Clive Mingham, Ling Qian, Derek Causon and David Ingram

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Clive Mingham, Ling Qian, Derek Causon and
David Ingram
Numerical Simulation of an OWSC Device Using a
Two-Fluid Free Surface Solver
Centre for Mathematical Modelling and Flow
Analysis, Manchester Metropolitan University, UK
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Acknowledgements

• EPSRC (UK) for funding the project
• Joint project (wave tank model tests) with Prof.
  Trevor Whittaker and Dr. Matt Folley, Queens
  University of Belfast.

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Talk Outline

• Background
• Numerics
• Solver
• Gridding
• Results
• Conclusions/future work

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Background

• Oscillating wave surge converter (OWSC) wave
  power device

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Background

• Accurate simulation of an OWSC can
• provide
• insight into the hydrodynamics
• assessment of its performance
• and needs to address
• moving (water/air) free surfaces
• complicated stationary and moving solid bodies

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AMAZON-SC Numerical Features

• Two fluid (water/air) free surface capturing
  solver based on the Cartesian cut cell mesh
• Each fluid is identified by density
• Solid stationary or moving bodies can be easily
  accommodated
• MMU code written in-house.

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Governing equations

• 2D incompressible, Euler equations with variable
  density.

b is the coefficient of artificial compressibility
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Discretisation

• The equations are discretised using a finite
  volume formulation
• Where Qi is the average value of Q in cell i
  (stored at the cell centre), Vi is the volume of
  the cell, Fij is the numerical flux across the
  interface between cells i and j and and Dlj is
  the length of side j.

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Convective fluxes

• The convective flux (Fij) is evaluated using
  Roes approximate Riemann solver.
• To ensure second order accuracy, MUSCL
  reconstruction is used
• where (x,y) is a point inside the cell ij, r is
  the coordinate vector of (x,y) relative to ij and
  DQij is the slope limited gradient.

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Time discretisation

• Euler implicit time discretisation is used
• together with an artificial time variable t (to
  ensure a
• divergence free velocity field) resulting in a
  linearised
• RHS.

This system of linear equations is solved using
an approximate LU factorisation.
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Boundary Conditions

• Boundary conditions implemented include
• Seaward boundary a solid moving paddle is used
  to generate waves (wave maker)
• Atmospheric boundary a constant atmospheric
  pressure gradient is applied
• Wall boundary for either vertical or horizontal
  walls at the domain boundary
• Solid (moving) internal body modelled using
  Cartesian cut cell techniques

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Cartesian Cut Cell Method

• Automatic mesh generation
• Boundary fitted
• Extends to moving boundaries

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Cartesian Cut Cells

• Input vertices of solid boundary (and domain)

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Cartesian Cut Cells

• Input vertices of solid boundary (and domain)
• Overlay background stationary Cartesian grid

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Cartesian Cut Cells

• Input vertices of solid boundary (and domain)
• Overlay Cartesian grid
• Identify Cut Cells and compute intersection
  points and other geometrical information.

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The vane as a wave maker
Xa 170 mm, Ya 437 mm, Cl 20 mm, f 53
degrees water depth 200 mm, thickness of vane
25mm. wave probe positioned 500 mm to the left of
the vane
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The vane as a wave maker
Rotation angle of the vane (from QUB test) as
input to the numerical simulation.
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The vane as a wave maker

• Water surface elevation at the probe position
  comparison with QUB tests

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The vane as a wave maker

• Animation showing velocity vectors and free
  surface position around the vane

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OWSC Device Modelling

• Flow conditions
  
• Still water depth H 20 cm
• Density of the vane m 1100 kg/m3
• Wave period T 1.6 seconds
• Velocity (horizontal) of wave maker
• U -0.2 (1-e(-5t)) sin(2pt/T)
• Angle of the backplane ? 45

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OWSC Device Modelling

• The motion of the vane is derived from the forces
  exerted on it by the surrounding water.

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Conclusions

• Initial results have been presented for
  simulation of the OWSC wave energy device using a
  surface capturing Cartesian cut cell method.
• AMAZON-SC
• Capable of modelling both water and air, as well
  as their interface
• Can handle both static and moving boundaries
  easily.
• The code shows promise for simulating a wide
  range of wave energy devices.

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Future Work

• Power takeoff simulation
• 2D parametric study of the OWSC device
• Extension to 3D with mesh adaptation