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-Drucker model

9. Arbitrary load and rigidity (cont.)

10. Arbitrary load and rigidity (cont.)

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

13. A rigid polygonal supercavitating hydrofoil

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

15. Method of successive approximations

16. Displacements, Pressure, Foil profile

17. Viscous effects: Boundary layer model

18. Karman-Pohlhausen method

19. Karman-Pohlhausen method (cont.)

20. Boundary layer on the cavity

21. conclusions
The Tulin single-spiral-vortex model has been employed to describe supercavitating flow 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