Giorgio Crasto University of Cagliari - ITALY Forest Modelling A canopy model for WindSim 4.5.
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Transcript of Giorgio Crasto University of Cagliari - ITALY Forest Modelling A canopy model for WindSim 4.5.
Giorgio Crasto
University of Cagliari - ITALY
Forest ModellingForest Modelling
A canopy model for WindSim 4.5
Giorgio Crasto
University of Cagliari - ITALY
Why the need for a canopy modelWhy the need for a canopy model
0,0
0,5
1,0
1,5
2,0
0,00 0,50 1,00 1,50u/uhc
h/h
c
Roughness Lenght z0 0,6m
0,0
0,5
1,0
1,5
2,0
0,0 0,5 1,0 1,5u'w'/u*2
h/h
c
Roughness Lenght z0 0,6m
Giorgio Crasto
University of Cagliari - ITALY
In the new canopy model of WindSim the In the new canopy model of WindSim the Canopy Layer is solved by the use of Canopy Layer is solved by the use of porosity and drag forces (sinks of porosity and drag forces (sinks of momentum)momentum)
The canopy is described by:The canopy is described by: Height of the canopy – hHeight of the canopy – hcc
The canopy is discretized with a caertain number The canopy is discretized with a caertain number of cells (uniform grid?) of cells (uniform grid?)
Underwood roughness length – zUnderwood roughness length – z00
Porosity – Porosity – Drag coefficients – C1 and C2Drag coefficients – C1 and C2
Giorgio Crasto
University of Cagliari - ITALY
Concept of PorosityConcept of Porosity
Given a Given a generic volumegeneric volume occupied by fluid and occupied by fluid and solid phases, its porosity solid phases, its porosity is defined as the ratio is defined as the ratio
volumeof fluidphases
Vol
Giorgio Crasto
University of Cagliari - ITALY
Given a Given a surface surface partially permeable, also a partially permeable, also a porosity for a 2D windbreak can be defined asporosity for a 2D windbreak can be defined as
S
areaholes
totalarea
Concept of PorosityConcept of Porosity
Giorgio Crasto
University of Cagliari - ITALY
Concept of PorosityConcept of Porosity
Once done an hypothesis on the structure Once done an hypothesis on the structure of the porous region, there is a of the porous region, there is a relation relation linking linking and and SS
x EAST
z HIGH
2
3S 1 1
Darcy’s velocity
Giorgio Crasto
University of Cagliari - ITALY
Every element of the canopy introduces Every element of the canopy introduces in the flow a sink of momentumin the flow a sink of momentum
So inside the canopy the momentum RANS So inside the canopy the momentum RANS equations present an additional termequations present an additional term
x
y
z
x xi t U
i i i
y yi t U
i i i
z zi t U
i i i
U UU p i S
x x x
U UU p j S
x x x
U UU p k g S
x x x
xU 3
NS
m
Advection Diffusion Additional forces: pressure gradient, gravity,
adittional sources
Giorgio Crasto
University of Cagliari - ITALY
The sinks of momentum depend upon The sinks of momentum depend upon porosity and velocity porosity and velocity
A classical approach (for high porous A classical approach (for high porous materials) is to consider the sinks of materials) is to consider the sinks of momentum proportional to the velocitymomentum proportional to the velocity
In the Darcy’s law the advective and In the Darcy’s law the advective and diffusive terms are neglected, so the gravitydiffusive terms are neglected, so the gravity
VCk
Darcy’s law
DV UCP UCS VU
Giorgio Crasto
University of Cagliari - ITALY
Sinks of momentum implemented in the Sinks of momentum implemented in the new version of WindSimnew version of WindSim
Sinks of momentum [N/mSinks of momentum [N/m33]: two terms]: two terms
UUC2ρUC1ρSU
viscous force
pressure force
Since the high Reynolds numbers
pressure >> viscous forces
Giorgio Crasto
University of Cagliari - ITALY
In the canopy model of WindSim 4.5 is possible to set the In the canopy model of WindSim 4.5 is possible to set the drag coefficients C1 and C2 wheredrag coefficients C1 and C2 where
s
1C1 dimensionsnoC2
typermeabili][mk
kkρ
μC1
2
Present modelPresent model
Giorgio Crasto
University of Cagliari - ITALY
How to estimate the porosity k?How to estimate the porosity k?
The relation k vs. The relation k vs. is proposed:is proposed:2
22
k C [m ]1
0
0,002
0,004
0,006
0,008
0,01
0,012
0 20 40 60 80 100
porosity (%)
2C 0,00450799m
In this way it’s possible to estimate the value of the drag coefficient C1 starting from a
given value of porosity
Giorgio Crasto
University of Cagliari - ITALY
0,0
0,5
1,0
1,5
2,0
0,00 0,25 0,50 0,75 1,00 1,25 1,50 1,75u/uhc
h/h
c
porosity 15% , C1 1.450E-01, C2 0 porosity 50%, C1 1.002E-02, C2 0
porosity 84%, C1 1.393E-03 , C2 0 porosity 100%
Giorgio Crasto
University of Cagliari - ITALY
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7
speed [m/s]
heig
ht [m
]
canopy 04b - C1 1,002E-02 canopy 06b - C1=C2=0,5E-02
Giorgio Crasto
University of Cagliari - ITALY
0,0
0,5
1,0
1,5
2,0
0,0 0,5 1,0 1,5u'w'/u*2
h/h
c
porosity 15%, C1 1.450E-01, C2 0 porosity 50%, C1 1.002E-02, C2 0
porosity 84%, C1 1.393E-03, C2 0 porosity 100%
Giorgio Crasto
University of Cagliari - ITALY
ConclusionsConclusions With the proposed canopy model is possible to With the proposed canopy model is possible to
estimate properly the dissipation of momentum estimate properly the dissipation of momentum and the production of turbulence inside a forestand the production of turbulence inside a forest
Further validations are needed in order to state Further validations are needed in order to state more precise guidelines for the choice of the more precise guidelines for the choice of the parameters C1 and C2 used togetherparameters C1 and C2 used together
Masts inside forestsMasts inside forests Wind farms close to forestsWind farms close to forests
A possible treatment of a canopy would be with A possible treatment of a canopy would be with additional sources in the transport equations of k additional sources in the transport equations of k and and