Uncertainty quantification of leakage characteristics of stepped labyrinth seals based on sparse PC-Kriging model
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Decheng Xu
,
Xiang Zhang
,
Zhongzhi Zhang
Abstract
Based on the sparse PC-Kriging method, a high-fidelity surrogate model was constructed to map the geometry of a stepped labyrinth seal to its leakage characteristics. Based on this surrogate model, Monte Carlo sampling was employed to analyze the impact of geometric errors on the uncertainty of the seal’s leakage characteristics and conduct sensitivity analysis. The results indicate that within a 99.7 % confidence interval, the maximum discharge coefficient can reach 0.584; compared to the baseline value of 0.52118, the worst-case scenario could lead to an approximate 12.1 % increase in the discharge coefficient, significantly increasing leakage. Sensitivity analysis reveals that the tip clearance of the fifth tooth exhibits the highest sensitivity to the discharge coefficient, approaching 80 % and dominating the response, while the remaining parameters show lower sensitivity, with 47 of them having sensitivities close to zero.
Funding source: Henan Provincial Science and Technology Research Program
Award Identifier / Grant number: Grant No.242102220042
Funding source: Guangdong Basic and Applied Basic Research Foundation
Award Identifier / Grant number: Grant No.2022A1515110055
Funding source: Graduate Education Innovation Foundation of Zhengzhou University of Aeronautics
Award Identifier / Grant number: Grant No. 2025CX82
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Research ethics: Not applicable.
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Informed consent: Informed consent was obtained from all individuals included in this study or their legal guardians or wards.
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Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Use of Large Language Models, AI and Machine Learning Tools: None declared.
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Conflict of interest: The authors state no conflict of interest.
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Research funding: This research was funded by the Henan Provincial Science and Technology Research Program (Grant No. 242102220042); Guangdong Basic and Applied Basic Research Foundation (Grant No. 2022A1515110055); and Graduate Education Innovation Foundation of Zhengzhou University of Aeronautics (Grant No. 2025CX82).
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Data availability: The data used for comparison in this study were obtained from previously published research articles, which are cited in the manuscript.
Nomenclature (SI UNITS)
- b
-
tooth tip width (mm)
- h
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tooth height (mm)
- H
-
step height (mm)
- r
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the radius of tooth tip fillet (mm)
- R
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the radius of tooth root fillet (mm)
- s
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tooth clearance (mm)
- t
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tooth pitch (mm)
- α
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tooth front angle (°)
- β
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tooth back angle (°)
Superscript
- left
-
left side of tooth
- right
-
right side of tooth
Subscripts
- i
-
The i-th tooth/step/chamber
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