Turbulence: a Challenging Problem of Wind Energy

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Turbulence a Challenging Problem of Wind Energy
J. Peinke, F. Böttcher, B. Lange U. Foken, D.
Heinemann Carl von Ossietzky University of
Oldenburg Institute of Physics Research and
Competence Center for Wind Energy of Uni
Oldenburg and Uni Hannover
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energy problem

• Global consumption of primary energy 400EJ/a
  400 1018 J/a
• Primary energy production
• 80 fossil sources
• 14 renewable (10 biomass)
• 6 nuclear
• Energy basic source for
• prosperity and poverty
• 1/5 of world population consume 2/3 of the
  energy available
• Worldwide conflicts
• Environmental conditions
• 400EJ/a 100 Gt (1021kg) CO2
• Club of Rome, Kyoto, EU commission -
• demand for reduction of using nonrenewable
  energy sources
• Government report on global changes of the
  environment
• www.iea.org www.iwr.de www.worldbank.org/energy
  www.ecn.nl/main.html www.iwr.de

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energy problem - 2 -
Electricity production of different power
stations
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Wind energy
Effective time of production onshore 2000 -
3000 h/a) offshore 6000 h/a (1 a 8760h)
Typical wind turbines rated energy 1- 2
MW
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challenges for the use of wind energy
fuel turbulent wind
For the efficient use of wind energy we need a
profound knowledge of atmospheric turbulence
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turbulence and wind energy
Large scales meso scales micro scales gt
100km _at_ 10 km lt 1 km
weather
fluctuations
boundary layer
Loads and short time fluctuations
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Large scale wind turbulence and power production
controllable
depending on weather

• Besides the fluctuations in the electricity
  network causes by the consumption -
• wind (and solar) energy add further fluctuations
  to the power supply

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Large scale wind turbulence -2-
Typical electric power consumption in North
Germany
Power demand - wind energy
no wind
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Load peakload
0
27
20
21
22
23
24
25
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Storm Janet gt100 wind energy changes within a
few hours to less than 20 due to emergency shut
down
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meso scale wind turbulence
Open problem the profile of the boundary layer on
the sea within a distance of some 10 km
(Influences of waves and cost?)
Measured data vs Monin Obukhov law
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micro scale wind turbulence

• small scale structures of wind turbulence may
  cause
• Loads on material,
• short time fluctuations of
• power production

• Extreme events like gusts

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micro scale wind turbulence -2-
velocity increments ur, ut
- spatial fluctuations
- temporal fluctuations
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Intermittency and probabilities of ur, ut
spatial fluctuations
temporal fluctuations
P(ut )
P(ur)
factor 106 !
Anormal, nongaussian statistics - intermittency
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Comparison between free field and wind tunnel
data

• Nongaussian statistics resembles statistics of
  local isotropic turbulence from laboratory
  experiments (stationary flow conditions)
• if wind data are conditioned to mean wind
  situations

Knowledge on isotropic turbulence can be used to
understand wind fluctuations like gusts
F. Böttcher, et.al. Boundary-Layer Meteorology
108, 163 (2003)
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isotropic turbulence
structure of small scale turbulence is commonly
investigated by the statistics of velocity
increments

• Kolmogorov 41
• refined Kolmogorov 62
• multiscaling property of turbulence

ESS-Scaling exponents zn for Rl 100 to 5000
zn
n
A. Arneodo et.al. Europhys. Lett (1996)
gt universal structure?
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On a complete stochastic analysis

• Traditional analysis by the structure functions
  lturngt or by the statistics p(ur,r) of velocity
  increments on distinct scales r,
• complete characterization - knowledge of joint
  probability
• Central question how are the relations between
  increments on different scales ri and rj?

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New concept - Markovian cascade process

• Stochastic cascade process in r
• results
• process is Markovian
• p(u1,r1 u2,r2un,rn) f( p(ui,ri uj,rj) )
• process equation Fokker-Planck equation
• process and p(u1 u2un) are given by
• Drift D(1)(u,r)
• Diffusion D(2)(u,r)
• which are measurable quantities

Ch. Renner, et.al. Journal of Fluid Mechanics
433 (2001)
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Verification
with the known Fokker-Planck equation it is
possible to determine numerically the
statistics p(u(r),r) and p(u(r1)u(r0)) and with
this the moments lturngt and the multipoint
statistics of the turbulent velocity filed
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Comparison between free field and wind tunnel
data

• Nongaussian statistics resembles statistics of
  local isotropic turbulence from laboratory
  experiments (stationary flow conditions)
• if wind data are conditioned to mean wind
  situations

Knowledge on isotropic turbulence can be used to
understand wind fluctuations like gusts
F. Böttcher, et.al. Boundary-Layer Meteorology
108, 163 (2003)
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summary

• Wind energy is a very promising renewable energy
  for the next decades
• Scientific challenges are connected with the
  understanding or meteorological turbulence
• It is shown that the small scale wind turbulence
  is closely linked to the fundamental problem of
  isotropic turbulence
• A Marcovian cascade process, as a new tool to
  investigate profoundly the multiscaling
  (multifractal) features turbulence, has been
  presented
• non equilibrium thermodynamics of complex
  structures like turbulence is given by the the
  Fokker-Planck equation

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Measured D(1)(u,r) and D(2)(u,r)
what is a(r,Re) b(r,Re) g(r,Re)
from D(1)(u,r) _at_ g(r) u(r) D(2)(u,r) _at_ a(r)
d(r ) u(r) b(r) u2(r) a(r,Re), d(r,Re) 0
as Re g(r,Re) follows a universal curve
r/l ( l Taylor length ) b(r,Re) strong Re
dependence Reynolds number (Rl85-1181)
Ch. Renner et.al., Phys. Rev. Lett. 89, (2002)
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Verification
with the known Fokker-Planck equation it is
possible to determine numerically the
statistics p(u(r),r) and p(u(r1)u(r0))
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Windenergy - 2 -
Istalled power in Europe 27 GW - Germany 12
GW - Spain 5 GW North America 5 GW -
USA 4.7 GW