Modeling of Oscillating Flow Past a Vertical Plate

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Modeling of Oscillating Flow Past a Vertical Plate
The 13th International Offshore and Polar
Engineering Conference ISOPE-2003, Hawaii,
May25-30, 2003

• Spyros A. Kinnas, Yi-Hsiang Yu, Hanseong Lee,
  Karan Kakar

Ocean Engineering Group, Department of Civil
Engineering The University of Texas at Austin,
Austin, TX, USA
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Overview

• Introduction
• Governing Equations, Boundary Conditions and
  Numerical Formulation.
• Comparison of results from the 2D unsteady Euler,
  Navier-Stokes Solvers with measurements.
• Visualization of separated flow field.
• Summary and future work.

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IntroductionMotivation Objectives

• Develop and validate a method for the prediction
  of the effects of bilge keels on FPSO Hull
  motion.

• Understand the physics of the unsteady separated
  flow about the bilge keels of a hull subject to
  roll motions, and predict the corresponding
  hydrodynamic coefficients.

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Motivation Objectives

• In this work, we apply and validate our model to
  a bilge keel (vertical plate) subject to
  horizontal sinusoidal inflow.

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Literature Review

• Numerical Work
• Gentaz et al. 1997
• Korpus and Falzarano 1997
• Vassalos et al. 2000
• Yeung et al. 1992, 1996, 1998, 2000, 2002
• Experiments on Vertical Plate
• -Keulegan and Carpenter 1958
• -Sarpkaya and OKeefe 1995

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Numerical FormulationGoverning Equation

• Non-Dimensional Navier-Stokes equations
• KC Keulegan-Carpenter number,
• Re Reynolds number,

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Numerical Method

• Finite Volume Method
• Nis Lax-Wendroff Method for time
• Artificial dissipation (viscosity) only in the
  case of Euler solver
• SIMPLE Method for pressure correction

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Euler and Navier-Stokes Solver

• Choi Kinnas 2000, Choi PhD thesis 2000
• -Development of Euler Solver and Navier-Stokes
  solver.
• Kakar MS thesis 2002
• Application of unsteady 2D Euler solver of flow
  over bilge keels for FPSO hull motion.

• Euler Solver Applied artificial viscosity
• Navier-Stokes Solver Viscous terms

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Force Calculation on the plate

• Morisons equation as follows Sarpkaya and
  OKeefe (1995)

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ResultsConvergence Study
At KC1
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Convergence Study
At KC1
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Force History comparison
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Drag coefficient for a range of KC (0.5 lt KC lt 10)
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Inertia coefficient for a range of KC (0.5 lt KC lt
10)
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Streamline vorticity contour at 0T/4 for KC1
ES
NS
Streamline vorticity contour at 1T/4 for KC1
ES
NS
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Streamline vorticity contour at 2T/4 for KC1
ES
NS
Streamline vorticity contour at 3T/4 for KC1
ES
NS
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Summary

• A finite volume method was applied to the
  solution of oscillating flow around a vertical
  flat plate. The same plate and tunnel dimensions
  as in the experiment of Sarpkaya and O'Keefe
  have been used.
• It was found, that either the Euler or the
  Navier-Stokes solver produced force coefficients
  and separated flow fields which were close to
  each other and also close to the measurements,
  especially for lower values of the
  Keulegan-Carpenter number.

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Summary

• For higher KC numbers, the viscous terms start to
  be more important, and the effects of turbulence
  may need to be taken into account.
• The Euler solver has already been extended in the
  case of FPSO hull sections, with and without
  bilge keels, and some preliminary results have
  been presented in Kinnas, et al., 12th Offshore
  Symposium, Texas section of the SNAME, 2003.

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Future Work

• Further investigations with different Re numbers
  and KC numbers.
• Continue with the extension in the case of FPSO
  hull sections to study the effects of bilge keels.

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The End