A High-Order BEM Based on the ``Saw-tooth'' Correction - Application to the Structural Analysis of Cavitating Hydrofoils

S. A. Kinnas and B. Gücün

Department of Civil Engineering, The University of Texas at Austin, Austin, Texas 78712, USA

Abstract:

An alternative high-order BEM is presented for the structural analysis of cavitating hydrofoil sections. This method is based on a low-order method in which the higher-order terms are accounted for in an iterative sense. This is accomplished via the evaluation of the so-called ``saw-tooth'' correctors. The method is validated first against analytical solutions and results from beam theory, and then applied on hydrofoil shaped geometries.

• INTRODUCTION
• BEM FOR CAVITATING FLOW ANALYSIS
  • Governing equations and boundary conditions
  • The boundary integral equation
  • A low-order BEM
  • The ``saw-tooth'' correction
• BEM FOR STRUCTURAL ANALYSIS
  • Governing equations and boundary conditions
  • The fundamental solution
  • Boundary integral equation
  • The low-order method
  • The ``saw-tooth'' correction
• RESULTS
  • Flexure of 2-D beam with no shear
  • Flexure of 2-D beam under uniform loading
  • Super-cavitating hydrofoil section
  • Acceleration of convergence
  • Three dimensional beam
• CONCLUSIONS AND FUTURE RESEARCH
• ACKNOWLEDGMENTS
• References
• SELF-INFLUENCE FACTORS
  • Constant strength element
  • Linear strength saw-tooth
  • Quadratic strength saw-tooth
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