Numerical Evaluation of Cavitation Erosion Intensity around NACA0015 Hydrofoil Based on Eulerian-Lagrangian Approach

Document Type : Article

Authors

D‌e‌p‌t. o‌f M‌e‌c‌h‌a‌n‌i‌c‌a‌l E‌n‌g‌i‌n‌e‌e‌r‌i‌n‌g S‌h‌a‌h‌i‌d R‌a‌j‌a‌e‌e T‌e‌a‌c‌h‌e‌r T‌r‌a‌i‌n‌i‌n‌g U‌n‌i‌v‌e‌r‌s‌i‌t‌y

Abstract

In this study, to investigate the intensity of cavitation-induced erosion, the bubble behavior around the NACA0015 2D hydrofoil was simulated from the Eulerian-Lagrangian perspective. Macroscopic examination of the cavitation flow was determined by a homogeneous mixture model (Eulerian method) and the trajectory of bubble motion based on the applied forces using Newton's second law and the development of numerical code (Lagrange method). One way to reduce the computational cost of the Lagrangian perspective is to use the Discrete Phase Model (DPM). In this method, the fluid is considered as a continuous environment, while the discrete phase is solved by tracing a large number of particles in the calculated flow field. The behavior of the bubble arises from the pressure gradient caused by the flow. Bubble oscillations were obtained from the modified Rayleigh-Plesset-Keller-Herring equation. This equation considers the compressible behavior of the bubble as the bubble collapse velocity approaches the speed of sound as well as the slip velocity between the bubble and the moving liquid. To pair the obtained results and solve them, the fourth-order Runge-Kutta method with variable time step was used, which increased the data solution speed up to 10 times. From the Keller& Kolodner relationship, a pressure wave emitted from the collapse of a spherical bubble, and the model of Soyama et al., the total energy of the cavitation-induced shocks, which is the result of the accumulation of all the shocks on each other, is obtained. The actual effects of flow for cavitation inception and erosion were investigated. Different cavitation numbers were used for cavitation inception with different radii. The results showed that the nucleation process occured in the cavitation inception numbers and the cavitation inception for flow with larger nuclei was visible better. As the cavitation number decreases, the bubble growth rate increases and as the bubble radius increases, the erosion intensity increases. At high cavitation numbers, the bubble oscillates around its initial radius; however, at the lowest cavitation number in this article, the number , we see an increase of nearly times the radius compared to the original radius. The erosion power of bubbles with an initial radius of is approximately times that of the erosion power of bubbles with an initial radius of and about times that of the initial bubbles of . The probable site of erosion is at the end of cavity at the hydrofoil level. As the bubbles increase in size, the number of collapses and their strength increase, and the dispersion of the distribution at the hydrofoil surface increases. The results were compared with other published works and had acceptable accuracy.

Keywords


1. Chahine K.K.G. , France, J.P. and Karimi, A. , \Advanced experimental and numerical techniques for cavitation erosion prediction", Fluid Mechanics and Its Applications, pp. 3-4, Springer Dordrecht Heidelberg New York London (2014). ISBN:978-94-017-8538-9 2. Franc, J.-P. and Michel, J.-M. \ Fundamentals of cavitation, Springer Science & Business Media" (2006). DOI:10.1007/1-4020-2233-6. 3. Knapp, R. Cavitation, New York (1970). 4. Kato, H., Konno, A., Maeda, M. and et al. \Possibility of quantitative prediction of cavitation erosion without model test", J. Fluids Eng. 118, pp. 582{588 (1996). DOI:10.1115/1.2817798. 5. Sagar, H. J. and Ould el Moctar.\Numerical simulation of aLaser-induced cavitation bubble near a solid boundary considering phase change", Sh.Technol. Res., 65(3), pp. 163-179 (2018). DOI: 10.1080/09377255.2018. 1473235. 6. Ochiai, N. \Numerical prediction of cavitation erosion in cavitating ow", Proceedings of the 7th International Symposium on Cavitation CAV2009-Paper. 67 (2009). 7. KazukiMaeda and TimColonius. \Eulerian lagrangian method for simulation of cloud cavitation", Division of Engineering and Applied Science, California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125, US (2018). DOI:org/10.1016/j.jcp.2018.05.02. 8. Rasthofer, U., Wermelinger, F., Karnakov P. and et al. \A computational study of the collapse of a cloud with 120500 Gas Bubbles in a Liquid" (2018). 9. Paquette, Yves. ,Fivel, M.C. ,Ghigliotti, G. ,Johnsen, E. and et al. \Fluid-Structure interaction in cavitation erosion", 10th International Symposium on Cavitation (CAV2018) , Baltimore, United States.(May 2018). (hal- 01692512). 10. Schnerr, G. H. and Sauer, J. \Physical and numerical modeling of unsteady cavitation dynamics," Fourth International Conference on Multiphase Flow, New Orleans, USA, pp. 1-12 (2001). 11. Plesset, M. S. and Prosperetti, A. \Bubble dynamics and cavitation," Annu. Rev. Fluid Mech., 9(1), pp. 145-185 (1977). DOI: 10.1146/annurev. .09.010177.001045. 12. Prosperetti, A. and Lezzi, A. \Bubble dynamics in a compressible liquid," J. Fluid Mech., 168, pp. 457-478 (1986). DOI: 10.1017/S0022112086000460. 13. Maxey, M. R. \Equation of motion for a small rigid sphere in a nonuniform ow," Phys. Fluids, 26(4), pp. 883 (1983). DOI: 10.1063/1.864230. 14. Haberman, W. L. and Morton, R. K. \An experimental investigation of the drag and shape of air bubbles rising in various liquids," Navy Dep. David Taylor Model Basin Washingt. DC, pp. 1-55 (1953). DOI: 10.5962/bhl.title.47521. 15. Hosseininejad S.S. \A CFD modeling of cavitation for ne particle otation", A thesis submitted in partial ful- llment of the requirements for the degree of doctor of philosophy in chemical engineering, pp. 83-85 (2016). 27 5. Sagar, H. J. and Ould el Moctar.\Numerical simulation of aLaser-induced cavitation bubble near a solid boundary considering phase change", Sh.Technol. Res., 65(3), pp. 163-179 (2018). DOI: 10.1080/09377255.2018. 1473235. """|}=R?=@L V}=UQi COW |OOa |UQQ@ 16. Keller, J.B. and Kolodner, I.I. \ Damping of underwater explosion bubble oscillations", J. Appl. Phys 27, pp.1152-1161 (1956). DOI:10.1063/1.1722221. 17. Soyama, H., Kumano, H., and Saka, M. \A new parameter to predict cavitation erosion," http//resolver. caltech. edu/cav2001 Sess. 002, pp. 1-8 (2001). 18. Van Rijsbergen, M. and Boorsma, A. \High speed video observations and acoustic impact measurements on a NACA0015 foil", Proceedings of the 8th International Symposium on Cavitation CAV2012 | Submission, 280, Singapore(August 13-16 2012). 19. Mahdi, M., Shams, M. and Ebrahimi, R. \Numerical simulation of scaling e ect on bubble dynamics in a turbulent ow around a hydrofoil", JAST, 3(2), pp. 67-75 (2006). 20. Ochiai, N., Iga, Y., Nohmi, M. and Ikohagi, T. \ Numerical prediction of cavitation erosion intensity in cavitating ows around a Clark Y 11.7% hydrofoil, J. Fluid Sci. Technol, 5, pp. 416-431 (2010). DOI:10.1299/jfst.5.416 (2010). 21. Bergeles, G., Li, J., Wang, L. and et al. \ An erosion aggressiveness index (EAI) based on pressure load estimation due to bubble collapse in cavitating ows within the RANS solvers" SAE Int. J. Engines, 8 pp. 2015-24- 2465 (2015). DOI:10.4271/2015-24-2465. 22. Knapp, R.T. \Recent investigations of the mechanics of cavitation and cavitation damage", Trans. ASME, 77, pp. 1045-1054 (1955). DOI:10.1016/0043-1648(58)90220- 5. 23. Ochiai, N., Iga, Y., Nohmi, M. and et al. \Study of quantitative numerical prediction of cavitation erosionin cavitating ow", Journal of Fluids Engineering., 135(1):(011302-1) (2013). DOI:10.1115/1.4023072.