. Compared to previous studies performed on
stationary parts, the rotating fan introduces surface source terms in addition to volume
source terms. Those surface source terms defined on a porous surface allow taking into
account the fan rotation as a boundary condition in the frequency acoustic computation.
Results obtained so far show the importance of the CFD quality. A great effort has to be
made in this step of the simulation to expect relevant results after acoustic propagation.
In addition, it would be interesting to investigate a simpler setup involving only a
blower, without the Mylar box; this would simplify the CFD and acoustic models and
help understand the important features of this aeroacoustic simulation.
ACKNOWLEDGEMENTS
The first author would like to acknowledge FFT support team, and in particular Diego
d’Udekem, for fruitful discussions about this study.
REFERENCES

1. Piellard, M. & Bailly, C. (2010) Several Computational Aeroacoustics solutions for
the ducted diaphragm at low Mach number. 16
th
AIAA/CEAS Aeroacoustics
Conference. AIAA paper 2010-3996.
2. Lighthill, M. (1952) On sound generated aerodynamically. Part I: General theory,
Proceedings of the Royal Society of London, Vol. A211, pp. 564-587.
3. Free Field Technologies (2009) Actran 10 User’s Guide.
4. Oberai, A. A., Roknaldin, F. & Hughes, T. J. R. (2000) Computational procedures for
determining structural-acoustic response due to hydrodynamic sources. Computer
Methods in Applied Mechanics and Engineering, Vol. 190, pp. 345-361.
5. Caro, S., Ploumhans, P. & Gallez, X. (2004) Implementation of Lighthill's Acoustic
Analogy in a finite/infinite elements framework. 10th AIAA/CEAS Aeroacoustics
Conference, AIAA Paper 2004-2891.
6. Ansys Fluent (2010) Ansys Fluent 12.1 User’s Guide.
7. ISO 10302:1996. Acoustics – Method for the measurement of airborne noise emitted
by small air-moving devices.
8. ISO 3745:1977. Acoustics – Determination of sound power levels of noise sources –
Precision methods for anechoic and hemi-anechoic rooms