Transcript Slide 1

CONSIDERATIONS
ABOUT THE ROLE OF
ATMOSPHERIC
STABILITY IN CFD
MODELS
C. Montavon, ANSYS UK
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Contents
Why
Effects
Atmospheric
stability
•Stable standard atmosphere
in free stream
•Surface heat fluxes
How
•Mountain waves
•Buoyancy terms in
•Possible changes in flow
momentum and
topology •Low Froude number
turbulence equations
•Affects
When
•Mixing
•Boundary layer height
•Always,
•Boundary layer
•More or less so depending on
regeneration
surface stability
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How: Stability implementation
• Continuity
• Momentum
gravity waves
 
U i  
  U kU i   
p
  eff
t
xk
xi
x j 




 U
U j
i


 x
xi
j



   g h    h  i 3

h
 
• Turbulence quantities (e.g. k-e)

 
 U j k        T   k
k  
t
x j
 x j  
 k  x j



  P  e

G
G 
 eff g  
 H  h z
2
e
 
 T  e 
e
e
 C 1e max G , 0 
 U j e          C 1e P  C 2 e 
 e  
k
t
x j
 x j  
 e   x j 
k
k


• Energy (potential temperature)
  
 T  

 U j      
   
t
x j
 x j  C p     x j



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


mixing, boundary
layer height
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Effects: Mountain waves
Potential temperature
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Effect: change in flow topology
Neutral
Stable
Low Froude number
•High terrain elevation
•Strong stability
•Low wind speed
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  u* / f L
Effect: reduced boundary layer
height, reduced mixing
• Equilibrium profiles on flat terrain, roughness z0, Coriolis parameter f
1
0.3
Nicholls,-9.7
1985 K /km
model,
model, -9.7 K/km
model,
-9.8 K/km
Nicholls, 1985
Hinze
dT /dz = -9.7 K/km
Duynkerke
dT /dz = -9 K/km
dT /dz = -9.7 K/km
model, -9.8 K/km
1.0
dT /dz = -9 K/km
Hinze
0.3
dT /dz = -8 K/km
Duynkerke
dT /dz = -6.5 K/km
dT /dz = -8 K/km
dT /dz = -6.5 K/km
0.2
z f/u *
zf/u
*
z f/u *
zf/u
*
0.2
0.5
0.5
0.1
0.1
0
0.0
0
0
0
0
0.5
5 1
- u'w'/u
k/u* *22
0
1.5
10
0.2
0.4
0.05
v'w'/u
*
 f/u
2
T
*
2
0.1
Eddy diffusivity
Turbulence kinetic energy
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  u* / f L
Effect: reduced boundary layer
height and momentum fluxes
• Equilibrium profiles on flat terrain, roughness z0, Coriolis parameter f
Nicholls, 1985
Increasing
free stream stability
Nicholls, 1985
0.3
dT /dz = -9.7 K/km
dT /dz = -9.7 K/km
dT /dz = -9 K/km
0.3
dT /dz = -8 K/km
dT /dz = -9 K/km
dT /dz = -6.5 K/km
dT /dz = -8 K/km
dT /dz = -6.5 K/km
0.2
z f/u *
z f/u *
0.2
0.1
0.1
0
0
0
0.5
- u'w'/u *
1
0
1.5
2
0.4
0.2
v'w'/u *
2
Vertical momentum fluxes
• Reduction of fluxes  expected slower boundary layer regeneration
downstream of forests or large arrays
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Effect: Boundary layer height
0.8
0.7
0.7-0.8
0.6
0.6-0.7
0.5
0.5-0.6
h/(u*/f) 0.4
0.4-0.5
0.3
0.3-0.4
0.2
0.2-0.3
0.1
  N / f
0
S1
0.1-0.2
0-0.1
25

75
Increasing free stream stability
100
1
ln
  u* / f L
Increasing surface stability
Source: C. Montavon, 1998, Simulation of atmospheric flows over complex terrain for wind power
potential assessment, Ph D thesis, EPF Lausanne, http://library.epfl.ch/en/theses/?nr=1855
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Example of An Suidhe
Normalised wind speed
Normalised TI
50m
30m
RMS error [%]
average over
anemometers
average highest
meas. Heights
average lowest
meas. Heights
Wind speed
ratio
TI ratio
8.9
12.8
6.6
7.6
12.0
18.4
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Stability in ANSYS CFD
• Free stream stability tested as part of WindModeller
developments
• Preliminary results
– Validation successful of mountain waves from 2D theoretical test
case (witch of Agnesi mountain profile)
– Application on real terrain (An Suidhe, Scotland), see poster
session for details
 inclusion of stability helped improve modelling accuracy,
particularly on the turbulence intensity predictions
 also observed strong sensitivity of results to domain vertical
extent when including stability. More work required to find best
configuration for top boundary condition.
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