Sogachev Andrey Wind Energy Division, Risø National Laboratory for Sustainable Energy, DTU,...
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Transcript of Sogachev Andrey Wind Energy Division, Risø National Laboratory for Sustainable Energy, DTU,...
Sogachev Andrey
Wind Energy Division, Risø National Laboratory for Sustainable Energy , DTU, Building 118, Box 49, DK-4000, Roskilde, Denmark, [email protected]
SCADIS (scalar distribution) model: overview
(Sogachev et al., 2002, 2004; Sogachev and Panferov, 2006; Sogachev et al., 2008, Sogachev 2009)
Basic equations:
momentum, heat,moisture,scalars (CO2, SO2, O3), turbulent kinetic energy (E)
One-and-a-half-order turbulence closurebased on equations of E and ε (dissipation rate) : ( E-l, E-ε.)
E-ω closure based on ω (ε/E) equation
Terrain-following coordinate system
Horizontal and vertical resolutions (depending on a specific problem)
SCADIS model: domain
q(t),T(t), C(t), V(t), U(t)
Clouds ( t )
T ( soil ), q ( soil ), FCO2
( soil ), V = 0 , U = 0
Q0
( t),
l o w e r b o u n d a r y c o n d i t i o n s
3 - 5 km
1 - 10 km
Upper boundary conditions
(Sogachev et al., 2002, 2004; Sogachev and Panferov, 2006; Sogachev et al., 2008, Sogachev 2009)
SCADIS model: physical processes in the model grid-cell
FCO2
E R H
G
y
f
x
f
¶
¶
¶
¶,
10 - 100 m
advection
y
f
x
f
,
(Sogachev et al., 2002, 2004; Sogachev and Panferov, 2006; Sogachev et al., 2008, Sogachev 2009)
Turbulence model: governing equations
.0
i
i
x
U
0
12 j ii i
j ijk j kj i j
u uU U PU U
t x x x
i
j
j
iijji x
U
x
UKEuu
3
2
E
iEijj P
x
EK
xx
EU
t
E
j
ijiE x
UuuP
iiuuE 21
l
EC
2343
EL P
CE
u 212
2 241 3 2 3Lu u u u u
iii uUU with
1 2jj i i
KU C P C
t x x x E
( , , )K f C E
( , , )l f C E
, ,El with
2
1 22 1
k
C C C
Accounting for plant drag and buoyancy: the traditional way
' 'vv
gB w
0
12 j ii i
j ijk j kj
ij i
u uU U PU U
x x xS
t
( Raupach and Shaw, 1982 )( ) ,i d iS c A z U U
?
j i
di
pjE
E E K EU P B
t x x xS S
*1 3 52 4 p dj
j i i
KU P C B
t x xC C S C S
EC
x E
1 2*1 1 max( ) /C C C C l l
( Apsley and Castro, 1997)
max 0.00027 g Cl U f (Blackadar, 1962)
Modelling of Askervein flow
Askervein Hill topographic map (brawn isolines) and dimensionless speed-up, ΔS estimated by SCADIS at z = 10 m above the ground (colored field). Figure 1 also shows the reference site (RS) (with ΔS = 0 ), the 210o wind direction in our simulations and the lines A, AA and B along which the measurements were made. Background of Figure 1 is taken from Castro et al., 2003.
Modelling of Askervein flow
Dimensionless speed-up, ΔS at z = 10 m above the ground along lines A (a) and AA (b). During measurements along line AA two different sets of instruments were used.
(a) (b)
?j Ej i E i
E E K EU P
t x x x
2ECK
ES
ECK
2
1 2 ?j Ej i i
KU C P C
t x x x E
1
2
0 C
CPE
( Ayotte et al., 1999 )
(Sogachev and Panferov., 2006)
Uncertainties: dissipation
Accounting for plant drag and buoyancy: the revised way
' 'vv
gB w
0
12 j ii i
j ijk j kj
ij i
u uU U PU U
x x xS
t
( Raupach and Shaw, 1982 )( ) ,i d iS c A z U U
1 2*1 1 max( ) /C C C C l l ( Apsley and Castro, 1997) max 0.00027 g Cl U f
0
dpS
jj i E i
S
E E K EU P B
t x x x
*1 2 1 2
*dj
j i i
KU P C C B
t x x x E EC C S
*15 2C CC *
13 2C CC 4 0C
1/ 212 ( )dd C cS A z U E (Sogachev and Panferov, 2006 )
(Blackadar, 1962)
(Sogachev 2009 )
dpS S (Seginer et al., 1976)
Accounting for plant drag and buoyancy: the revised way
... ?E
Pt
... ? ? ?E
Pt
*1 2? ?... P
t EC C
2*1
*21 ?
... PCt E
CC
C
E
2
2
1
2*
1
*
1
...
( )B d
P CCt E
C B a a SE
C
Treatment of the plant drag
a)
0 6 12
z / h
0
5
10
c)
0 3 6
b)
-1.0 -0.5 0.0
d)
| U | / u*
0 3 6
z / h
0
1
2e)
< u'w' > / u*2
-1.0 -0.5 0.0
f)
E / u*2
0 3 6
(after Sogachev and Panferov, 2006)
◄Furry hill wind-tunnel experiment(Finnigan and Brunet, 1995)
▲The Pine forest canopy (Katul and Chang, 1999)
►The Elora corn canopy (Wilson et al., 1982; Wilson, 1988)
a)
A h0 2 4
z / h
0
1
2
3
d)
< u'w' > / u*2
-1.0 -0.5 0.0
z / h
0
1
c)
E / u*2
0 3 6
b)
U / u*
0 4 8
e)
U / u*
0 2
f)
E / u*2
0 2 4
b)
|U| / u*
0 3 60.0
0.5
1.0
1.5
c)
< u'w' > / u*2
-1.0 -0.5 0.0
z / h
0.0
0.5
1.0
1.5d)
E / u*2
0 3 60.0
0.5
1.0
1.5
a)
A h
0 10 20
z / h
0.0
0.5
1.0
1.5
Treatment of the plant drag
(Sogachev and
Panferov, 2006)
4
2
6
x / h-10 0 10 20 30
z / h
0.0
0.5
1.0
1.5
2.0
2.5
3.0
1.0
0.5
1.5
1.0
0.5
x / h-10 0 10 20 30
10
5
x / h-10 0 10 20 30
U ( m s-1 ) l ( m ) E ( m2 s-2 )
a) E-l model
4
2
6
x / h-10 0 10 20 30
z / h
0.0
0.5
1.0
1.5
2.0
2.5
3.0
5
10
x / h
-10 0 10 20 30
1.0
1.00.5
1.0
0.5
0.5
x / h
-10 0 10 20 30
U ( m s-1 ) l ( m ) E ( m2 s-2 )
b) E- model
SCADIS reproduces the experimental variation in length scales
The basic requirement of K-theory – that the length scale of the mixing process be substantially smaller than that of the inhomogeneity in the mean scalar or momentum gradient (Corrsin 1974) – is not violated for disturbed flow and for slow spatial variation of cdA (Finnigan and Belcher, 2004).
Verification: low-roughness surface
Converse Prandtl number
1 4
1.35 /(1. 1.35Ri) for Ri 0
1.35 (1 15Ri ) for Ri 0
(Businger et al. 1971, Sogachev et al. 2002)
Wind speed ( m s-1 )Fig. 1 (a) ABL wind evolution and (b) surface characteristics: u* and Monin-Obukhov length, L, during fair weather over low-roughness land derived by E-ω model.
Uncertainties: Turbulent Prandtl number, Pr versus Ri
21Pr ( )z
UP B K Ri B
z
211 Pr ( )z Ri R
UP B K
zi
Verification: low-roughness surface
(Paulson, 1970)
0*
0
( ) lnzu z z
U zz L L
22ln 1 / 2 ln 1 / 2
2arctan / 2 0
5 0
X X
zz XLL
z z
L L
1 4
where 1 15z
XL
Fig. 2 (a) Wind evolutions and (b) wind profiles for different hours in the atmospheric surface layer during fair weather over low-roughness land derived by E-ω and analytical models.
Uncertainties: buoyancy inside canopy
1/ 212 ( )dd cS A z U EC (Sogachev and Panferov, 2006 )
? 12 (Ri)const C f 1 2 1 212 12 (Ri)C const C f