© 2010 ANSYS, Inc. All rights reserved. 1 ANSYS, Inc. Proprietary© 2010 ANSYS, Inc. All rights reserved. 1 ANSYS, Inc. Proprietary

CONSIDERATIONS ABOUT THE ROLE OF ATMOSPHERIC STABILITY IN CFD MODELS

CONSIDERATIONS ABOUT THE ROLE OF ATMOSPHERIC STABILITY IN CFD MODELS

C. Montavon, ANSYS UKC. Montavon, ANSYS UK

© 2010 ANSYS, Inc. All rights reserved. 2 ANSYS, Inc. Proprietary

Contents

Atmospheric stability

Why

How

When

Effects

• Stable standard atmosphere in free stream

• Surface heat fluxes

• Buoyancy terms in momentum and turbulence equations

• Mountain waves• Possible changes in flow

topology• Affects

• Mixing• Boundary layer height• Boundary layer

regeneration

• Low Froude number

• Always,• More or less so depending

on surface stability

© 2010 ANSYS, Inc. All rights reserved. 3 ANSYS, Inc. Proprietary

How: Stability implementation

• Continuity • Momentum

• Turbulence quantities (e.g. k-e)

• Energy (potential temperature)

i

j

j

ieff

jiik

ki x

U

x

U

xp

xUU

xU

t

Px

k

xkU

xk

t jk

T

jj

j

j

T

pjj

j xCxU

xt

k

CPk

Cxx

Uxt j

T

jj

j

2

21

3ihh

hg

G

0,max1 Gk

C

z

gG

hH

eff

gravity waves

mixing, boundary layer height

© 2010 ANSYS, Inc. All rights reserved. 4 ANSYS, Inc. Proprietary

Effects: Mountain waves

Potential temperaturePotential temperature

© 2010 ANSYS, Inc. All rights reserved. 5 ANSYS, Inc. Proprietary

Effect: change in flow topology

NeutralNeutral StableStable

Low Froude number• High terrain elevation• Strong stability• Low wind speed

© 2010 ANSYS, Inc. All rights reserved. 6 ANSYS, Inc. Proprietary

Effect: reduced boundary layer height, reduced mixing

• Equilibrium profiles on flat terrain, roughness z0, Coriolis parameter f

Lfu /*

- u'w'/u* 2

0

0.1

0.2

0.3

0 0.5 1 1.5

zf/u

*

Nicholls, 1985

dT/dz = -9.7 K/km

dT/dz = -9 K/km

dT/dz = -8 K/km

dT/dz = -6.5 K/km

v'w'/u* 2

0

0.1

0.2

0.3

0 0.2 0.4

zf/u

*

Nicholls, 1985

dT/dz = -9.7 K/km

dT/dz = -9 K/km

dT/dz = -8 K/km

dT/dz = -6.5 K/km

0.0

0.5

1.0

0 0.05 0.1Tf/u*

2

zf/u

*

model, -9.7 K /km

model, -9.8 K/km

Hinze

Duynkerke

0

0.5

1

0 5 10k/u*

2

zf/u

*

model, -9.7 K/km

model, -9.8 K/kmHinze

Duynkerke

Turbulence kinetic energyTurbulence kinetic energy Eddy diffusivityEddy diffusivity

© 2010 ANSYS, Inc. All rights reserved. 7 ANSYS, Inc. Proprietary

Effect: reduced boundary layer height and momentum fluxes

• Equilibrium profiles on flat terrain, roughness z0, Coriolis parameter f

• Reduction of fluxes expected slower boundary layer regeneration downstream of forests or large arrays

Lfu /*

- u'w'/u* 2

0

0.1

0.2

0.3

0 0.5 1 1.5

zf/u

*

Nicholls, 1985

dT/dz = -9.7 K/km

dT/dz = -9 K/km

dT/dz = -8 K/km

dT/dz = -6.5 K/km

v'w'/u* 2

0

0.1

0.2

0.3

0 0.2 0.4

zf/u

*

Nicholls, 1985

dT/dz = -9.7 K/km

dT/dz = -9 K/km

dT/dz = -8 K/km

dT/dz = -6.5 K/km

Vertical momentum fluxesVertical momentum fluxes

Increasing free stream stability

© 2010 ANSYS, Inc. All rights reserved. 8 ANSYS, Inc. Proprietary

1S10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

h/(u*/f)

ln

0.7-0.8

0.6-0.7

0.5-0.6

0.4-0.5

0.3-0.4

0.2-0.3

0.1-0.2

0-0.1

Effect: Boundary layer height

Increasing free stream stability Increasing surface stability

Lfu /*fN /

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

25

75

100

© 2010 ANSYS, Inc. All rights reserved. 9 ANSYS, Inc. Proprietary

Example of An Suidhe

Normalised wind speedNormalised wind speed Normalised TINormalised TI

50m50m

30m30m

10m10m

 RMS error [%]Wind speed 

ratio TI  ratioaverage over anemometers 8.9 12.8average highest meas. Heights 6.6 7.6average lowest meas. Heights 12.0 18.4

© 2010 ANSYS, Inc. All rights reserved. 10 ANSYS, Inc. Proprietary

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.