The Thermoviscous Acoustics, Boundary Mode Interface

The interface (

), found under the branch (

) when adding a physics interface, is used to compute and identify propagating and non-propagating modes in waveguides and ducts. The interface performs a boundary mode analysis on a given boundary including the thermal and viscous loss effects that are important in the acoustic boundary layer near walls.

The interface is applied at boundaries which represent the cross section or the inlet of a waveguide or duct of small dimensions. It solves for the acoustic variations of pressure p, velocity u, and temperature T, as well as the out-of-plane wave number kn of the modes. Near walls, viscous losses and thermal conduction become important because boundary layers exists. The thickness of these layers is known as the viscous and thermal penetration depth. For this reason, it is necessary to include thermal conduction effects and viscous losses explicitly in the governing equations. The Thermoviscous Acoustics, Boundary Mode interface is, for example, used when setting up sources in systems with small ducts like hearing aids or mobile devices. It can also be used to identify the propagating wave number and characteristic impedance of a duct cross section and use that information in the homogenized Narrow Region Acoustics model in The Pressure Acoustics, Frequency Domain Interface.

The Thermoviscous Acoustics, Boundary Mode interface solves the equations defined by the linearized Navier-Stokes equations (linearized continuity, momentum, and energy equations), in quiescent background conditions, on boundaries, searching for the out-of-plane wave numbers at a given frequency. All gradients in the governing equations are expressed in terms of the in-plane gradient and the out-of-plane wave number that is being solved for. Due to the detailed description necessary when modeling thermoviscous acoustics, the model simultaneously solves for the acoustic pressure p, the velocity variation u (particle velocity), and the acoustic temperature variations T. The interface is available on boundaries for 3D and on edges for 2D axisymmetric geometries.

	For details about the governing equations see the Theory Background for the Thermoviscous Acoustics Branch.

When this physics interface is added, these default nodes are also added to the — , , and . Then, from the toolbar, add other nodes that implement, for example, boundary conditions and sources. You can also right-click to select physics features from the context menu.

The is the default physics interface name.

The 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 field. The first character must be a letter.

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

Expand the section to see the equations solved for with the specified. The default selection is is set to . The available studies are selected under .

See the settings for Sound Pressure Level Settings for the Pressure Acoustics, Frequency Domain interface.

To display this section, click the button (

) and select . From the list select the element order for the , the , and the . The default uses elements for the pressure and for the velocity field and the temperature variations.

In order for the system to be numerically stable, it is important that the order for the pressure degree of freedom (DOF) is one lower than the velocity field. Per default, the velocity components and the temperature share the same element order as they vary similarly over the same length scale in the acoustic boundary layer. Therefore, both typically require the same spatial accuracy.

	Increase the element order to, for example, quadratic for the pressure and cubic for the velocity and temperature dofs. This can add additional accuracy but it also adds additional degrees of freedom compared to the default setting and will be computationally more expensive.

This physics interface defines these dependent variables (fields), the p, the u and its components, and the T. The names can be changed but the names of fields and dependent variables must be unique within a model.