Predicting and Understanding the Breakdown of Linear Flow Models

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Predicting and Understanding the Breakdown of
Linear Flow Models

• P. Stuart, I. Hunter, R. Chevallaz-Perrier, G.
  Habenicht
• 19 March 2009

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Why Try to Predict when Linear Flow Models Fail?

• Computational Fluid Dynamics Analysis
  (nonlinear) is more time consuming than running
  most linear models.

• Predicting the breakdown of linear models helps
  prioritise CFD analysis to those sites who need
  it most.

• Assessing linear model breakdown helps the
  interpretation of subsequent CFD analysis as many
  of the critical features of the flow are
  identified ahead of time.

• The breakdown of linear models is normally
  associated which phenomena with series
  consequences for turbines i.e. high turbulence
  and vertical wind shear. There is much insight to
  be gained by comparing CFD and linear models.

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What is a Linear Hill?
If the wind flow over a hill can be assumed to be
linear then the effects of a single hill can be
decomposed into several smaller hills.
Models like WASP / MS3DJH decompose real terrain
into many sinusoidal hills, solve them
individually and then recombine to get their
final solution.
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Why does linear theory break down?
The linear theory (from which both WASP and
MS3DJH are derived) simplifies the governing flow
equations under the assumption of small terrain
slope.
The velocity is decomposed as follows
perturbation
undisturbed
(Jackson and Hunt, 1975)
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Methodology

• Calculate flow over idealised hills using both
  CFD and linear models for incrementally
  increasing slopes and tree heights.

MS3DJH / RES Roughness
Linear
CFD

• Establish guidelines for where linear models
  fail by comparing to CFD.

• Use simple geometrical considerations to assess
  likely impact on real sites.

• Confirm predicted effects using CFD.

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Computer code
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Breakdown of Linear Behaviour for a 2D Symmetric
Hill
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Comparison of 2D and 3D Symmetric Hills
c.f. Kaimal and Finnigan (1994) 2D Critical
slope 18, 3D Critical Slope 20.
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Variation of Critical Terrain Slope with Tree
Height (2D Symmetric Hill)
Critical angle for recirculation reduced by ¼
per metre of tree height.
c.f. Kaimal and Finnigan (1994) 2D Critical
slope 10 for a very rough hill.
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Variation of Critical Terrain Slope with Tree
Height (2D Symmetric Hill)
Critical angle for linear model break down
reduced by ½ per metre of tree height.
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Consequences of Linear Model Breakdown
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Case Study 1 Complex Terrain Short Trees
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Case Study 2 Complex Terrain No Trees

• No trees, critical angle fRfN16

Transient CFD Turbulence
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Case Study 3 Complex Terrain With Tall Trees
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Case Study 4 Complex Terrain With Tall Trees
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Case Study 4 Complex Terrain With Tall Trees
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Conclusions

• CFD indicates critical angle for recirculation
  is reduced by around ¼ per metre of tree height.

• CFD indicates critical angle for linear model
  breakdown is reduced by around ½ per metre of
  tree height.

• Considering the critical angle and using simple
  geometry can provide an extremely useful insight
  into where linear models are likely to fail. This
  helps identify where it is necessary to apply CFD.

• Comparison with measurements demonstrates the
  value of the analysis.

• Terrain assessment method can produce false
  positives, but CFD analysis provides
  clarification.

• This presentation summarises 7 to 8 years of
  experience of learning how to take advantage of
  CFD modelling within RES

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