Ling Qian Clive Mingham Derek Causon David Ingram

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Ling Qian Clive Mingham Derek Causon David
Ingram
Numerical Simulation of a Wave Driven Rotating
Vane Using a Two-Fluid Solver
by
of
Centre for Mathematical Modelling and Flow
Analysis, Manchester Metropolitan University, UK
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Acknowledgements

• EPSRC (UK) for funding the project
• Trevor Whittaker and Matt Folley
• Queens University, Belfast, U. K.

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Outline

• Background
• - the wave energy device
• - modelling issues
• Numerics
• Solver
• Gridding
• Results
• Conclusions

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Wave Energy Device

• - is based on the pendular principle.

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Modelling Issues

• Device simulation has to model
• Complex flow including
• wave breaking
• vortex formation
• air entrainment
• Complicated geometry
• Moving solid bodies

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Numerics AMAZON-SC

• Written in-house
• Two fluid, time accurate, conservation law based,
  flow code utilising the surface capturing
  approach
• Cartesian cut cell techniques are used to
  represent solid static or moving boundaries

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Governing Equations

• - 2D incompressible, Euler equations with
  variable
• density.

b is the coefficient of artificial compressibility
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Spatial discretisation

• - finite volume formulation.
• where,
• Qi is the average value of Q in cell i
• Vi is the area of cell i,
• Dlj is the length of side j,
• Fij is the numerical flux across the interface
  between cells i and j.

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Spatial discretisation

• Convective fluxes (Fij) are evaluated using Roes
  approximate Riemann solver
• To ensure second order accuracy, MUSCL
  reconstruction is used

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Time discretisation

• implicit backward Euler scheme with an artificial
  time variable t and a linearised RHS.

The resulting block penta-diagonal system is
solved using an approximate LU factorisation.
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Computer Implementation

• A Jameson-type dual time iteration is used to
• eliminate t at each real (outer) iteration and
• recover a divergence free velocity field.

The code vectorises and currently
simulations take about 2 hours per wave to run on
an NEC SX6i deskside supercomputer (!)
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Boundary Conditions

• Seaward boundary a solid moving paddle is used
  to generate waves
• Atmospheric boundary a constant atmospheric
  pressure gradient is applied. Spray and water
  passing out of this boundary are lost from the
  computation.
• Landward boundary a solid wall boundary
  condition is used.
• Bed and wave energy device modelled using
  Cartesian cut cell techniques.

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Cartesian Cut Cell Mesh

• Step 1) Input vertices of solid boundary (and
  domain)

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Cartesian Cut Cell Mesh

• Step 2) Overlay Cartesian mesh

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Cartesian Cut Cell Mesh

• Step 3) Identify Cut Cells and compute
• intersection points.

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Cartesian Cut Cell Mesh

• Advantages
• Automatic mesh generation
• Body fitted
• Moving body capability (remesh at each time step)

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Results Wave Paddle Test

• Waves generated by a moving paddle using
  AMAZON-SC

Numerical and experimental wave heights
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Results Device Simulation
Simulation of a wave driven rotating vane using
AMAZON-SC
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Conclusions 1

• Initial results have been presented for
  non-linear simulation of a rotating vane wave
  energy device using a surface capturing method in
  a Cartesian cut cell framework
• The method can model
• both water and air and their interface
• static and moving boundaries

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Conclusions 2

• Detailed comparisons with small scale
  experimental tests are in progress
• The numerical model is generic and can be used
  to model a wide range of wave energy and other
  devices
• Project details can be found at
• http//www.owsc.ac.uk/