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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 - PowerPoint PPT Presentation
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LARGE DEFLECTION OF A SUPERCAVITATING HYDROFOIL
Yuri AntipovDepartment of Mathematics Louisiana State UniversityBaton Rouge, Louisiana
Singapore, August 16, 2012
OUTLINE
1. A supercavitating curvilinear elastic hydrofoil: Tulin’s type model
2. Solution for a thin circular elastic hydrofoil3. 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-BISSHOPP-DRUCKER 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