1. Sedan Interior Acoustics
© 2013 COMSOL. All rights reserved.

2. Background and Motivation
This is a model that solves for the acoustic field inside a car where the sound source is placed at a speaker location.
The model enables the user to get a frequency response at any point in the car. This is useful when optimizing for speaker locations with respect to mirror sources (sound reflections in the windscreen), damping and other factors.
The model solves in the frequency domain up to around 2-3 kHz.

3. Geometry The geometry is one of a generic sedan car interior.
Seats highlighted.

4. Geometry
The geometry is imported from a parasolid file (.x_b) and a few Virtual Geometry operations are performed to optimize the geometry for meshing and modeling.
import geometry

5. Absorbing and damping boundaries
Cars have many surfaces that are not sound-hard but rather act as absorbers. The seats are for example made of a porous material like, for example, foam covered with tissue or leather.
These surfaces may be modeled by an impedance condition defined by the normal impedance Zn(f) (Pas/m). The normal impedance is a complex-valued function that is function of the frequency.
The normal impedance is related to the reflection coefficient R (complex ratio of reflected to incident pressure) as:
The absorption coefficient, , is a real-valued quantity describing the amount of absorbed energy at a surface. It is related to the reflection coefficient as:
𝑍 𝑛 =𝜌𝑐 1+𝑅 1−𝑅
𝛼=1− |𝑅| 2

6. Absorbing and damping boundaries
The surface properties are best described by the reflection coefficient or the surface impedance, as they contain both amplitude and phase information.
These data may be obtained either by measurements (e.g., in an impedance tube) or by simulations (see, for example, the Porous Absorber model in the Model Library).
Absorbing surfaces are often only characterized by their absorption coefficient (f). Because it has no phase information ( is unknown), this impedance is only an approximate description of the acoustic surface properties:
arbitrarily setting   0 will result in a real-valued impedance. This is NOT the fully correct description and may result in erroneous results. The importance of the phase decreases with increasing frequency.
In the model, the absorption coefficient (f) is defined as an interpolation function under Global Definitions and we crudely assume   0.
Data inspired by measurements found in T. J. Cox and P. D’Antonio, Acoustic Absorbers and Diffusers, Taylor and Francis (2009).
𝑍 𝑛 =𝜌𝑐 1+|𝑅| 1−|𝑅| with 𝑅 = 𝑒 𝑖𝜃 1−𝛼

7. Modeling Interfaces
Pressure acoustics in the frequency domain is used.
Simple normal acceleration boundary conditions for the sources and impedance conditions for the absorbing materials.
Sound hard boundaries (default) for the remaining boundaries.

8. Mesh and solver Settings
In acoustics, the computational mesh must resolve the acoustic wavelength. The requirement is to have at least 5 to 6 elements per wave length.
This means that for increasing frequencies (decreasing wave length) the mesh becomes denser and denser, resulting in computationally more expensive models.
The maximal mesh size is given by:
The mesh size is defined under: Global Definitions > Parameters
ℎ 𝑚𝑎𝑥 = 𝜆 6 = 𝑐 6𝑓

9. Mesh and solver Settings
For large acoustic problems it is efficient to use an iterative solver with the geometric multigrid pre-conditioner.
Decrease the relative tolerance (also lower than shown here) to get a more converged solution. This is important for higher frequencies with many standing modes.

10. Results Pressure distribution on the interior surfaces. f = 100 Hz

11. Results
f = 200 Hz
Sound pressure level distribution on interior surface.
f = 600 Hz

12. Results
Pressure isosurfaces inside car.

13. Results
Sound pressure level on cut planes.

14. Results
Energy flow with intensity vector from sound sources.

15. Results
Pressure distribution on car seats.

16. Results: Response
Data in cut point (see under Data Sets) as function of frequency.
For a sweep define the mesh in relation to the maximal study frequency.
Define a frequency range for the study:

17. Results: Response
Zoom see next slides.

18. Results: Response
Rounded resonance peaks are clear and due to the losses at the impedance boundaries.

19. Results: Response
Rounded resonance peaks are clear and due to the losses at the impedance boundaries.