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

cs.LGSep 23, 2026

CFD Correction of Open Tip Clearance Flow in a Compressor Cascade Using VAE Latent Space Adaptation

Authors: Xiang Zuo, Hefang Deng, Caiyan Chen, Honglin He, Mingmin Zhu, Songan Zhang, Jinfang Teng

Organizations: School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China · Global Institute of Future Technology, Shanghai Jiao Tong University, Shanghai 200240, China

Abstract

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.

Figures & tables

Figure 1 : Schematic of the experimental facility.

Figure 2 : Endwall motion in the cascade test section [ 4 ] .

Figure 3 : CDA blade profile and coordinate definitions.

Parameter	Symbol	Value
Blade chord	C	60 mm
Axial chord	$C_{\mathrm{ax}}$	51.96 mm
Stagger angle	$\beta_{s}$	30 ∘
Blade pitch	t	41.27 mm
Passage height	H	70 mm
Aspect ratio	h/C	1.17

Table 1 : Principal geometrical parameters of the cascade

Case	Incidence ( ∘ )	Tip clearance (% span)	Ma	Disk speed (rpm)
1	0	5	0.3	0
2	0	5	0.3	900
3	0	7.14	0.3	0
4	0	7.14	0.3	900
5	0	7.14	0.5	0
6	0	7.14	0.5	900

Table 2 : Paired CFD–experiment operating conditions

Figure 4 : Computational domain and reference locations.

Variable	Symbol	Range	Type
Inlet incidence angle	i	$-$ 7 ∘ to 7 ∘	Continuous
Tip clearance	s	1.42% to 7.14% of blade span	Continuous
Inlet Mach number	Ma	0.3 to 0.8	Continuous
Endwall rotational speed	n	0 or 900 rpm	Discrete

Table 3 : Parameter ranges for the CFD dataset

Panel of Figure 5 — Figure 5 : Architecture of the two-stage CFD correction model.

Item	Setting
Dataset split	141 training cases; 25 validation cases
Optimizer	AdamW
Initial learning rate	1 $\times$ 10 -4
Batch size	8
Maximum epochs	300
$\beta_{\mathrm{KL}}$	1 $\times$ 10 -4

Table 4 : Stage 1 VAE training settings

Figure 6 : Schematic of the observation operator.

Loss term	Weight	Role
Observation consistency $\mathcal{L}_{\mathrm{obs}}$	1.0	Fit the experimental measurements
Latent regularization $\mathcal{L}_{\mathrm{reg}}$	1 $\times$ 10 -4	Limit the latent correction magnitude
Full-field preservation $\mathcal{L}_{\mathrm{field}}$	1 $\times$ 10 -4	Stabilize unobserved regions
Gradient constraint $\mathcal{L}_{\mathrm{grad}}$	0.005	Preserve local first-order continuity

Table 5 : Stage 2 loss weights

Figure 7 : Distribution of Stage 1 reconstruction errors on the 25 held-out CFD samples.

Figure 8 : Representative Stage 1 reconstruction.

Metric	Before correction (mean $\pm$ SD)	After correction (mean $\pm$ SD)	Improvement (%) (mean $\pm$ SD)
MAE	0.133478 $\pm$ 0.022167	0.047329 $\pm$ 0.012506	63.00 $\pm$ 12.77
RMSE	0.171729 $\pm$ 0.023534	0.062099 $\pm$ 0.014686	62.46 $\pm$ 12.69
Relative $L_{2}$	0.510767 $\pm$ 0.051110	0.187061 $\pm$ 0.050893	—

Table 6 : Summary of the current 12-fold leave-one-condition-out results

Panel of Figure 9 — Figure 9 : Experimental observations and CFD-based predictions before and after correction at four operating conditions.

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Efficient Adaptation of ROMs for Unsteady Flows Using Data Assimilation

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We propose an efficient retraining strategy for a parameterized Reduced Order Model (ROM) that attains accuracy comparable to full retraining while requiring only a fraction of the computational time and relying solely on sparse observations of the full system. The architecture employs an encode-process-decode structure: a Variational Autoencoder (VAE) to perform dimensionality reduction, and a transformer network to evolve the latent states and model the dynamics. The ROM is parameterized by an external control variable, the Reynolds number in the Navier-Stokes setting, with the transformer exploiting attention mechanisms to capture both temporal dependencies and parameter effects. The probabilistic VAE enables stochastic sampling of trajectory ensembles, providing predictive means and uncertainty quantification through the first two moments. After initial training on a limited set of dynamical regimes, the model is adapted to out-of-sample parameter regions using only sparse data. Its probabilistic formulation naturally supports ensemble generation, which we employ within an ensemble Kalman filtering framework to assimilate data and reconstruct full-state trajectories from minimal observations. We further show that, for the dynamical system considered, the dominant source of error in out-of-sample forecasts stems from distortions of the latent manifold rather than changes in the latent dynamics. Consequently, retraining can be limited to the autoencoder, allowing for a lightweight, computationally efficient adaptation procedure with very sparse fine-tuning data.

Abstract

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