vibro-aero-acoustic simulation of side mirror wind...

Vibro-aero-acoustic simulation of side mirror wind noise and strategies to evaluate pressure contributions

J. Jacqmot1, Y. Detandt1, G. Lielens1, D. Copiello1 1 MSC Software Belgium

Rue E. Francqui, 9, B-1425, Mont-Saint-Guibert, Belgium

e-mail: [email protected]

Abstract The sound pressure levels due to flow turbulence generated by the A-pillar and the side mirror is assessed

by means of simulations up to 6,000 Hz. The pressure perturbations that arise around a generic vehicle

model are propagated up to the side windows, inducing vibrations of the window’s surfaces. Those

vibrations then create the interior noise.

The finite element model used to simulate those phenomenon is presented along with the results that have

been validated against measurements. The content of the pressure field in terms of wavelengths is analyzed using two different methods: the wave number decomposition and the pellicular mode decomposition.

1 Introduction

In the past, wind noise was considered as a noise source only in the higher frequency range and a noise issue

when a vehicle is traveling at mid to high speed. With the recent advances in the automotive field, this is

not true anymore. The aeroacoustic noise can be a major source both in the low frequency range and for low

speed vehicles. This is caused by many factors. For example, vehicle noise sources typically affecting the

low frequency range have been greatly reduced (e.g. the powertrain and the exhaust) or are no more present

in new electric and hybrid cars. Moreover, the efforts of reducing weights of (among others) windshield and side windows are leading to an increasing interest to the side mirror noise.

This type of noise can be split in two contributions acting on the side window: a turbulent contribution

caused by the aerodynamic pressure fluctuations acting directly on the walls and an acoustic contribution

due to the noise generated by the turbulent structures themselves and propagating to the car surface.

Modifying the turbulent structure outside the vehicle does not ensure that the interior noise is affected as

the acoustic part might remain unchanged. Indeed, the acoustic part is also known to be more effective in

transmission through the side windows.

The simulation of such problem relies on two main factors:

Accurate representation of the turbulent flow field around the A-pillar and the side mirror

Realistic simulation of side windows vibrations and the acoustic propagation into the car interior

With rapid advancement in Computational Fluid Dynamic (CFD) techniques and hardware capabilities over

the last 5 to 10 years, accurate evaluations of the flow field on an actual vehicle shape moving at a realistic speed (e.g. 130 km/h) over a reasonable portion of the frequency range of interest is feasible.

The underlying physics of the two phenomena are quite different, so are the numerical solutions developed

to assess them. Numerous studies have illustrated the challenges in solving such problem accurately

[3, 4, 6, 9, 10]. In this paper, different techniques to address the aforementioned factors are presented along

with the interior noise analysis. These techniques can be used in a practical configurations in the automotive

industry.

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The CFD calculation performed to compute the pressure fields on the side windows is mentioned here and

the results are validated against measurements. Two different methods are proposed to discriminate the

acoustic from the turbulent part of the pressure field. A supplementary method to efficiently store the

transfer functions between the exterior and interior acoustic pressure is presented discussed.

This paper is subdivided as follows: the vibro-acoustic model and its experimental validation through

hammer shock test are described in sections 2 and 3 respectively; methods used for detecting the pressure

wall fluctuations acting on the window are described in section 4; the aero-vibro-acoustic results and their

correlation with measurements are discussed in section 5; section 6 of this paper presents two different

numerical methods to distinguish the acoustic and the turbulent contributions on real case applications and

section 7 will describe an efficient method allowing to assess the interior noise level by post-processing the

acoustic component of the incident pressure field. Finally, the APE formulation for computing the wall

pressure fluctuations from incompressible CFD solutions is discussed in section 8. Conclusions are provided in section 9.

2 Vibro-acoustic model description

The pressure fluctuations generated by the flow over the A-pillar and the turbulent wave behind the side-

mirror induce unsteady forces acting on the side-window which vibrates. These vibrations generate acoustic

waves propagating in the car cavity. The experimental set-up used for the validation of the calculation

sequence is illustrated in Figure 1. Detailed description about the set-up can be found in [1]. The Actran software package is used for the definition and the solution of the complete F.E. model.

Figure 1: Photograph of the generic vehicle model

A vibro-acoustic model is created based on the following assumptions:

The side window is the only flexible part of the model and made of standard mono-layered glass

material

The supporting structure on which the window is glued is infinitively rigid

Acoustic cavity is airtight (no air leakage)

The glue is a uniform layer of 2 mm thick by 5 mm wide on the whole perimeter of the window’s

glass

It has not been possible to measure the exact material properties of the glue (Young modulus and loss factor)

and therefore it has been decided to use those two parameters as variables to improve the correlations

between simulations and measurements for the hammer shock test as described in section 3. Starting from

conventional polymeric glue material properties, the parameters are calibrated in a realistic range to fit to

hammer shock tests measurements.

332 PROCEEDINGS OF ISMA2016 INCLUDING USD2016

Figure 2: Glue Young Modulus and Loss Factor used

The reverberation time inside the cavity has been measured and it has been introduced in the finite element

(F.E.) model as a volume dissipation rate. The walls have been assumed to be perfectly reflecting (rigid).

One can deduce the dissipation factor using the method described in [10] based on the formula below:

𝑬𝟎

𝑷𝟎=

𝑹𝑻𝟔𝟎

𝒍𝒏(𝟏𝟎𝟔) and 𝜽 =

𝟏𝑬𝟎𝑷𝟎

×𝟐𝝅𝒇

where 𝑹𝑻𝟔𝟎 is the frequency dependent reverberation time for a 60dB decay, 𝑬𝟎 the acoustic energy stored

in the car cavity over one period, and 𝑷𝟎 the acoustic power dissipated in the car cavity over one period.

3 Hammer shock test correlation with measurements

Hammer shock tests have been performed by hitting the window multiple times at different locations with

a small hammer equipped with a sensor. The force applied by the hammer as well as the pressure at different

points inside the car cavity have been measured. The transfer functions between the impact force and the

pressure inside the car are the main information used to calibrate the numerical model.

Figure 3 shows a good overall correlation between the F.E. model and the experimental results. The plots

are averaged over ten load locations and five pressure microphone positions.

Figure 3: Transfer function between cavity pressure and input force (narrow band and 1/3 octave band)

Another way to assess the accuracy of the model is to evaluate the transfer function between an acoustic

volume flow source (e.g. omni-directional acoustic source) and the interior pressure for both simulation and

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AEROACOUSTICS AND FLOW NOISE 333

measurements. The interior noise levels are expected to be driven by the acoustic component of the wind

pressure load as explained in section 4. Therefore, evaluating the transfer functions is more relevant to assess

the accuracy of the F.E. model. In author opinion, these type of measurements are easier to perform

compared to the potentially operator-dependent, and repetitive hammer shock classical test procedure.

4 Pressure wall fluctuations

The wall pressure fluctuations on the car windows caused by the wind are commonly divided into two different types of contribution:

The acoustic contribution, defined based on “large” acoustic wavelengths (typically 34 cm at

1000 Hz) and relatively small amplitude (around 0.1 Pa for typical side mirror applications)

The turbulent contribution, defined based on “small” wavelengths (typically a 3 - 4 cm at 1000 Hz)

and relatively high amplitude (100 – 1000 Pa)

The acoustic pressure propagates over longer distances compared to the turbulence and due to its larger

wavelengths is able to interact much more efficiently with the side window’s structural bending

wavelengths. Therefore, the vibration of the windows and the subsequently generated interior noise are

driven by the exterior acoustic contribution. These phenomena will be demonstrated later in this paper with several methods.

One of the objectives of many Computer Aided Engineering (CAE) teams is to improve the end-

users’ comfort by minimizing the interior noise level. An accurate evaluation of the acoustic contribution is

mandatory to achieve this objective. The exterior acoustic pressure level can help to determine which

configuration (geometry, yaw angle, speed) is the noisiest without actually performing the interior acoustic computation as described later in this paper (see section 6 and 7).

The flow around a vehicle is generally computed using CFD tools based on volume finite difference or

Lattice Boltzmann method (LBM). Providing that the simulations are compressible (and that parameters

such as cell size, time step, material properties are suited for such solver), the results include acoustic

information. Both methods can be considered as direct method for this specific application as both the

acoustic and turbulent contributions of the pressure are assessed at the same stage of the computation.

In some specific cases, one may prefer to use an incompressible solver while using volume finite difference.

This approach will allow the increase in mesh size and time step, as well as improving the overall efficiency

of the CFD computation. As acoustics is related to compressibility effects, the incompressible solution is

not resolving acoustics. Lighthill analogy can then be used as presented in [2, 3, 4, 8, 9]. This two-steps

procedure is commonly referred to as a hybrid method since a CFD code is used to compute the unsteady

flow field and an acoustic code is used to compute the aero-acoustic sources and their propagations up to

the side window. As Lighthill equation is derived from Navier-Stokes equations, the turbulent part is

involved in the Lighthill solution, in particular in source region. Section 8 of this paper presents the Acoustic

Perturbation Equations (APE) technology that filters the turbulent terms from the acoustic propagation operator.

In the framework of this paper, two CFD calculations results are utilized:

CFD model 1 solved using an incompressible solver (OpenFOAM software package) having

relatively large elements (4 mm in the volume around the windows and 1 mm directly on the

window surface). The results are available for a duration of 0.05 s with a 2e-5 s time step.

CFD model 2 solved using a compressible flow solver (StarCCM+ software package). Overall, the

element sizes are smaller compared to CFD model 1. The element sizes in the area close to the

window is about 0.5 mm. The results were available on a much longer time history of 0.4 s.

This paper uses mostly the results from CFD model 2 because they are based on a model with finer mesh

and longer time history, which makes them more accurate. The CFD model 1 results will be used mainly

for the APE evaluation in section 8.


The duration of the CFD time sample is important as the vibro-acoustic calculation is performed in the

frequency domain. Because of the nature of Fourier transform, the longer the time signal, the smaller the

minimum frequency, and the smaller is the frequency step. Moreover, the time signal is divided into multiple

overlapping time intervals. It is important to note that the exact same process is applied in the measurement tools for an even longer duration of the measured signal.

5 Aero-vibro acoustic simulation results

The side window surface in the validated vibro-acoustic model presented in section 2 is excited with pressure

information provided by CFD model 2, which was solved using the compressible solver. In Figure 4, the

pressure information is averaged over five microphone locations inside the vehicle and compared to the measured values up to 6,000 Hz.

Figure 4: Interior Noise Level due to wind noise (left: narrow band, right: 1/3 octave band)

The correlation is very good for the whole frequency range with excellent agreement between 150 Hz and

3500 Hz both in terms of 1/3 octave band results and narrow band results. Moreover, the total pressure

(dominated by the turbulent contribution in terms of amplitude) has been measured on the exterior side of

the windows using microphones flushed mounted on the windows’ surface. A comparison between the

exterior CFD pressure and the measurements is shown in Figure 5. In this analysis, two important things are observed:

The pressure is not constant over the entire microphone area. Therefore, the numerical solution is

averaged over the microphone surface instead of using the local value at its center.

The compressible CFD pressure and the measured results are in good agreement up to 3,000 - 4,000

Hz. Note that this is the total pressure and not the acoustic pressure, which is supposed to dominate

the interior cavity pressure. Based on this observation, it is concluded that the correlation of the

interior noise level prediction can be negatively impacted by a slightly less accurate CFD input data.


Figure 5: Pressure on the exterior face of the window

6 Wall pressure decomposition

As mentioned previously, the difference between hydrodynamic and acoustic pressures is important and

should be computed accurately. One of the most popular method to perform this type of separation is to use

the wavenumber decomposition (WND). Using a set of sine functions, the pressure field can be decomposed

over a flat rectangular surface located on the window. The specifics about the method are explained in

details in [1, 5, 6].

Figure 6: Wavenumber Decomposition Sub-Surface

This method is applied on the compressible CFD results containing both the acoustic and hydrodynamic

pressure components. The wavenumber decomposition usage is limited to a rectangular shape flat surface

as illustrated in Figure 6. An example of a wavenumber decomposition result at 2000 Hz is shown in Figure

7.

Figure 7: Wave Number Decomposition Plot at 2000 Hz


As expected for this type of plot, the acoustic contribution is concentrated on a disk centered at (kx,ky) =

(0,0) with a radius of 2 𝜋 𝑓 𝑐⁄ with 𝑓 being the frequency (2000 Hz in the illustration) and 𝑐 being the speed

of sound (340 m/s). The turbulent contribution is located on a vertical region located at 𝑘𝑥 = 2 𝜋 𝑓 ‖�̅�‖⁄ , ‖�̅�‖ being the norm of the wind velocity vector on the window (130 km/h in this case).

Figure 8: Locus Identification for Wave Number Decomposition

The acoustic level at each frequency is generally computed by integrating the component on a disk enclosing

the acoustic locus. The hydrodynamic contribution is then calculated by summing all the remaining values

after the acoustic component has been removed. This operation can be performed for each frequency and

the values are plotted as a function of frequency (see Figure 9). As expected, the turbulent contribution is dominating the total pressure by a factor of ~25dB.

Figure 9: Acoustic and Turbulent Contribution of Wall Pressure Fluctuations

Another method [5] can also be used to decompose both contributions on the pressure. The Pellicular Mode

Decomposition (PMD) makes use of a set of numerical modes related to the acoustic wavelength of an

infinitively thin air layer located on the window surface. In finite element framework, the modal extraction

solver is be able to efficiently calculate the solutions of the following equation:

𝐾𝐿(𝜙𝑖(𝑥, 𝑦, 𝑧)) = 𝜆𝑖𝑀𝐿(𝜙𝑖(𝑥, 𝑦, 𝑧))

where 𝐾𝐿and 𝑀𝐿 are the so-called acoustic stiffness and mass operators respectively, and 𝜙𝑖(𝑥, 𝑦, 𝑧) and 𝜆𝑖

denote a particular eigenvector/eigenvalue pair. Any pressure field 𝑝(𝑥, 𝑦, 𝑧) (acoustic or turbulent) along

the window surface 𝑆 can be expanded as:

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𝑝(𝑥, 𝑦, 𝑧) = ∑ 𝜙𝑖(𝑥, 𝑦, 𝑧)𝑥𝑝𝑖𝐿

𝑖=1

where 𝑥𝑝𝑖 is the participation factor of the mode 𝜙𝑖(𝑥, 𝑦, 𝑧) and 𝐿 is the number of retained pellicular modes.

The participation factor 𝑥𝑝𝑖 can be obtained using the orthonormality:

𝑥𝑝𝑖 = ∫ 𝜙𝑖(𝑥, 𝑦, 𝑧)𝑝(𝑥, 𝑦, 𝑧)𝑑𝑆

𝑆

In Figure 10, the PMD participation factors are presented with the pellicular mode natural frequency as the

x-axis and the frequency of extraction as the y-axis.

Figure 10: Pellicular Mode Decomposition Plot

Based on the definition of the pellicular plot, the two pressure contributions are located at two specific locus

as illustrated in Figure 11. As for WND, the acoustic component is integrated over a triangular area (red in

left part of Figure 11) which encloses the acoustic region. All of the participation factors located outside the

acoustic region are integrated to build the hydrodynamic turbulent part.

Figure 11: Locus Identification for Pellicular Mode Decomposition

Unlike the wave number decomposition, the pellicular mode pressure decomposition can be applied to any

window geometry. The shapes are not limited to rectangles and the surface can be curved in 3D. In this

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particular case, the PMD method is applied on the same exact surface as the WND for comparison purposes. Additionally, the PMD is also applied on a complete window as shown in Figure 12.

Figure 12: Acoustic contributions comparison between methods

Performing WND and PMD calculations on the same surface geometries resulted in very similar pressure

components. The PMD performed on a full scale window gave slightly different results as they are

calculated using a larger surface involving an additional acoustic contribution generated by the A-pillar turbulences.

Another key advantage of the PMD is the ability to reconstruct the pressure field after removing the turbulent

component. The acoustic pressure field is reconstructed as shown in Figure 13 by summing only the

contributions in the acoustic region (see Figure 11). The smaller turbulent wavelengths that were previously dominating the pressure field are filtered out to reveal the acoustic pressure field.

Figure 13: Filtering wall pressure fluctuation by pellicular mode method

This filtered pressure field can then be used to directly load the vibro-acoustic model (presented in section 2)

instead of loading it with the full unfiltered pressure field. In Figure 14, it is observed that the filtered

pressure field provided similar interior noise level except at low frequencies. At these frequencies, the

number of pellicular modes available to perform the filtering is limited. In this example, the fifth pellicular

mode has a natural frequency around 500 Hz. This makes the separation of the acoustic and turbulent

pressure components more complex and the filtering is too sharp. Also, although the transparency of the

window is multiple order of magnitude lower for shorter wavelengths than for acoustical wavelengths, it is

not nil. As turbulent (short wavelength) pressure fluctuation have a larger amplitude than acoustic pressure

fluctuation, the relative net effect of both types of pressure fluctuation on cavity response is complex to

predict. However, Figure 14 clearly shows that the acoustic component corresponds to the main dominant

contributor inside the car cavity.


Figure 14: Interior pressure Field based on filtered or unfiltered exterior pressure field

A drawback of the PMD method is the handling of a large number of numerically evaluated modes. A large

number of modes is required to represent the turbulent pressure contribution which has small wavelengths.

Calculating the modes of the windows does not require intensive CPU nor RAM resources. However, the

projection of a very large number of pressure samples in this very large base requires a few integration

procedures, which are computationally intensive compared to the WND method. One can reduce this

negative effect by limiting the modal extraction of the pellicular modes up to 1.5 times the maximum

frequency of interest. Based on this reduced modes, the PMD performance becomes equivalent to the WND

method.

7 Pellicular solution sequence

The pellicular modes are very convenient to analyze and decompose the pressure field on the external side

of the windows. A relatively small set of modes (200 – 300 modes) and the orthogonality property of this

sub-space can be used to load the vibro-acoustic model and determine the transfer function of each

individual pellicular modes shape in the frequency range of interest.

The visualization of these transfer functions is illustrated in Figure 18. The y-axis is the frequency of interest,

the x-axis is the natural frequency associated with the pellicular mode shapes. For this simulation, the

pellicular modes are normalized in order to directly determine the transfer functions.


Figure 15: Pellicular modes transfer functions for interior acoustic pressure

These transfer functions show two interesting patterns:

1. A straight line with a slope of 1 (dashed white line). The acoustic transfer function is higher around

this line because the acoustic wavelengths on the excitation side match the acoustic wavelengths in

the car cavity. The interior acoustic pressure increases noticeably.

2. A parabolic line (dotted white line). This line corresponds to the coincidence between the excitation

mode wavelengths and the glass bending wavelengths. The bending wavelength of the window can

be estimated based on the bending wavelength of an infinite plate using the following formula:

𝜆𝑏𝑒𝑛𝑑 =𝑐𝑏𝑒𝑛𝑑

𝑓 with 𝑐𝑏𝑒𝑛𝑑 = √𝜔ℎ√

𝐸

12𝜌(1−𝜐2)

𝑓 is the frequency, 𝜔 omega is the angular frequency, ℎ is the thickness of the glass layer, 𝐸, 𝜌 and

𝜐 are the Young modulus, density, and Poisson ratio of the glass respectively.

3. The turbulent locus represented by the straight (solid white) line with a slope of 0.11 features very

low transfer function coefficients above 2000Hz. As a consequence, above this frequency, the

turbulent contributions are not transmitted through the window. This is also explaining the

difference observed in Figure 14.

When the two lines (parabolic and straight) intersect, the external acoustic wavelength corresponds to the

structure bending wavelength of the window and the interior acoustic wavelength. This frequency is known

as the coincidence or the critical frequency. An increase of the interior pressure is often observed around

this frequency and can be evaluated analytically using the aforementioned formula.

The distinction between acoustic and turbulent pressure is quite obvious when observing the pellicular wave

decomposition diagram on Figure 10. However, there is still some small contributions at wavelength

between the acoustic and turbulent locus. Even if this content is small in amplitude, the transmission to the

interior cavity can be very efficient when it match the bending wavelength of the structure, which of the

same size in this frequency range. By definition, this effect only appears below the coincidence frequency

as illustrated in Figure 16.

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Figure 16: Pressure Content located between Acoustic and Turbulent Locus has efficient transmission characteristic to generate interior noise

Once the transfer functions have been evaluated and analyzed, the participation factors of the pellicular

pressure decomposition can be used to get the final interior pressure. The interior SPL can be calculated

simply by taking the product of the exterior pressure participation factors and the transfer function of the

pellicular modes matrices:

𝑝𝑗 = ∑ Π𝑖𝑗(𝜔)

𝐿

𝑖=1

𝑥𝑝𝑖

𝑝𝑗 is the interior pressure at location 𝑗, Π𝑖𝑗 the interior pressure at location 𝑗 when the pellicular mode

𝜙𝑖(𝑥, 𝑦, 𝑧) is used to excite the window and 𝑥𝑝𝑖 is the participation factor of mode 𝜙𝑖 for the exterior pressure

field. 𝐿 is the number of pellicular modes considered in the pressure decomposition.

An efficient numerical procedure has been implemented in the Actran software package to perform this

operation. The transfer functions evaluation (200-300 functions) requires similar CPU time compared to

the direct solution but with an increase in RAM consumption. With this solution sequence, a second

configuration can be assessed based on a few minutes post-processing run whereas in direct solution it would

require the same computational resource as the first calculation. The interior pressure level provided by this

specific solution sequence is very similar to the standard solution sequence with a maximum difference

observed to be below 0.1 dB per frequency.

8 Acoustic perturbation equation formulation

The simulation process used to compute the acoustic pressure field around the vehicle in this section is

different compared to the previous sections. It is based on the incompressible data discussed in section 4. The simulation set-up is based on a hybrid computation similar to the one presented in [2].

The flow fluctuations are characterized by their associated length scales. If the length scale is large, it

corresponds to the acoustic fluctuations (length scales is in the order of 𝑙 = 𝑐 𝑓⁄ ). If the length scale is short,

the fluctuations correspond to the hydrodynamic fluctuations (𝑙 = 𝑈 𝑓⁄ ). Since the Lighthill equations are

derived from the compressible Navier-Stokes equations, all length scales are present in the solution.

However, as the hydrodynamic fluctuations decay rapidly outside of the source region, the far field pressure only exhibits the acoustic fluctuations.

For analysis purposes, it is convenient to discard the hydrodynamic part of the pressure field. An original

decomposition procedure has been proposed by Ewert et al. [7] to filter the right hand side such that only

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the acoustic modes are exciting the system and not the hydrodynamic contributions. The filtering method is

based on the fact that acoustic fluctuations propagate at a different speed than the hydrodynamic modes.

The set of equations is rearranged such that a new right hand side corresponds to the filtered aero-acoustic

sources:

𝜕2𝑝

𝜕𝑡2− 𝑐2

𝜕2𝑝

𝜕𝑥𝑖𝜕𝑥𝑖= −

𝜕2𝜙3

𝜕𝑡2

where 𝜙3 is computed by solving the following equation :

𝜕2𝜙3

𝜕𝑥𝑖𝜕𝑥𝑖= −

𝜕2𝜌𝑣𝑖𝑣𝑗

𝜕𝑥𝑖𝜕𝑥𝑖

The right hand side of Eqn. 7 corresponds to the turbulent contributions designed to only generate acoustic

fluctuations in near and far field. The APE right hand side can be used in a standard aero-acoustic simulation, the propagation operator being the same as for non-convected acoustic propagation.

Figure 17 shows the exterior acoustic pressure field solved based on the standard right hand side of

Lighthill’s equation (left plot) and one solved using the right hand side of APE equation (right plot). It can

be clearly observed that most of the short wavelength (high amplitude) contributions associated with the turbulent part have been filtered in the APE method.

Figure 17: 1500 Hz Pressure based on Lighthill RHS (left) and APE RHS (right), different scales

The efficiency of the filtering procedure is visible on wavenumber decomposition diagram (see Figure 18)

on which the turbulent contribution region has been cleared.

Figure 18: 1500 Hz WND based on Lighthill RHS (left) and APE RHS (right), same scale for both images

The interior cavity pressure field can then be evaluated based on the two windows pressure fields calculated

by either the standard Lighthill equation or the APE equation. As illustrated in Figure 19, the resulting

interior SPLs are similar except at low frequencies. This may be explained by the fact that below 1500 Hz,

wavelength smaller than the acoustic wavelength can interact with structural modes at low frequency as seen in Figure 14 and as explained previously.

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Figure 19: Interior Noise level based on Lighthill source term and APE source term

9 Conclusions

In this paper, a complete methodology to assess the interior noise level of car due to wind noise up to

6000 Hz with good correlations against measurements has been presented. The simulation process involves

several steps each being described in details and compared against measurements. Moreover, detailed

analyses have been performed to better understand the influence of acoustic and turbulent contributions of pressure fields with the window structure as well as the cavity modes.

This paper demonstrates and highlights the importance of the acoustic contribution to the interior noise.

This phenomenon has also been observed in other publications. However, for frequencies that are lower

than the coincidence frequency, pressure content having a wavelength between the hydrodynamic and the acoustic wavelength may still interact with the window having a bending wavelength of similar order.

Acknowledgements

The authors would like to thank the German CAA Working Group consisting of Audi, Daimler, Porsche and Volkswagen for their collaboration on this project and their provision of CFD and measurements data.

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