# 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
```python
# 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
)
)
]
```