Frozen rotor method
Frozen rotor method: Theoretical Foundations
Overview
The Frozen Rotor method has a cool name, but what does it actually do?
It's a method for performing steady-state analysis while keeping the relative position between the rotating and stationary components fixed. The rotor blade coordinates are placed in a rotating frame, and the stator blade coordinates are placed in a stationary frame, but at the interface, information is passed "as is" without taking a circumferential average.
What's the difference from Mixing Plane?
| Method | Interface Treatment | Blade Count Constraint | Computational Cost | Accuracy |
|---|---|---|---|---|
| Frozen Rotor | Fixed position, direct interpolation | Pitch ratio correction needed if 1 pitch differs | Low | Position-dependent |
| Mixing Plane | Circumferential mass averaging | Any pitch ratio | Low | Smooths circumferential fluctuations |
| Sliding Mesh | Rotation with time progression | Integer pitch ratio is desirable | High | Most accurate |
When to Use It
In what situations is Frozen Rotor used?
It is suitable for the following cases.
- High-speed screening in the initial design stage: Faster than Mixing Plane when comparing many shape candidates
- Centrifugal machines with volutes: Volutes are non-axisymmetric, making Mixing Plane difficult to apply. Frozen Rotor provides an estimate of blade-volute interaction.
- Hydraulic turbines: Evaluation of interaction with the draft tube
So it's useful when Mixing Plane can't be used, like with volutes.
Yes. However, the results depend on the relative position between the blades and the volute. For accurate evaluation, you should either calculate with multiple relative positions and average, or ultimately move to Sliding Mesh.
Frozen Rotor Settings in CFX
Please tell me the steps to set up Frozen Rotor in CFX.
Simply set the domain interface type to "Frozen Rotor". If the pitch ratio is not 1:1, automatic scaling is performed via the "Pitch Change" option. As a note, the mesh pitch of the GGI surfaces should be roughly aligned. Large discrepancies increase interpolation error.
History of Turbomachinery CFDโFrom the 1970s Slim Slot Method to 3D Inviscid Analysis
Attempts to analyze internal flows in turbomachinery using CFD began in the 1970s. Initially, due to computer limitations, 2D analysis of blade rows was mainstream, and 3D blade shapes could not be considered. The turning point was the development of the precursor code to ANSYS Fluent in the late 1970s and the 3D inviscid (Euler equations) turbomachinery analysis achieved by Denton (1982) on an IBM mainframe. Furthermore, in the 1990s, Harvey & Denton, Arnone, and others realized viscous analysis including unsteady rotor-stator interference, establishing the prototype of modern turbomachinery CFD (RANS + sliding mesh). The Frozen Rotor method was born within this history as a "reasonable first choice for steady-state approximation" and continues to live on as a standard method in the design exploration phase even 50 years later in the modern era.
Computational Methods for Frozen rotor method
Position Dependency Issue
Is it true that Frozen Rotor results change depending on blade position?
It's true. For example, in a centrifugal pump, the head can change by 5-10% depending on whether the blade is directly in front of the volute tongue (cutoff) or offset. This is a fundamental limitation of Frozen Rotor.
So it's not reliable?
Reporting the result from a single position directly as a performance value is risky. It is recommended to calculate 3-5 phases at intervals of 1/3 to 1/2 of the blade pitch and take the average.
Pitch Ratio Correction
What is pitch ratio?
It's the ratio of the angle of one pitch between the rotor and stator. For example, if the rotor has 7 blades (pitch 51.4 degrees) and the stator has 12 blades (pitch 30 degrees), the pitch ratio is 51.4/30=1.71. In Frozen Rotor, this pitch difference on both sides of the interface must be handled in some way.
In CFX, setting the Pitch Ratio on the interface triggers scaling interpolation in the circumferential direction. However, accuracy degrades significantly if the pitch ratio exceeds 2.
Choosing Between Mixing Plane and Frozen Rotor
How do you choose in practice?
| Situation | Recommended Method |
|---|---|
| Axisymmetric diffuser / No volute | Mixing Plane |
| Centrifugal pump with volute | Frozen Rotor (multiple phases) โ Sliding Mesh |
| Multi-stage axial flow | Mixing Plane |
| Parametric study in preliminary design | Frozen Rotor (fast) |
| Pressure pulsation / noise evaluation | Sliding Mesh (mandatory) |
Ultimately, it's safe to verify with Sliding Mesh.
Exactly. Frozen Rotor is positioned as "fast estimation," Mixing Plane as "stable steady-state approximation," and Sliding Mesh as "physically correct unsteady analysis."
Numerical Settings for the Frozen Rotor MethodโInterface Handling and Convergence Tips
The Frozen Rotor method is a steady-state analysis method with the MRF fixed under the assumption of circumferential uniformity between the rotor and stator. In implementation, the handling of the "rotor-stator interface" determines accuracy. At this interface, coordinate transformation (from rotating to stationary frame) is performed, but when the circumferential flow is non-uniform (e.g., strong wake interference), the assumption fails, and "circumferential dependency" occurs where results change when evaluated at different circumferential positions. The countermeasure is to perform Frozen Rotor calculations at multiple circumferential positions and take the circumferential average (Pitch Average). Also, since the interpolation accuracy of flow variables at the interface affects results, comparative verification with Sliding Mesh (more accurate) is recommended for critical areas.
Frozen rotor method in Practice
Centrifugal Pump Model Configuration
How do you set up the full model for a centrifugal pump?
A typical configuration is as follows.
- Suction Pipe: Stationary domain, non-rotating
- Impeller: Rotating domain, MRF or Sliding Mesh
- Volute: Stationary domain, non-axisymmetric
- Impeller-Volute Interface: Frozen Rotor (steady) or Sliding Mesh (unsteady)
Because the volute is non-axisymmetric, Mixing Plane cannot be applied. This is why Frozen Rotor is valued.
How do you create the mesh for the volute?
The volute's cross-sectional shape changes in a spiral pattern, so it cannot be created with TurboGrid. Use unstructured mesh from Ansys Meshing or Fluent Meshing, or automatic mesh from STAR-CCM+. For quality, it's advantageous to create a hexa-dominant mesh by sweeping cross-sectional shapes along the sweep direction.
Volute Tongue (Cutoff) Handling
What's difficult about the area near the cutoff (tongue)?
The tongue is a region where the impeller outlet flow and recirculating flow collide, with steep pressure gradients. The mesh needs to be particularly refined here. Also, in Frozen Rotor, the flow field changes significantly depending on the relative position between the blade and the tongue, so Sliding Mesh is essential for pressure pulsation evaluation.
Creating a Performance Map
Can you create an H-Q curve for a centrifugal pump using Frozen Rotor?
It's possible, but it's recommended to take the average of multiple phases at each flow rate point. The procedure is as follows.
1. For the design flow rate, perform Fro
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