Pressure Acoustics
The Pressure Acoustics node adds the equations for time-harmonic (frequency domain) and eigenfrequency acoustics modeling of classical acoustics solving Helmholtz equation. In the Settings window, define the properties for the acoustics model such as material properties and bulk attenuation. Define the so-called Model Inputs to the properties including the absolute background pressure and temperature, that is the quiescent ambient properties.
The advanced fluid models are defined using individual physics feature nodes: Poroacoustics, Narrow Region Acoustics, and Anisotropic Acoustics. In the time domain nonlinear effects can be included using the Nonlinear Acoustics (Westervelt) Contributions node.
For details about some of the available fluid models, see Theory for the Equivalent Fluid Models.
For more information about using variables during the results analysis, see Postprocessing Variables.
Model Inputs
Select, User defined (the default), Common model input, or an input from another physics interface, if applicable.
The values of the quiescent (or background) Temperature T (SI unit: K) and Absolute pressure pA (SI unit: Pa) are entered in the Model Inputs section if required by the material properties (other inputs like relative humidity or salinity can also appear). The values of the model inputs can influence the material properties like, for example, the density and speed of sound, depending on their definition in the Materials node. In general, if the model includes a material property that depends on a model input, the corresponding text field will be enabled.
Details about the Model Input and the Default Model Inputs are found in the Global and Local Definitions chapter of the COMSOL Multiphysics Reference Manual.
If Ideal gas is selected as the Fluid model, both the Temperature T and Absolute pressure pA fields are enabled. In this case this input option is always available.
In addition, the Temperature T and Absolute pressure pA can be picked up from another physics interface where the fields have been calculated. For example, select a temperature field defined by a Heat Transfer interface or a Nonisothermal Flow interface (if any). Or, if applicable, select a pressure as defined by a Fluid Flow interface present in the model. For example, select Absolute pressure (spf) to use the absolute pressure defined by a Laminar Flow interface spf.
The input to the Model Inputs fields influences the value of the material parameters in the model. Typically, the density ρ and the speed of sound c in the model depend on the absolute pressure and/or the temperature. Picking up any of those from another physics interface typically results in space dependent quantities ρ = ρ(x) and c = c(x).
Detailed convected acoustic models that take into account the full background flow (including the movement of the fluid) are available among the Aeroacoustics Interfaces. For flow-induced noise simulations based on the Lighthill analogy see the Aeroacoustic Flow Source.
Pressure Acoustics Model
To define the properties of the fluid, select a Fluid model from the list:
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Linear elastic (the default) for defining the classical lossless fluid: Go to Linear Elastic Fluid Model.
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User-defined attenuation for defining losses through an attenuation coefficient: Go to User-Defined Attenuation Fluid Model.
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Atmosphere attenuation defines the standard attenuation of atmospheric (moist) air:
Go to Atmosphere Attenuation Fluid Model.
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Ocean attenuation defines attenuation in the seawater of the ocean: Go to Ocean Attenuation Fluid Model.
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Viscous, Thermally conducting, and Thermally conducting and viscous defines the classical thermoviscous attenuation model: Go to Thermally Conducting and/or Viscous Fluid Model.
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General dissipation defines losses through the sound diffusivity: Go to General Dissipation Fluid Model.
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Ideal gas to define the properties of an ideal gas: Go to Ideal Gas Fluid Model.
The theory for the fluid models is in the section Theory for the Equivalent Fluid Models.
The fluid models represent different bulk loss or attenuation mechanisms (applied in a homogenized way) or ways of defining the properties of the fluid. Some of these models are sometimes referred to as equivalent fluid models. The loss model can be a theoretical model or a model based on measurement data for the attenuation in the fluid like the atmosphere or the ocean.
Losses in porous materials are defined in Poroacoustics. Thermoviscous boundary layer losses in narrow regions of constant cross section (like waveguides) can be modeled using Narrow Region Acoustics.
Linear Elastic Fluid Model
Linear elastic is the default. When the material parameters are real values, this corresponds to a lossless compressible fluid. From the Specify list, select Density and speed of sound (the default), Impedance and wave number, or Bulk modulus and density. To add user-defined losses, in a general way, specify the properties as complex-valued data.
For each of the following, the default values (when applicable), are taken From material or for User defined, enter other values or expressions.
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For Density and speed of sound, define the Speed of sound c (SI unit: m/s) and Density ρ (SI unit: kg/m3).
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For Impedance and wave number, define the Characteristic acoustic impedance Z (SI unit: Pa·s/m) and enter a Wave number k (SI unit: rad/m).
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For Bulk modulus and density, define the Effective bulk modulus K (SI unit: Pa) and Density ρ (SI unit: kg/m3). Selecting User defined is well suited for entering the properties of a user-defined porous material fluid model. Predefined porous models exist in the Poroacoustics domain feature.
User-Defined Attenuation Fluid Model
The User-defined attenuation model adds a user-defined attenuation to the fluid. This data is typically based on experimental data for the attenuation coefficient α. Adding attenuation makes the wave number k complex valued. For example, a plane wave p(x) moving in the x direction is attenuated according to
When the attenuation is defined in Np per unit length, the wave has a spatial exponential decay governed by the attenuation coefficient.
Do not confuse the amplitude attenuation coefficient α with the intensity attenuation coefficient m most often defined in room acoustics. The two are simply related through 2α = m. The difference stems from how the intensity scales in the propagation direction: I(x) = I0·exp(-2αx) = I0·exp(-mx).
The default Speed of sound c (SI unit: m/s) and Density ρ (SI unit: kg/m3) are taken From material. For User defined, enter other values or expressions for one or both options.
Select an Attenuation type: Attenuation coefficient, Np per unit length (the default) to define an attenuation coefficient α in Np/m (nepers per meter), Attenuation coefficient, dB per unit length to define an attenuation coefficient α in dB/m (decibel per meter), or Attenuation coefficient, dB per wavelength to define an attenuation coefficient α in dB/λ (decibel per wavelength). The last option is often used in underwater acoustics and uses a slightly different formulation than the first two, see the theory section. For any selection, enter a value or expression in the Attenuation coefficient α field.
Theory: User-Defined Attenuation Fluid Model
Atmosphere Attenuation Fluid Model
The Atmospheric attenuation model defines attenuation in atmospheric air that follows the ANSI standard S1.26-2014, see Ref. 6 (Appendix B), 43, 44, and 45 for details. The model describes attenuation due to thermal and viscous effects (primarily pure air), the relaxation processes for nitrogen and oxygen, and the dependency on atmospheric pressure (absolute pressure), temperature, and relative humidity. The attenuation in air is important for propagation over large distances and for high frequency processes. This also means that the attenuation effect is more important in ray tracing simulations where propagation can be simulated over much larger distances, see The Ray Acoustics Interface.
When the model is selected the Model Input section includes inputs for the Temperature T (SI unit: K), the Absolute pressure pA (SI unit: Pa), and the Relative humidity (SI unit: 1). In the Pressure Acoustic Model section the default Speed of sound c (SI unit: m/s) and Density ρ (SI unit: kg/m3) are taken From material. For User defined, enter other values or expressions for one or both options.
Ocean Attenuation Fluid Model
The Ocean attenuation model defines attenuation in seawater of the ocean. The model is based on a semianalytical model with parameters that are based on extensive measurement data. It includes effects due to viscosity in pure water, the relaxation processes of boric acid and magnesium sulfate, as well as depth, temperature, practical salinity, and pH value. For further details, see Ref. 46, 47, 48, 49, and 50. The ocean attenuation model is important in ray tracing simulations where propagation can be simulated over much larger distances, see The Ray Acoustics Interface.
When the model is selected, the Model Input section includes inputs for the Temperature T (SI unit: K), the Depth D (SI unit: m), and the Practical salinity Sp (SI unit: 1); the default is 35. In the Pressure Acoustic Model section, the default Speed of sound c (SI unit: m/s) and Density ρ (SI unit: kg/m3) are taken From material. For User defined, enter other values or expressions for one or both options. Enter a value for the pH value pH (SI unit: 1); the default is 8.
The Practical salinity is defined on the Practical Salinity Scale. It represents a specific way of measuring salinity through electric conductivity. Practical salinity is a unit-less quantity, although it can be thought of as given in units of g/kg. The default value for the Practical salinity Sp is 35. For details see Ref. 56.
For a discussion about air and water materials as commonly used in acoustics, the attenuation in (sea) water and (humid) air, and other material properties, see the Acoustic Properties of Fluids chapter of this manual.
Thermally Conducting and/or Viscous Fluid Model
The Viscous, the Thermally conducting, and the Thermally conducting and viscous fluid models essentially add the same attenuation model. Here, the attenuation is due to bulk viscous and/or thermal losses. This type of model is relevant in highly viscous fluids or thermally conducting fluids when acoustic waves are traveling over large distances (relative to the wavelength). This is not a model for viscous and thermal boundary layer losses in narrow regions (see Narrow Region Acoustics). The models define the classical thermoviscous attenuation αtv properties of a fluid and can be applied in cases when, for example, relaxation processes are not important. The classical thermoviscous amplitude attenuation is given by
In atmospheric air or salt water where relaxation processes are important use the Atmosphere attenuation or the Ocean attenuation model as they capture these effects and also their dependency on, for example, relative humidity or salinity.
For each of the following (when applicable), the default values are taken From material. For User defined, enter other values or expressions for any or all options.
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Speed of sound c (SI unit: m/s).
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Density ρ (SI unit: kg/m3).
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Heat capacity at constant pressure Cp (SI unit: J/(kg·K)).
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Ratio of specific heats γ (dimensionless).
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Thermal conductivity k (SI unit: W/(m·K)).
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Dynamic viscosity μ (SI unit: Pa·s).
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Bulk viscosity μB (SI unit: Pa·s).
It is possible to assess the magnitude of the losses due to thermal conduction and viscosity, that is, the power dissipation density (SI unit: W/m3). This is done during the analysis process by plotting the variables for:
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Viscous power dissipation density (acpr.diss_visc)
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Thermal power dissipation density (acpr.diss_therm)
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Combined total power dissipation density (acpr.diss_tot)
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Viscous Fluid Model
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Thermally Conducting Fluid Model
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Thermally Conducting and Viscous Fluid Model
General Dissipation Fluid Model
For General dissipation enter the Speed of sound c (SI unit: m/s), the Density ρ (SI unit: kg/m3), and the Sound diffusivity δ (SI unit: m2/s). By default they are taken From material and for User defined enter other values or expressions.
The sound diffusivity is automatically calculated for the classical thermoviscous case using either the Viscous, Thermally conducting or the Thermally conducting and viscous options (see below). For nonideal fluids like tissue, the sound diffusivity is measured directly instead and can be entered with the General dissipation.
Ideal Gas Fluid Model
For Ideal Gas, you can edit the Model Inputs section. For each of the following, the default values are taken From material. For User defined, enter other values or expressions for any or all options.
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Select a Gas constant type: Specific gas constant Rs (SI unit: J/(kg·K) (the default) or Mean molar mass Mn (SI unit: kg/mol). For Mean molar mass, the molar gas constant (universal gas constant) R = 8.314 J/(mol·K) is used as the built-in physical constant.
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From the Specify Cp or γ list, select Heat capacity at constant pressure Cp (SI unit: J /(kg·K)) (the default) or Ratio of specific heats γ. For common diatomic gases such as air, γ = 1.4 is the standard value.