Sliding Mesh Method
Sliding Mesh Method: Theoretical Foundations
Overview
I often hear about Sliding Mesh in unsteady turbomachinery analysis, but how is it different from MRF?
MRF fixes the rotor position to obtain a pseudo-steady solution, while Sliding Mesh physically rotates the mesh in the rotating domain at each time step. It interpolates information at the non-conformal interface.
So it's called Sliding Mesh because the mesh slides at the interface, right?
Correct. This allows physical capture of blade-to-blade interactions (wake passage, potential interference). It's an essential method for predicting pressure fluctuations and unsteady blade surface loads.
Interface Handling
How is the interpolation at the interface done?
At each time step, the overlap between the rotating and stationary interface meshes is calculated, and fluxes are conservatively interpolated. CFX's Transient Rotor-Stator uses GGI-based weighted interpolation. Fluent's Sliding Mesh uses face-to-face intersection detection for interpolation.
Scope of Application
In what cases is Sliding Mesh essential?
| Analysis Objective | Sliding Mesh Necessity |
|---|---|
| Design point efficiency prediction | Not required (MRF/Mixing Plane is sufficient) |
| Pressure fluctuations due to blade passing | Essential |
| Wake-blade interference | Essential |
| Unsteady blade surface loads (vibration evaluation) | Essential |
| Noise prediction (FW-H input) | Essential |
| Surge/Stall | Essential (full annulus) |
The Birth of the Sliding Mesh Method—The Dawn of Unsteady Rotor-Stator Interference CFD
The industrial adoption of the Sliding Mesh method began in the late 1990s. Prior to that, turbomachinery CFD was limited to steady-state frozen rotor or mixing plane methods, unable to capture unsteady rotor-stator interactions (wake interference, potential interference). The turning point was when ANSYS Fluent, in version 5 (1998), first fully implemented the Sliding Interface feature as a commercial CFD tool. This enabled the transport of vortices from rotor to stator, calculation of BPF (Blade Passing Frequency) fluctuating forces, and prediction of acoustic pressure fluctuations. In modern turbomachinery development (stall analysis for jet engine compressors, hydraulic pulsation reduction in pumps), unsteady sliding mesh has become an indispensable tool, a method that changed the common sense of CFD over the 25 years since its 1998 implementation.
Computational Methods for Sliding Mesh Method
Determining the Time Step
How do you decide the time step for Sliding Mesh?
A general guideline is 20 to 50 time steps per blade passage.
Example: 3000rpm, 12 blades, 30 steps/blade passage → $\Delta t = 60/(3000 \times 12 \times 30) = 55.6 \mu s$
What if a finer resolution is needed?
For noise prediction or DES/LES, resolution up to the 10th harmonic of BPF is required, demanding 100 to 200 steps per blade passage.
Determining Periodic Steady State
How many revolutions should be calculated to be sufficient?
Judge by monitoring pressure fluctuations.
1. Place a pressure monitor at an appropriate point (e.g., near cutoff)
2. Overlay and compare pressure waveforms from two consecutive revolutions
3. If the amplitude change is within 2%, it's considered periodic steady state
Typically stabilizes in 5 to 15 revolutions. Using initial values from MRF or Frozen Rotor steady-state solutions can shorten this to 3 to 5 revolutions.
Handling Pitch Ratio
What if the blade count ratio between rotor and stator is not an integer?
Ideally, a full annulus model is used, but computational cost becomes enormous. One method is to create a sector model based on the greatest common divisor of blade counts. For example, rotor 7 blades, stator 12 blades → greatest common divisor is 1, requiring full annulus. But rotor 6 blades, stator 12 blades → greatest common divisor is 6, allowing calculation with a 1/6 sector.
CFX's Time Transformation method and FINE/Turbo's NLH method are techniques that can approximate unsteady interference with a single pitch calculation even for non-integer pitch ratios.
Numerical Implementation of the Sliding Mesh Method—The Role of AMI and Flux Correction
The Sliding Mesh method couples the boundary between the rotating rotor domain and the stationary stator domain using an "Arbitrary Mesh Interface (AMI)," updating the relative mesh positions at the boundary each time step to compute unsteady rotor-stator interference. Variable interpolation at the AMI is done via bilinear interpolation or weighted least squares (WLS), but when interface cells are non-conformal, "Flux Correction" is required for flux conservation. In OpenFOAM, AMI surface flux correction is automated, but it's known that mass conservation error can accumulate after more than two rotor revolutions, so periodic additional pressure correction settings are recommended.
Sliding Mesh Method in Practice
Extracting Pressure Fluctuations
How do you evaluate pressure fluctuations from Sliding Mesh results?
Follow these steps.
1. Place pressure monitors at points of interest (volute wall, pipe connection, etc.)
2. Sample data from 2 to 5 revolutions after reaching periodic steady state
3. Perform spectral analysis via FFT (Fast Fourier Transform)
4. Evaluate peak amplitudes at BPF and its harmonics
What is a normal amplitude for BPF?
It depends on the machine type, but for centrifugal pumps, a typical BPF pressure amplitude is 1–5% of the average head. Exceeding this poses a risk of pipe vibration or structural resonance.
Unsteady Blade Surface Loads
Can unsteady forces on blade surfaces also be evaluated?
Output the time history of force components (x, y, z) acting on each blade surface and perform spectral analysis via FFT. If blade natural frequencies coincide with BPF harmonics, there is a risk of resonance (flutter).
Post-Processing Notes
What should I be careful about in Sliding Mesh post-processing?
| Note | Details |
|---|---|
| Output Frequency | Saving every time step creates enormous files. Thin out to a frequency satisfying the Nyquist condition for the frequencies needed for BPF analysis |
| Rotating/Stationary Frame Conversion | Convert rotating frame data to stationary frame for display in CFD-Post |
| Phase Averaging | Average the same phase across multiple revolutions to obtain a phase-locked flow field |
| Animation | Create videos of Mach number or Q-criterion isosurfaces in inter-blade passages to confirm vortex structure propagation |