skip to main content
research-article

Simulation of cavitating fluid–Structure interaction using SPH–FE method

Published: 01 July 2020 Publication History

Abstract

In the present paper, a modified version of SPH–FE is proposed to study the cavitating fluid interaction with the convergent–divergent nozzle. The additional terms of mass/momentum transfer, surface tension and pressure based phase change are added to the standard SPH equations to track the growth, convection and collapse of the cavitation phenomenon. Due to using the particle-based method for the fluid, no transitional phase is defined and the certain particle phase is determined by the absolute pressure value in comparison with vapor pressure. The comparison of the results of modified SPH with those of finite volume as a grid-based method shows that the cavitating region can be accurately modeled in the convergent–divergent nozzle. Then, the interaction of cavitating fluid flow–nozzle wall is simulated by the improved SPH–FE algorithm for the different types of steel where the good agreement is obtained in comparison with the other similar numerical methods. Also, it is concluded that considering cavitation in the fluid flow can generally change the nozzle behavior slightly and increase the stress values inside its body.

References

[1]
Adami S., Hu X.Y., Adams N.A., A new surface-tension formulation for multi-phase SPH using a reproducing divergence approximation, J. Comput. Phys. 229 (13) (2010) 5011–5021.
[2]
Ahuja V., Hosangadi A., Arunajatesan S., Simulations of cavitating flows using hybrid unstructured meshes, J. Fluids Eng. 123 (2) (2001) 331–340.
[3]
Arndt R.E., Cavitation in fluid machinery and hydraulic structures, Annu. Rev. Fluid Mech. 13 (1) (1981) 273–326.
[4]
Attaway S.W., Heinstein M.W., Swegle J.W., Coupling of smooth particle hydrodynamics with the finite element method, Nucl. Eng. Des. 150 (2–3) (1994) 199–205.
[5]
Batchelor G.K., An Introduction to Fluid Dynamics, Cambridge university press, 2000.
[6]
Blessing M., König G., Krüger C., Michels U., Schwarz V., Analysis of flow and cavitation phenomena in diesel injection nozzles and its effects on spray and mixture formation, SAE Trans. (2003) 1694–1706.
[7]
Canelas R.B., Crespo A.J., Domínguez J.M., Ferreira R.M., Gómez-Gesteira M., SPH–DCDEM model for arbitrary geometries in free surface solid–fluid flows, Comput. Phys. Comm. 202 (2016) 131–140.
[8]
Cleary P.W., Monaghan J.J., Conduction modelling using smoothed particle hydrodynamics, J. Comput. Phys. 148 (1) (1999) 227–264.
[9]
Colagrossi A., Landrini M., Numerical simulation of interfacial flows by smoothed particle hydrodynamics, J. Comput. Phys. 191 (2) (2003) 448–475.
[10]
Cummins S.J., Rudman M., An SPH projection method, J. Comput. Phys. 152 (2) (1999) 584–607.
[11]
Das A.K., Das P.K., Modeling of liquid–vapor phase change using smoothed particle hydrodynamics, J. Comput. Phys. 303 (2015) 125–145.
[12]
De Vuyst T., Vignjevic R., Campbell J.C., Coupling between meshless and finite element methods, Int. J. Impact Eng. 31 (8) (2005) 1054–1064.
[13]
Deshpande M., Feng J., Merkle C.L., Cavity flow predictions based on the Euler equations, J. Fluids Eng. 116 (1) (1994) 36–44.
[14]
Deshpande M., Feng J., Merkle C.L., Numerical modeling of the thermodynamic effects of cavitation, J. Fluids Eng. 119 (2) (1997) 420–427.
[15]
Donea J., Giuliani S., Halleux J.P., An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid–structure interactions, Comput. Methods Appl. Mech. Engrg. 33 (1–3) (1982) 689–723.
[16]
Dular M., Bachert R., Stoffel B., Širok B., Experimental evaluation of numerical simulation of cavitating flow around hydrofoil, Eur. J. Mech. B Fluids 24 (4) (2005) 522–538.
[17]
Federico I., Marrone S., Colagrossi A., Aristodemo F., Antuono M., Simulating 2D open-channel flows through an SPH model, Eur. J. Mech. B Fluids 34 (2012) 35–46.
[18]
Fourey G., Oger G., Le Touzé D., Alessandrini B., Violent fluid–structure interaction simulations using a coupled SPH/FEM method, in: IOP Conference Series: Materials Science and Engineering, vol. 10(1), IOP Publishing, 2010, 012041.
[19]
Gingold R.A., Monaghan J.J., Smoothed particle hydrodynamics: theory and application to non-spherical stars, Mon. Not. R. Astron. Soc. 181 (3) (1977) 375–389.
[20]
Gröbelbauer H.P., Fanneløp T.K., Britter R.E., The propagation of intrusion fronts of high density ratios, J. Fluid Mech. 250 (1993) 669–687.
[21]
Groenenboom P.H., Cartwright B.K., Hydrodynamics and fluid–structure interaction by coupled SPH-FE method, J. Hydraul. Res. 48 (S1) (2010) 61–73.
[22]
Hejranfar K., Ezzatneshan E., Fattah-Hesari K., A comparative study of two cavitation modeling strategies for simulation of inviscid cavitating flows, Ocean Eng. 108 (2015) 257–275.
[23]
Hou T.Y., Shi Z., An efficient semi-implicit immersed boundary method for the Navier–Stokes equations, J. Comput. Phys. 227 (20) (2008) 8968–8991.
[24]
Hou G., Wang J., Layton A., Numerical methods for fluid–structure interaction—a review, Commun. Comput. Phys. 12 (2) (2012) 337–377.
[25]
Hron J., Turek S., A monolithic FEM/multigrid solver for an ALE formulation of fluid–structure interaction with applications in biomechanics, in: Fluid–Structure Interaction, 2006, pp. 146–170.
[26]
Hu D., Long T., Xiao Y., Han X., Gu Y., Fluid–structure interaction analysis by coupled FE–SPH model based on a novel searching algorithm, Comput. Methods Appl. Mech. Engrg. 276 (2014) 266–286.
[27]
Johnson G.R., Linking of Lagrangian particle methods to standard finite element methods for high velocity impact computations, Nucl. Eng. Des. 150 (2–3) (1994) 265–274.
[28]
Kalateh F., Attarnejad R., A new cavitation simulation method: dam-reservoir systems, Int. J. Comput. Methods Eng. Sci. Mech. 13 (3) (2012) 161–183.
[29]
Kalateh F., Koosheh A., Comparing of loose and strong finite element partitioned coupling methods of acoustic fluid–structure interaction: concrete dam-reservoir system, KSCE J. Civ. Eng. 21 (3) (2017) 807–817.
[30]
Kalateh F., Koosheh A., Application of SPH-FE method for fluid–structure interaction using immersed boundary method, Eng. Comput. 35 (8) (2018) 2802–2824.
[31]
Kalateh F., Koosheh A., Finite element analysis of flexible structure and cavitating nonlinear acoustic fluid interaction under shock wave loading, Int. J. Nonlinear Sci. Numer. Simul. 19 (5) (2018) 459–473.
[32]
Khorasanizade S., Sousa J.M.M., An innovative open boundary treatment for incompressible SPH, Internat. J. Numer. Methods Fluids 80 (3) (2016) 161–180.
[33]
S. Khorasanizade, J.M.M. Sousa, J.F. Pinto, On the use of a time-dependent driving force in SPH simulations, in: Proceedings of 7th International SPHERIC Workshop, 2012.
[34]
Kim J.H., Nishida K., Hiroyasu H., Characteristics of the internal flow in a diesel injection nozzle, Int. J. Fluid Mech. Res. 24 (1–3) (1997).
[35]
Kinnas S.A., Fine N.E., A numerical nonlinear analysis of the flow around two-and three-dimensional partially cavitating hydrofoils, J. Fluid Mech. 254 (1993) 151–181.
[36]
Kunz R.F., Boger D.A., Stinebring D.R., Chyczewski T.S., Lindau J.W., Gibeling H.J., et al., A preconditioned Navier–Stokes method for two-phase flows with application to cavitation prediction, Comput. & Fluids 29 (8) (2000) 849–875.
[37]
Liang C., Huang J., Shi W., A new treatment for boundary of laminar flow inlet or outlet in SPH, J. Softw. Eng. 8 (2014) 321–327.
[38]
CRC Handbook of Chemistry and Physics, vol. 85, CRC press, 2004.
[39]
Long T., Hu D., Wan D., Zhuang C., Yang G., An arbitrary boundary with ghost particles incorporated in coupled FEM–SPH model for FSI problems, J. Comput. Phys. 350 (2017) 166–183.
[40]
Long T., Hu D., Yang G., Wan D., A particle-element contact algorithm incorporated into the coupling methods of FEM-ISPH and FEM-WCSPH for FSI problems, Ocean Eng. 123 (2016) 154–163.
[41]
Lucy L.B., A numerical approach to the testing of the fission hypothesis, Astron. J. 82 (1977) 1013–1024.
[42]
May R.W.P., Cavitation in hydraulic structures: Occurrence and prevention, 1987.
[43]
Mikola R.G., Sitar N., Next generation discontinuous rock mass models: 3-D and rock-fluid interaction, in: Frontiers of Discontinuous Numerical Methods and Practical Simulations in Engineering and Disaster Prevention, 2013, pp. 81–90.
[44]
Monaghan J.J., Simulating free surface flows with SPH, J. Comput. Phys. 110 (2) (1994) 399–406.
[45]
Monaghan J.J., Smoothed particle hydrodynamics, Rep. Prog. Phys. 68 (8) (2005) p. 1703.
[46]
Monaghan J.J., Kocharyan A., SPH Simulation of multi-phase flow, Comput. Phys. Comm. 87 (1–2) (1995) 225–235.
[47]
Monteleone A., Monteforte M., Napoli E., Inflow/outflow pressure boundary conditions for smoothed particle hydrodynamics simulations of incompressible flows, Comput. & Fluids 159 (2017) 9–22.
[48]
Mori Y., Peskin C.S., Implicit second-order immersed boundary methods with boundary mass, Comput. Methods Appl. Mech. Engrg. 197 (25) (2008) 2049–2067.
[49]
Morris J.P., Simulating surface tension with smoothed particle hydrodynamics, Int. J. Numer. Methods Fluids 33 (3) (2000) 333–353.
[50]
Nugent S., Posch H.A., Liquid drops and surface tension with smoothed particle applied mechanics, Phys. Rev. E 62 (4) (2000) 4968.
[51]
Ozbulut M., Yildiz M., Goren O., A numerical investigation into the correction algorithms for SPH method in modeling violent free surface flows, Int. J. Mech. Sci. 79 (2014) 56–65.
[52]
Peng X., Yu P., Chen G., Xia M., Zhang Y., Development of a coupled DDA–SPH method and its application to dynamic simulation of landslides involving solid–fluid interaction, Rock Mech. Rock Eng. (2019) 1–19.
[53]
Peskin C.S., Flow patterns around heart valves: a numerical method, J. Comput. Phys. 10 (2) (1972) 252–271.
[54]
Peskin C.S., Numerical analysis of blood flow in the heart, J. Comput. Phys. 25 (3) (1977) 220–252.
[55]
Ren B., Jin Z., Gao R., Wang Y.X., Xu Z.L., SPH-DEM modeling of the hydraulic stability of 2D blocks on a slope, J. Waterw. Port Coast. Ocean Eng. 140 (6) (2013).
[56]
Ritchie B.W., Thomas P.A., Multiphase smoothed-particle hydrodynamics, Mon. Not. R. Astron. Soc. 323 (3) (2001) 743–756.
[57]
Robinson M., Ramaioli M., Luding S., Fluid–particle flow simulations using two-way-coupled mesoscale SPH–DEM and validation, Int. J. Multiph. Flow 59 (2014) 121–134.
[58]
Sato K., Shimojo S., Detailed observations on a starting mechanism for shedding of cavitation cloud, 2003.
[59]
Shi Y., Pan G., Huang Q., Du X., Numerical simulation of cavitation characteristics for pump-jet propeller, J. Phys. Conf. Ser. 640 (1) (2015).
[60]
Srinivasan V., Salazar A.J., Saito K., Numerical simulation of cavitation dynamics using a cavitation-induced-momentum-defect (CIMD) correction approach, Appl. Math. Model. 33 (3) (2009) 1529–1559.
[61]
Stockie J.M., Wetton B.T., Stability analysis for the immersed fiber problem, SIAM J. Appl. Math. 55 (6) (1995) 1577–1591.
[62]
Stockie J.M., Wetton B.R., Analysis of stiffness in the immersed boundary method and implications for time-stepping schemes, J. Comput. Phys. 154 (1) (1999) 41–64.
[63]
Takashi N., Hughes T.J., An arbitrary Lagrangian-Eulerian finite element method for interaction of fluid and a rigid body, Comput. Methods Appl. Mech. Engrg. 95 (1) (1992) 115–138.
[64]
Trulev A.V., Trulev Y.V., Theoretical fundamentals of cavitation in turbomachines, Chem. Pet. Eng. 33 (2) (1997) 189–195.
[65]
Tu C., Peskin C.S., Stability and instability in the computation of flows with moving immersed boundaries: a comparison of three methods, SIAM J. Sci. Stat. Comput. 13 (6) (1992) 1361–1376.
[66]
Valizadeh A., Shafieefar M., Monaghan J.J., Neyshaboori S.A.A.S., Modeling two-phase flows using SPH method, J. Appl. Sci. 8 (21) (2008) 3817–3826.
[67]
Venkateswaran S., Lindau J.W., Kunz R.F., Merkle C.L., Computation of multiphase mixture flows with compressibility effects, J. Comput. Phys. 180 (1) (2002) 54–77.
[68]
Ventikos Y., Tzabiras G., A numerical method for the simulation of steady and unsteady cavitating flows, Comput. & Fluids 29 (1) (2000) 63–88.
[69]
Wang W., Chen G., Zhang Y., Zheng L., Zhang H., Dynamic simulation of landslide dam behavior considering kinematic characteristics using a coupled DDA-SPH method, Eng. Anal. Bound. Elem. 80 (2017) 172–183.
[70]
Xu Y., Yu C., Liu F., Liu Q., A coupled NMM-SPH method for fluid–structure interaction problems, Appl. Math. Model. (2019).
[71]
Yang X.F., Liu M.B., Improvement on stress instability in smoothed particle hydrodynamics, Acta Phys. Sin. 61 (2012).
[72]
Yuan W., Sauer J., Schnerr G.H., Modeling and computation of unsteady cavitation flows in injection nozzles, Mec. Ind. 2 (5) (2001) 383–394.
[73]
Zhang G., Wang S., Sui Z., Sun L., Zhang Z., Zong Z., Coupling of SPH with smoothed point interpolation method for violent fluid–structure interaction problems, Eng. Anal. Bound. Elem. 103 (2019) 1–10.
[74]
Zienkiewicz O.C., Paul D.K., Hinton E., Cavitation in fluid–structure response (with particular reference to dams under earthquake loading), Earthq. Eng. Struct. Dyn. 11 (4) (1983) 463–481.

Cited By

View all

Index Terms

  1. Simulation of cavitating fluid–Structure interaction using SPH–FE method
        Index terms have been assigned to the content through auto-classification.

        Recommendations

        Comments

        Information & Contributors

        Information

        Published In

        cover image Mathematics and Computers in Simulation
        Mathematics and Computers in Simulation  Volume 173, Issue C
        Jul 2020
        120 pages

        Publisher

        Elsevier Science Publishers B. V.

        Netherlands

        Publication History

        Published: 01 July 2020

        Author Tags

        1. Cavitating flow
        2. Fluid–structure interaction
        3. Smoothed particle hydrodynamics (SPH)
        4. Finite element method (FEM)
        5. Immersed boundary
        6. Multi-phase fluid
        7. Phase change

        Qualifiers

        • Research-article

        Contributors

        Other Metrics

        Bibliometrics & Citations

        Bibliometrics

        Article Metrics

        • Downloads (Last 12 months)0
        • Downloads (Last 6 weeks)0
        Reflects downloads up to 08 Feb 2025

        Other Metrics

        Citations

        Cited By

        View all

        View Options

        View options

        Figures

        Tables

        Media

        Share

        Share

        Share this Publication link

        Share on social media