The Pressure Acoustics, Frequency Domain Interface

The Pressure Acoustics, Frequency Domain (acpr) interface (), found under the Pressure Acoustics branch () when adding a physics interface, is used to compute the pressure variation for propagation of acoustic waves in fluids at quiescent background conditions. It is suited for all frequency-domain simulations with harmonic variations of the pressure field.

The physics interface can be used for linear acoustics described by a scalar pressure variable. It includes domain conditions to model losses in a homogenized way, so-called fluid models for porous materials, as well as losses in narrow regions. Domain features also include background incident acoustic fields as well as domain monopole and dipole sources. The plane wave attenuation behavior of the acoustic waves may be entered as a user-defined quantity, or defined to be bulk viscous and thermal losses.

The physics interface solves the Helmholtz equation in the frequency domain for given frequencies, or as an eigenfrequency or modal analysis study.

An acoustics model can be part of a larger multiphysics model that describes, for example, the interactions between structures and acoustic waves. This physics interface is suitable for modeling acoustics phenomena that do not involve fluid flow.

The sound pressure p, which is solved for in pressure acoustics, represents the acoustic variations (or excess pressure) to the ambient pressure. In the absence of flow, the ambient pressure is simply the static absolute atmospheric pressure of 105 Pa.

When the geometrical dimensions of the acoustic problems are reduced from 3D to 2D (planar symmetry or axisymmetric) or to 1D axisymmetric, it is possible to specify an out-of-plane wave number kz and a circumferential wave number m, when applicable. In this case the wave number used in the equations keq contains both the ordinary wave number k as well as the out-of-plane wave number and circumferential wave number, when applicable.

The following table lists the names and SI units for the most important physical quantities in the Pressure Acoustics, Frequency Domain interface:

Table 11-1: Pressure Acoustics, Frequency Domain Interface Physical Quantities

Quantity	Symbol	SI Unit	Abbreviation
Pressure	p	Pascal	Pa
Density	ρ	kilogram/meter3	kg/m3
Frequency	f	Hertz	Hz
Wave number	k	1/meter	1/m
Dipole source	qd	newton/meter3	N/m3
Monopole source	Qm	1/second2	1/s2
Speed of sound	c	meter/second	m/s
Specific acoustic impedance	Z	pascal-second/meter	Pa·s/m
Normal acceleration	an	meter/second2	m/s2
Source location	r0	meter	m
Wave direction	nk	(dimensionless)	1

In the following descriptions of the functionality in this physics interface, the subscript c in ρc and cc (the density and speed of sound, respectively) denotes that these can be complex-valued quantities in models with damping.

When this physics interface is added, these default nodes are also added to the Model Builder— Pressure Acoustics Model, Sound Hard Boundary (Wall), and Initial Values.

Then, from the Physics toolbar, add other nodes that implement, for example, boundary conditions and point conditions. You can also right-click Pressure Acoustics to select physics features from the context menu.

Physics Nodes — Equation Section

Settings

The Label is the default physics interface name.

The Name is used primarily as a scope prefix for variables defined by the physics interface. Refer to such physics interface variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different physics interfaces, the name string must be unique. Only letters, numbers, and underscores (_) are permitted in the Name field. The first character must be a letter.

The default Name (for the first physics interface in the model) is acpr.

Equation

Expand the Equation section to see the equations solved for with the Equation form specified. The default selection is Equation form set to Study controlled. The available studies are selected under Show equations assuming.

•	For Study controlled, the scaling and nonreflecting boundary settings are optimized for the numerical performance of the different solvers.

•	For Frequency domain, enter the settings as described in Scaling Factor and Nonreflecting Boundary Condition Approximation.

Pressure Acoustics Equation Settings

•	For 1D axisymmetric components, the default Out-of-plane wave number kz (SI unit: rad/m) is 0 rad/m. The default Circumferential wave number m (dimensionless) is 0. The pressure has the form:

•	For 2D axisymmetric components, the default Circumferential wave number m (dimensionless) is 0. The pressure has the form:

•	For 2D components, the default Out-of-plane wave number kz (SI unit: rad/m) is 0 rad/m. The pressure has the form:

Scaling Factor and Nonreflecting Boundary Condition Approximation

For all component dimensions, and if required, click to expand the Equation section, then select Frequency domain as the Equation form and enter the settings as described below.

The default Scaling factor Δ is 1/ω2 and Non-reflecting boundary condition approximation is Second order. These values correspond to the equations for a Frequency Domain study when the equations are study controlled.

To get the equations corresponding to an Eigenfrequency study, change the Scaling factor Δ to 1 and the Non-reflecting boundary conditions approximation to First order.

Sound Pressure Level Settings

The zero level on the dB scale varies with the type of fluid. That value is a reference pressure that corresponds to 0 dB. This variable occurs in calculations of the sound pressure level Lp based on the root mean square (rms) pressure prms, such that

where pref is the reference pressure and the star (*) represents the complex conjugate. This is an expression valid for the case of harmonically time-varying acoustic pressure p.

Select a Reference pressure for the sound pressure level based on the fluid type:

•	Use reference pressure for air to use a reference pressure of 20 μPa (20·10−6 Pa).

•	Use reference pressure for water to use a reference pressure of 1 μPa (1·10−6 Pa).

•	User-defined reference pressure to enter a reference pressure pref, SPL (SI unit: Pa). The default value is the same as for air, 20 μPa.

Dependent Variables

This physics interface defines one dependent variable (field), the Pressure p. If required, edit the name, which changes both the field name and the dependent variable name. If the new field name coincides with the name of another pressure field in the model, the interfaces share degrees of freedom and dependent variable name. The new field name must not coincide with the name of a field of another type, or with a component name belonging to some other field.

Discretization

To display this section, click the Show button () and select Discretization.

• Domain, Boundary, Edge, Point, and Pair Nodes for the Pressure Acoustics, Frequency Domain Interface • Theory for Pressure Acoustics, Frequency Domain

Eigenmodes of a Room: Application Library path COMSOL_Multiphysics/Acoustics/eigenmodes_of_room