Assisted Turbulence Modeling via Data Assimilation and Machine Learning for Turbomachinery Flows

What it claims

The framework is built and tested on CME2, a single-stage, low-speed axial compressor rig at Arts et Métiers in Lille. The authors are Tom Moussie, Pierric Joseph and Marcello Meldi (Univ. Lille, CNRS, ONERA, Arts et Métiers, Centrale Lille). It corrects Spalart-Allmaras RANS with a learned volume forcing term f_i added to the momentum equation. The abstract states two outcomes. A single neural network keeps global accuracy, but near the blade tips its error can exceed that of baseline RANS. A Mixture of Experts gives discrepancy that is systematically lower than baseline RANS and close to the MFEnKF state estimate.

How it works

The test case has a 30-blade rotor, a 40-blade stator, a 275 mm casing radius and a 0.5 mm tip gap. At the 3,200 rpm design point it runs at 5.3 kg/s, a pressure ratio of about 1.03, inlet Mach 0.12 and rotor-tip Mach 0.28.

Observations are 2D2C PIV on three constant-radius planes: P1 at 18%, P2 at 51% and P3 at 79% of blade height. These hold 8,180, 6,944 and 8,090 points, with 0.5 mm vector spacing. Each field is the average of 100 acquisitions, and PIV uncertainty is about 3%.

The two simulation fidelities run in OpenFOAM:

1. Low fidelity is steady RANS with a SIMPLE solver and a Multiple Reference Frame for rotor rotation.
2. High fidelity is unsteady DDES (C_DES = 0.65) with a PIMPLE solver and an Arbitrary Mesh Interface between the rotating and static grids.

flowchart LR
  A[PIV planes P1-P3] --> D[MFEnKF]
  B[Many steady RANS] --> D
  C[Few DDES runs] --> D
  D --> E[NN: forcing term]
  E --> F{Error near tips}
  F -->|single NN| G[Can exceed RANS]
  F -->|Mixture of Experts| H[Below RANS everywhere]

The MFEnKF state estimate trains NNs that follow the approach of Villiers et al. Inputs are local velocity, velocity gradients and turbulent viscosity, and the output is the forcing term. The goal is to keep DA-level accuracy without needing experimental data at run time.

Evidence

Two operating-point uncertainties bound any comparison with experiment: mass flow is known to ±0.06 kg/s (±1% of design) and pressure rise to ±12.5 Pa (±0.4%). The fetched text ends in Section 3. It contains no error tables, no network sizes and no training cost, so the abstract's comparative claims cannot be checked here.

Limits

The authors call CME2 geometrically simpler than operating machines. Results come from one rig and one operating point. Experimental data covers only three 2D planes, which is a small part of the domain, so the assimilated state away from these planes depends on the simulations. The introduction notes that ML-corrected RANS models often fail to generalise to other test cases, and the fetched text shows no test on another geometry or operating condition. No code or data release is mentioned.