Theory for the Wall Boundary Condition
See Wall for the node settings. Note that some modules have additional theory sections describing options available with that module.
Slip
The No Slip condition assumes that there are no viscous effects at the slip wall and hence, no boundary layer develops. From a modeling point of view, this is a reasonable approximation if the important effect of the wall is to prevent fluid from leaving the domain. Mathematically, the constraint can be formulated as:
The no-penetration term takes precedence over the Neumann part of the condition and the above expression is therefore equivalent to
expressing that there is no flow across the boundary and no viscous stress in the tangential direction.
For a moving wall with translational velocity utr, u in the above equations is replaced by the relative velocity urel = u−utr.
Sliding Wall
The sliding wall option is appropriate if the wall behaves like a conveyor belt; that is, the surface is sliding in its tangential direction. The wall does not have to actually move in the coordinate system.
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In 2D, the tangential direction is unambiguously defined by the direction of the boundary, but the situation becomes more complicated in 3D. For this reason, this boundary condition has slightly different definitions in the different space dimensions.
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For 2D and 2D axisymmetric components, the velocity is given as a scalar Uw and the condition prescribes
where t = (ny , −nx) for 2D and t = (nz, −nr) for axial symmetry.
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For 3D components, the velocity is set equal to a given vector uw projected onto the boundary plane:
The normalization makes u have the same magnitude as uw even if uw is not exactly parallel to the wall.