Abstract
To weaken the influence of profile error on compressor aerodynamic performance, especially on pressure ratio and efficiency, a robust design method considering profile error is built to improve the robustness of aerodynamic performance of the blade. The characteristics of profile error are random and small-scaled, which means that to evaluate the influence of profile error on blade aerodynamic performance is a time-intensive and high-precision work. For this reason, non-intrusive polynomial chaos (NIPC) and Kriging surrogate model are introduced in this robust design method to improve the efficiency of uncertainty quantification (UQ) and ensure the evaluate accuracy. The profile error satisfies the Gaussian distribution, and NIPC is carried out to do uncertainty quantification since it has advantages in prediction accuracy and efficiency to get statistical behavior of random profile error. In the integrand points of NIPC, several surrogate models are established based on Latin hypercube sampling (LHS) + Kriging, which further reduces the costs of optimization design by replacing calling computational fluid dynamic (CFD) repeatedly. The results show that this robust design method can significantly improve the performance robustness in shorter time (40 times faster) without losing accuracy, which is meaningful in engineering application to reduce manufacturing cost in the premise of ensuring the aerodynamic performance. Mechanism analysis of the robustness improvement samples carried out in current work can help find out the key parameter dominating the robustness under the disturbance of profile error, which is meaningful to further improvement of compressor robustness.
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Gao L.M., Cai Y.T., Xu H.L., et al., Uncertainty quantification of airfoil considering manufacturing error. Journal of Aerospace Power, 2017, 32(9): 2253–2259. (in Chinese)
Bolotov M.A., Pechenin V.A., Ruzanov N.V., Uncertainties in measuring the compressor-blade profile in a gas-turbine engine. Russian Engineering Research, 2016, 36(12): 1058–1065.
Chen B., Yang T., Feng T., Ontology-based aero-engine compressor blade manufacturing quality analyzing. International Conference on Computational Intelligence and Software Engineering, IEEE, Wuhan, China, 2009, DOL 10.1109/CISE.2009.5366278.
Clayton R.D.L., Effects of manufacturing deviation on core compressor blade performance. Virginia Polytechinic Institute and State University, Blacksburg, USA, 2009.
Chen Y., Gao J., Deng H., et al., Spatial statistical analysis and compensation of machining errors for complex surfaces. Precision Engineering, 2013, 37(1): 203–212.
Wang P., Li S., Zhang D., et al., The machining error control of blade shape based on multivariate statistical process control. Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture, 2015, 229(11): 1912–1924.
Lange A., Voigt M., Vogeler K., Probabilistic CFD simulation of a high-pressure compressor stage taking manufacturing variability into account. ASME Turbo Expo 2010, Power for Land, Sea, and Air, Glasgow, UK, 2010, pp. 617–628. DOI: 10.1115/GT2010-22484.
Gao L.M., Cai Y.T., Zeng R.H., et al., Effects of blade machining error on compressor cascade aerodynamic performance. Journal of Propulsion Technology, 2017, 38(3): 525–531. (in Chinese)
Wang H., Huang L., Yao C., et al., Integrated analysis method of thin-walled turbine blade precise machining. International Journal of Precision Engineering & Manufacturing, 2015, 16(5): 1011–1019.
Eric A. Dow, Wang Q.Q., Simutaneous robust design and tolerancing of compressor blades. Proceedings of the ASME Turbo Expo 2014, Dusseldorf, North Rhine-Westphalia, Germany, 2014, pp. 1–12. DOI: 10.1115/GT2014-25795.
Taguchi G., Elsayed E.A., Hsiang T.C., Quality engineering in production systems. McGraw-Hill, New York, 1989. DOI: 10.1080/00401706.1990.10484745.
Mcallister C.D., Simpson T.W., Multidisciplinary robust design optimization of an internal combustion engine. Journal of Mechanical Design, 2003, 125(1): 39–41.
Khodaygan S., Sharafi M., A new approach for the reliability-based robust design optimization of mechanical systems under the uncertain conditions. SAE Technical Paper, 2018-01-0615.
Wu X., Zhang W., Song S., Robust aerodynamic shape design based on an adaptive stochastic optimization framework. Structural & Multidisciplinary Optimization, 2017, 57(3): 1–13.
David M., Pietro B., Jaikumar L., Carlo L.B., Propagation of uncertainties through wind turbine models for robust design optimization. 35th Wind Energy Symposium, Grapevine, Texas, USA, 2017, pp. 1–10. DOI: 10.2514/6.2017-1849.
Giulia A., Ilya A., Andreas F.B., Robust design optimization of a low pressure turbine rotor discs secondary air system. Proceedings of the ASME Turbo Expo, Charlotte, North Carolina, USA, 2017, pp. 1–12. DOI: 10.1115/GT2017-63289.
Kumar A., Keane A.J., Nair PB., et al., Robust design of compressor fan blades against erosion. ASME Journal of Mechanical Design, 2006, 128(4): 864–873.
Kumar A., Nair P.B., Keane A.J., et al., Robust design using Bayesian Monte Carlo. International Journal for Numerical Methods in Engineering, 2008, 73(11): 1497–1517.
Keane A.J., Comparison of several optimization strategies for robust turbine blade design. Journal of Propulsion & Power, 2012, 25(5): 1092–1099.
Keane A.J., Cokriging for robust design optimization. AIAA Journal, 2012, 50(11): 2351–2364.
Mattia P., Sergio C.M., Dimitrov G.M., Comparative analysis of uncertainty propagation methods for robust engineering design. Tetrahedron Letters, 2007, 33(43): 6537–6540.
Campobasso M.S., Minisci E., Caboni M., Aerodynamic design optimization of wind turbine rotors under geometric uncertainty. Wind Energy, 2014, 19(1): 1–15.
Smola A.J., Schölkopf B., A tutorial on support vector regression. Statistics and Computing, 2004, 14(3): 199–222.
[24] Loeven G.J.A., Bijl H., Probabilistic collocation used in a two-step approached for efficient uncertainty quantification in computational fluid dynamics. Computer Modeling in Engineering & Sciences, 2008, 36(3): 193–212.
Loeven A., Bijl H., An efficient framework for uncertainty quantification in CFD using probabilistic collocation. 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Paim Springs, California, USA, 2009, pp. 1–10. DOI: 10.2514/6.2009-2275.
Xiu D., Karniadakis G.E., Modeling uncertainty in flow simulations via generalized polynomial chaos. Journal of Computational Physics, 2003, 187(1): 137–167.
Zhao K., Gao Z.H., Huang J.T., et al., Uncertainty quantification and robust design of airfoil based on polynomial chaos technique. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(1): 10–19. (in Chinese)
Fusi F., Guardone A., Quaranta G., et al., Multi-fidelity physics-based method for robust optimization with application to a hovering rotor airfoil. AIAA Journal, 2015, 52(11): 1–18.
Wang J., Wen S., Li T., et al., Multidisciplinary design optimization to reduce erosion of blades in a mixed flow fan. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 2014, 228(1): 64–82.
Kamenik J., Voutchkov I., Toal D.J.J., et al., Robust turbine blade optimization in the face of real geometric variations. Journal of Propulsion and Power, 2018, 34(6): 1479–1493.
Li Z., Liu Y., Agarwal R.K., Robust optimization design of single-stage transonic axial compressor considering the manufacturing uncertainties. ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018 June 11–15, Oslo, Norway, 2018, pp. 1–12. DOI: 10.1115/GT2018-75415.
Lin X.J., Shan C.W., Wang Z.Q., et al., Measurement techniques of coordinate measuring machine for blade surface of aero-engine. Computer Integrated Manufacturing Systems, 2012, 18(1): 125–131.
Cai Y.T., Gao L.M., Ma C., et al., Uncertainty quantification on compressor blade considering manufacturing error based on NIPC method. Journal of Engineering Thermophysics, 2017, 38(3): 490–497. (in Chinese)
Dow E., Wang Q., The implications of tolerance optimization on compressor blade design. Journal of Turbomachinery, 2015, 137(10): 101008-1-101008-7.
Yan Y., Zhu P.Y., Song L.M., et al., Uncertainty quantification of cascade manufacturing error based non-stationary Gaussian process. Journal of Propulsion Technology, 2017, 38(8): 1767–1775. (in Chinese)
Kumar A., Keane A.J., Nair P.B., et al., Efficient robust design for manufacturing process capability. Proceeding of the 6th ASMO-UK/ISSMO International Conference on Engineering Design Optimization, 2006, pp. 242–250.
Farokhi S., Aircraft propulsion. second ed. West Sussex, John Wiley & Sons Ltd, 2014.
Francesco M., Carnevale M., D'Ammaro A., et al., Uncertainty quantification in computational fluid dynamics and aircraft engines, first ed., Springer International Publishing, Heidelberg, 2015. DOI: 10.1007/978-3-319-14681-2.
Eldred M.S., Burkard J., Comparison of non-intrusive polynomial chaos and stochastic collocation methods for uncertainty quantification. 47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, Florida, USA, 2009, pp. 1–20. DOI: 10.2514/6.2009-976.
Ouyang J., Numerical analysis, Higher Education Press, Beijing, 2009.
Zhang W., Hao X., Lei H.E., The parametric design of turbine blade based on NURBS. Machine Design & Manufacturing Engineering, 2013, 42(8): 23–26. (in Chinese)
Yang X.D., Bo L., Zhang G.C., et al., Optimization of aspirated airfoil based on artificial bee colony algorithm and NURBS. Journal of Aerospace Power, 2014, 29(8): 1855–1862.
Guo X.Y, Zhang H.J., Dai R., Airship shape optimization with NURBS and gradient based algorithms. Journal of Aerospace Power, 2011, 26(12): 2812–2819.
Sein M. L., Interpolation of spatial data: some theory for Kriging. Springer, New York, 1999. DOI: 10.1007/978-1-4612-1494-6.
Huang D., Allen T.T., Notz W.I., Zeng N., Global optimization of stochastic black-box systems via sequential Kriging meta-models. Journal of Global Optimization, 2006, 34(2006): 441–466.
Kuhnt S., Steinberg D.M., Design and analysis of computer experiments. AStA Advances in Statistical Analysis, 2010, 94(4): 307–309.
Mckay M.D., Beckman R. J., Conover W.J., A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 2000, 42(1): 55–61.
Park J.S., Optimal Latin-hypercube designs for computer experiments. Journal of Statistical Planning & Inference, 1994, 39(1): 95–111.
Johnson M.E., Moore L.M., Ylvisaker D., Minimax and maximin distance designs. Journal of Statistical Planning & Inference, 1990, 26(2): 131–148.
Label & tolerance of Blade and airfoil, and surface roughness of blade. Aviation Industry Standard of China, Beijing, China, 1999.
Acknowledgments
The authors would like to express appreciation for the support of the National Natural Science Foundation of China (NSFC) under the Grant No. 51790512; the Overseas Expertise Introduction Project for Discipline Innovation (111 Project) under Grant No. B17037; Industry-University-Research Cooperation Project of Aero Engine Corporation of China (AECC) under Grant No. HFZL2018CXY011-1 and MUT.
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Gao, L., Ma, C. & Cai, Y. A Robust Blade Design Method based on Non-Intrusive Polynomial Chaos Considering Profile Error. J. Therm. Sci. 28, 875–885 (2019). https://doi.org/10.1007/s11630-019-1185-6
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DOI: https://doi.org/10.1007/s11630-019-1185-6