The Pressure Acoustics, Frequency Domain (acpr) interface (), found under the Pressure Acoustics branch () when adding a physics interface, is used to compute the pressure variations for the 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 equivalent fluid models, for porous materials as well as losses in narrow regions (waveguides or slits). The plane wave attenuation behavior of the acoustic waves may also be entered as a user-defined quantity, or based on the losses in the atmosphere or ocean. Effective anisotropic material properties can be modeled with an effective anisotropic density formulation. Domain features also include Background Pressure Field, heat sources, a Flame Model, as well as general user-defined monopole and dipole domain sources. An Aeroacoustic Flow Source or flow-induced noise source from turbulence can be included when coupled to an LES or DES simulation (this requires the CFD Module).

The physics interface solves the Helmholtz equation in the frequency domain for given frequencies, or as an eigenfrequency or mode analysis study. The harmonic variation of all fields and sources is given by eiωt using the +iω convention.

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

The governing equations and boundary conditions are formulated using the total pressure pt with a so-called scattered field formulation. In the presence of a Background Pressure Field defining a background pressure wave pb (this could, for example, be an incident plane wave), the total acoustic pressure pt is the sum of the pressure solved for p (which is then equal to the scattered pressure ps) and the background pressure wave: pt = p+pb. The equations then contain the information about both the scattered field and the background pressure field.

When the geometrical dimensions of the acoustic problems are reduced from 3D to 2D (planar symmetry or axisymmetry) or to 1D axisymmetry, it is possible to specify an out-of-plane wave number kz and an azimuthal mode number m (sometimes referred to as the circumferential mode number), 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 kz and azimuthal wave number km = m/r, when applicable.

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, Frequency Domain to select physics features from the context menu.

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.

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

Select to Enable physics symbols (selected per default). This shows the physics symbols, like for example, normals or symmetry planes in the Graphics window when applicable.

In this section you can add out-of-plane information defining an out-of-plane wave number kz or an azimuthal wave number km = m/r through the mode number m. Add if applicable:

Note that when performing a mode analysis study in 2D (solving for the out-of-plane wave number) the Out-of-plane wave number property is not used as this is now the variable solved for.

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 Nonreflecting 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 Nonreflecting boundary conditions approximation to First order.

Select the Port sweep settings as:

The Activate port sweep option is used to compute the full scattering matrix when Port conditions are used. For more details see The Port Sweep Functionality subsection. The section only exists for 3D and 2D axisymmetry.

Select the Mode shape normalization as Amplitude normalized (the default) or Power normalized. This setting controls if the mode shapes are normalized to have a unit maximum amplitude or carry unit power. The selection determines how the scattering matrix is to be interpreted.

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:

Enter a value or expression for the Typical wave speed for perfectly matched layers cref (SI unit m/s). The default is real(acpr.c_c) and the value is automatically taken from the material model. If several materials or material models are used it is best practice to add one PML for each. This will ensure that the typical wavelength is continuous within each PML feature.

From the list select the element order and type (Lagrange or serendipity) for the Pressure, the default is Quadratic Lagrange.

To see all settings in this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box.

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.