Abstract
As a high-dimensional complex nonlinear dynamic system, the analysis of the essence of flow has always been a difficult problem, especially in the flow including phase change. In recent years, it has become a feasible method to reduce the dimension of flow structure by reduced-order modeling (ROM) methods. In this paper, through the cavitation numerical simulation of NACA0015 hydrofoil, two ROM methods are used to reduce and restore three different cavitation respectively-proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD). The applicability of two methods in cavitation is discussed and reasons are analyzed. The results show that for stable cavitation, POD, DMD methods can accurately restore the flow field of a few modes with high energy. For unstable cavitation, only POD method can restore real flow field well. This situation is mainly due to the fact that POD, DMD method are applicable to different energy ratios, and different main mode selection criterion of DMD will lead to different main mode. ROM can greatly simplify the complexity of flow. Selecting a reasonable ROM can improve the accuracy of a small amount of database, and provide a basis for intelligent prediction of flow analysis.
Similar content being viewed by others
References
Luo X. W., Ji B., Tsujimoto Y. A review of cavitation in hydraulic machinery [J]. Journal of Hydrodynamics, 2016, 28(3): 335–358.
Wang F. J. Analysis method of flow in pumps and pumping stations [M]. Beijing, China: China Water & Power Press, 2020 (in Chinese).
Sreedhar B. K., Albert S. K., Pandit A. B. Cavitation damage: Theory and measurements–A review [J]. Wear, 2017, 372: 177–196.
Malekshah E. H., Wróblewski W., Bochon K. et al. Experimental analysis on dynamic/morphological quality of cavitation induced by different air injection rates and sites [J]. Physics of Fluids, 2023, 35(1): 013335.
Simanto R. I. A., Hong J. W., Kim K. S. et al. Experimental investigation on cavitation and induced noise of two-dimensional hydrofoils with leading-edge protuberances [J]. Physics of Fluids, 2023, 34(12): 124115.
Knapp R. T., Daily J. W., Hammitt F. G. Cavitation [M]. New York: McGraw-Hill, 1970.
Ye B., Wang Y., Huang C.. Numerical study of the pressure wave-induced shedding mechanism in the cavitating flow around an axisymmetric projectile via a compressible multiphase solver [J]. Ocean Engineering, 2019, 187: 106179.
Russell P. S., Barbaca L., Venning J. A. et al. A. Influence of nucleation on cavitation inception in tip leakage flows [J]. Physics of Fluids, 2023, 35(1): 013341.
Huai W. X., Zhang J., Katul G. G. et al. The structure of turbulent flow through submerged flexible vegetation [J]. Journal of Hydrodynamics, 2019, 31(2): 274–292.
Li D. Y., Chang H., Zuo Z. G. et al. The effect of humpback whalelike leading-edge protuberances number on stall control mechanism of NACA 634-021 airfoil [J]. Large Electric Machine and Hydraulic Turbine, 2020, 4: 1–9 (in Chinese).
Ji B., Luo X., Arndt R. E. A. et al. Large eddy simulation and theoretical investigations of the transient cavitating vortical flow structure around a NACA66 hydrofoil [J]. International Journal of Multiphase Flow, 2015, 68: 121–134.
Ji B., Luo X., Wu Y. et al. Numerical analysis of unsteady cavitating turbulent flow and shedding horse-shoe vortex structure around a twisted hydrofoil [J]. International Journal of Multiphase Flow, 2013, 51: 33–43.
Lei T. T., Cheng H. Y., Ji B. et al. Numerical assessment of the erosion risk for cavitating twisted hydrofoil by three methods [J]. Journal of Hydrodynamics, 2021, 33(4): 698–711.
Cheng H. Y., Bai X. R., Long X. P. et al. Large eddy simulation of the tip-leakage cavitating flow with an insight on how cavitation influences vorticity and turbulence [J]. Applied Mathematical Modelling, 2020, 77: 788–809.
Taira K., Brunton S. L., Dawson S. T. M. et. al. Modal analysis of fluid flows: An overview [J]. AIAA Journal, 2017, 55(12): 4013–4041.
Taira K., Hemati M. S., Brunton S. L. et. al. Modal analysis of fluid flows: Applications and outlook [J]. AIAA Journal, 2020, 58(3): 998–1022.
Peng C., Tian S. C., Li G. S. Determination of the shedding frequency of cavitation cloud in a submerged cavitation jet based on high-speed photography images [J]. Journal of Hydrodynamics, 2021, 33(1): 127–139.
Kutz J. N., Brunton S. L., Brunton B. W. et al. Dynamic mode decomposition: Data-driven modeling of complex systems [M]. Philadelphia, USA: Society for Industrial and Applied Mathematics, 2016.
Wu Y., Tao R., Yao Z. et al. Application and comparison of dynamic mode decomposition methods in the tip leakage cavitation of a hydrofoil case [J]. Physics of Fluids, 2023, 35(2): 023326.
Li X., Liu Y., Kou J. et al. Reduced-order thrust modeling for an efficiently flapping airfoil using system identification method [J]. Journal of Fluids and Structures, 2017, 69: 137–153.
Kou J., Zhang W., Liu Y. et al. The lowest Reynolds number of vortex-induced vibrations [J]. Physics of Fluids, 2017, 29(4): 041701.
Yin T., Giorgio P., Pei J. et al. Numerical investigation of unsteady cavitation around a twisted hydrofoil [J]. International Journal of Multiphase Flow, 2021, 135: 103506.
Liu Y., Long J., Wu Q. et al. Data-driven modal decomposition of transient cavitating flow [J]. Physics of Fluids, 2021, 33(11): 113316.
Wu J., Deijlen L., Bhatt A. et al. Cavitation dynamics and vortex shedding in the wake of a bluff body [J]. Journal of Mechanics, 2021, 917: A26.
Giorgi M. G. D., Fontanarosa D., Ficarella A. Characterization of unsteady cavitating flow regimes around a hydrofoil, based on an extended Schnerr’Sauer model coupled with a nucleation model [J]. International Journal of Multiphase Flow, 2019, 115: 158–180.
Liu M., Tan L., Cao S. Dynamic mode decomposition of cavitating flow around ALE 15 hydrofoil [J]. Renewable Energy, 2019, 139: 214–227.
Angelo C., Cristina B., Emilio R. et al. Thermal cavitation experiments on a NACA 0015 hydrofoil [J]. Experiments in Fluids, 2006, 128(2): 326–331.
Celik I. B., Ghia U., Roache P. J. et al. Procedure for estimation and reporting of uncertainty due to discretization in CFD applications [J]. Journal of Fluids Engineering, 2008, 130(7): 078001.
Oberkampf W. L., Roy C. J. Verification and validation in scientific computing [M]. Cambridge, UK: Cambridge University Press, 2010.
Wang X. W., Fan Z. Y., Tang Z. Q. et al. Drag reduction and hairpin packets of the turbulent boundary layer over the superhydrophobic-riblets surface [J]. Journal of Hydrodynamics, 2021, 33(3): 621–635.
Kou J., Zhang W. Dynamic mode decomposition with exogenous input for data-driven modeling of unsteady flows [J]. Physics of Fluids, 2019, 31(5): 057106.
Acknowledgement
This work was supported by the Chinese Universities Scientific Fund (Grant No. 2021TC107).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest: The authors declare that they have no conflict of interest.
Ethical approval: This article does not contain any studies with human participants or animals performed by any of the authors.
Informed consent: Informed consent was obtained from all individual participants included in the study.
Additional information
Project supported by the National Natural Science Foundation of China (Grant No. 52079142, 51909131).
Biography: Yan-zhao Wu (1996-), Male, Master
Rights and permissions
About this article
Cite this article
Wu, Yz., Tao, R., Zhu, D. et al. Comparative study of reduced-order modeling method for the cavitating flow over a hydrofoil. J Hydrodyn 35, 679–699 (2023). https://doi.org/10.1007/s42241-023-0046-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s42241-023-0046-7