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Large deflection of a supercavitating hydrofoil

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

LARGE DEFLECTION OF A SUPERCAVITATING HYDROFOIL

Yuri AntipovDepartment of Mathematics Louisiana State UniversityBaton Rouge, Louisiana

Singapore, August 16, 2012

Page 2: Large deflection of a  supercavitating  hydrofoil

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

Page 3: Large deflection of a  supercavitating  hydrofoil

A SUPERCAVITATING ELASTIC HYDROFOIL

Page 4: Large deflection of a  supercavitating  hydrofoil

TULIN’S SINGLE-SPIRAL-VORTEX CLOSURE MODEL

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POTENTIAL THEORY MODEL

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ELASTIC DEFORMATION MODEL: SHELL THEORY

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LARGE DEFLECTION OF A BEAM: BARTEN-BISSHOPP-DRUCKER MODEL

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GENERALIZATION OF THE BARTEN-BISSHOPP-DRUCKER MODEL

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ARBITRARY LOAD AND RIGIDITY (CONT.)

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ARBITRARY LOAD AND RIGIDITY (CONT.)

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NON-LINEARITY OF THE COUPLED FLUID-STRUCTURE INTERACTION PROBLEM

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A RIGID POLYGONAL SUPERCAVITATING HYDROFOIL

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NUMERICAL RESULTS FOR A RIGID POLYGONAL FOIL ZEMLYANOVA & ANTIPOV (SIAM J APPL MATH, 2012)

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METHOD OF SUCCESSIVE APPROXIMATIONS

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DISPLACEMENTS, PRESSURE, FOIL PROFILE

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VISCOUS EFFECTS: BOUNDARY LAYER MODEL

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KARMAN-POHLHAUSEN METHOD

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KARMAN-POHLHAUSEN METHOD (CONT.)

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BOUNDARY LAYER ON THE CAVITY

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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


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