2Background 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.
3Geometry The geometry is one of a generic sedan car interior. Seats highlighted.
4GeometryThe 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
5Absorbing 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) (Pas/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−𝑅𝛼=1− |𝑅| 2
6Absorbing 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
7Modeling InterfacesPressure 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.
8Mesh 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 > Parametersℎ 𝑚𝑎𝑥 = 𝜆 6 = 𝑐 6𝑓
9Mesh 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.
10Results Pressure distribution on the interior surfaces. f = 100 Hz
11Resultsf = 200 HzSound pressure level distribution on interior surface.f = 600 Hz