0
Research Papers: CFD and VIV

Numerical Simulation of Water-Entry and Sedimentation of an Elliptic Cylinder Using Smoothed-Particle Hydrodynamics Method

[+] Author and Article Information
Roozbeh Saghatchi

Department of Mechanical Engineering,
Babol University of Technology,
Babol, 45136-74334Iran
e-mail: r.saghatchi@aut.ac.ir

Jafar Ghazanfarian

Department of Mechanical Engineering,
University of Zanjan,
University Boulevard,
Zanjan, 45371-38791Iran
e-mail: j.ghazanfarian@znu.ac.ir

Mofid Gorji-Bandpy

Department of Mechanical Engineering,
Babol University of Technology,
Babol, 45136-74334Iran
e-mail: gorji@nit.ac.ir

1Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING Manuscript received July 19, 2012; final manuscript received February 7, 2014; published online April 1, 2014. Assoc. Editor: Antonio C. Fernandes.

J. Offshore Mech. Arct. Eng 136(3), 031801 (Apr 01, 2014) (10 pages) Paper No: OMAE-12-1074; doi: 10.1115/1.4026844 History: Received July 19, 2012; Revised February 07, 2014

This paper studies the two-dimensional water-entry and sedimentation of an elliptic cylinder using the subparticle scale (SPS) turbulence model of a Lagrangian particle-based smoothed-particle hydrodynamics (SPH) method. The motion of the body is driven by the hydrodynamic forces and the gravity. The present study shows the ability of the SPH method for the simulation of free-surface-involving and multiphase flow problems. The full Navier–Stokes equation, along with the continuity equation, have been solved as the governing equations of the problem. The accuracy of the numerical code is verified using the case of the water-entry and exit of a circular cylinder. The numerical simulations of the water-entry and sedimentation of the vertical and horizontal elliptic cylinder with the diameter ratio of 0.75 are performed at the Froude numbers of 0, 2, 5, and 8, and the specific gravities of 0.5, 0.75, 1, 1.5, 1.75, 2, and 2.5. The effect of the governing parameters and vortex shedding behind the elliptic cylinder on the trajectory curves, velocity components within the flow field, rotation angle, the velocity of ellipse, and the deformation of free-surface have been investigated in detail.

FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Sames, P. C., Muzaferija, S., Peric, M., and Schellinr, T. E., 1999, “Application of a Two-Fluid Finite Volume Method to Ship Slamming,” ASME J. Offshore Mech. Arct. Eng., 121(1), pp. 47–52. [CrossRef]
Lee, M., Longoria, R., and Wilson, D., 1997, “Ballistic Waves in High-Speed Water Entry,” J. Fluids Struct., 11(7), pp. 819–844. [CrossRef]
Faltinsen, O. M., Landrini, M., and Greco, M., 2002, “Green Water Loading on an FPSO,” ASME J. Offshore Mech. Arct. Eng., 124(2), pp. 97–103. [CrossRef]
Zio, E., Baraldi, P., and Patelli, E., 2006 “Assessment of the Availability of an Offshore Installation by Monte Carlo Simulation,” Int. J. Pressure Vessels Piping, 83(4), pp. 312–320. [CrossRef]
Glowinski, R., Pan, T. W., Hesla, T., and Joseph, D., 1999, “A Distributed Lagrange Multiplier/Fictitious Domain Method for Particulate Flows,” Int. J. Multiphase Flow, 25(5), pp. 755–794. [CrossRef]
Mirzaii, I., and Passandideh-Fard, M., 2012, “Modeling Free Surface Flows in Presence of an Arbitrary Moving Object,” Int. J. Multiphase Flow, 39, pp. 216–226. [CrossRef]
Yan, H., Liu, Y., Kominiarczuk, J., and Yue, D. K. P., 2009, “Cavity Dynamics in Water Entry at Low Froude Numbers,” J. Fluid Mech., 641, pp. 441–461. [CrossRef]
Truscott, T. T., and Techet, A. H., 2009, “Water Entry of Spinning Spheres,” J. Fluid Mech., 625, pp. 135–165. [CrossRef]
Worthington, A. M., 1908, A Study of Splashes, Longmans, Green & Co., New York.
Von Kármán, T., 1929, “The Impact on Seaplane Floats During Landing,” National Advisory Committee for Aeronautics, Washington, DC.
Seddon, C., and Moatamedi, M., 2006 “Review of Water Entry With Applications to Aerospace Structures,” Int. J. Impact Eng., 32(7), pp. 1045–1067. [CrossRef]
Schnitzer, E., and Hathaway, M. E., 1953, “Estimation of Hydrodynamic Impact Loads and Pressure Distributions on Bodies Approximating Elliptical Cylinders With Special Reference to Water Landings of Helicopters,” National Advisory Committee for Aeronautics, Washington, DC.
Feng, J., Hu, H. H., and Joseph, D. D., 1994, “Direct Simulation of Initial Value Problems for the Motion of Solid Bodies in a Newtonian Fluid. Part 1. Sedimentation,” J. Fluid Mech., 261, pp. 95–134. [CrossRef]
JuárezV. L. H., 2001, “Numerical Simulation of the Sedimentation of an Elliptic Body in an Incompressible Viscous Fluid,” C.R. Acad. Sci., Ser. IIb, 329(3), pp. 221–224. [CrossRef]
Vazquez, J., and Williams, A., 1994, “Hydrodynamic Loads on a Three-Dimensional Body in a Narrow Tank,” ASME J. Offshore Mech. Arct. Eng., 116(3), pp. 117–121 [CrossRef]
Nobari, M., and Ghazanfarian, J., 2009, “A Numerical Investigation of Fluid Flow Over a Rotating Cylinder With Cross Flow Oscillation,” Comput. Fluids, 38(10), pp. 2026–2036. [CrossRef]
Ghazanfarian, J., and Nobari, M., 2009, “A Numerical Study of Convective Heat Transfer From a Rotating Cylinder With Cross-Flow Oscillation,” Int. J. Heat Mass Transfer, 52(23–24), pp. 5402–5411. [CrossRef]
Nobari, M., and Ghazanfarian, J., 2010, “Convective Heat Transfer From a Rotating Cylinder With Inline Oscillation,” Int. J. Therm. Sci., 49(10), pp. 2026–2036. [CrossRef]
Ghazanfarian, J., and Abbassi, A., 2011, “Numerical Investigation of Flow Over a Square Cylinder With Moving Walls and Incident Angle by CBS Method,” Proceedings of the 16th International Conference on Finite Elements in Flow Problems (FEF 2011), March 23–25, Munich, Germany.
Li, S., and Liu, W. K., 2004, Meshfree Particle Methods, Springer, New York.
Saghatchi, R., Gorji-Bandpy, M., and Ghazanfarian, J., 2012, “Water Impact and Sedimentation of Solid Bodies in a Newtonian Fluid Using SPH Method,” Proceedings of International Conference on Mechanical Engineering and Advanced Technologies (ICMEAT2012), Isfahan, Iran, Oct. 10–12.
Ghazanfarian, J. and Saghatchi, R., 2014, “SPH Simulation of Fluid-Structure Interaction of Flow Past a Water-Leaving Rotating Circular Cylinder,” Proceedings of National Conference on Mechanical Engineering of Iran (NCMEI2014), Shiraz, Iran.
Gomez-Gesteira, M., Crespo, A., Rogers, B., Dalrymple, R., Dominguez, J., and Barreiro, A., 2012, “SPHysics Development of a Free-Surface Fluid Solver. Part 2: Efficiency and Test Cases,” Comput. Geosci., 48, pp. 300–307. [CrossRef]
Gomez-Gesteira, M., Rogers, B., Crespo, A., Dalrymple, R., Narayanaswamy, M., and Dominguez, J., 2012, “SPHysics Development of a Free-Surface Fluid Solver. Part 1: Theory and Formulations,” Comput. Geosci., 48, pp. 289–299. [CrossRef]
Gingold, R. A. and Monaghan, J. J., 1977, “Smoothed Particle Hydrodynamics-Theory and Application to Non-Spherical Stars,” R. Astron. Soc., 181, pp. 375–389.
Monaghan, J., 2012, “Smoothed Particle Hydrodynamics and Its Diverse Applications,” Annu. Rev. Fluid Mech., 44(1), pp. 323–346. [CrossRef]
Monaghan, J. J., 1992, “Smoothed Particle Hydrodynamics,” Annu. Rev. Astron. Astrophys., 30, pp. 543–574. [CrossRef]
Wendland, H., 1995, “Piecewise Polynomial, Positive Definite and Compactly Supported Radial Functions of Minimal Degree,” Adv. Comput. Math., 4(1), pp. 389–396. [CrossRef]
Dalrymple, R. and Rogers, B., 2006, “Numerical Modeling of Water Waves With the SPH Method,” Coastal Eng., 53(23), pp. 141–147. [CrossRef]
Monaghan, J., and Kos, A., 1999, “Solitary Waves on a Cretan Beach,” J. Waterw. Port Coast. Ocean Eng., 125(3), pp. 145–155. [CrossRef]
Rogers, B. D. and Dalrymple, R. A., 2008, SPH Modeling of Tsunami Waves, World Scientific, Singapore, pp. 75–100.
Bonet, J., and Lok, T. S., 1999, “Variational and Momentum Preservation Aspects of Smooth Particle Hydrodynamic Formulations,” Comput. Meth. Appl. Mech. Eng., 180(12), pp. 97–115. [CrossRef]
Cummins, S. J., and Rudman, M., 1999, “An SPH Projection Method,” J. Comput. Phys., 152(2), pp. 584–607. [CrossRef]
Colagrossi, A. and Landrini, M., 2003, “Numerical Simulation of Interfacial Flows by Smoothed Particle Hydrodynamics,” J. Comput. Phys., 191(2), pp. 448–475. [CrossRef]
Monaghan, J., 1994, “Simulating Free Surface Flows With SPH,” J. Comput. Phys., 110(2), pp. 399–406. [CrossRef]
Greenhow, M. and Lin, W. M., 1983, “Nonlinear-Free Surface Effects: Experiments and Theory,” Cambridge Department of Ocean Engineering, Massachusetts Institute of Technology, Report No. 83–19.
Zhu, X., Faltinsen, O. M., and Hu, C., 2006, “Water Entry and Exit of a Horizontal Circular Cylinder,” ASME J. Offshore Mech. Arct. Eng., 129(4), pp. 253–264. [CrossRef]
Vandamme, J., Zou, Q., and Reeve, D., 2011, “Modeling Floating Object Entry and Exit Using Smoothed Particle Hydrodynamics,” J. Waterw. Port Coast. Ocean Eng., 137(5), pp. 213–224. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Comparison of the free-surface deformation during water-entry of a half-buoyant cylinder. Right column, experimental result from Ref. [36]; left column, CIP numerical data obtained from Ref. [37]; middle column, results of the present SPH method; first row at t = 0.33 s and second row at t = 0.42 s.

Grahic Jump Location
Fig. 2

Comparison of the free-surface deformation during water-entry of a neutrally buoyant cylinder. Right column, experimental results [36]; left column, CIP numerical data obtained from Ref. [37]; middle column, results of the present SPH method; first row at at t = 0.5 s and second row at t = 0.75 s.

Grahic Jump Location
Fig. 3

Comparison of the temporal variation of the depth of penetration of the cylinder falling in the still water obtained from the present study and other numerical and experimental data. Experimental data extracted from Ref. [36]; CIP numerical data obtained from Ref. [37].

Grahic Jump Location
Fig. 4

Definition of the coordinate system and initial velocity of the cylinder

Grahic Jump Location
Fig. 5

Vortex shedding pattern behind the cylinder

Grahic Jump Location
Fig. 6

(a) Trajectory, (b) deflection angle versus nondimensional time, and (c) local Froude number versus time for the horizontal cylinder for various specific gravities

Grahic Jump Location
Fig. 7

A sequence of the sedimentation of the vertical elliptical cylinder for SG = 1.5

Grahic Jump Location
Fig. 8

(a) Trajectory, (b) deflection angle versus nondimensional time, and (c) local Froude number versus time for the vertical cylinder and various specific gravities

Grahic Jump Location
Fig. 9

Comparison of the nondimensional depth of penetration with nondimensional time for two cases of vertical and horizontal elliptical cylinders and different specific gravities

Grahic Jump Location
Fig. 10

A sequence of the splash and water surface deformation during the water-entry of the horizontal elliptical cylinder for Fr = 5 and SG = 0.5

Grahic Jump Location
Fig. 11

Time variation of the (a) nondimensional depth, and (b) vertical nondimensional velocity of the horizontal elliptical cylinder for various specific gravities during the water-entry case

Grahic Jump Location
Fig. 12

A sequence of the splash and water surface deformation during the water-entry of the vertical elliptical cylinder for Fr = 5 and SG = 0.5

Grahic Jump Location
Fig. 13

Time variation of the (a) nondimensional depth, and (b) vertical nondimensional velocity of the vertical elliptical cylinder for various specific gravities during the water-entry problem

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In