Surface Reaction Equations on Deforming Geometries
If a Surface Reaction interface is used in conjunction with a Deformed Geometry or a Moving Mesh (ale) interface the boundary concentration can either be assumed to be transported with the deforming geometry (moving mesh), with no compensation for the stretching (the Compensate for boundary stretching check box is not selected), or the species can be assumed to “float” on the mesh (the Compensate for boundary stretching check box is selected, which is the default). In the latter case the following is assumed in regards to the coupling between the surface species and bulk species and the mesh movement:
•
Expansion or contraction of the boundary dilutes or increases concentration of the species, respectively, so that the surface integral (in spatial coordinates) of the species is kept constant.
•
Tangential mesh movement has no impact on the local concentration in spatial coordinates, that is, the tangential transport of surface and bulk species does not move with the mesh in the tangential direction.
In order to comply with the additional contributions to the mass balance, equations are added. First, the following terms are added to the right-hand side of
Equation 5-43
and
Equation 5-44
, respectively.
where
∂
A
is the infinitesimal mesh area segment (area scale factor). The above terms account for the concentration change due to a fractional area change.
Second, the resulting unwanted tangential convection, imposed by the mesh movement, is compensated for by the adding following terms to the right-hand side of
Equation 5-43
and
Equation 5-44
, respectively:
where
v
t
,mesh
is the mesh velocity in the tangential direction.
This convectional term needs often to be stabilized using methods such as streamline diffusion or isotropic diffusion.
