Introduction to the Equivalent Fluid Models
It is possible to define the properties of a fluid in several ways in pressure acoustics. In a Pressure Acoustics domain feature attenuation properties for the bulk fluid may be specified. Acoustic losses in porous materials are modeled by homogenizing the porous matrix and saturating fluid, and are defined by the Poroacoustics domain feature (frequency domain only). The viscous and thermal losses that occur in the acoustic boundary layer can be modeled in a homogenized way using the Narrow Region Acoustics domain feature (frequency domain only). The different ways of defining the properties of a fluid are called fluid models. They are also often referred to as equivalent fluid models.
Losses and damping occur when acoustic waves propagate in a porous material (where material refers to the homogenization of a fluid and a porous solid) because of bulk viscous and thermal properties, or because of thermal and viscous losses in the acoustic boundary layer at walls in narrow ducts. The purpose of the fluid model is to mimic a special loss behavior by defining a complex-valued density ρc and speed of sound cc. These are often frequency dependent.
In a Pressure Acoustics domain feature, the default Linear elastic fluid model (see Linear Elastic Fluid Model) enables you to specify a linearly elastic fluid using either the density ρ and speed of sound c, the impedance Z and wave number k, or the equivalent bulk modulus K and the density ρ. When any of these material parameters are complex-valued, damping is introduced.
It is always necessary to specify a set of two parameters (for example Z and k) or conditions in order to calculate the complex speed of sound and complex density needed to specify a fluid model. The choice of parameters typically depend on the application and which equivalent fluid is being modeled. For example:
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It is possible to determine the complex wave number k and impedance Z from directly measuring it 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.
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The option to define the equivalent bulk modulus K and density ρ is often used when characterizing the propagation of acoustic waves in a porous material. These parameters may be determined from measurements or by defining an analytical model expression.
The linear elastic fluid model enables the user to enter any desired fluid models with the desired combination of fluid properties. It is the most general fluid model. You may enter any user-defined analytical expressions for your favorite equivalent fluid model or use measurement data to represent the lossy behavior of the fluid.
Propagation in General Fluid with Bulk Losses
The options are (see About the Pressure Acoustics Fluid Models and the settings for the Pressure Acoustics node):
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Linear elastic: define density and speed of sound, impedance and wave number, or equivalent bulk modulus and density.
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Linear elastic with attenuation: define an attenuation parameter for the fluid.
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Ideal gas is also available but not described here. This fluid model is used to specify the fluid properties by selecting a gas constant type and selecting between entering the heat capacity at constant pressure or the ratio of specific heats. See Ideal Gas Fluid Model for details.
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Viscous and/or thermally conducting fluids (bulk losses): the losses are due to viscous losses, thermal conduction, or the combined thermal conduction and viscous losses in the bulk of the fluid.
Propagation in porous Materials
A series of fluid models exist for describing the propagation of pressure waves in porous materials. These range from fully empirical models to semianalytical/empirical models with varying degree of complexity. See Poroacoustics and About the Poroacoustics Models for more detail.
Propagation in Narrow Regions, Narrow Tubes, or Waveguides
See Narrow Region Acoustics and About the Narrow Region Acoustics Models. The losses are due to absorption/dissipation in the acoustic boundary layer (thermal and viscous losses). The losses are smeared on the domain in a homogenized way.