DTU Wind Energy22 January 2020 M.Kelly / 10 years of stability research
> a decade of atmospheric stability research: From p(L–1) to a(Iu , z/L) to proxies to entrainment…
(…“what’s it good for?” )
Dr. Mark KellyRisø Lab/Campus, DTU Wind Energy
for VindKraftNet, 22 Jan. 20201
DTU Wind Energy22 January 2020 M.Kelly / 10 years of stability research
> a decade of atmospheric stability research: From p(L–1) to a(Iu , z/L) to proxies to entrainment…
(…where stability is useful, and where it isn’t?)
Dr. Mark KellyRisø Lab/Campus, DTU Wind Energy
for VindKraftNet, 22 Jan. 20202
Risø DTU, Technical University of DenmarkRisø DTU, Technical University of Denmark
Motivation…
• (Wind energy):
3 17 May 2010From M-O theory to long-term mean wind profiles
real, ‘physical’ parameters
representative winds, Power
Better describe the long-term profile, § over different ranges of conditions § up to larger heights
(2010)
Risø DTU, Technical University of DenmarkRisø DTU, Technical University of Denmark
Modelling and issues
• Microscale (CFD): • large-scale effects missing:
• Realistic forcing (varies in x,y,z,t)• Phenomena from above • Two-way interaction among scales
• Non-stationarity
• Mesoscale: • Lots of physics is unresolved – sub-grid parameterization• PBL schemes have problems
• Un-representative stability / surface interaction• Give improper distributions of stability, other parameters…• Not optimized for wind• ABL top mis-represented
16 March 2011Mark Kelly: "Tall" wind and siting issues4
model/obs. frequency of shear exponent
Risø DTU, Technical University of DenmarkRisø DTU, Technical University of Denmark
Motivation…
• Fundamental concept: for nonlinear functions,
Þ Mean form of Monin-Obukhov stability correction cannot simply use a mean Obukhov length !
→ For long-term profiles, need something else/more…
5 17 May 2010From M-O theory to long-term mean wind profiles
( )( )f x f x¹z zL L
y yæ öæ öç ÷ç ÷ ç ÷è ø è ø
¹
Risø DTU, Technical University of DenmarkRisø DTU, Technical University of Denmark
Long-term adaptation of M-O theory
M-O profile:
Make it long-term:
6 17 May 2010From M-O theory to long-term mean wind profiles
Need the probability distribution of stability, P(L−1)
Risø DTU, Technical University of DenmarkRisø DTU, Technical University of Denmark
A general form for stability distributions:
7 17 May 2010From M-O theory to long-term mean wind profiles
211
12
( ) exp(1 )
LCP L n Ca
a
ss
-- ± ±
±±
±
é ùæ öê úç ÷= -ê úç ÷G + è øë û
where
with scale parameter
1 ,3
a =
à analytically obtain profile0/U u*
3, 1C C- += =
Risø DTU, Technical University of DenmarkRisø DTU, Technical University of Denmark8
…general form of stability distributions P(L−1)
17 May 2010From M-O theory to long-term mean wind profiles
Risø DTU, Technical University of DenmarkRisø DTU, Technical University of Denmark9
…using stability distribution model P(L−1) :
17 May 2010From M-O theory to long-term mean wind profiles
(Høvsøre)
à Need to account for ABL depth h
Risø DTU, Technical University of DenmarkRisø DTU, Technical University of Denmark
Generalize “tall profile” theory: (we adapt Gryning et al. 2007)
Make it long-term:
10 17 May 2010From M-O theory to long-term mean wind profiles
Use effective h, G (or Lmid) in lieu of P(h) , P(G)
Risø DTU, Technical University of DenmarkRisø DTU, Technical University of Denmark11
Long-term ASL and “tall profiles” via P(L−1)
Høvsøre (land sectors)
Hamburg (residential sectors)
17 May 2010From M-O theory to long-term mean wind profiles
DTU Wind Energy, Technical University of Denmark, Risø campus
How well does it extrapolate?
Mark Kelly EWEA (Vienna)12 5 Feb 2013
Abs.%Error in wind speed, vs. relative extrapolation distance:
2012
DTU Wind Energy, Technical University of Denmark, Risø campus
How well does it extrapolate?
Mark Kelly EWEA (Vienna)13 5 Feb 2013
Abs.Error in power density, vs. relative extrapolation distance:
DTU Wind Energy, Technical University of Denmark, Risø campus
How well does it extrapolate, with added flux info?
Mark Kelly EWEA (Vienna)14 5 Feb 2013
%Error in wind speed, vs. relative extrapolation distance:
DTU Wind Energy, Technical University of Denmark, Risø campus
… stability affects k-profilesCorrected/adapted Weiringa89-like formulation
5 Feb 2013 Mark Kelly EWEA (Vienna) 15
10
1 10
1 ( ) ( /1 p) x )( er
hr
rz z z zkz z z z
k zz k f zké ùæ ö- -+ -ê úç ÷- -
+ -øë û
=è
2012-13
DTU Wind Energy, Technical University of Denmark16
buoyancy in RANS (with forests): add B
( )
0dpS
jj i E i S
E E K EU P Bt x x xj e
s-
é ùæ ö¶ ¶ ¶ ¶ ê ú+ - = - + +ç ÷ ê ú¶ ¶ ¶ ¶è ø ê úë û
!"#
1/ 212 ( )dd C cS A z U Eµ= (Sogachev and Panferov, 2006 )
(Sogachev, Kelly, LeClerc 2012 )
dpS US E= µ (Seginer et al., 1976)
( )*1 3 4 52j d d
j i i
KU P C B S St x x
Cx
CEC
ECj
jj j j j
j j j j jesæ ö¶ ¶ ¶ ¶ é ù+ - = - + + -ç ÷ ë ûç ÷¶ ¶ ¶ ¶è ø
( )1 2i iC C Cj j j ja g= - +
( ) ( )23
2 11 1 ( / ) for 0, 1
1 / for 0, 1MY
MY
C C C Ri B
Ri Pj j j jg e
ae
ì é ù- + - - £ ®ï ë û= í- > ®ïî
! !
! !
4 0a = 5 1a =
( γφ = {1, 0} for φ = {ε, ω})
3PS Uµ
In consistent way ‘extra’ coefficients appearing in the supplementary equationshave to be presented as
( )1 1 2*1 ( ) / MYC C CC j j jj = + - -! ! 1 MYa = -! ! 2 0a =Compare with
2012
Risø DTU, Technical University of DenmarkRisø DTU, Technical University of Denmark 17
Improving k-e/k-w (RANS) with stability
( )*
11 PrgB p p d d
B BRiP Y P B S Sa a a a-
= =+ + + + +
( )1 2i BC C Cj j j ja g= - +
( ) ( )2 2 11 1 ( / ) for 0, 1
1 / for 0, 1MY
B
MY
C C C Ri B
Ri Pj j j jg e
ae
ì é ù- + - - £ ®ï ë û= í- > ®ïî
! !
! !
( γφ = {1, 0} for φ = {ε, ω})
Stable limit
( ) ( ) ( )* 11 1 2 1 1 2 1 1 2 1
, ,
2 1.35Pr
1 1.35g g B g
B gg cr g cr B g
Ri Ri RiC C C C Ri C C C C C C
Ri Ri Rij j j j j j j j j j
aa
a-
é ù ×¢ º + - = + - + = + -ê ú
+ê úë û
*, 1
1Prg cr
B
Ria -º 1
, Prg g cr B gRi Ri Ria -= 1*
1.35Pr1 1.35B gRia
- =+ *
,
1.351 1.35
g B g
g cr B g
Ri RiRi Ri
aa
=+
Convective limit treat T later…more research…
,/ MY g g crRi Ri®! !
( )/ 1 ?MY P B TP® - + +! !
2012-3make consistent with length-scale limitation: for ABL flows (coefficient aB on B)
Risø DTU, Technical University of DenmarkRisø DTU, Technical University of Denmark
unsteady (diurnal) RANS result (Sogachev & Kelly, 2012)
Aug 2012Flow Center update18
DTU Wind Energy, Technical University of Denmark, Risø campus
Turbulence, shear, and stability
A “decomposition” of the problem
Balance of TKE (Turbulent Kinetic Energy) !
• Surface-layer limit
where
using
21-Oct 2014
*0 02 2
0 *0 *0
( )/
u gz w TU u U u U z
qa
k q- -!
0de dUuw B Tdt dz
e= = - + + -
( )z B TU uw
ea - -® =
-
0( / )B g wq q=
1Uz TIL e
é ù» + -ê úë û*02.5U us »
( )2*0 0u uwº -
19
2014
DTU Wind Energy, Technical University of Denmark, Risø campus
Stability and shear
ASL (10-40m)
• Can map stability to shear in ASL
20
11 1 5( )
5 | |( )
1zP L
zP La
a a+
--
+
++ ++
+
+»
-
June 2014 / Torque from Wind
P(L-1)
2014
DTU Wind Energy, Technical University of Denmark, Risø campus
Stability and shear
ASL (10-40m) above ASL (60-160m)
• Can map stability to shear in ASL; NOT at current hub heights L ...
21 June 2014 / Torque from Wind
DTU Wind Energy, Technical University of Denmark, Risø campus
A “decomposition” of the problem
Balance of TKE (Turbulent Kinetic Energy) !
• Surface-layer limit
where
using
21-Oct 2014
*0 02 2
0 *0 *0
( )/
u gz w TU u U u U z
qa
k q- -!
0de dUuw B Tdt dz
e= = - + + -
( )z B TU uw
ea - -® =
-
0( / )B g wq q=
1Uz TIL e
é ù» + -ê úë û*02.5U us »
( )2*0 0u uwº -
22
DTU Wind Energy, Technical University of Denmark, Risø campus
(mean) TI ↔ shear
21-Oct 2014
Extended ASL theory (stability-modified profile, TKE): where
0
01 ( )II
ca a a=
+ -0 0 * 0( / )u UI a uka k s a= =
23
DTU Wind Energy, Technical University of Denmark, Risø campus
2014-15 shear/TI Summary
• Above ASL, can get <I> estimate from <α>, with IEC Iref
– Depends on effective roughness (z0 + hills); stability
• Variability: σα ~ 1/U ;
• TI is more important for input to loads (Dimitrov et al 2014)
– P(α) significant for fatigue loads in low-TI conditions
– P(α) can drive blade-tip deflection for extreme-TI
• P(α) è power curve modification
Mark Kelly May 201524
DTU Wind Energy, Technical University of Denmark, Risø campus
buoyant vs. ‘old’ Mann model
A.Chougule / Mark Kelly25 2015
2015stability included in RDT (extra equation), old: 3 parameters
2 extra parameters (Ri, 𝜖") (L, 𝜖, Γ)
DTU Wind Energy22 January 2020 M.Kelly / 10 years of stability research
when is stability “useful” [in Wind Energy] ?
• i.e. when is it a valuable ‘metric’ or input?• often ‘blamed’, but might not need to be accounted for directly…
• a few applications where stability is (less/more) helpful –turbulence length scale, loads inputs–turbulence estimation from {shear, 1/L} in simple places –RANS simulations for wind
»ensemble / statistically-driven–vertical extrapolation (for some/depends) –top-down (entrainment) effects…–LOTS of indirect stuff (wakes, blockage, terrain)
26
DTU Wind Energy, Technical University of Denmark
Stability & TI: obs. vs. IEC”-1” (+Mann-model)
• Affects the shear/turbulence strength, and turb.length scale (L) – G, L (from spectral fits to sonic data) deviate from IEC…– IEC-prescribed s1 (pink) also bad in non-neutral
27 Mark Kelly May 2016
DTU Wind Energy, Technical University of Denmark
Mann-model / for IEC turbulence
28 Mark Kelly May 2016
from Sathe+Mann et al. (2013)
measured su , L , per {U,stability class}
Wind Energy Dept., Technical University of Denmark
…finding Mann-model parameters (without spectra)
• Also account for stability effects, without flux obs., – Using basic/neutral turbulence model
• Peña et al (2010) tried mixing-length concept: • ℓ∗ =
)∗⁄+, +- , with 𝐿 = 1.7 ℓ∗
but note that )∗,
depends on stability (ℓ∗ →3-
4 ⁄- 5in ASL limit)
• For 𝑎) ≡ ⁄𝜎) 𝑢∗ and ⁄𝑐; ≡ 𝐿 ℓ∗ get𝐿 = <=
>?
@?⁄+, +-
– Find 𝑐; ≃ 𝑎) ≃ 2.3 , 𝐿 ≃ @?
⁄+, +-= 𝑧 EFGH
IFGHfor typical range of Γ
– ASL: 𝐿|KLM → 𝑐;𝜅𝑧 = ⁄3𝛼 2 ⁄P Q𝜅𝑧 <=@?,FGHR.S>?@THF
⁄P U
→ 𝜎),VWX= 𝜎YXV ⁄𝑐; 1.1 ⁄U P
but 𝜎),VWX ∝ Γ𝜎YXV…
14 Mar 2018Mark Kelly / RAM29
2018
DTU Wind Energy, Technical University of Denmark
…finding turbulence length-scale, without spectra
P(LMM)P(1.7u* /|dU/dz|)P(2.3u* /|dU/dz|)P(σu /|dU/dz|)
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30 Mark Kelly / RAM 14 Mar 2018
𝐿 ≃ @?⁄+, +-
= 𝑧 EFGHIFGH
(for ABL range of Γ) à don’t need stability; this info is
contained within 𝜎) , 𝑑𝑈/𝑑𝑧
Wind Energy Dept., Technical University of Denmark
…finding Obukhov length (without sonics or ∂T/dz ?!?)
• note that )∗, depends on stability (ℓ∗ →3-
4 ⁄- 5 in M-O limit)
ignoring turb.transport (𝑇/𝜖): à
– recall
– Stability without a sonic anem. or heat flux obs.!
• Get 𝜓 ⁄𝑧 𝐿 → ℓ in terms of obs. 𝑈, 𝜎,, 𝛼– à modified 𝜓/correction above ASL
• but not so accurate above ASL, non-ideal places– …need to deal with Turb.transport (𝑇/𝜖)
dimensionless TKE balance : (κ au) α ≈ IU [1 + z /L - cT T /ϵ]
May 2016Mark Kelly / RAM31
-0.010 -0.005 0.000 0.005 0.010
-0.010
-0.005
0.000
0.005
0.010
0.015
0.020
LMO-1 (m-1 )
z-1 (α/I u
-1)(m
-1)
2016
Wind Energy Dept., Technical University of Denmark
…finding Obukhov length (without sonics or ∂T/dz ?!?)
– )∗,
depends on stability
• Limited success without 1/L, even at simple site:
dimensionless TKE balance : (κ au) α ≈ IU [1 + z /L - cT T /ϵ]
May 2016Mark Kelly / RAM32
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
u* (m/s)
σ U/2.3
z=80m, land
0.0 0.2 0.4 0.6 0.8 1.0-0.2
0.0
0.2
0.4
0.6
0.8
1.0
u*
σ U2.3
1-(κα)
-1T
ϵ
z=80m, land
Wind Energy Dept., Technical University of Denmark
…finding Obukhov length (without sonics or ∂T/dz ?!?)
– )∗,
depends on stability
• Limited success without 1/L, even at simple site:
dimensionless TKE balance : (κ au) α ≈ IU [1 + z /L - cT T /ϵ]
May 2016Mark Kelly / RAM33
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
u* (m/s)
σ U/2.3
z=80m, land
0.0 0.2 0.4 0.6 0.8 1.0-0.2
0.0
0.2
0.4
0.6
0.8
1.0
u*
σ U2.3
1-(κα)
-1T
ϵ
z=80m, land
-0.015 -0.010 -0.005 0.000 0.005 0.010 0.015
-0.015
-0.010
-0.005
0.000
0.005
0.010
0.015
LMO-1 (m-1 )
L MO
-1(α,I u,z,TT MS)(m-1
)
right: modification and inclusion of Turb.transport (𝑇/𝜖)
improves our 1/L estimate !
Wind Energy Dept., Technical University of Denmark
…finding Obukhov length (without sonics or ∂T/dz ?!?)
– )∗,
depends on stability
• Limited utility, even at simple site:
dimensionless TKE balance : (κ au) α ≈ IU [1 + z /L - cT T /ϵ]
May 2016Mark Kelly / RAM34
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
u* (m/s)
σ U/2.3
z=80m, land
0.0 0.2 0.4 0.6 0.8 1.0-0.2
0.0
0.2
0.4
0.6
0.8
1.0
u*
σ U2.3
1-(κα)
-1T
ϵ
z=80m, land
-0.015 -0.010 -0.005 0.000 0.005 0.010 0.015
-0.015
-0.010
-0.005
0.000
0.005
0.010
0.015
LMO-1 (m-1 )
L MO
-1(α,I u,z,TT MS)(m-1
)
recall 2014 result:0
01 ( )II
ca a a=
+ -
DTU Wind Energy, Technical University of Denmark
Probabilistic ABL modelling via RANS
• First try: ensemble of atmospheric-stability states – stability most influences flow field
• shear/profile • wake
– We know how to model stability (𝐿aR) and its PDF; • 𝑃(𝐿aR) has universal shape [Kelly+Gryning 2010]
• We know e.g. limits of effect on shear [Kelly et al 2014]
• summing 𝐿aR regimes: works for modeling 𝑈(𝑧) [Kelly+Troen 2015,16]
• Turbine noise propagation application
ΔSPL(𝑟, 𝑓) = ∑l 𝑎l𝑃 𝐿laR ΔSPL(𝑟, 𝑓|𝐿laR)
Cross Cutting Activity: Wind Turbine Noise35 6 Jan.2017
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DTU Wind Energy, Technical University of Denmark
ABL modelling : flow fields
• ScaDis: RANS w/2-eqn. turbulence model [Sogachev et al 2002…]
– Advanced stability treatment ; satisfies M-O theory [Sogachev+Kelly 2012]
– Captures ABL ’top’ (T-inversion)
– Radiation/clouds also
– Mean fields or diurnal cycles
– Actuator disc à turbulent wake
Cross Cutting Activity: Wind Turbine Noise36 6 Jan.2017
U(m/s)
2.5
5.0
7.5
10.0
12.5
15.0
U(m/s)
2
4
6
8
DTU Wind Energy, Technical University of Denmark
ABL modelling : flow fields
• ScaDis: RANS w/2-eqn. turbulence model [Sogachev et al 2002…]
– Advanced stability treatment ; satisfies M-O theory [Sogachev+Kelly 2012]
– Captures ABL ’top’ (T-inversion)
– Radiation/clouds also
– Mean fields or diurnal cycles
– Actuator disc à turbulent wake
Cross Cutting Activity: Wind Turbine Noise37 6 Jan.2017
U(m/s)
2.5
5.0
7.5
10.0
12.5
15.0
U(m/s)
2
4
6
8
U(m/s)
2
4
6
8
DTU Wind Energy, Technical University of Denmark
Application: turbine noise propagation
• Parabolic Equation (PE): 2-D spectral solver – Frequency-dependent propagation (refractive) – Sound-speed profile (from 𝑈(𝑧) and 𝑇(𝑧))– Acoustic ground impedance [grass]– Input: ScaDis mean flow fields– Source:
• Distributed / lumped: 3 heights (46m, 80m, 114m) • Source spectrum
– Plus geometrical spreading, molec.absorption:
SPL 𝑓, 𝑟 = LW 𝑓 − 10 ln 4𝜋𝑟U − 𝛼 𝑓 𝑟 + Δ𝐿(𝑓, 𝑟)
Cross Cutting Activity: Wind Turbine Noise38 6 Jan.2017
50 100 500 100092
93
94
95
f (Hz)
LW(dB)
Turbine source level
DTU Wind Energy, Technical University of Denmark
results…stable cases
• stable cases
• Colored lines: – with/out T(z) in PE
– Very stable case (blue lines): • less sound, more loss… à loss reduced by including T(z)
– Weakly stable case (red/orange): • Not much change by including T(z) in PE calcs
Cross Cutting Activity: Wind Turbine Noise39 6 Jan.2017
500 1000 1500 2000 2500 300030
35
40
45
50
r(m)
SPL(dB
)
Stable Cases, 2 with T(z) [ExpMAv]
DTU Wind Energy, Technical University of Denmark
Results…
• Re-weighting SPL’s for other sites/climatologies
Cross Cutting Activity: Wind Turbine Noise40 6 Jan.2017
500 1000 1500 2000 2500 3000
35
40
45
50
r(m)
SPL(dB
)
weighted-mean for different P(1/L)-��� -��� -��� -��� ��� ���
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DTU Wind Energy22 January 2020 M.Kelly / 10 years of stability research
Top-down stability effect• Strength of capping inversion (Nc), and ABL depth
– LES confirm
41
0 2 4 6 8 10 12
S[m/s]
0
0.2
0.4
0.6
0.8
1
1.2
z/z i[−
]
log-lawnew formLES
-10 0 10 20 30
E% log−law[%]
0
0.2
0.4
0.6
0.8
1
1.2
z/z i[−
]
ABCDFGHIJKLMNOPQR
-20 -10 0 10 20
E%newform[%]
0
0.2
0.4
0.6
0.8
1
1.2
z/z i[−
]
ABCDFGHIJKLMNOPQR
DTU Wind Energy22 January 2020 M.Kelly / 10 years of stability research
Top-down stability effect• Strength of capping inversion (Nc), and ABL depth
– LES confirm
42
0 2 4 6 8 10 12
S[m/s]
0
0.2
0.4
0.6
0.8
1
1.2
z/z i[−
]
log-lawnew formLES
-20 -10 0 10 20
E%newform[%]
0
0.2
0.4
0.6
0.8
1
1.2
z/z i[−
]
ABCDFGHIJKLMNOPQR
à need to measure stability from above …1/L from surface is part of the story
DTU Wind Energy22 January 2020 M.Kelly / 10 years of stability research
when is stability “useful” [in Wind Energy] ?
• i.e. when is it a valuable ‘metric’ or input?• often ‘blamed’; sometimes no need to be account for it directly…
• a few applications where stability is (less/more) helpful/usable input–turbulence length scale, loads inputs–mean turbulence estimation {shear, 1/L} in simple terrain–RANS simulations for wind
»statistically-driven ensembles using P(1/L) not yet over complex terrain…
–vertical extrapolation (at large z2/z1 where shear fails) –top-down (entrainment) effects…–LOTS of indirect stuff (wakes, blockage, terrain)
43
DTU Wind Energy22 January 2020 M.Kelly / 10 years of stability research
EXTRA Slides
44
DTU Wind Energy, Technical University of Denmark
Mann-model implied s1 (via shear)
• Eddy-lifetime has implicit shear• IEC-recommended constants inconsistent with shear-independence Here:
Using obs. s1(L,G should deviate…)
45 Mark Kelly May 2016