Meshing the Boundary Layer
When modeling using the Thermoviscous Acoustics interfaces, several length scales become important when setting up the mesh.
Secondly, there is the thickness of the viscous and thermal boundary layers. In order for the model to include the correct amount of damping, the boundary layers need to be resolved. Ideally this is done using a Boundary Layers mesh. The Thickness of first boundary layer and the Number of boundary layers should be set such that they resolve the boundary layer at the specific modeling frequency. Remember that the boundary layer thickness scales as one over the square root of the frequency.
See the Boundary Layers section in the COMSOL Multiphysics Reference Manual for more details.
Finally, it is important to consider the thickness of the boundary layer compared to the physical dimensions of the model, for example, the viscous boundary layer thickness δv compared to the tube radius a. This is sometimes known as the Womersley number
.
where δv is the viscous boundary layer thickness and Pr is the Prandtl number. If the Womersley number is very small, say Wo < 0.1, the effect associated with the losses in the viscous boundary layer can normally be disregarded. In this case, the boundary layer do not need to be meshed and a Slip condition can be used instead of a No-slip condition. The same is true for the thermal boundary layer thickness compared to the tube radius. Here, an Isothermal condition can be replaced by an Adiabatic condition.
If the No-slip or Isothermal conditions are kept (when Wo < 0.1), then remember to add at least one boundary layer mesh that is of roughly the size of the acoustic boundary layer. If this is not done, erroneous losses can be introduced in the model.