in Arbitrary Domains Lasse Gilling and Søren R K Nielsen Department of Civil Engineering Aalborg University Denmark Niels N Sørensen National Laboratory for Sustainable Energy RisøDTU Denmark ID: 792262
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Slide1
Generation of Synthetic Turbulence in Arbitrary Domains
Lasse Gilling and Søren R. K. Nielsen
Department of Civil Engineering, Aalborg University, Denmark
Niels N. Sørensen
National Laboratory for Sustainable Energy, Risø-DTU, Denmark
lg@civil.aau.dk
Slide2Generation of Synthetic Turbulence in Arbitrary Domains – Outline
Motivation
Description of the method
Comparison with the Mann and Sandia methodsExamplesConclusions
2
Slide3Motivation
Turbulent inflow condition for CFD simulation of a rotating section of a wind turbine blade
Mann and Sandia methods cannot be used due to computer memory requirement
A large saving is obtained by only generating the needed part of the velocity field
3
Slide4Method for Generating the
Turbulence
Introduce cross-covariance tensor
Collect correlation information for all points
Fourier transform and
factorization
Introduce random phases and amplitudes and FFT
4
Connell (1982):
R
a
(r)
and
R
l
(r)
given
by von Karman (1948)
They are also denoted
f(r)
and
g(r)
Slide5Method for Generating the
Turbulence
Introduce cross-covariance tensor
Collect correlation
information for all pointsFourier
transform
and
factorization
Introduce
random
phases
and amplitudes and FFT5
Slide6Method for Generating the
Turbulence
Introduce cross-covariance tensor
Collect correlation information for all points
Fourier transform
and
factorization
Introduce
random
phases
and amplitudes and FFT
6
Next,
S
(f)
is factored by an eigenvalue decomposition:
K
(t)
is Fourier transformed:
Slide7Method for Generating the
Turbulence
Introduce cross-covariance tensor
Collect correlation information for all points
Fourier transform and factorization
Introduce
random
phases
and amplitudes and FFT
7
H
(f)
contains spectral information
d
W
(f)
contains random amplitudes and phases
Slide8Comparison
with
the Mann and Sandia Methods
Sandia method:Can be modified to generate incom-pressible turbulence
Uses 1D FFT
Points can be clustered in rotor plane
Number of entries
Mann method:
Generates incompressible turbulence
Uses 3D FFT
Points are required to be placed equidistant in a 3D Cartesian grid
Number of entries
8
Present method:
G
enerates incompressible turbulence
Uses 1D FFT
Points can be placed freely
and move in time
Number of entries
N
t
: Number of time steps,
N,M:
Number of points in rotor plane,
M
>>
N
Slide9Example 1
9
Generate turbulence along a single rotating blade
Slide10Example 2
Generate turbulence as in the figure
8×8 points in a 1×1m
2 area (in the rotorplane)512 time steps
Diameter: 80 m
Required RAM: 72MB
Generate the same
field with Mann: 4.3GB
10
Slide11Conclusions
Proposed method can generate synthetic turbulence
Correct spatial correlation
Correct spectraIncompressible fieldLower memory requirement allows finer resolution in rotor area and time
11
Slide12Generation of Synthetic Turbulence in Arbitrary Domains
Lasse Gilling and Søren R. K. Nielsen
Department of Civil Engineering, Aalborg University, Denmark
Niels N. SørensenNational Laboratory for Sustainable Energy, Risø-DTU, Denmarklg@civil.aau.dk