AIAA 2010-3995
16th AIAA/CEAS Aeroacoustics Conference
Validation of a Hybrid CAA Method: Noise Generated
by a Flap in a Simplified HVAC Duct
Corentin Carton de Wiart ∗ and Philippe Geuzaine†
Cenaero, rue des Frères Wright 29, 6041, Gosselies, Belgium
Yves Detandt‡ , Julien Manera §and Stéphane Caro¶
Free Field Technologies, rue Emile Francqui 1, 1435, Mont-Saint-Guibert, Belgium
Yves Marichalk and Grégoire Winckelmans∗∗
Institute of Mechanics, Materials, and Civil Engineering (iMMC), Université catholique de Louvain (UCL),
1348 Louvain-La-Neuve, Belgium
This paper reports on the validation of a hybrid computational aeroacoustics (CAA)
method on a benchmark of a simplified HVAC duct. An acoustic analogy is adopted and
an in-house unstructured flow solver is coupled to the Actran commercial finite element
solver. Two acoustic analogies are compared: the Lighthill and the Möhring analogies. The
sensitivity study on the numerical setup results in a set of parameters that improves significantly the agreement between the numerical acoustic results obtained with the Lighthill
analogy and the experiment. The same agreement is obtained using the Möhring analogy.
Finally, a study on the parameters of the Fourier transform shows that reasonable results
can be obtained on this case at a low cost using a short duration CFD or with a sampling
in agreement with the highest frequency of interest.
I.
Introduction
The approach followed in this paper consists in using an acoustic analogy, as first proposed by Lighthill.1
Acoustic analogies rest on the assumption that the noise generation and propagation are decoupled, that is,
flow generated noise does not impact the internal dynamics of the flow. In practice, using an acoustic analogy
is a two-steps procedure. In the first step, an unsteady CFD analysis is used to compute the aerodynamic
sources. The second step consists in computing the propagation and radiation of these aerodynamic sources.
In order to perform the high Reynolds number flow analysis for complex geometries, Cenaero has developed a parallel implicit solver, called Argo, for three-dimensional compressible flows on unstructured
tetrahedral meshes. A special care has been devoted to develop accurate discretization methods that perform properly for unsteady flow applications, especially for turbulence using Large Eddy Simulation (LES).
For instance, the spatial discretization is based on a kinetic energy conserving discretization2 ensuring a low
level of artificial dissipation. As the wall-resolved LES is known to be too expensive near the walls in terms
of grid resolution, Cenaero has implemented a RANS-LES approach. The near-wall region is treated in
RANS and a LES model is recovered away from this zone. This leads to grid requirements in line with pure
RANS simulations. The selected RANS-LES method is the Delayed Detached-Eddy Simulation (DDES)3
approach, based on the one-equation Spalart-Allmaras model.4 In this version of the DES, the switching
∗ Research
Scientist, CFD-Multiphysics group and Ph. D. student, UCL, AIAA Member
Leader, CFD-Multiphysics group
‡ Research Scientist, AIAA Member
§ Research Scientist, AIAA Member
¶ Research Scientist, AIAA Member
k Ph. D. student, F.R.S. - F.N.R.S fellow
∗∗ Professor, President of iMMC, AIAA Member
† Group
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between the RANS and the LES region depends not only on the grid resolution but also on turbulent flow
properties. The spatial discretization has also been modified, the kinetic energy conserving scheme is used
in the LES region of the flow and an upwind scheme (AUSM) is used in the RANS region.
Within an acoustic analogy framework, a popular approach for the propagation and radiation of the
aerodynamic sources is to rely on explicit integral methods, amongst which the most famous is the FfowcsWilliams and Hawkings equation. There are however several limitations to such techniques since they are
practically limited to pure exterior radiation problems as they can hardly be used in interior problems (e.g.
in ducts). These limitations have pushed Free Field Technologies (FFT) to implement an alternate method5
in the finite element code Actran. The method is based on the variational formulation of the Lighthill
equation, is designed to be used for exterior or interior problems with or without liners, and has been shown
to possess the potential to handle industrial problems.6–8 FFT has recently implemented the Möhring analogy in Actran. As in the Lighthill analogy, Möhring uses a scalar equation directly derived from the
Navier-Stokes equations but with the ability to handle higher Mach number flows (M > 0.2), where the
convection and refraction effects cannot be neglected.
The acoustic sources captured by the CFD have to be transferred to the acoustic mesh, the sources being
the divergence of the Lighthill tensor or the Möhring source term. FFT has developed a mapping approach
ensuring the conservation of the integral of the source term.9 With this method, it is expected that the
mesh in the source region can be coarser than when using linear interpolation. At the limit, the constraint
on the mesh in the source region is fully relaxed, leaving propagation to be the only criterion to design the
acoustic mesh. A previous contribution10 investigated the accuracy of the proposed CAA methodology and
the conservative mapping was compared to the linear interpolation of the sources. The main benchmark
used for these investigations was the noise generated by a Helmholtz resonator placed in a duct.
The objective of the present contribution is to further validate the proposed CAA methodology, using two
different acoustic analogies. The effects of the parameters of the CFD on the acoustic result are first studied.
For those investigations, only the Lighthill analogy is considered. The mesh strategy and its influence on the
computational setup is explained. Then, the Lighthill analogy is compared to the Möhring analogy using
the CFD case whose noise prediction best fits the experiment. Finally, the influence of the sampling of the
source term on the noise prediction are shown, as well as the duration of the flow computation which directly
drives the frequency accuracy.
II.
Computational aeroacoustics
The theory5, 11, 12 behind the formulations used in Actran is briefly summarised hereafter, more details
about those formulations can be found in the Actran manual.13 Two acoustic analogies are considered:
the Lighthill analogy and the Möhring analogy.
II.A.
The Lighthill analogy
Starting from the mass and momentum conservation equations, it is possible to derive Lighthill’s equation
without any assumption, as in the beginning of the original paper.1 The final equation is a true wave
equation whose right-hand side term is the simplified Lighthill’s tensor
2
∂ 2 Tij
∂ 2 ρa
2 ∂ ρa
−
a
=
,
0
∂t2
∂xi ∂xi
∂xi ∂xj
(1)
with some classical assumptions, valid only in the case of a low Mach number and a high Reynolds number
flow where isentropic assumptions are reasonable from an acoustic point of view, the source term gives
Tij ' ρ0 vi vj .
II.B.
(2)
The Möhring analogy
The Möhring’s equation14 is derived from the Navier-Stokes equations. The final equation is a scalar equation
whose left-hand side corresponds to acoustic wave propagation in the presence of a heterogeneous flow. The
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right-hand side corresponds to flow fluctuations which are considered as acoustic sources. The equation gives
∂
ρ0 Dba
ρ0 v0 Dba
ρ0
+
∇
−
∇b
=R
(3)
a
∂t ρ2T c2 Dt
ρ2T c2 Dt
ρ2T
with v0 the mean velocity, ρ0 the mean density and c the sound speed. ba is the scaled total enthalpy
fluctuations and is defined by
DBa
Dba
= ρT
,
Dt
Dt
1
Ba = ha + kva k2
2
(4)
with ha and va the fluid enthalpy and velocity fluctuations. The material derivative is computed using v0 .
In this analogy, the acoustic variable is the fluid total enthalpy. This one can be connected to the acoustic
pressure with the energy equation:
1 ∂pa
DBa
=
.
(5)
Dt
ρ0 ∂t
The source term R is computed within the CFD. Neglecting the entropy noise sources, the source term gives
R = −∇
II.C.
1
(ρv × (∇ × v) − ∇τ )
ρT
(6)
Methodology
The whole computational aeroacoustics process can be summarised as follows:
1. One CFD is performed from a statistically converged solution with ∆t (time step) and ∆T (duration)
driven by acoustic. From that CFD, the primary variables (velocity, temperature, density, pressure)
are computed by Argo for each time step and written in the EnsightGold format on everypoint of the
CFD mesh;
2. The conservative mapping9, 10 from the CFD mesh to the CA mesh, the computation of the divergence
of the Lighthill tensor and/or the Möhring source terms is performed by iCFD, a package which comes
with the standard distribution of Actran.
3. The Fourier transform of the source term is also done within iCFD, using filters if needed;
4. The user launches the Actran simulation, which gives a direct access to all acoustic fields in the finite
and infinite elements, including some energy indications.
To avoid a great amount of data storage, the conservative mapping and the CFD are done simultaneously.
III.
Simplified HVAC duct
The consortium of the German car manufacturers Audi, BMW, Daimler, Porsche and Volkswagen have
investigated the feasibility of correctly predicting the aerodynamically generated noise within an HVAC
system. Experiments as well as fluid and acoustic computations have been carried out. The results have
been presented by the consortium9, 15 and showed a fair agreement. This case is thus a good benchmark to
validate the coupling between Actran and Argo.
III.A.
Experimental setup
The experimental setup is briefly described in this section. More details can be found in Jäger et al.15 The
setup is composed of a square duct section with an elbow and a flap. The dimension of the duct in the elbow
region is given in Fig. 1. To ensure a fully turbulent flow in the region of interest, a 3 meter long duct is
installed before the elbow. An adaptor with turbulence tripping is connected between the duct and the fan
allowing a smooth transition from the circular cross section to the square cross section. Finally, to reduce
efficiently the fan noise, two mufflers in tandem configuration are placed between the fan and the adaptor.
The full setup is described in Fig. 2 An averaged inlet velocity of 7.5 m/s is imposed at the inlet using a
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Figure 1. Dimension of the simplified HVAC duct in the elbow region (Jäger et al.15 ).
Figure 2. Experimental setup (Jäger et al.15 ).
variable speed fan.
Fluid dynamic measurements as well as pure acoustic measurements have been performed using this
setup. Fig. 3 shows the PIV setup and the position of the microphones near the flap and the elbow. For the
Figure 3. Measurements setup (Jäger et al.15 ).
acoustic measurements, dB values are available in the far-field region. Microphones turning around the exit
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of the duct gives 289 measures at different positions with a frequency resolution of 0.625 Hz. The average of
the results of those measurements are used to compare the experiment with the numerical noise prediction.
III.B.
III.B.1.
CFD setup
Geometry
The computational domain is presented in Fig. 4. To ensure a fully developed flow in the duct and to avoid
the effect of the elbow on the inflow condition, the 3 meter duct of the experiment is taken into account in
the computation.
Figure 4. Geometry of the computational domain.
III.B.2.
Boundary conditions
Fig. 5 shows the boundaries and their associated conditions. As the velocity at the inflow is uniform, a slip
wall is used at the beginning of the duct to avoid an possible influence of the development of the boundary
layer on the inflow condition. A non-reflective boundary condition16 is set at the outflow to damp the vortical
structures of the jet.
III.B.3.
Mesh and computations
Three simulations have been performed on this geometry and those boundary conditions (see Tab. 1). The
simulations differ on the mesh refinements and boundary layer mesh definition. The first computation
Table 1. Parameters of the meshes and the three CFD
Boundary layer mesh
Wallfunction
Refinement size around the elbow [mm]
Total number of nodes [M]
CFD1
CFD2
CFD3
y+ ' 1
No
2 10−3
5.83
y + ' 30 − 40
Yes
2 10−3
3.43
y + ' 30 − 40
Yes
10−3
4.72
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Figure 5. Boundary conditions.
(CFD1) has been done on a preliminary mesh with local refinements around the elbow and in the jet. A
finer refinement box is placed around the flap to capture correctly the vortical structures created around it
(see Fig. 6). A boundary layer mesh is applied on the no-slip walls of the duct and the flap. This boundary
layer mesh is set to obtain y + ' 1 and a growth rate equal to r = 1.2. The second computation (CFD2)
Figure 6. Mesh with local refinement.
is done using wall functions on the walls of the duct in order to get a less expensive computation. The
refinement boxes of the mesh, as well as the boundary layer mesh around the flap, remain the same than
those of the first case, only the parameters that define the boundary layer mesh of the duct are different
from the first case. This boundary layer mesh is designed to reach a y + ' 30 − 40. The third case (CFD3)
is also designed to use wall functions on the walls of the duct. The only difference with the second case is a
refinement box around the elbow. The size of this refinement box is the same as the one around the flap.
The turbulence modelling used for both computations is the DDES based on the Spalart-Allmaras model.
The convective term of the equations is treated with an AUSM flux in the RANS region and a central scheme
in the LES region. The time step is set to ∆t = 4.10−5 s.
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III.C.
CA setup
The geometry of the computational acoustic domain includes the whole duct, the muffler, the flap and
the opening in the anechoic room. The mesh is made of quadratic tetrahedron and is designed to solve
frequencies up to 2kHz. The number of element is 105 . The computational domain and the mesh used
are presented in Fig. 7. The mesh is finer near the wall in order to represent better the geometry. The
Figure 7. Computational domain and surface mesh.
interpolation of the sources from the CFD mesh to the CA mesh is done with iCFD with a conservative
method and are transformed into the frequency domain using a Hanning windowing. Infinite elements are
used at the inlet of the domain (the mufflers) and at the outlet (anechoic room). To avoid truncation effects,
the sources are damped smoothly using a spatial filtering. For more details in the Actran setup, see Caro et
al.9 The computational time is 2 minutes per frequency on one CPU and requires 4GB of RAM. Numerical
microphones are placed at the same positions as in the experiment. The average of the values measured by
those microphones are used to compare the numerical noise prediction to the experiment.
III.D.
III.D.1.
Results
Preliminary results
The acoustic results of the CFD1 are shown on Fig. 8. The low and medium frequency region (up to 1kHz)
Figure 8. Comparison between the SPL obtained with Actran and that measured from the experiment. CFD1 is sample
on 0.2s giving a frequency resolution of 5Hz.
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is well represented although the peaks are overestimated. The high frequency range as well as the peak
at 1550Hz are quite underestimated. To understand this behaviour, it is necessary to locate the source
of this high frequency peak. The microphones placed in the duct can give important information on the
localisation of the acoustic sources. Fig. 9 presents the spectra of the microphones 2 and 4 in the duct. The
two microphones are located around the two major sources: after the flap and around the elbow. The high
frequency peak is present on the experimental curve of the microphone 4 but not on that of the microphone
2. The source region of the high frequency peak is thus located around the elbow (see Fig. 3).
Figure 9. Pressure fluctuations for the CFD1 case (left: microphone 2, right: microphone 4).
The analysis of the vortical structures computed within the CFD showed that the elbow region is mainly
steady, resulting in a no production of acoustic noise in this region. Fig. 10 shows the z-component of the
vorticity at the middle of the duct. We can see that the shearlayer separating from the elbow is totally
steady.
Figure 10. Snapshot of the instantaneous field of the z-component of the vorticity for the CFD1 case.
In Fig. 11, the 3-dimensional vortical structures are presented using a λ2 iso-contour. The snapshot
confirms the steadiness in the elbow region. Investigations showed that the Detached Eddy Simulation
model often prevents the shearlayers to develop the Kelvin-Helmholtz instabilities.
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Figure 11. Snapshot of the λ2 iso-contour coloured with the velocity for the CFD1 case.
III.D.2.
Reduction of the CFD cost with wall function
A well known way to reduce the cost of a CFD while keeping a reasonable accuracy is the use of wall
functions. In this case (CFD2), a wall function based on the Reichardt’s law is applied on the walls of the
duct. Fig. 12 shows a snapshot of the vorticity (z-component) of the CFD2. With the wall function, the
Figure 12. Snapshot of the instantaneous field of the z-component of the vorticity for the CFD2 case.
shearlayer coming from the elbow is unstable. This could be explained by the numerical instabilities created
by the wall function. The same behaviour is observed for the 3-dimensional vortical structures, presented
with iso-contour of λ2 on Fig. 13. This unsteadiness does not lead to a high frequency peak at 1550kHz as
observed in the experiment. Fig. 14 presents the result of the acoustic computation based on the sources of
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Figure 13. Snapshot of the λ2 iso-contour coloured with the velocity for the CFD2 case.
the CFD2. The low frequency peak is still underpredicted and the broadband noise is similar to that of the
CFD1. Nevertheless, the same result is obtained at a lower cost.
Figure 14. Comparison between the SPL obtained with Actran and that measured from the experiment. CFD2 is
sample on 0.2s giving a frequency resolution of 5Hz.
III.D.3.
Refinement in the elbow region
As well as in the CFD1, the high frequency peak is captured by the CFD2, only the amplitude of the peak is
not as high as in the experiment. A reason could be the coarse mesh around the elbow. As the high frequency
sound is generated by small structures in the flow, if the mesh size is close to the size of those structures,
the turbulence model could damp them resulting in noise underprediction. Therefore, a computation with a
refinement in the elbow region is studied in the CFD3 case.
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Because the refinement in the elbow region is expensive in terms of mesh points, the boundary layer mesh
with wall functions around the elbow of the CFD2 is kept in this case. On Fig. 15, the acoustic result is
shown for CFD3. The refinement in the elbow region greatly improves the results. The high-frequency peak
Figure 15. Comparison between the SPL obtained with Actran and that measured from the experiment. CFD3 is
sample on 0.2s giving a frequency resolution of 5Hz.
is no longer underestimated from the CFD compared to the experiment and the broadband noise is well
represented.
The same behaviour is present on the pressure fluctuations at the wall of the duct. Fig. 16 shows pressure
fluctuations in the frequency domain of the microphones 2, 4 and 6. For the microphone 4, the high frequency
Figure 16. Pressure fluctuations on microphone 2 (upper left), 4 (upper right) and 6 (down).
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peak is present but the low and medium frequency range seems more “turbulent” than in the experiment.
Nevertheless, those fluctuations do not appear in the sound radiated.
In Fig. 17, the λ2 iso-contour is presented. The improvement compared to the CFD1 and the CFD2 case
is obvious. The mesh captures smaller vortical structures and the flow is unsteady after the elbow. The
same behaviour can be observed in Fig. 18.
Figure 17. Snapshot of the λ2 iso-contour coloured with the velocity for the CFD3 case.
Figure 18. Snapshot of the instantaneous field of the z-component of the vorticity for the CFD3 case.
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Fig. 19 presents the acoustic pressure at 120Hz and 1550Hz. This result shows the importance of the
Figure 19. Acoustic pressure at 120Hz (left) and 1550Hz (right). The colorbars are saturated between [−1, 1] (left) and
[−0.005, 0.005] (right).
infinite elements at the inlet of the duct (numerical representation of the mufflers). The acoustic waves going
back into the duct are much stronger than those radiated away from the outlet. In agreement with the noise
prediction given by the microphone (Fig.15), the low pressure sound is much stronger than that of the high
pressure (values saturated between [−1, 1] at 120Hz and between [−0.005, 0.005] at 1550Hz).
The zoom on the source region gives a good idea of the position of the sources. Most of them are localised
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around the flap. Nevertheless, the noise source is not null near the elbow. Investigations showed that most
of the high frequency sound (> 1kHz) comes from the shearlayers of the flap, the low and medium frequency
sound (< 1kHz) is created by the vortical interactions near the exit of the duct.
IV.
Comparison between the Lighthill and the Möhring analogies
Fig. 20 shows the acoustic results in the far-field computed with the Lighthill and the Möhring analogies
using the CFD3. As expected the broadband noise is very similar. Indeed, the Mach number of this flow is
very low, meaning the convection effects are minimal.
Figure 20. Comparison between the SPL obtained with Actran with the Lighthill analogy, that obtained with the
Möhring analogy and the experiment. The frequency resolution is 5Hz.
V.
Influence of the CFD sampling and duration on the noise prediction
As the region of interest of the acoustic computation goes up to 2kHz and the frequential range of the
CFD goes up to 12.5kHz, it is interesting to study the influence of the sampling of the CFD on the acoustic
result. Indeed, sampling the CFD source term is interesting to minimise the computational resources (time
and disk space).
Three acoustic computations, using the Lighthill analogy, are carried out to compare the effect of the
CFD sampling on the results. The first computation is done using every time step available, giving a time
step of the DFT equal to the half of that of the CFD (∆tDF T = 21 ∆tCF D , as recommended for low Mach
number flow), giving a frequency range going up to 25kHz. The other computations are done using the CFD
results every two and four time steps, giving a frequency range going up, respectively, to 6250 and 3125Hz.
The computations are compared on Fig. 21. The curves are very similar, even in the high frequency
range. In this case, the sampling of the CFD does not influence the acoustic results.
The CFD duration is also an interesting parameter to study. The computational cost of the CFD, as well
as that of the CA (the frequency resolution directly depends on the CFD duration), grows linearly with time.
Then, the CFD duration has to be chosen to capture the minimal frequency of interest. Fig. 22 compares
the acoustic result of each CFD compared to that of the experiment. It is interesting to see that the 0.1s
duration CFD already gives a reasonable result. The longer the CFD is, the better the noise is captured, also
at high frequencies. In this case, the best frequency resolution (2.5Hz) gives a better representation of the
broadband noise, although some peaks are overestimated (as well as the noise predicted with the Möhring
analogy). Nevertheless, this overestimation can be explained by the differences between the numerical and the
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Figure 21. Comparison between the SPL obtained with Actran using different time step for the DFT.
Figure 22. Comparison between the SPL obtained with Actran using different CFD duration.
experimental setup. The walls of the duct are not completely rigid, contrary to the numerical representation
of the walls. The numerical setup is then more sensitive to resonance.
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VI.
Conclusion and perspectives
This paper shows the capability of Argo combined with Actran to predict correctly the noise created
within a HVAC system. It also shows the importance of the refinement in some regions of the CFD mesh
needed to capture correctly the noise sources in the high frequency range. A coarse mesh in a source region
results in an underprediction of the noise. Numerical results shows that for this case the use of wall function
is advantageous. While the wall function is only applied on the wall of the duct in this study, future works
will investigate its use on the flap. If the methodology is validated, LES computations using multiscale
subgrid models will be studied. Indeed, as the RANS region of the DDES model is reduced for computations
with wall functions, LES methods should give the same result at lower cost.
Numerical results also shows good agreement between the Möhring and the Lighthill analogies.
Finally, a study on the parameters of the Fourier transform shows that reasonable results can be obtained
on this case at a low cost using a short duration CFD or with a sampling in agreement with the highest
frequency of interest.
Acknowledgment
The authors would like to thank the owners of the test case and experimental results, who agreed to share
them with us. The first two authors acknowledge the support by the Walloon Region and the European
regional development fund (ERDF) under contract N◦ ECV12020022015F.
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