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Large deflection of a supercavitating hydrofoil

Large deflection of a supercavitating hydrofoil. Yuri Antipov Department of Mathematics Louisiana State University Baton Rouge, Louisiana Singapore, August 16, 2012. Outline. 1. A supercavitating curvilinear elastic hydrofoil: Tulin’s type model

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Large deflection of a supercavitating hydrofoil

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  1. Large deflection of a supercavitating hydrofoil • Yuri Antipov • Department of Mathematics • Louisiana State University • Baton Rouge, Louisiana • Singapore, August 16, 2012

  2. Outline • 1. A supercavitating curvilinear elastic hydrofoil: Tulin’s type model • 2. Solution for a thin circular elastic hydrofoil • 3. Nonlinear model on large deflection of an elastic foil • 4. Viscous effects: a boundary layer model

  3. A supercavitating elastic hydrofoil

  4. Tulin’s single-spiral-vortex closure model

  5. Potential theory model

  6. Elastic deformation model: shell theory

  7. Large deflection of a beam: Barten-Bisshopp-Drucker model

  8. Generalization of the Barten-Bisshopp-Druckermodel

  9. Arbitrary load and rigidity (cont.)

  10. Arbitrary load and rigidity (cont.)

  11. Non-linearity of the coupled fluid-structure interaction problem

  12. A rigid polygonal supercavitating hydrofoil

  13. Numerical results for a rigid polygonal foil Zemlyanova & Antipov (SIAM J Appl Math, 2012)

  14. Method of successive approximations

  15. Displacements, Pressure, Foil profile

  16. Viscous effects: Boundary layer model

  17. Karman-Pohlhausen method

  18. Karman-Pohlhausen method (cont.)

  19. Boundary layer on the cavity

  20. conclusions • The Tulinsingle-spiral-vortex model has been employed to describe supercavitatingflow past an elastic hydrofoil • The nonlinear equation of large deflection of an elastic beam (‘elastica’) has been solved exactly in terms of elliptic functions • The method of conformal mappings and the Riemann-Hilbert formalism have been used to solve the cavitation problem in closed form • The fluid-structure interaction problem has been solved by the method of successive approximations • The Prandtl boundary layer equations and the Karman-Pohlhausen method have been applied to derive a nonlinear first-order ODE for the shearing stress on the foil. On the cavity boundary, the shearing stress has been found explicitly

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