Almost every computational fluid dynamics problem is defined under the limits of initial and boundary conditions. When constructing a staggered grid, it is common to implement boundary conditions by adding an extra node across the physical boundary. The nodes just outside the inlet of the system are used to assign the inlet conditions and the physical boundaries can coincide with the scalar control volume boundaries. This makes it possible to introduce the boundary conditions and achieve discrete equations for nodes near the boundaries with small modifications.
The most common boundary conditions used in computational fluid dynamics are
Consider the case of an inlet perpendicular to the x direction.
Fig.3 v-velocity cell at intake boundary|alt=|none | Fig.4 pressure correction cell at intake boundary|alt=|none |
If flow across the boundary is zero:
Normal velocities are set to zero
Scalar flux across the boundary is zero:
In this type of situations values of properties just adjacent to the solution domain are taken as values at the nearest node just inside the domain.
Consider situation solid wall parallel to the x-direction:
Assumptions made and relations considered-
thumb|Fig.7 v-cell at physical boundary j=3 |
Turbulent flow:
[math]\displaystyle{ y^+ \gt 11.63\, }[/math].
in the log-law region of a turbulent boundary layer.
[math]\displaystyle{ y^+ \lt 11.63\, }[/math].
Important points for applying wall functions:
These conditions are used when we don’t know the exact details of flow distribution but boundary values of pressure are known
For example: external flows around objects, internal flows with multiple outlets, buoyancy-driven flows, free surface flows, etc.
Considering the case of an outlet perpendicular to the x-direction -
thumb|Fig. 13 v-control volume at an exit boundary | Fig. 14 pressure correction cell at an exit boundary |
In fully developed flow no changes occurs in flow direction, gradient of all variables except pressure are zero in flow direction
The equations are solved for cells up to NI-1, outside the domain values of flow variables are determined by extrapolation from the interior by assuming zero gradients at the outlet plane
The outlet plane velocities with the continuity correction
[math]\displaystyle{ U_{NI,J} = U_{NI-1,J}\frac{M_{in}}{M_{out}}\, }[/math].
Original source: https://en.wikipedia.org/wiki/Boundary conditions in computational fluid dynamics.
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