Damping
Fluids like air or water — by far the most common media in acoustics simulations — exhibit practically no internal damping (so-called bulk attenuation) over the number of wavelengths that can be resolved with the finite element method and in the audio frequency range. However, in ultrasound applications or when using ray tracing to model room and underwater acoustics, these become important.
In smaller systems, damping takes place through interaction with solids, either because of friction between the fluid and a porous material filling the domain, or because acoustic energy is transferred to a surrounding solid where it is absorbed. In systems with small length scales, significant losses can occur in the viscous and thermal acoustic boundary layer at walls.
Atmosphere and Ocean Attenuation
When performing ray acoustics simulations or modeling ultrasound applications, the bulk or internal attenuation of atmospheric air or the ocean sea water can be modeled using the built-in Atmosphere attenuation or the Ocean attenuation models. Both models are semi analytical and fitted to extensive experimental data. The atmosphere model complies with the ANSI standard.
For further details about material properties and attenuation models see the Acoustic Properties of Fluids chapter.
Porous Absorbing Materials
For frequency-domain modeling, the most convenient and compact description of a damping material (where material here refers to the homogenization of a fluid and a porous solid) is given by its complex wave number k and complex impedance Z, both functions of frequency. Knowing these properties, define a complex speed of sound as cc = ω/k and a complex density as ρc = kZ/ω. Defining ρc and cc results in a so-called equivalent-fluid model or fluid model.
It is possible to directly measure the complex wave number and impedance in an impedance tube in order to produce curves of the real and imaginary parts (the resistance and reactance, respectively) as functions of frequency. These data can be used directly as input to COMSOL Multiphysics interpolation functions to define k and Z.
Sometimes acoustic properties cannot be obtained directly for a material you want to try in a model. In that case you must resort to knowledge about basic material properties independent of frequency. Several empirical or semi-empirical models exist in COMSOL Multiphysics and can estimate the complex wave number and impedance as function of material parameters. These models are defined in the Poroacoustics domain feature of the Pressure Acoustics interfaces — for example, the Johnson–Champoux–Allard model and the Delany–Bazley–Miki models; the latter uses frequency and flow resistivity as input.
The Acoustics Module includes a series of fluid models that are described in Pressure Acoustics and Theory for the Equivalent Fluid Models. In addition, The Poroelastic Waves Interface can be used for detailed modeling of the propagation of coupled pressure and elastic waves in porous materials.
Boundary Layer Absorption (Thermoviscous acoustics)
In systems of small dimensions (or at low frequencies) the size of the acoustic boundary layer (the viscous and thermal acoustic penetration depth) that exists at all walls can become comparable to the physical dimensions of the modeled system. In air the boundary layer thickness is 0.22 mm at 100 Hz. This is typically the case inside miniature transducers, condenser microphones, in MEMS systems, in tubing for hearing aids, or in narrow gaps of vibrating structures.
For such systems, it is often necessary to use a more detailed model for the propagation of the acoustics waves. This model is implemented in the Thermoviscous Acoustics Interfaces. In simple cases for sound propagating in long ducts of constant cross sections, the losses occurring at the boundaries can be smeared out on the fluid using one of the fluid models of the Narrow Region Acoustics domain feature. For geometries with curved surfaces and nonconstant cross sections an alternative is to use the Thermoviscous Boundary Layer Impedance boundary condition, also available in Pressure Acoustics.
More details on the detailed acoustic model for viscous and thermal losses are described in Thermoviscous Acoustics Interfaces. See the boundary layer absorption fluid models in Narrow Region Acoustics for simplified modeling in uniform waveguide structures or the Thermoviscous Boundary Layer Impedance boundary condition.
Damping at Boundaries
The losses associated with the acoustic field often stem from the interaction with boundaries, for example, when interacting with a rubber material. In this case, it may be necessary to include the acoustic-structure interaction using the appropriate multiphysics coupling. Another way of including the losses is to use an impedance boundary condition. The Acoustics Module provides a series of impedance models to model, for example, the human ear, human skin, or a simple mechanical lumped RCL system.