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Higher order hydrodynamic interaction between two slender bodies in potential flow

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Abstract

In this paper, we apply the slender body theory to study the effect of higher order hydrodynamic interactions between two slender bodies of revolution moving in close proximity, in an unbounded, inviscid, and incompressible fluid. We compare between leading and second-order approximations, as well as approximate and exact separation distances. The total solution is found to be valid for both small and large lateral separation distances. The contribution of the higher order forces is found to be relatively small for large separation distances, though significant for small separation distances. Comparisons with measurements and simulations are satisfactory.

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References

  1. Taylor GI (1928) The force acting on a body placed in a curved and converging stream fluid. Proc R Soc Lond A 120:260

    Article  MATH  Google Scholar 

  2. Newton RN (1960) Some notes on interaction effects between ships close aboard in deep water. In: Proceedings of first symposium on ship maneuverability, DTMB Report 1461, Washington, D.C., pp 1–24 (1960)

  3. Silverstein BL (1957) Linearized theory of the interaction of ships. Institute of Engineering Research, University of California, Berkeley, Calif, Tech. Rep., Series 82, Issue 3

  4. Collatz G (1963) Potential theoretische Unter suchnung der hydrodynamicschen Wechselwirkung zweier Schiffskorper. Jahrbuch Schiffsbautechnischen Gesellschaft 57:281–329

    Google Scholar 

  5. Dand IW (1974) Some aspects of maneuvering in collision situation in shallow water. In: Proceedings of tenth symposium on naval hydrodynamics, Cambridge MA. Office of Naval Research, Washington, pp 261–275 (1974)

  6. Tuck EO (1978) Hydrodynamic problems of ships in restricted waters. Annu Rev Fluid Mech 10:33–44

    Article  Google Scholar 

  7. Newman JN (1965) The force and moment on a slender body of revolution moving near a wall. Naval Ship R&D Centre Rep. 2127

  8. Newman JN (1972) Some theories for ship maneuvering. International symposium on directional stability and control of bodies moving in water, London, pp 34–42

  9. Wang S (1974) Forces and moment on a moored vessel. In: Tenth symposium on naval hydrodynamics, Cambridge MA. Office of Naval Research, Washington, pp 62–69

  10. Wang QX (1992) Analysis of slender bodies of revolution with curved-ground effect and waving-water effect. Fluid Dyn Res 9:235–254

    Article  Google Scholar 

  11. Milne-Thomson LM (1968) Theoretical hydrodynamics, 5th edn. The Macmillan Press LTD, pp XVI, XVII, 528–530 (1968)

  12. Munk MM (1924) The aerodynamic forces on airship hulls. NACA Rep. 184

  13. Lighthill MJ (1954) General theory of high speed aerodynamics. In: High-speed aerodynamics and jet propulsion, vol 6. Princeton Univ. Press, Princeton, pp sect. E, pp 462–477

  14. Cole JD, Messiter AF (1957) Expansion procedures and similarity laws for transonic flow; I. slender bodies at zero incidence. Z Angew Math Physik 88:1–25

  15. Dyke MV (1959) Second-order theory-axisymmetric flow, Tech. Rep. NASA R-47

  16. Barrows TM (1971) Progress on the ram-wing concept, with emphasis on lateral dynamics, Tech. rep., US Dept. Trans. Rep

  17. Tuck EO (1975) Matching problems involving flow through small holes. Adv Appl Mech 15:89–158

    MathSciNet  Google Scholar 

  18. Norrbin NH (1974) Bank effects on a ship moving through a short dredged channel. In: Tenth symposium on naval hydrodynamics, Cambridge MA. Office of Naval Research, Washington, pp 71–88 (1974)

  19. Newman JN (1970) Applications of slender-body theory in ship hydrodynamics. Annu Rev Fluid Mech 2:67–94

    Article  Google Scholar 

  20. Ogilvie TF (1974) Slender-ship theory. Workshop on slender-body theory, part 1: free surface effects, Tech. rep., University of Michigan, Department of Naval Architecture and Marine Engineering, p 13

  21. Ogilvie TF (1977) Singular perturbation problems in ship hydrodynamics. Adv Appl Mech 17:92–187

    Google Scholar 

  22. Tuck EO, Newman JN (1974) Hydrodynamic interactions between ships. In: Cooper R, Doroff S (eds) In: Tenth symposium on naval hydrodynamics. U.S. Government Printing Office, Washington, pp 35–70

  23. Yeung RW (1978) On the interactions of slender ships in shallow water. J Fluid Mech 85:143–159

    Article  MATH  MathSciNet  Google Scholar 

  24. Yeung RW, Tan WT (1980) Hydrodynamic interactions of ships with fixed obstacles. J Ship Res 24:50–59

    Google Scholar 

  25. Kijima K (1979) Hydrodynamic interactions between two lifting bodies. Japan Soc Naval Archit 58:187–197

    Google Scholar 

  26. Kijima K, Furukawa Y, Qing H (1991) The interaction effects between two ships in the proximity of bank wall. The Japan Society of Naval Architects and Ocean Engineers, vol 81, pp 101–112

  27. Faltinsen OM, Newman JN, Vinje T (1995) Nonlinear-wave loads on a slender vertical cylinder. J Fluid Mech 289:179–198

    Article  MATH  Google Scholar 

  28. Fontaine E, Faltinsen OM, Cointe R (2000) New insight into the generation of ship bow waves. J Fluid Mech 421:15–38

    Article  MATH  MathSciNet  Google Scholar 

  29. Becker LE, Koehler SA, Stone HA (2003) On self-propulsion of micro-machines at low reynolds number: Purcells three-link swimmer. J Fluid Mech 490:15–35

    Article  MATH  MathSciNet  Google Scholar 

  30. Chen XN, Sharma SD, Stuntz N (2003) Zero wave resistance for ships moving in shallow channels at supercritical speeds. Part 2. Improved theory and model experiment. J Fluid Mech 478:111–124

    MATH  Google Scholar 

  31. Lighthill MJ (1960) Note on the swimming of slender fish. J Fluid Mech 9:305

    Article  MathSciNet  Google Scholar 

  32. Newman JN, Wu TY (1973) A generalized slender-body theory for fish-like form. J Fluid Mech 57:673–697

    Article  MATH  Google Scholar 

  33. Weihs D (2004) Dolphin drafting hydrodynamics. J Biol 3:1–16

    Article  Google Scholar 

  34. Wang QX (2007) An analytical solution for two slender bodies of revolution translating in very close proximity. J Fluid Mech 582:223–251

    Article  MATH  MathSciNet  Google Scholar 

  35. Nathman JK, Matarrese M (2004) Hybrid grid (structured and unstructured) calculations with a potentialbased panel method. In: AIAA Paper 2004-4836

  36. Newman JN (1977) Marine hydrodynamics, 3rd edn. The MIT Press, Cambridge

    Google Scholar 

  37. Rattanasiri P, Wilson PA, Phillips AB (2014) Numerical investigation of a fleet of towed AUVs. Ocean Eng 80C:25–35. doi:10.1016/j.oceaneng.2014.02.001

    Article  Google Scholar 

  38. Rattanasiri P, Wilson PA, Phillips AB (2012) Numerical Investigation of the influence of propeller to the interference drag of twin prolate spheroids at various longitudinal offsets and transverse separations. In: USYS’12: 4th international conference on underwater system technology, Southampton

  39. Hoerner SF (1965) Fluid-dynamic drag: practical information on aerodynamic drag and hydrodynamic resistance. Published by the author

  40. Hucho WH, Ahmed SR (1998) Aerodynamics of road vehicles: from fluid mechanics to vehicle engineering, 4th edn. The Society of Automative Engineers, Warrendale

    Google Scholar 

  41. Molland AF, Utama IKA (2002) Experimental and numerical investigations of a pair of ellipsoids in close proximity. In: Proceedings of the Institute of Mechanical Engineers, Part M: Journal of Engineering for Maritime Environment (2002)

  42. Kadri U (2005) The flow field and forces on two slender bodies moving in close proximity, M.Sc. Thesis, Technion Libraries, Israel Institute of Technology, Haifa

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Acknowledgments

The research is based on an M.Sc. thesis submitted by U.K. to the Graduate School of the Technion-Israel Institute of Technology, 2005.

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Correspondence to Usama Kadri.

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Kadri, U., Weihs, D. Higher order hydrodynamic interaction between two slender bodies in potential flow. J Mar Sci Technol 20, 249–256 (2015). https://doi.org/10.1007/s00773-014-0275-0

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  • DOI: https://doi.org/10.1007/s00773-014-0275-0

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