Abstract
Fluid flow in centrifugal compressors is complex and turbulent, making it difficult to achieve a robust equipment design. In this work, a computational fluid dynamics (CFD) analysis is conducted on the periodical domain of a CO2 centrifugal compressor impeller and vaneless diffuser, with a 2.85:1 pressure ratio, using ANSYS CFX. The fluid flow is assumed to be steady state, turbulent, and three dimensional. Since polar angles are not considered in the traditional one-dimensional analysis, eight polar angles on hub and shroud were considered for modeling, sensitivity analysis, and optimization. After numerical verification and validation, a sequential sensitivity analysis (SA) was performed to identify non-influential variables. From the same design of experiment (DoE) used by the Morris qualitative SA, a response surface (RS) was trained to perform a quantitative SA by the smoothing spline ANOVA (SS-ANOVA) method. The Morris method was found to be more conservative than SS-ANOVA, keeping more variables as influent for the analysis. Both methods agreed on influential variables ranking. Low computational effort was required to submit the RS to a constrained optimization procedure using the NSGA-II method. The polytropic efficiency of the optimal centrifugal compressor configuration increased 0.7%, keeping the pressure ratio above 2.85, and the required power and outlet temperature below the base compressor. The impact of the polar angles at trailing edge on output variables is higher than leading edge. The optimal centrifugal compressor found is submitted to different mass flow rates and the overall performance for the optimal angles of the trailing edge and leading edge of the impeller was higher than the base compressor. The strategy adopted herein related to qualitative and quantitative sensitivity analysis coupled with response surface and the constrained optimization was shown to be robust, which can be applied to high-dimensional CFD models to reduce the computational cost with suitable results regarding fluid flow phenomena.
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References
ANEEL (2020) Ranking Nacional de Tarifas. https://www.aneel.gov.br/ranking-das-tarifas
ANSYS (2006) CFX - Solver Theory Guide. ANSYS, Inc., Canonsburg
Aungier RH (1995) A fast, accurate real gas equation of state for fluid dynamic analysis applications. J Fluids Eng 117:277–281. https://doi.org/10.1115/1.2817141
Benini E, Toffolo A, Lazzaretto A (2006) Experimental and numerical analyses to enhance the performance of a microturbine diffuser. Exp Thermal Fluid Sci 30:427–440. https://doi.org/10.1016/j.expthermflusci.2005.09.003
Bilal N (2014) Implementation of Sobol ’ s method of global sensitivity analysis to a compressor simulation model. In: International Compressor Engineering Conference. Purdue, pp. 1–10
Blanchette L, Khadse A, Mohagheghi M, Kapat JS (2016) Two types of analytical methods for a centrifugal compressor impeller for supercritical CO2 power cycles. In: 14th International Energy Conversion Engineering Conference AIAA. American Institute of Aeronautics and Astronautics, Salt Lake City, USA
Campolongo F, Cariboni J, Saltelli A (2007) An effective screening design for sensitivity analysis of large models. Environ Model Softw 22:1509–1518. https://doi.org/10.1016/j.envsoft.2006.10.004
Campolongo F, Saltelli A, Cariboni J (2011) From screening to quantitative sensitivity analysis. A unified approach. Comput Phys Commun 182:978–988. https://doi.org/10.1016/j.cpc.2010.12.039
Casey M, Robinson C (2008) A new streamline curvature throughflow method for radial turbomachinery. In: Turbo Expo. ASME, Berlin
Casey M, Robinson C (2013) A method to estimate the performance map of a centrifugal compressor stage. J Turbomach 135:1–10. https://doi.org/10.1115/1.4006590
Celik IB, Ghia U, Roache PJ et al (2008) Procedure for estimation and reporting of uncertainty due to discretization in CFD applications. J Fluids Eng 130:1–4. https://doi.org/10.1115/1.2960953
Ciuffo B, Casas J, Montanino M et al (2013) Gaussian process metamodels for sensitivity analysis of traffic simulation models. J Transp Res Board 2390:87–98. https://doi.org/10.3141/2390-10
Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6:182–197. https://doi.org/10.1109/4235.996017
Dezan DJ, Yanagihara JI, Jenovencio G, Salviano LO (2018) Parametric investigation of heat transfer enhancement and pressure loss in louvered fins with longitudinal vortex generators. Int J Therm Sci 135:533–545. https://doi.org/10.1016/j.ijthermalsci.2018.09.039
Ge Q, Ciuffo B, Menendez M (2014) Combining screening and metamodel-based methods: an efficient sequential approach for the sensitivity analysis of model outputs. Reliab Eng Syst Saf 134:334–344. https://doi.org/10.1016/j.ress.2014.08.009
Gu C (2002) Smoothing spline ANOVA models. Springer-Verlag, New York
Haykin S (1999) Neural networks - a comprehensive foundation. Pearson Education, Hamilton
He X, Zheng X (2016) Performance improvement of transonic centrifugal compressors by optimization of complex three-dimensional features. J Aerosp Eng. https://doi.org/10.1177/0954410016673395
Ibaraki S, Matsuo T, Kuma H et al (2002) Aerodynamics of a transonic centrifugal compressor impeller. In: Turbo Expo. ASME, Amsterdam, pp 1–8
Javed A, Pecnik R, Van Buijtenen JP (2016) Optimization of a centrifugal compressor impeller for robustness to manufacturing uncertainties. J Eng Gas Turbines Power 138:1–11. https://doi.org/10.1115/1.4033185
Jensen HA, Mayorga F, Papadimitriou C (2015) Reliability sensitivity analysis of stochastic finite element models. Comput Methods Appl Mech Eng 296:327–351. https://doi.org/10.1016/j.cma.2015.08.007
Kim YJ, Gu C (2004) Smoothing spline Gaussian regression: more scalable computation via efficient approximation. J R Stat Soc 66:337–356. https://doi.org/10.1046/j.1369-7412.2003.05316.x
Kim JH, Choi JH, Kim KY (2009) Design optimization of a centrifugal compressor impeller using radial basis neural network method. Proceedings of ASME Turbo Expo 2009: Power for Land, Sea and Air, Orlando, Florida
Kleijnen JPC (2009) Sensitivity analysis of simulation models. Center Discussion Paper Series No. 2009-11. https://doi.org/10.2139/ssrn.1340449
Knopp T, Alrutz T, Schwamborn D (2006) A grid and flow adaptive wall-function method for RANS turbulence modelling. J Comput Phys 220:19–40. https://doi.org/10.1016/j.jcp.2006.05.003
Kulkarni S, Beach TA, Skoch GJ (2013) Computational study of the CC3 impeller and vaneless diffuser experiment. In: 49th AIAA/ASME/SAE/ASEE Joint Propulsion Conference. American Institute of Aeronautics and Astronautics, pp 1–12
Li X, Zhao Y, Liu Z (2019) A novel global optimization algorithm and data-mining methods for turbomachinery design. Struct Multidiscip Optim 60:581–612. https://doi.org/10.1007/s00158-019-02227-5
Marconcini M, Rubechini F, Arnone A, Ibaraki S (2008) Numerical investigation of a transonic centrifugal compressor. J Turbomach 130:1–9. https://doi.org/10.1115/1.2752186
McKay MD, Beckman RJ, Conover WJ (1979) Comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21:239–245. https://doi.org/10.1080/00401706.1979.10489755
Menter FR (1994) Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J 32:1598–1605. https://doi.org/10.2514/3.12149
Menter FR (2009) Review of the shearstress transport turbulence model experience from an industrial perspective. International Journal of Computational Fluid Dynamics 23(4):305–316. https://doi.org/10.1080/10618560902773387
Monje B, Sánchez D, Savill M, et al (2014) A design strategy for supercritical CO2 compressors. In: ASME Turbo Expo 2014. ASME, Dusseldorf
Morris MD (1991) Factorial sampling plans for preliminary computational experiments. Technometrics 33:161–174. https://doi.org/10.1177/001872086700900503
Rasmussen CE, Williams CKI (2006) Gaussian processes for machine learning. The MIT Press, Massachusetts Institute of Technology
Ratto M, Pagano A (2010) Using recursive algorithms for the efficient identification of smoothing spline ANOVA models. Adv Stat Anal 94:367–388. https://doi.org/10.1007/s10182-010-0148-8
Rigoni E (2007) Technical report of radial basis functions response surfaces. ESTECO, Italy
Rigoni E (2014) Technical report of stepwise regression RSM. ESTECO, Italy
Rigoni E, Ricco L (2011) Technical report of smoothing spline ANOVA for variable screening. ESTECO, Italy
Robinson C, Casey M, Hutchinson B, Steed R (2012) Impeller-diffuser interaction in centrifugal compressors. In: Turbo Expo. ASME, Copenhagen, pp 1–11
Saltelli A, Ratto M, Andres T et al (2008) Global sensitivity analysis. The Primer. John Wiley & Sons Ltd, Chichester
Salviano LO, Dezan DJ, Yanagihara JI (2015) Optimization of winglet-type vortex generator positions and angles in plate-fin compact heat exchanger: response surface methodology and direct optimization. Int J Heat Mass Transf 82:373–387. https://doi.org/10.1016/j.ijheatmasstransfer.2014.10.072
Vanrolleghem PA, Mannina G, Cosenza A, Neumann MB (2015) Global sensitivity analysis for urban water quality modelling: terminology, convergence and comparison of different methods. J Hydrol 522:339–352. https://doi.org/10.1016/j.jhydrol.2014.12.056
Villa-Vialaneix N, Follador M, Ratto M, Leip A (2012) A comparison of eight metamodeling techniques for the simulation of N2O fluxes and N leaching from corn crops. Environ Model Softw 34:51–66. https://doi.org/10.1016/j.envsoft.2011.05.003
Wang XD, Hirsch C, Kang S, Lacor C (2011) Multi-objective optimization of turbomachinery using improved NSGA-II and approximation model. Comput Methods Appl Mech Eng 200:883–895. https://doi.org/10.1016/j.cma.2010.11.014
Xu L, Lu Z, Li L, Shi Y (2019) Sensitivity analysis method for model with correlated inputs and multivariate output and its application to aircraft structure. Comput Methods Appl Mech Eng 355:373–404. https://doi.org/10.1016/j.cma.2019.06.015
Acknowledgements
This work was supported by the National Agency of Petroleum, Natural Gas and Biofuels (ANP) and Shell Brazil Ltda., through the Investment in Research, Development and Innovation Clause, contained in contracts for Exploration, Development, and Production of Oil and Natural Gas.
Code availability (software)
ANSYS software used in the present work is licensed for Sao Paulo State University for Customer number #1068625. ModeFrontier codes used in the present work are licensed for Sao Paulo State University for Customer ID: F44D3080FAB4.
Funding
Jurandir Itizo Yanagihara would like to acknowledge CNPq (National Council for Scientific and Technological Development - Brazil) for research grant 306364/2020-4.
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The quasi-optimal sampling and elementary effects methods codes were implemented in software R and are available as supplementary material. The SS-ANOVA method and response surface training methods are available in software ModeFRONTIER.
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Salviano, L.O., Gasparin, E.E., Mattos, V.C.N. et al. Sensitivity analysis and optimization of a CO2 centrifugal compressor impeller with a vaneless diffuser. Struct Multidisc Optim 64, 1607–1627 (2021). https://doi.org/10.1007/s00158-021-02914-2
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DOI: https://doi.org/10.1007/s00158-021-02914-2