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
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
A SUPERCAVITATING ELASTIC HYDROFOIL
TULIN’S SINGLE-SPIRAL-VORTEX CLOSURE MODEL
POTENTIAL THEORY MODEL
ELASTIC DEFORMATION MODEL: SHELL THEORY
LARGE DEFLECTION OF A BEAM: BARTEN-BISSHOPPDRUCKER MODEL
GENERALIZATION OF THE BARTEN-BISSHOPP-DRUCKER MODEL
ARBITRARY LOAD AND RIGIDITY (CONT.)
ARBITRARY LOAD AND RIGIDITY (CONT.)
NON-LINEARITY OF THE COUPLED FLUID-STRUCTURE
INTERACTION PROBLEM
A RIGID POLYGONAL SUPERCAVITATING HYDROFOIL
NUMERICAL RESULTS FOR A RIGID POLYGONAL FOIL
ZEMLYANOVA & ANTIPOV (SIAM J APPL MATH, 2012)
METHOD OF SUCCESSIVE APPROXIMATIONS
DISPLACEMENTS, PRESSURE, FOIL PROFILE
VISCOUS EFFECTS: BOUNDARY LAYER MODEL
KARMAN-POHLHAUSEN METHOD
KARMAN-POHLHAUSEN METHOD (CONT.)
BOUNDARY LAYER ON THE CAVITY
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