Supriya Ghosh (Editor)

Boundary conditions in CFD

Updated on
Edit
Like
Comment
Share on FacebookTweet on TwitterShare on LinkedInShare on Reddit
Boundary conditions in CFD

Almost every computational fluid dynamics problem is defined under the limits of initial and boundary conditions. For implementation of boundary conditions when we construct a staggered grid we add an extra node across the physical boundary in order to get,

Contents

  • The nodes just outside the inlet of the system are used to assign the inlet conditions
  • The physical boundaries can coincide with the scalar control volume boundaries.

    • This allow us to introduce the boundary conditions and achieve discretion equations for nodes near boundary with small modifications.

    Most common boundary conditions used in computational fluid dynamics are

  • Intake conditions
  • Symmetry conditions
  • Physical boundary conditions
  • Cyclic conditions
  • pressure conditions
  • exit conditions

    • Intake boundary conditions

    We are considering the case of an inlet perpendicular to the x-direction -

  • For the first u, v, φ-cell all links to neighboring nodes are active, so there is no need of any modifications to discretion equations.
  • At one of the inlet node absolute pressure is fixed and made pressure correction to zero at that node.
  • Generally computational fluid dynamics codes estimate k and ε with approximate formulate based on turbulent intensity between 1 and 6% and length scale

    • Symmetry boundary condition

    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.

    physical boundary conditions

    Consider situation solid wall parallel to the x-direction:

    Assumptions made and relations considered-

  • The near wall flow is considered as laminar and the velocity varies linearly with distance from the wall
  • No slip condition: u = v = 0.
  • In this we are applying the “wall functions” instead of the mesh points.

    • Turbulent flow:

    y + > 11.63 .

    in the log-law region of a turbulent boundary layer.

    Laminar flow :

    y + < 11.63 .

    Important points for applying wall functions:

  • The velocity is constant along parallel to the wall and varies only in the direction normal to the wall.
  • No pressure gradients in the flow direction.
  • High Reynolds number
  • No chemical reactions at the wall

    • cyclic boundary condition

  • We take flux of flow leaving the outlet cycle boundary equal to the flux entering the inlet cycle boundary
  • Values of each variable at the nodes at upstream and downstream of the inlet of the inlet plane are equal to values at the nodes at upstream and downstream of the outlet plane.

    • Pressure boundary condition

    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.

  • The pressure corrections are taken zero at the nodes.

    • exit boundary conditions

    Considering the case of an outlet perpendicular to the x-direction -

    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

    U N I , J = U N I − 1 , J M i n M o u t .

    References

    Boundary conditions in CFD Wikipedia
    (Text) CC BY-SA