Periodic Boundary Condition

Periodic Boundary Condition#

The Periodic boundary condition links two separate boundaries so that flow exiting one boundary enters the other, enabling simulation of infinitely repeating geometry with a reduced computational domain.

Available Options#

Option

Description

Applicable

Periodicity Type

Type of periodicity (translational or rotational)

always

Axis of rotation

Rotation axis for rotational periodicity

Periodicity type is Rotational

Assigned surfaces

Matching pairs of boundaries to be treated as periodic

always

Detailed Descriptions#

Periodicity Type#

Defines the geometric relation between periodic boundaries.

  • Options:

    • Translational

    • Rotational

  • Default: Translational

Note: Translational periodicity is typically used for linear arrays, while rotational periodicity is used for circular arrangements.

Axis of rotation#

The axis about which rotational periodicity is applied.

  • Required when Rotational is selected.

  • Example: Vector (0, 0, 1) for rotation around the z-axis.

Note: The rotation angle is determined automatically from the mesh geometry.

Assigned surfaces#

Matching pairs of boundaries that will be treated as periodic interfaces.

  • Required.

  • Accepted types: Pairs of Surface objects

  • Example: front_plane AND back_plane

Note: The mesh must be conformal at periodic interfaces, meaning nodes on paired surfaces must match exactly after applying the periodic transformation.

💡 Tips

Mesh Preparation for Periodic Boundaries

  • Conformal mesh requirement:

    • The mesh must be conformal at periodic interfaces

    • Nodes on paired surfaces must match exactly after applying the periodic transformation (translation or rotation)

    • Ensure your mesh generator creates matching node distributions on both periodic surfaces

  • For Translational Periodicity:

    • Ensure identical node positions on both surfaces, offset only by the translation vector

  • For Rotational Periodicity:

    • Ensure nodes on both surfaces match exactly when one surface is rotated to align with the other

Common Applications

  • Translational Periodicity:

    • Airfoil or blade cascades

    • Heat exchanger channels

    • Infinite arrays of elements

    • Channel flow with repeating features

  • Rotational Periodicity:

    • Single blade passage in turbomachinery

    • Sectional analysis of axisymmetric components

    • Propeller/rotor blade analysis using one blade

    • Components with cyclic symmetry

Performance Considerations#

  • Periodic boundaries typically reduce computational cost significantly

  • For rotational cases, ensure sufficient sector size to capture relevant flow features

  • Verify that periodicity is a valid assumption for your flow physics

❓ Frequently Asked Questions

  • How do I determine if periodicity is appropriate for my simulation?

    Periodicity is appropriate when:

    • Your geometry repeats in a regular pattern

    • Flow conditions are expected to be identical across the repeating units

    • You’re interested in the fully developed flow rather than entrance/exit effects

    • The problem has no major asymmetries that would invalidate the periodic assumption

  • What mesh requirements must be met for periodic boundaries?

    Periodic boundaries require conformal meshes:

    • Nodes on paired surfaces must match exactly after applying the periodic transformation

    • The node count must be identical on both periodic surfaces

    • Ensure your mesh generator creates matching node distributions when generating periodic boundaries

  • Can I use periodicity with other boundary conditions?

    Yes, periodic boundaries are often combined with:

    • Wall conditions for solid surfaces

    • Inflow/outflow for the flow direction perpendicular to the periodic directions

    • Symmetry planes for additional domain reduction

  • How many repeating units should I include in my periodic simulation?

    For most cases, a single repeating unit is sufficient. However, include multiple units when:

    • Vortex shedding or instabilities with wavelengths larger than one unit are expected

    • Flow features may develop with periodicity different from the geometric periodicity

    • Investigating possible asymmetric solutions in nominally periodic configurations

  • Can I use periodicity for time-dependent simulations?

    Yes, periodicity works for both steady and unsteady simulations, but:

    • Ensure that time-dependent phenomena respect the periodic assumption

    • For some unsteady flows (e.g., vortex shedding), include enough repeating units to capture the correct wavelength

    • Consider phase-lag periodicity for turbomachinery with relative motion between components

  • What’s the difference between periodicity and symmetry?

    • Periodicity connects two separate boundaries, simulating infinite repetition

    • Symmetry reflects flow across a single plane, imposing the condition that flow doesn’t cross that plane

    • Use periodicity for repeating patterns, symmetry for mirror-image configurations

🐍 Python Example Usage

 
# Example of translational periodicity
translational_periodic = fl.Periodic(
    name="x_direction_periodicity",
    surface_pairs=[
        (volume_mesh["left_face"], volume_mesh["right_face"])
    ],
    spec=fl.Translational()
)

# Example of rotational periodicity
rotational_periodic = fl.Periodic(
    name="blade_passage_periodicity",
    surface_pairs=[
        (volume_mesh["passage_minus"], volume_mesh["passage_plus"])
    ],
    spec=fl.Rotational(
        axis_of_rotation=(0, 0, 1)  # Rotation around z-axis
    )
)

# Example with multiple periodic pairs
multi_periodic = fl.Periodic(
    name="multi_direction_periodicity",
    surface_pairs=[
        (volume_mesh["left_face"], volume_mesh["right_face"]),
        (volume_mesh["bottom_face"], volume_mesh["top_face"])
    ],
    spec=fl.Translational()
)

# Example of turbomachinery setup with periodicity
def create_turbo_boundaries():
    return [
        fl.Wall(
            name="blade_surface",
            entities=volume_mesh["blade"],
            heat_spec=fl.HeatFlux(0 * fl.u.W / fl.u.m**2)  # Adiabatic wall
        ),
        fl.Inflow(
            name="inlet",
            entities=[volume_mesh["inlet"]],
            total_temperature=300 * fl.u.K,
            spec=fl.TotalPressure(
                value=150000 * fl.u.Pa
            )
        ),
        fl.Outflow(
            name="outlet",
            entities=volume_mesh["outlet"],
            spec=fl.Pressure(
                value=101325 * fl.u.Pa
            )
        ),
        fl.Periodic(
            name="blade_passage",
            surface_pairs=[
                (volume_mesh["periodic_minus"], volume_mesh["periodic_plus"])
            ],
            spec=fl.Rotational(
                axis_of_rotation=(1, 0, 0)  # Rotation around x-axis
            )
        )
    ]
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