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CFD Correction of Open Tip Clearance Flow in a Compressor Cascade Using VAE Latent Space Adaptation
Xiang Zuo, Hefang Deng, Caiyan Chen, Honglin He, Mingmin Zhu, Songan Zhang, Jinfang Teng
TL;DR
Sparse measurements and local CFD–experiment discrepancies make open tip clearance loss-field correction challenging. The paper combines a learned CFD-field representation with latent-space adaptation and sparse observation-space supervision; current 12-fold results report mean foldwise improvement exceeding 62% for multiple metrics.
Problem
Method
The method adapts a frozen VAE latent representation using paired CFD–experiment data and maps corrected fields to actual measurement locations and pitchwise windows for observation-space supervision.
Source: §4 · p. 10, §6 · p. 18Results
Mean foldwise improvement exceeds 62.00% for multiple metrics in the current 12-fold results.
Source: §6 · p. 18Takeaways & Limitations
The VAE prior and sparse experimental observations support non-intrusive field correction with a small number of paired samples.
Source: §6 · p. 18Checkpoint selection and early stopping should rely only on training data, but the current results precede a strictly fixed model-selection procedure.
Source: §4.5 · p. 14
Abstract
from arXiv · showhide
CFD predictions of open tip clearance flow in compressor cascades are subject to discrepancies relative to experiments, while experimental observations are sparse and high-resolution experimental ground truth is unavailable. This study proposes a non-intrusive correction method based on a variational autoencoder (VAE) and latent-space adaptation. A VAE is first trained using a dataset of 166 parametrically sampled CFD total pressure loss fields to learn a low-dimensional statistical representation of these fields. The VAE is then frozen, and a low-rank latent-space adapter is trained using only 12 paired CFD--experiment operating conditions. An observation operator maps the corrected high-resolution fields to the experimental observation space, allowing supervision to be applied only at the available measurement locations and within the measured pitchwise windows. In the current 12-fold cross-validation, the mean absolute error decreases from 0.1335 to 0.0473, the root mean square error from 0.1717 to 0.0621, and the relative $L_2$ error from 0.5108 to 0.1871. These results indicate that the method improves agreement between CFD predictions and sparse experimental observations of open tip clearance flow without modifying the RANS solver or constructing artificial high-resolution experimental labels.
1 Introduction
Open tip clearance produces complex exit-loss fields that vary with operating conditions, while measurements are sparse and CFD predictions can differ locally from experiments. The study addresses the challenge of correcting these fields non-intrusively with few paired CFD–experiment conditions.
1 Introduction
- Loss location, extent, and magnitude depend jointly on clearance, inlet conditions, and endwall motion, so one representative condition cannot describe other geometries and operating states.The cited studies report effects from moving endwalls, upstream wakes, and inlet-boundary-layer thickness.Source: §1 · pp. 1–2
- Sparse probe measurements and experimental costs limit operating-condition coverage, while RANS and URANS can differ from measurements in local loss magnitudes and spatial distributions.Higher-fidelity large eddy simulation resolves unsteady structures in greater detail but is too computationally expensive for large parametric datasets.Source: §1 · p. 2
- Prior correction approaches either update the numerical solution or learn post-CFD mappings, but open tip clearance applications have few paired CFD–experiment conditions for training.Solution-coupled approaches generally incorporate measurement constraints into the solver or an iterative inversion procedure.Source: §1 · p. 2
- The proposed non-intrusive method trains a VAE on 166 parametrically sampled RANS loss fields, then adapts its frozen latent representation using 12 paired conditions and an observation-space consistency loss.The observation operator maps corrected high-resolution fields to actual experimental measurement locations and pitchwise windows.Source: §1 · p. 3
2 Experimental Facility and Data Acquisition
The study uses a moving-endwall linear cascade and paired exit traverses to evaluate CFD correction across operating conditions. Measurements remain discrete observations, so processing aligns them to a single-pitch window for comparison in observation space.
2 Experimental Facility and Data Acquisition
- The facility combines air supply and flow conditioning with a cascade test section, moving-endwall system, probe traverse, and pressure acquisition.A large-radius rotating disk provides the moving endwall; 0 and 900 rpm represent stationary and moving conditions.Source: §2 · p. 3
2.1 Test Cascade and Paired Operating Conditions
- The test uses highly loaded controlled-diffusion airfoil blades with clearance between blade tips and the rotating disk; 12 paired conditions have complete exit traverses.The conditions vary incidence, tip clearance, Mach number, and endwall rotation, but are not a full factorial design because 5% clearance cases are available only at Ma = 0.3.Source: §2.1 · p. 3
2.2 Measurement System and Procedure
- Five-hole probe traverses sample the exit plane on a 16 × 21 grid, giving 336 locations per condition, with 2.5 mm pitchwise and 2 mm spanwise spacing.The probe is positioned 0.4C downstream of the blade trailing edge; measurements are time-averaged after a settling period.Source: §2.2 · pp. 5–6
2.3 Experimental Data Processing
- The total pressure loss coefficient is a normalized local exit total-pressure deficit referenced to inlet total and static pressures and is the CFD-correction target.Paired experimental observations are shifted and cropped to a single-pitch window without interpolation into a high-resolution full field; an observation operator maps predictions to those locations.Source: §2.3 · p. 6
3 CFD Simulations and Flow Field Dataset Construction
The section describes the CFD domain, numerical setup, and field processing, then explains how the resulting CFD and paired experimental datasets support the two training stages.
3.1 Computational Domain and Reference Planes
- The computational domain uses one blade passage with pitchwise periodic boundaries, extending from 2.52C upstream to 2C downstream of the blade.The inlet reference plane is 0.45C upstream of the leading edge, and the extraction plane is 0.4C downstream of the trailing edge.Source: §3.1 · p. 6, Figure 4 · p. 7
3.2 Mesh Configuration and Grid Independence
- The same multiblock structured-mesh specification is used across cases, with local refinement near blades, endwalls, and the tip clearance.The mesh is regenerated for each clearance while retaining topology and node allocation; a separate grid-independence study is not repeated here.Source: §3.2 · p. 7
3.3 Numerical Method and Boundary Conditions
- Steady three-dimensional compressible RANS uses the SST k–ω turbulence model with γ–Reθ transition modeling and prescribed inlet and outlet conditions.The CFD cases use pitchwise periodic boundaries; the moving endwall is modeled as a translating planar wall.Source: §3.3 · pp. 7–8
3.4 Parametric Sampling and Generation of the Stage 1 CFD Dataset
- The study generates 200 cases from incidence, clearance, Mach number, and endwall-speed settings, retaining 166 valid CFD results after convergence and data checks.Latin hypercube sampling covers the three continuous parameters; endwall speed has two levels, 0 and 900 rpm.Source: §3.4 · p. 8
3.5 Extraction and Resampling of Total Pressure Loss Fields
- The exit total-pressure-loss field is extracted 0.4C downstream of the trailing edge and resampled onto a common 120 × 68 grid after alignment.The original structured-grid locations vary with tip clearance, so coordinate directions and passage and wake locations are made consistent before interpolation.Source: §3.5 · pp. 8–9
3.6 Datasets for the Two Training Stages
- Stage 1 uses 166 unpaired CFD fields to train the VAE, while Stage 2 uses 12 paired CFD–experiment cases to train an adapter with the VAE frozen.The learned correction represents aggregate discrepancies between CFD predictions and observations, not one isolated error source or turbulence-model parameter.Source: §3.6 · p. 9
4 CFD Correction Using a VAE and Latent Space Adaptation
The method adapts CFD predictions to sparse experimental observations by learning a CFD-field prior, then correcting its latent representation without changing the RANS solver. Its observation-space supervision and structural constraints keep the correction tied to measured locations while retaining a high-resolution CFD-based field.
4 CFD Correction Using a VAE and Latent Space Adaptation
- A two-stage, non-intrusive model learns CFD field structure first, then uses sparse experiments to correct it without changing the RANS equations, boundary conditions, or turbulence model.The approach addresses the mismatch between spatially complete CFD fields and sparse measurements by retaining CFD spatial structure while fitting the observed discrepancy.Source: §4 · pp. 9–10
4.1 A VAE Based Generative Prior for CFD Fields
- The Stage 1 VAE learns a continuous, low-dimensional representation from 166 parametrically sampled CFD fields, without using experimental data.A reconstruction objective and KL regularization balance field reconstruction with latent-space regularity.Source: §4.1 · pp. 10, 12
4.2 Low Rank Latent Space Adapter
- With only 12 paired cases, Stage 2 freezes the VAE and trains a low-rank adapter to predict residual latent corrections from the CFD code and operating conditions.The adapter conditions on incidence, tip clearance, inlet Mach number, and endwall rotational speed; its low-rank mapping limits the correction directions.Source: §4.2 · p. 12
4.3 Observation Operator for Sparse Experimental Data
- The observation operator aligns the CFD grid with the measured window and interpolates predictions to actual measurement locations, avoiding artificial full-field experimental labels.It uses fixed, differentiable inverse-distance weights from four neighbors, allowing measurement errors to backpropagate through the decoder to the adapter.Source: §4.3 · pp. 12–13
4.4 Joint Loss Function and Structural Constraints
- Stage 2 combines measurement error with constraints on latent shifts, full-field deviation, and error-field gradients to stabilize corrections where experiments provide little information.The field and gradient terms stabilize unobserved regions and suppress local jaggedness without requiring the corrected field to reproduce the original CFD field.Source: §4.4 · p. 13
4.5 Leave One Condition Out Training with Limited Paired Data
- Twelve-fold leave-one-condition-out evaluation trains each adapter on 11 conditions and tests on the remaining condition, but current quantitative conclusions await a strictly fixed model-selection procedure.The stated procedure should select checkpoints and stop training using only the training portion, with the held-out condition evaluated once.Source: §4.5 · p. 14
4.6 Evaluation Metrics and Visualization
- Evaluation compares predictions with experiment only in observation space using MAE, RMSE, and relative L2 error; the full corrected field is not high-resolution experimental ground truth.Visualizations compare measurements and predictions within the observed region, while the complete field is inspected for anomalous changes rather than validated point by point.Source: §4.6 · p. 14
5 Results and Discussion
The VAE reconstruction preserves dominant high-loss structures, while latent-space correction reduces observation-space errors across the 12 folds. In four illustrated conditions, corrected high-loss regions generally move closer to measurements while retaining smooth transitions.
5.1 Stage 1 Reconstruction Performance
- For 25 held-out CFD samples, the VAE preserved principal high-loss locations, extents, and spatial gradients, with errors concentrated near peaks and region edges.Figure 8 shows a representative reconstruction; Figure 7 presents RMSE and MAE distributions across the held-out samples.Source: §5.1 · p. 15, Figure 7 · p. 15, Figure 8 · p. 16
5.2 Stage 2 Correction Performance
- 63.00% MAE and 62.46% RMSE mean foldwise improvement rates; both metrics improved in all 12 held-out conditions.Improvement varied across folds, with the lowest values around 34%.Source: §5.2 · p. 15, Table 6 · p. 16
5.3 Corrections in the Experimental Window and Full Field
- Across four illustrated conditions, corrected high-loss regions generally moved closer to measurements in position and coverage while retaining smooth spatial transitions.All four illustrated conditions show improvement; the adapter adjusts local structures rather than uniformly scaling the total pressure loss coefficient.Source: §5.3 · p. 16, Figure 9 · p. 17
6 Conclusions
Latent-space adaptation substantially reduces observation-space errors for unseen paired conditions, while the sparse observation operator maps measurements to corrected high-resolution fields. The VAE representation preserves dominant structures, supporting CFD correction with sparse experimental data.
Conclusions
- For 25 CFD samples excluded from training, the VAE preserved principal high-loss locations, extents, and overall spatial gradients.Errors occurred mainly near loss peaks and high-loss-region edges.Source: §6 · p. 18
- The sparse observation operator maps corrected high-resolution fields to measurement locations and pitchwise windows, avoiding interpolated high-resolution experimental labels.The passage notes that full-field label construction could introduce additional errors.Source: §6 · p. 18
- Mean foldwise improvement exceeded 62.00% for multiple metrics, reducing observation-space errors for unseen paired conditions.Similar MAE and RMSE improvements indicate reductions in both overall measurement discrepancy and larger local errors.Source: §6 · p. 18
- The VAE prior provides high-resolution structural constraints, while experimental observations constrain latent-representation adaptation, supporting correction with few paired samples.The stated conclusion is that the method enables CFD correction using sparse experimental data.Source: §6 · p. 18