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Journal of Hydrodynamics

, Volume 18, Issue 1, pp 45–48 | Cite as

Exact variational formulation of free-surface gravity flow around hydrofoils accounting for surface tension

  • Gao-Lian Liu
Session A1
  • 1 Downloads

Abstract

A variational principle family using stream function is formulated for the free surface hydrofoil flow under gravity, taking full advantage of the functional variation with variable domain for handling the free surface and accounting exactly for the surface tension. This theory offers a new theoretical basis for the finite element analysis of free surface flow accounting for the surface tension effect.

Key words

free surface flow variational principle finite element method hydrodynamics surface tension 

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References

  1. [1]
    O’Carroll, M.J. (1980), “A VP for Ideal Flow over a Spillway,” Int’l J. Num. Meth. Engrg, Vol. 15, No. 5, pp. 767–769.MathSciNetCrossRefGoogle Scholar
  2. [2]
    Liu, G.L. (1992), “The Hybrid problem of Free-Surface Gravity Spillway Flow Treated by VPs with Variable Domain: (I) Potential Formulation,” J.Hydrodynamics (Series B), Vol. 4, No. 3, pp. 118–122zbMATHGoogle Scholar
  3. [3]
    Liu, G.L. (1986), “A Unified Theory of Hybrid Problems for Fully 3-D Incompressible Rotor-Flow Based on VPs with Variable Domain,” ASME J.Engrg. for GT & Power, Vol. 108, No. 2, pp. 254–256.CrossRefGoogle Scholar
  4. [4]
    Liu, G.L. (1987), “New VP Families for Direct, Inverse & Hybrid Problems of Free Surface Gravity Flow over a Spillway,” Turbulence Measurements & Flow Modelling, C.J. Chen et al. (eds.), Hemisphere Publ. Corp., New York, pp. 323–332.Google Scholar
  5. [5]
    Liu, G.L. (1997), “Variable-domain variational finite element method: A general approach to free/moving boundary problems in heat and fluid flow.” Nonlinear Analysis, Vol. 30, No. 8, 5229–5239.MathSciNetCrossRefGoogle Scholar
  6. [6]
    Liu, G.L. (1992), “VPs and GVPs for fully 3-D transonic flow with shocks in a turbo-rotor, Pt. I: Potential flow.” Acta Mechanica, Vol. 95, 117–130.CrossRefGoogle Scholar
  7. [7]
    Luke, J.C. (1967), “A VP for a Fluid with a Free Surface,” J. Fluid Mech., Vol. 27, No. 2. pp. 395–397.MathSciNetCrossRefGoogle Scholar
  8. [8]
    Varoglu, E. & Finn, W.D.L. (1978), “Variable Domain FE Analysis of Free Surface Gravity Flow,” Computers & Fluids, Vol. 6, No. 2, pp. 103–114.CrossRefGoogle Scholar
  9. [9]
    Washizu, K. et al. (1977), “Application of FEM to Some Free Surface Flow problems,” FE in Water Resources, W.G. Gray et al. (eds.), pp. 4, 247–266.Google Scholar
  10. [10]
    Liu, G.L. (2000), “Derivation & Transformation of VP with emphasis on inverse and hybrid problems in fluid mechanics: A systematic approach,” Acta Mech., Vol. 140, No. 1, pp. 73–89.CrossRefGoogle Scholar
  11. [11]
    Courant, R. & Hibert, D. (1953), Methods of Math. Physics. Vol. 1, Interscience Publ., New York.Google Scholar
  12. [12]
    Liu, G.L. & Zhang, D.F. (1987), “Numerical Methods for Solving Inverse Problem of Heat Conduction with Unknown Boundary Based on VPs with Variable Domain,” Num. Meth. for Thermal Problems, Vol. 5, R.W. Lewis et al. (eds.), Pineridge Press, UK, pp. 284–295.Google Scholar
  13. [13]
    Liu, G.L. (1989), “The hybrid problem of free-surface gravity spillway flow treated by VPs with variable domain: (II)stream function formulation,” Proc. 7 th Int. Conf. FEM in Flow Problem, 1989Google Scholar
  14. [14]
    White, F.M. (1974), Viscous Fluid Flow, McGraw-Hill.Google Scholar
  15. [15]
    Chen, K.M. et al. (1984), “A variational FE analysis of blade-to-blade flow in cascades with splitter blades on an arbitrary streamsheet of revolution.” Computational Methods in Turbomachinery, IMechE, Paper No. C64/84, UK, pp. 230–236Google Scholar
  16. [16]
    Liu, G.L., “Free-surface gravity flow around hydrofoils accounting for surface tension: A variational approach.” Proc. 4 TH Int. Workshop on Ship Hydrodynamics, Sept. 24–7, 2005, Shanghai, China, pp. 89–92Google Scholar

Copyright information

© China Ship Scientific Research Center 2006

Authors and Affiliations

  • Gao-Lian Liu
    • 1
  1. 1.Institute of MechanicsShanghai UniversityShanghaiChina

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