Abstract
A numerical approach for modelling cavitating flows over moving hydrodynamic surfaces is presented. The operating fluid is modelled as an isothermal homogeneous mixture of water vapor and liquid phases. The flow field is governed by the Navier–Stokes equations along with a transport equation for the vapor volume fraction. The Arbitrary Lagrangian-Eulerian description of the continuum is adopted to handle fluid flow simulations on moving domains. The residual based variational multiscale method is used to model the turbulent flow together with wall modelling implemented by the weak imposition of the no-slip boundary condition. Merkle and Zwart cavitation models are implemented and compared. First, a cavitating flow over a 3D hemispherical fore-body is modeled to perform a detailed comparison between two models. Next, the cavitating flow over the INSEAN E779A marine propeller is modeled and results are compared to available experimental data showing good agreement.
Similar content being viewed by others
References
Burrill LC (1951) Sir Charles Parsons and cavitation. The Institute of Marine Engineers, Transactions, vol LXIII, no 8
Kuiper G (1997) Cavitation research and ship propeller design. Appl Sci Res 58(1–4):33–50
Krella AK, Zakrzewska DE (2018) Cavitation erosion-phenomenon and test rigs. Adv Mater Sci 18(2):15–26
Goldstein S (1929) On the vortex theory of screw propellers. Proc R Soc Lond Ser A Contain Pap Math Phys Charact 123(792):440–465
Schoenherr KE (1939) Propulsion and propellers. Princ Naval Archit 2:148–150
Lerbs HW (1952) Moderately loaded propellers with a finite number of blades and a arbitrary distribution of circulations. Trans SNAME 60:73–123
Eckhardt MK, Morgan WB (1955) A propeller design method. SNAME Trans 63:1955
van Manen JD (1957) Fundamentals of ship resistance and propulsion. Int Shipbuild Progr 4(35):371–391
Lerbs HW (1955) Propeller pitch correction arising from lifting surface effect. Technical report, David Taylor Model Basin Washington DC
Nelson DM (1964) A lifting-surface propeller design method for high-speed computers. Technical report, Naval Ordnance Test Station China Lake CA
Morgan WB, Silovic V, Denny SB (1968) Propeller lifting-surface corrections. Technical report, Hydro and Aerodynamics Lab Lyngby (Denmark) Hydrodynamics Section
Kuiper G (1981) Cavitation inception on ship propeller models. Ph.D. Thesis, Technische Hogeschool Delft
Tulin MP (1953) Steady two-dimensional cavity flows about slender bodies. David W. Taylor Model Basin, Washington DC, USA, Department of the Navy, Research and Development Report 834
Geurst JA, Verbrugh PJ (1959) A note on camber effects of a partially cavitated hydrofoil. Int Shipbuild Progr 6(61):409–414
Geurst JA (1961) Linearized theory of two-dimensional cavity flows. Technical report, Technische Hogeschool Delft
Fabula AG (1962) Thin-airfoil theory applied to hydrofoils with a single finite cavity and arbitrary free-streamline detachment. J Fluid Mech 12(2):227–240
Tulin MP (1963) Supercavitating flows-small perturbation theory. Technical report, Hydronautics Inc Laurel MD
Wade RB (1967) Linearized theory of a partially cavitating plano-convex hydrofoil including the effects of camber and thickness. J Ship Res 11(1):20–27
Kinnas SA (1985) Non-linear corrections to the linear theory for the prediction of the cavitating flow around hydrofoils. Ph.D Thesis, Massachusetts Institute of Technology
Kinnas SA et al (1991) Leading-edge corrections to the linear theory of partially cavitating hydrofoils. J Ship Res 35(01):15–27
Tulin MP, Chun CH (1980) New application of cavity flow theory. In: 13th Symposium on naval hydrodynamics, Tokyo, pp 107–132
Widnall SE et al (1966) Unsteady loads on supercavitating hydrofoils of finite span. J Ship Res 10(02):107–118
Lee C-S (1979) Predicton of steady and unsteady performance of marine propellers with or without cavitation by numerical lifting-surface theory. Ph.D. Thesis, Massachusetts Institute of Technology
Lee C-S (1980) Prediction of the transient cavitation on marine propellers by numerical lifting-surface theory. In: Proceedings of 13th symposium on naval hydrodynamics, pp 41–64
Breslin JP, Kerwin JE (1983) Theoretical and experimental propeller-induced hull pressures arising from intermittent blade cavitation loading and thickness. Technical report, Maritime Technical Information Facility
Kerwin JE (1986) Marine propellers. Annu Rev Fluid Mech 18(1):367–403
Kerwin JE (1961) The solution of propeller lifting surface problems by vortex lattice methods. Technical report, Massachusetts Institute of Technology Cambridge Dept of Naval Architecture and Marine Engineering
Kerwin JE, Lee C-S (1978) Prediction of steady and unsteady marine propeller performance by numerical lifting-surface theory. Technical report, Society of Naval Architects and Marine Engineers
Szantyr JA (1985) A new method for the analysis of unsteady propeller cavitation and hull surface pressures. R Inst Naval Arch Trans 127
Kinnas SA, Fine NE (1989) Theoretical prediction of midchord and face unsteady propeller sheet cavitation. In: International conference on numerical ship hydrodynamics, 5th, pp 685–700
Kinnas SA et al (1992) A general theory for the coupling between thickness and loading for wings and propellers. J Ship Res 36(01):59–68
Kinnas SA, Lee H, Young YL (2003) Modeling of unsteady sheet cavitation on marine propeller blades. Int J Rotat Mach 9(4):263–277
Hess JL, Valarezo WO (1985) Calculation of steady flow about propellers using a surface panel method. J Propul Power 1(6):470–476
Lee J (1987) A potential based panel method for the analysis of marine propellers in steady flow. Ph.D. Thesis, Massachusetts Institute of Technology
Fine NE (1992) Nonlinear analysis of cavitating propellers in nonuniform flow. Ph.D. Thesis, Massachusetts institute of Technology
Kinnas SA, Fine NE (1992) A nonlinear boundary element method for the analysis of unsteady propeller sheet cavitation. In: Proceedings of the 19th symposium on naval hydrodynamics, pp 717–737
Lee H, Kinnas SA, Gu H, Natarajan S (2003). Numerical modeling of rudder sheet cavitation including propeller/rudder interaction and the effects of a tunnel. In: Fifth international symposium on cavitation (CAV 2003) proceedings, pp CAV03–GS–12–005
Young YL, Kinnas SA (2001) A BEM for the prediction of unsteady midchord face and/or back propeller cavitation. J Fluids Eng 123(2):311–319
Lee H, Kinnas SA (2004) Application of a boundary element method in the prediction of unsteady blade sheet and developed tip vortex cavitation on marine propellers. J Ship Res 48(1):15–30
Lee H, Kinnas SA (2005) Unsteady wake alignment for propellers in nonaxisymmetric flows. J Ship Res 49(3):176–190
Salvatore F, Greco L, Calcagni D (2011). Computational analysis of marine propeller performance and cavitation by using an inviscid-flow BEM model. In: Second international symposium on marine propulsors (SMP2011), Hamburg, Germany, pp 72–79
Vaz G, Hally D, Huuva T, Bulten N, Muller P, Becchi P, Herrer J, Whitworth S, Macé R, Korsström A (2015) Cavitating flow calculations for the E779A propeller in open water and behind conditions: code comparison and solution validation. In: Proceedings of the 4th international symposium on marine propulsors (SMP15), Austin, TX, USA, pp 330–345
Perali P, Lloyd T, Vaz G (2016). Comparison of uRANS and BEM-BEM for propeller pressure pulse prediction: E779A propeller in a cavitation tunnel. In: Proceedings of the 19th numerical towing tank symposium, pp 90–95
Vaz G, de Campos J, Bosschers J, de Eça L (2005)Instituto Superior de Ciências do Trabalho e da Empresa. Modelling of sheet cavitation on hydrofoils and marine propellers using boundary element methods
Carlton J (2018) Marine propellers and propulsion. Butterworth-Heinemann
Kubota A, Kato H, Yamaguchi H (1992) A new modelling of cavitating flows: a numerical study of unsteady cavitation on a hydrofoil section. J Fluid Mech 240:59–96
Merkle CL (1998) Computational modelling of the dynamics of sheet cavitation. In: Proceedings of the 3rd international symposium on cavitation, Grenoble, France, 1998, pp 307–313
Kunz RF, Boger DA, Stinebring DR, Chyczewski TS, Lindau JW, Gibeling HJ, Venkateswaran S, Govindan TR (2000) A preconditioned Navier–Stokes method for two-phase flows with application to cavitation prediction. Comput Fluids 29(8):849–875
Schnerr GH, Sauer J (2001) Physical and numerical modeling of unsteady cavitation dynamics. In: Fourth international conference on multiphase flow, vol 1. ICMF New Orleans
Singhal AK, Athavale MM, Li H, Jiang Y (2002) Mathematical basis and validation of the full cavitation model. J Fluids Eng 124(3):617–624
Zwart PJ, Gerber AG, Belamri T , et al (2004) A two-phase flow model for predicting cavitation dynamics. In: Fifth international conference on multiphase flow, Yokohama, Japan, vol 152
Abdel-Maksoud M, SVA P M B (2003). Numerical and experimental study of cavitation behaviour of a propeller. Jahrbuch der Schiffbautechnischen Gesellschaft, pp 35–43
Pope SB (2000) Turbulent flows. Cambridge University Press, Cambridge
Salvatore F, Streckwall H, Van Terwisga T (2009) Propeller cavitation modelling by CFD-results from the VIRTUE 2008 Rome workshop. In: Proceedings of the first international symposium on marine propulsors, Trondheim, Norway, pp 22–24. Citeseer
Salvatore F, Pereira F, Felli M, Calcagni D, Di Felice F (2006) Description of the INSEAN E779A propeller experimental dataset. Technical report, INSEAN Tech. rep. 2006-085
Heinke HJ, Lubke L (2011) The SMP 2011 workshop on cavitation and propeller performance-case 2, propeller open water performance and cavitation behaviour. In: Proceedings of first workshop on cavitation and propeller performance, the second international symposium on marine propulsors, SMP, pp 36–42
Gaggero S, Villa D (2017) Steady cavitating propeller performance by using OpenFOAM, StarCCM+ and a boundary element method. Proc Inst Mech Eng Part M J Eng Maritime Environ 231(2):411–440
Reboud J-L, Stutz B, Coutier O (1998) Two phase flow structure of cavitation: experiment and modeling of unsteady effects. In: 3rd international symposium on cavitation CAV1998, Grenoble, France, vol 26, pp 203–208
Coutier-Delgosha O, Fortes-Patella R, Reboud J-L (2003) Evaluation of the turbulence model influence on the numerical simulations of unsteady cavitation. J Fluids Eng 125(1):38–45
Bensow RE, Bark G (2010) Implicit LES predictions of the cavitating flow on a propeller. J Fluids Eng 132(4)
Lu N-X, Bensow RE, Bark G (2014) Large eddy simulation of cavitation development on highly skewed propellers. J Mar Sci Technol 19(2):197–214
Kurobe Y (1983) Measurement of cavity volume and pressure fluctuations on a model of the training ship “Seiun-Maru” with reference to full scale measurement. Rep Ship Res Inst 20(6)
Yu C, Wang Y, Huang C, Wu X, Du T (2017) Large eddy simulation of unsteady cavitating flow around a highly skewed propeller in nonuniform wake. J Fluids Eng 139(4)
Asnaghi A, Svennberg U, Bensow RE (2018) Numerical and experimental analysis of cavitation inception behaviour for high-skewed low-noise propellers. Appl Ocean Res 79:197–214
Yilmaz N, Atlar M, Khorasanchi M (2019) An improved mesh adaption and refinement approach to cavitation simulation (MARCS) of propellers. Ocean Eng 171:139–150
Hughes TJR, Mazzei L, Jansen KE (2000) Large eddy simulation and the variational multiscale method. Comput Vis Sci 3(1–2):47–59
Bazilevs Y, Calo VM, Cottrell JA, Hughes TJR, Reali A, Scovazzi G (2007a) Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comput Methods Appl Mech Eng 197(1–4):173–201
Calo VM (2004) Residual-based multiscale turbulence modeling: finite volume simulations of bypass transition. Ph.D. Thesis, Stanford University Stanford, CA
Motlagh YG, Ahn HT, Hughes TJR, Calo VM (2013) Simulation of laminar and turbulent concentric pipe flows with the isogeometric variational multiscale method. Comput Fluids 71:146–155
Bazilevs Y, Yan J, De Stadler M, Sarkar S (2014a) Computation of the flow over a sphere at Re= 3700: A comparison of uniform and turbulent inflow conditions. J Appl Mech 81(12)
Akkerman I, Bazilevs Y, Kees CE, Farthing MW (2011) Isogeometric analysis of free-surface flow. J Comput Phys 230:4137–4152
Akkerman I, Bazilevs Y, Benson DJ, Farthing MW, Kees CE (2012a) Free-surface flow and fluid-object interaction modeling with emphasis on ship hydrodynamics. J Appl Mech 79
Akkerman I, Dunaway J, Kvandal J, Spinks J, Bazilevs Y (2012b) Toward free-surface modeling of planing vessels: simulation of the Fridsma hull using ALE-VMS. Comput Mech 50:719–727
Augier B, Yan J, Korobenko A, Czarnowski J, Ketterman G, Bazilevs Y (2015) Experimental and numerical FSI study of compliant hydrofoils. Comput Mech 55:1079–1090. https://doi.org/10.1007/s00466-014-1090-5
Yan J, Augier B, Korobenko A, Czarnowski J, Ketterman G, Bazilevs Y (2016a) FSI modeling of a propulsion system based on compliant hydrofoils in a tandem configuration. Comput Fluids 141:201–211. https://doi.org/10.1016/j.compfluid.2015.07.013
Yan J, Korobenko A, Deng X, Bazilevs Y (2016b) Computational free-surface fluid-structure interaction with application to floating offshore wind turbines. Comput Fluids 141:155–174. https://doi.org/10.1016/j.compfluid.2016.03.008
Yan J, Deng X, Korobenko A, Bazilevs Y (2017) Free-surface flow modeling and simulation of horizontal-axis tidal-stream turbines. Comput Fluids 158:157–166. https://doi.org/10.1016/j.compfluid.2016.06.016
Zhu Q, Yan J (2019) A moving-domain CFD solver in fenics with applications to tidal turbine simulations in turbulent flows. Comput Math Appl. https://doi.org/10.1016/j.camwa.2019.07.034
Bayram AM, Bear C, Bear M, Korobenko A (2020) Performance analysis of two vertical-axis hydrokinetic turbines using variational multiscale method. Comput Fluids. https://doi.org/10.1016/j.compfluid.2020.104432
Bayram AM, Korobenko A (2020) Variational multiscale framework for cavitating flows. Comput Mech 66:49–67. https://doi.org/10.1007/s00466-020-01840-2
Zhu Q, Xu F, Xu S, Hsu M-C, Yan J (2020) An immersogeometric formulation for free-surface flows with application to marine engineering problems. Comput Methods Appl Mech Eng. https://doi.org/10.1016/j.cma.2019.112748
Bazilevs Y, Ming-Chen Hsu I, Akkerman S, Wright K, Takizawa B, Henicke T. Spielman, Tezduyar TE (2011) 3D simulation of wind turbine rotors at full scale. Part I: geometry modeling and aerodynamics. Int J Numer Methods Fluids 65:207–235. https://doi.org/10.1002/fld.2400
Takizawa K, Henicke B, Tezduyar TE, Hsu M-C, Bazilevs Y (2011a) Stabilized space-time computation of wind-turbine rotor aerodynamics. Comput Mech 48:333–344. https://doi.org/10.1007/s00466-011-0589-2
Takizawa K, Henicke B, Montes D, Tezduyar TE, Hsu M-C, Bazilevs Y (2011b) Numerical-performance studies for the stabilized space-time computation of wind-turbine rotor aerodynamics. Comput Mech 48:647–657. https://doi.org/10.1007/s00466-011-0614-5
Bazilevs Y, Takizawa K, Tezduyar TE (2013) Computational fluid–structure interaction: methods and applications. Wiley, February ISBN 978-0470978771. https://doi.org/10.1002/9781118483565
Takizawa K, Tezduyar TE, McIntyre S, Kostov N, Kolesar R, Habluetzel C (2014a) Space–time VMS computation of wind-turbine rotor and tower aerodynamics. Comput Mech 53:1–15. https://doi.org/10.1007/s00466-013-0888-x
Takizawa K, Bazilevs Y, Tezduyar TE, Hsu M-C, Øiseth O, Mathisen KM, Kostov N, McIntyre S (2014b) Engineering analysis and design with ALE-VMS and space-time methods. Arch Comput Methods Eng 21:481–508. https://doi.org/10.1007/s11831-014-9113-0
Takizawa K (2014) Computational engineering analysis with the new-generation space–time methods. Comput Mech 54:193–211. https://doi.org/10.1007/s00466-014-0999-z
Bazilevs Y, Takizawa K, Tezduyar TE, Hsu Ming-Chen, Kostov N, McIntyre S (2014b) Aerodynamic and FSI analysis of wind turbines with the ALE-VMS and ST-VMS methods. Arch Comput Methods Eng 21:359–398. https://doi.org/10.1007/s11831-014-9119-7
Takizawa K, Tezduyar TE, Mochizuki H, Hattori H, Mei S, Pan L, Montel K (2015a) Space–time VMS method for flow computations with slip interfaces (ST-SI). Math Models Methods Appl Sci 25:2377–2406. https://doi.org/10.1142/S0218202515400126
Korobenko A, Bazilevs Takizawa K, Tezduyar TE (2019) Computer modeling of wind turbines: 1. ALE-VMS and ST-VMS aerodynamic and FSI analysis. Arch Comput Methods Eng 26(1099):1059. https://doi.org/10.1007/s11831-018-9292-1
Bazilevs Y, Takizawa K, Tezduyar TE, Hsu M-C, Otoguro Y, Mochizuki H, Wu MCH (2020a) Wind turbine and turbomachinery computational analysis with the ALE and space-time variational multiscale methods and isogeometric discretization. J Adv Eng Comput 4:1–32. https://doi.org/10.25073/jaec.202041.278
Bazilevs Y, Takizawa K, Tezduyar TE, Ming-Chen Hsu, Otoguro Y, Mochizuki H, Wu MCH (2020) bALE and space–time variational multiscale isogeometric analysis of wind turbines and turbomachinery. In: Grama A, Sameh A (eds) Parallel algorithms in computational science and engineering, modeling and simulation in science, engineering and technology. Springer, Berlin, pp 195–233. https://doi.org/10.1007/978-3-030-43736-7_7
Otoguro Y, Mochizuki H, Takizawa K, Tezduyar TE (2019a) Space–time variational multiscale isogeometric analysis of a tsunami-shelter vertical axis wind turbine. in preparation
Ravensbergen M, Bayram AM, Korobenko A (2020a) The actuator line method for wind turbine modelling applied in a variational multiscale framework. Comput Fluids. https://doi.org/10.1016/j.compfluid.2020.104465
Ravensbergen M, Helgedagsrud TA, Bazilevs Y, Korobenko A (2020b) A variational multiscale framework for atmospheric turbulent flows over complex environmental terrains. Comput Methods Appl Mech Eng. https://doi.org/10.1016/j.cma.2020.113182
Bazilevs Y, Korobenko A, Yan J, Pal A, Gohari SMI, Sarkar S (2015a) ALE-VMS formulation for stratified turbulent incompressible flows with applications. Math Models Methods Appl Sci 25:2349–2375. https://doi.org/10.1142/S0218202515400114
Korobenko A, Yan J, Gohari SMI, Sarkar S, Bazilevs Y (2017) FSI simulation of two back-to-back wind turbines in atmospheric boundary layer flow. Comput Fluids 158:167–175. https://doi.org/10.1016/j.compfluid.2017.05.010
Takizawa K, Bazilevs Y, Tezduyar TE, Korobenko A (2020a) Computational flow analysis in aerospace, energy and transportation technologies with the variational multiscale methods. J Adv Eng Comput 4:83–117. https://doi.org/10.25073/jaec.202042.279
Takizawa K, Bazilevs Y, Tezduyar TE, Korobenko A (2020b) Variational multiscale flow analysis in aerospace, energy and transportation technologies. In: Grama A, Sameh A (eds) Parallel algorithms in computational science and engineering, modeling and simulation in science, engineering and technology. Springer, Berlin, pp 235–280. https://doi.org/10.1007/978-3-030-43736-7_8
Bazilevs Y, Korobenko A, Deng X, Yan J (2016) FSI modeling for fatigue-damage prediction in full-scale wind-turbine blades. J Appl Mech 83 (6)
Korobenko A, Hsu M-C, Akkerman I, Bazilevs Y (2013a) Aerodynamic simulation of vertical-axis wind turbines. J Appl Mech. https://doi.org/10.1115/1.4024415
Bazilevs Y, Korobenko A, Deng X, Yan J, Kinzel M, Dabiri JO (2014c) FSI modeling of vertical-axis wind turbines. J Appl Mech 10(1115/1):4027466
Bazilevs Y, Hsu M-C, Kiendl J, Wüchner R, Bletzinger K-U (2011b) 3D simulation of wind turbine rotors at full scale. Part II: fluid-structure interaction modeling with composite blades. Int J Numer Methods Fluids 65:236–253
Hsu M-C, Akkerman I, Bazilevs Y (2011) High-performance computing of wind turbine aerodynamics using isogeometric analysis. Comput Fluids 49:93–100
Bazilevs Y, Hsu M-C, Scott MA (2012) Isogeometric fluid-structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines. Comput Methods Appl Mech Eng 249–252:28–41
Hsu M-C, Akkerman I, Bazilevs Y (2014a) Finite element simulation of wind turbine aerodynamics: validation study using NREL Phase VI experiment. Wind Energy 17:461–481
Korobenko A, Hsu M-C, Akkerman I, Tippmann J, Bazilevs Y (2013b) Structural mechanics modeling and FSI simulation of wind turbines. Math Models Methods Appl Sci 23:249–272
Bazilevs Y, Korobenko A, Deng X, Yan J (2015b) Novel structural modeling and mesh moving techniques for advanced FSI simulation of wind turbines. Int J Numer Methods Eng 102:766–783. https://doi.org/10.1002/nme.4738
Korobenko A, Bazilevs Y, Takizawa K, Tezduyar TE (2018) Recent advances in ALE-VMS and ST-VMS computational aerodynamic and FSI analysis of wind turbines. In: Tezduyar TE (ed) Frontiers in computational fluid-structure interaction and flow simulation: research from lead investigators under forty-2018, Modeling and simulation in science, engineering and technology. Springer, Berlin, pp 253–336. https://doi.org/10.1007/978-3-319-96469-0_7
Yu Y, Zhang YJ, Takizawa K, Tezduyar TE, Sasaki T (2020) Anatomically realistic lumen motion representation in patient-specific space–time isogeometric flow analysis of coronary arteries with time-dependent medical-image data. Comput Mech 65:395–404. https://doi.org/10.1007/s00466-019-01774-4
Terahara T, Takizawa K, Tezduyar TE, Tsushima A, Shiozaki K (2020a) Ventricle-valve-aorta flow analysis with the space–time isogeometric discretization and topology change. Comput Mech 65:1343–1363. https://doi.org/10.1007/s00466-020-01822-4
Takizawa K, Terahara T, Tezduyar TE (2020c) Space–time flow computation with contact between the moving solid surfaces. To appear in a special volume to be published by Springer
Takizawa K, Tezduyar TE, Terahara T, Sasaki T (2018a) Heart valve flow computation with the space-time slip interface topology change (ST-SI-TC) method and isogeometric analysis (IGA). In: Wriggers P, Lenarz T (eds) Biomedical technology: modeling, experiments and simulation. Lecture notes in applied and computational mechanics. Springer, Berlin, pp 77–99. https://doi.org/10.1007/978-3-319-59548-1_6
Takizawa K, Tezduyar TE, Terahara T, Sasaki T (2017a) Heart valve flow computation with the integrated space–time VMS, slip interface, topology change and isogeometric discretization methods. Comput Fluids 158:176–188. https://doi.org/10.1016/j.compfluid.2016.11.012
Takizawa K, Tezduyar TE, Uchikawa H, Terahara T, Sasaki T, Shiozaki K, Yoshida A, Komiya K, Inoue G (2018b) Aorta flow analysis and heart valve flow and structure analysis. In: Tezduyar TE (ed) Frontiers in computational fluid-structure interaction and flow simulation: research from lead investigators under forty—2018, Modeling and simulation in science, engineering and technology. Springer, Berlin, pp 29–89. https://doi.org/10.1007/978-3-319-96469-0_2
Takizawa K, Bazilevs Y, Tezduyar TE, Hsu M-C (2019a) Computational cardiovascular flow analysis with the variational multiscale methods. J Adv Eng Comput 3:366–405. https://doi.org/10.25073/jaec.201932.245
Hughes TJR, Takizawa K, Bazilevs Y, Tezduyar TE, Hsu M-C (2019) Computational cardiovascular analysis with the variational multiscale methods and isogeometric discretization. In: Grama A, Sameh A (eds) Parallel algorithms in computational science and engineering, Modeling and simulation in science, engineering and technology. Springer, Berlin
Terahara T, Takizawa K, Tezduyar TE, Bazilevs Y, Hsu M-C (2020b) Heart valve isogeometric sequentially-coupled FSI analysis with the space-time topology change method. Comput Mech 65:1167–1187. https://doi.org/10.1007/s00466-019-01813-0
Suito H, Takizawa K, Huynh VQH, Sze D, Ueda T (2014) FSI analysis of the blood flow and geometrical characteristics in the thoracic aorta. Comput Mech 54:1035–1045. https://doi.org/10.1007/s00466-014-1017-1
Suito H, Takizawa K, Huynh VQH, Sze D, Ueda T, Tezduyar TE (2016) A geometrical-characteristics study in patient-specific FSI analysis of blood flow in the thoracic aorta. In: Bazilevs Y, Takizawa K (eds) Advances in computational fluid-structure interaction and flow simulation: new methods and challenging computations, Modeling and simulation in science, engineering and technology. Springer, Berlin, pp 379–386. https://doi.org/10.1007/978-3-319-40827-9_29
Takizawa K, Tezduyar TE, Uchikawa H, Terahara T, Sasaki T, Yoshida A (2019b) Mesh refinement influence and cardiac-cycle flow periodicity in aorta flow analysis with isogeometric discretization. Comput Fluids 179:790–798. https://doi.org/10.1016/j.compfluid.2018.05.025
Takizawa K, Schjodt K, Puntel A, Kostov N, Tezduyar TE (2012a) Patient-specific computer modeling of blood flow in cerebral arteries with aneurysm and stent. Comput Mech 50:675–686. https://doi.org/10.1007/s00466-012-0760-4
Takizawa K, Schjodt K, Puntel A, Kostov N, Tezduyar TE (2013a) Patient-specific computational analysis of the influence of a stent on the unsteady flow in cerebral aneurysms. Comput Mech 51:1061–1073. https://doi.org/10.1007/s00466-012-0790-y
Takizawa K, Bazilevs Y, Tezduyar TE, Long CC, Marsden AL, Schjodt K (2014c) ST and ALE-VMS methods for patient-specific cardiovascular fluid mechanics modeling. Math Models Methods Appl Sci 24:2437–2486. https://doi.org/10.1142/S0218202514500250
Hsu M-C, Kamensky D, Bazilevs Y, Sacks MS, Hughes TJR (2014b) Fluid-structure interaction analysis of bioprosthetic heart valves: significance of arterial wall deformation. Comput Mech 54:1055–1071. https://doi.org/10.1007/s00466-014-1059-4
Hsu M-C, Kamensky D, Xu F, Kiendl J, Wang C, Wu MCH, Mineroff J, Reali A, Bazilevs Y, Sacks MS (2015) Dynamic and fluid-structure interaction simulations of bioprosthetic heart valves using parametric design with T-splines and Fung-type material models. Comput Mech 55:1211–1225. https://doi.org/10.1007/s00466-015-1166-x
Kamensky D, Hsu M-C, Schillinger D, Evans JA, Aggarwal A, Bazilevs Y, Sacks MS, Hughes TJR (2015) An immersogeometric variational framework for fluid-structure interaction: application to bioprosthetic heart valves. Comput Methods Appl Mech Eng 284:1005–1053
Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006) Isogeometric fluid-structure interaction analysis with applications to arterial blood flow. Comput Mech 38:310–322
Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid-structure interaction: theory, algorithms, and computations. Comput Mech 43:3–37
Bazilevs Y, Gohean JR, Hughes TJR, Moser RD, Zhang Y (2009a) Patient-specific isogeometric fluid-structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device. Comput Methods Appl Mech Eng 198:3534–3550
Bazilevs Y, Hsu M-C, Benson D, Sankaran S, Marsden A (2009b) Computational fluid-structure interaction: methods and application to a total cavopulmonary connection. Comput Mech 45:77–89
Bazilevs Y, Hsu M-C, Zhang Y, Wang W, Liang X, Kvamsdal T, Brekken R, Isaksen J (2010a) A fully-coupled fluid-structure interaction simulation of cerebral aneurysms. Comput Mech 46:3–16
Bazilevs Y, Hsu M-C, Zhang Y, Wang W, Kvamsdal T, Hentschel S, Isaksen J (2010b) Computational fluid–structure interaction: methods and application to cerebral aneurysms. Biomech Model Mechanobiol 9:481–498
Hsu M-C, Bazilevs Y (2011) Blood vessel tissue prestress modeling for vascular fluid-structure interaction simulations. Finite Elem Anal Des 47:593–599
Takizawa K, Henicke B, Puntel A, Spielman T, Tezduyar TE (2012b) Space–time computational techniques for the aerodynamics of flapping wings. J Appl Mech 10(1115/1):4005073
Takizawa K, Henicke B, Puntel A, Kostov N, Tezduyar TE (2012c) Space-time techniques for computational aerodynamics modeling of flapping wings of an actual locust. Comput Mech 50:743–760. https://doi.org/10.1007/s00466-012-0759-x
Takizawa K, Henicke B, Puntel A, Kostov N, Tezduyar TE (2013b) Computer modeling techniques for flapping-wing aerodynamics of a locust. Comput Fluids 85:125–134. https://doi.org/10.1016/j.compfluid.2012.11.008
Takizawa K, Kostov N, Puntel A, Henicke B, Tezduyar TE (2012d) Space-time computational analysis of bio-inspired flapping-wing aerodynamics of a micro aerial vehicle. Comput Mech 50:761–778. https://doi.org/10.1007/s00466-012-0758-y
Takizawa K, Tezduyar TE, Kostov N (2014d) Sequentially-coupled space-time FSI analysis of bio-inspired flapping-wing aerodynamics of an MAV. Comput Mech 54:213–233. https://doi.org/10.1007/s00466-014-0980-x
Takizawa K, Tezduyar TE, Buscher A, Asada S (2014e) Space–time interface-tracking with topology change (ST-TC). Comput Mech 54:955–971. https://doi.org/10.1007/s00466-013-0935-7
Takizawa K, Tezduyar TE, Buscher A (2015b) Space-time computational analysis of MAV flapping-wing aerodynamics with wing clapping. Comput Mech 55:1131–1141. https://doi.org/10.1007/s00466-014-1095-0
Takizawa K, Montes D, Fritze M, McIntyre S, Boben J, Tezduyar TE (2013c) Methods for FSI modeling of spacecraft parachute dynamics and cover separation. Math Models Methods Appl Sci 23:307–338. https://doi.org/10.1142/S0218202513400058
Takizawa K, Montes D, McIntyre S, Tezduyar TE (2013d) Space-time VMS methods for modeling of incompressible flows at high Reynolds numbers. Math Models Methods Appl Sci 23:223–248. https://doi.org/10.1142/s0218202513400022
Takizawa K, Tezduyar TE, Hattori H (2017b) Computational analysis of flow-driven string dynamics in turbomachinery. Comput Fluids 142:109–117. https://doi.org/10.1016/j.compfluid.2016.02.019
Komiya K, Kanai T, Otoguro Y, Kaneko M, Hirota K, Zhang Y, Takizawa K, Tezduyar TE, Nohmi M, Tsuneda T, Kawai M, Isono M (2019) Computational analysis of flow-driven string dynamics in a pump and residence time calculation. IOP Conf Ser Earth Environ Sci. https://doi.org/10.1088/1755-1315/240/6/062014
Kanai T, Takizawa K, Tezduyar TE, Komiya K, Kaneko M, Hirota K, Nohmi M, Tsuneda T, Kawai M, Isono M (2019a) Methods for computation of flow-driven string dynamics in a pump and residence time. Math Models Methods Appl Sci 29:839–870. https://doi.org/10.1142/S021820251941001X
Takizawa K, Tezduyar TE, Otoguro Y, Terahara T, Kuraishi T, Hattori H (2017c) Turbocharger flow computations with the space–time isogeometric analysis (ST-IGA). Comput Fluids 142:15–20. https://doi.org/10.1016/j.compfluid.2016.02.021
Otoguro Y, Takizawa K, Tezduyar TE (2017) Space-time VMS computational flow analysis with isogeometric discretization and a general-purpose NURBS mesh generation method. Comput Fluids 158:189–200. https://doi.org/10.1016/j.compfluid.2017.04.017
Otoguro Y, Takizawa K, Tezduyar TE (2018) A general-purpose NURBS mesh generation method for complex geometries. In: Tezduyar TE (ed) Frontiers in computational fluid-structure interaction and flow simulation: research from lead investigators under forty–2018, Modeling and simulation in science, engineering and technology. Springer, Berlin, pp 399–434. https://doi.org/10.1007/978-3-319-96469-0_10
Otoguro Y, Takizawa K, Tezduyar TE, Nagaoka K, Mei S (2019b) Turbocharger turbine and exhaust manifold flow computation with the space–time variational multiscale method and isogeometric analysis. Comput Fluids 179:764–776. https://doi.org/10.1016/j.compfluid.2018.05.019
Otoguro Y, Takizawa K, Tezduyar TE, Nagaoka K, Avsar R, Zhang Y (2019c) Space-time VMS flow analysis of a turbocharger turbine with isogeometric discretization: computations with time-dependent and steady-inflow representations of the intake/exhaust cycle. Comput Mech 64:1403–1419. https://doi.org/10.1007/s00466-019-01722-2
Takizawa K, Tezduyar TE (2016) New directions in space-time computational methods. In: Bazilevs Y, Takizawa K (eds) Advances in computational fluid-structure interaction and flow simulation: new methods and challenging computations, Modeling and simulation in science, engineering and technology. Springer, Berlib, pp 159–178. https://doi.org/10.1007/978-3-319-40827-9_13
Takizawa K, Tezduyar TE, Asada S, Kuraishi T (2016) Space-time method for flow computations with slip interfaces and topology changes (ST-SI-TC). Comput Fluids 141:124–134. https://doi.org/10.1016/j.compfluid.2016.05.006
Kuraishi T, Takizawa K, Tezduyar TE (2018) Space-time computational analysis of tire aerodynamics with actual geometry, road contact and tire deformation. In: Tezduyar TE (ed) Frontiers in computational fluid-structure interaction and flow simulation: research from lead investigators under forty–2018, Modeling and simulation in science, engineering and technology. Springer, Berlin, pp 337–376. https://doi.org/10.1007/978-3-319-96469-0_8
Kuraishi T, Takizawa K, Tezduyar TE (2019a) Tire aerodynamics with actual tire geometry, road contact and tire deformation. Comput Mech 63:1165–1185. https://doi.org/10.1007/s00466-018-1642-1
Kuraishi T, Takizawa K, Tezduyar TE (2019b) Space-time computational analysis of tire aerodynamics with actual geometry, road contact, tire deformation, road roughness and fluid film. Comput Mech 64:1699–1718. https://doi.org/10.1007/s00466-019-01746-8
Tezduyar TE, Takizawa K, Kuraishi T (2020). Space–time computational FSI and flow analysis: 2004 and beyond. To appear in a special volume to be published by Springer
Takizawa K, Tezduyar TE, Kanai T (2017d) Porosity models and computational methods for compressible-flow aerodynamics of parachutes with geometric porosity. Math Models Methods Appl Sci 27:771–806. https://doi.org/10.1142/S0218202517500166
Kanai T, Takizawa K, Tezduyar TE, Tanaka T, Hartmann A (2019b) Compressible-flow geometric-porosity modeling and spacecraft parachute computation with isogeometric discretization. Comput Mech 63:301–321. https://doi.org/10.1007/s00466-018-1595-4
Aydinbakar L, Takizawa K, Tezduyar TE, Matsuda D (2021a) U-duct turbulent-flow computation with the ST-VMS method and isogeometric discretization. Comput Mech 67:823–843. https://doi.org/10.1007/s00466-020-01965-4
Aydinbakar L, Takizawa K, Tezduyar TE, Kuraishi T (2021b) Space-time VMS isogeometric analysis of the Taylor–Couette flow. Comput Mech 67:1515–1541. https://doi.org/10.1007/s00466-021-02004-6
Cen H, Zhou Q, Korobenko A (2021) Variational multiscale framework for cavitating flows. Comput Fluids. https://doi.org/10.1016/j.compfluid.2020.104765
Takizawa K, Tezduyar TE (2012) Computational methods for parachute fluid-structure interactions. Arch Comput Methods Eng 19:125–169. https://doi.org/10.1007/s11831-012-9070-4
Takizawa K, Fritze M, Montes D, Spielman T, Tezduyar TE (2012e) Fluid-structure interaction modeling of ringsail parachutes with disreefing and modified geometric porosity. Comput Mech 50:835–854. https://doi.org/10.1007/s00466-012-0761-3
Takizawa K, Tezduyar TE, Boben J, Kostov N, Boswell C, Buscher A (2013e) Fluid-structure interaction modeling of clusters of spacecraft parachutes with modified geometric porosity. Comput Mech 52:1351–1364. https://doi.org/10.1007/s00466-013-0880-5
Takizawa K, Tezduyar TE, Boswell C, Tsutsui Y, Montel K (2015c) Special methods for aerodynamic-moment calculations from parachute FSI modeling. Comput Mech 55:1059–1069. https://doi.org/10.1007/s00466-014-1074-5
Takizawa K, Tezduyar TE, Boswell C, Kolesar R, Montel K (2014f) FSI modeling of the reefed stages and disreefing of the Orion spacecraft parachutes. Comput Mech 54:1203–1220. https://doi.org/10.1007/s00466-014-1052-y
Takizawa K, Tezduyar TE, Kolesar R, Boswell C, Kanai T, Montel K (2014g) Multiscale methods for gore curvature calculations from FSI modeling of spacecraft parachutes. Comput Mech 54:1461–1476. https://doi.org/10.1007/s00466-014-1069-2
Takizawa K, Tezduyar TE, Kolesar R (2015d) FSI modeling of the Orion spacecraft drogue parachutes. Comput Mech 55:1167–1179. https://doi.org/10.1007/s00466-014-1108-z
Rouse H, McNown JS (1948). Cavitation and pressure distribution: head forms at zero angle of yaw. Technical report, State University of Iowa
Rayleigh Lord. VIII (1917) On the pressure developed in a liquid during the collapse of a spherical cavity. Lond Edinb Dublin Philos Mag J Sci 34(200):94–98
Plesset MS, Prosperetti A (1977) Bubble dynamics and cavitation. Annu Rev Fluid Mech 9(1):145–185
Yeckel A, Derby JJ (1999) On setting a pressure datum when computing incompressible flows. Int J Numer Methods Fluids 29(1):19–34
Owis FM, Nayfeh AH (2001). Numerical simulation of super-and partially-cavitating flows over an axisymmetric projectile. In: 39th aerospace sciences meeting and exhibit, p 1042
Owis FM, Nayfeh AH (2004) Numerical simulation of 3-D incompressible, multi-phase flows over cavitating projectiles. Eur J Mech-B/Fluids 23(2):339–351
Brooks AN, Hughes TJR (1982) Streamline upwind/Petrov–Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Comput Methods Appl Mech Eng 32:199–259
Akin J, Tezduyar TE, Ungor M, Mittal S (2003) Stabilization parameters and Smagorinsky turbulence model. J Appl Mech 70(1):2–9
Tezduyar TE, Sathe S (2003) Stabilization parameters in SUPG and PSPG formulations. J Comput Appl Mech 4(1):71–88
Tezduyar TE (2007) Finite elements in fluids: stabilized formulations and moving boundaries and interfaces. Comput Fluids 36(2):191–206
Tezduyar TE, Ramakrishnan S, Sathe S (2008) Stabilized formulations for incompressible flows with thermal coupling. Int J Numer Methods Fluids 57(9):1189–1209
Hsu M-C, Bazilevs Y, Calo VM, Tezduyar TE, Hughes TJR (2010) Improving stability of stabilized and multiscale formulations in flow simulations at small time steps. Comput Methods Appl Mech Eng 199(13–16):828–840
Takizawa K, Tezduyar TE, Otoguro Y (2018c) Stabilization and discontinuity-capturing parameters for space-time flow computations with finite element and isogeometric discretizations. Comput Mech 62:1169–1186. https://doi.org/10.1007/s00466-018-1557-x
Otoguro Y, Takizawa K, Tezduyar TE (2019d) Element length calculation in B-spline meshes for complex ceometries. Comput Mech, submitted
Hughes TJR, Mallet M, Akira M (1986) A new finite element formulation for computational fluid dynamics: II. Beyond SUPG. Comput Methods Appl Mech Eng 54(3):341–355
Tezduyar TE, Park YJ (1986) Discontinuity-capturing finite element formulations for nonlinear convection–diffusion–reaction equations. Comput Methods Appl Mech Eng 59(3):307–325
Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43(5):555–575
Bazilevs Y, Hughes TJR (2007) Weak imposition of Dirichlet boundary conditions in fluid mechanics. Comput Fluids 36(1):12–26
Bazilevs Y, Michler C, Calo VM, Hughes TJR (2007) Weak Dirichlet boundary conditions for wall-bounded turbulent flows. Comput Methods Appl Mech Eng 196(49–52):4853–4862
Chung J, Hulbert GM (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-\(\alpha \) method. J Appl Mech
Jansen KE, Whiting CH, Hulbert GM (2000) A generalized-\(\alpha \) method for integrating the filtered Navier–Stokes equations with a stabilized finite element method. Comput Methods Appl Mech Eng 190(3–4):305–319
Saad Y (2003) Iterative methods for sparse linear systems, vol 82. SIAM
Kim S-E (2008) A multiphase approach to turbulent cavitating flow. In: Proceedings of 27th symposium on Naval Hydrodynamics, Seoul, Korea, 2008, pp 572–589
Guaily AG, Epstein M (2013) Boundary conditions for hyperbolic systems of partial differentials equations. J Adv Res 4(4):321–329
Ayyad M, Guaily A, Hassanein MA (2020). Stabilized variational formulation of an oldroyd-B fluid flow equations on a graphic processing unit (GPU) architecture. Comput Phys Commun, p 107495
Wagner W, Kretzschmar H-J (2007) International steam tables-properties of water and steam based on the industrial formulation IAPWS-IF97: Tables, algorithms, diagrams, and CD-ROM electronic steam tables-all of the equations of IAPWS-IF97 including a complete set of supplementary backward equations for fast calculations of heat cycles, boilers, and steam turbines. Springer
Celik IB, Ghia U, Roache PJ, Freitas CJ (2008) Procedure for estimation and reporting of uncertainty due to discretization in CFD applications. J Fluids Eng Trans ASME 130(7)
Acknowledgements
A. Bayram and A. Korobenko were supported by NSERC Discovery Grant, RGPIN-2017-03781. We thank Dr. Francesco Salvatore from CNR-INSEAN for providing INSEAN E779A dataset. We thank Compute Canada and Advanced Research Computing (ARC) at the University of Calgary for providing HPC resources that have contributed to the research results reported in this paper.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Bayram, A., Korobenko, A. A numerical formulation for cavitating flows around marine propellers based on variational multiscale method. Comput Mech 68, 405–432 (2021). https://doi.org/10.1007/s00466-021-02039-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00466-021-02039-9