Generation of Synthetic Turbulence in Arbitrary Domains Lasse Gilling and Søren R. K. Nielsen...
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Transcript of Generation of Synthetic Turbulence in Arbitrary Domains Lasse Gilling and Søren R. K. Nielsen...
![Page 1: Generation of Synthetic Turbulence in Arbitrary Domains Lasse Gilling and Søren R. K. Nielsen Department of Civil Engineering, Aalborg University, Denmark.](https://reader033.fdocuments.us/reader033/viewer/2022052509/56649cec5503460f949b8d79/html5/thumbnails/1.jpg)
Generation of Synthetic Turbulence in Arbitrary Domains
Lasse Gilling and Søren R. K. NielsenDepartment of Civil Engineering, Aalborg University, Denmark
Niels N. SørensenNational Laboratory for Sustainable Energy, Risø-DTU, Denmark
![Page 2: Generation of Synthetic Turbulence in Arbitrary Domains Lasse Gilling and Søren R. K. Nielsen Department of Civil Engineering, Aalborg University, Denmark.](https://reader033.fdocuments.us/reader033/viewer/2022052509/56649cec5503460f949b8d79/html5/thumbnails/2.jpg)
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Generation of Synthetic Turbulence in Arbitrary Domains – Outline
• Motivation• Description of the method• Comparison with the
Mann and Sandia methods
• Examples• Conclusions
![Page 3: Generation of Synthetic Turbulence in Arbitrary Domains Lasse Gilling and Søren R. K. Nielsen Department of Civil Engineering, Aalborg University, Denmark.](https://reader033.fdocuments.us/reader033/viewer/2022052509/56649cec5503460f949b8d79/html5/thumbnails/3.jpg)
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Motivation
• 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
![Page 4: Generation of Synthetic Turbulence in Arbitrary Domains Lasse Gilling and Søren R. K. Nielsen Department of Civil Engineering, Aalborg University, Denmark.](https://reader033.fdocuments.us/reader033/viewer/2022052509/56649cec5503460f949b8d79/html5/thumbnails/4.jpg)
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Method 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
Connell (1982):
Ra(r) and Rl(r) givenby von Karman (1948)
They are also denoted f(r) and g(r)
![Page 5: Generation of Synthetic Turbulence in Arbitrary Domains Lasse Gilling and Søren R. K. Nielsen Department of Civil Engineering, Aalborg University, Denmark.](https://reader033.fdocuments.us/reader033/viewer/2022052509/56649cec5503460f949b8d79/html5/thumbnails/5.jpg)
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Method 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
![Page 6: Generation of Synthetic Turbulence in Arbitrary Domains Lasse Gilling and Søren R. K. Nielsen Department of Civil Engineering, Aalborg University, Denmark.](https://reader033.fdocuments.us/reader033/viewer/2022052509/56649cec5503460f949b8d79/html5/thumbnails/6.jpg)
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Method 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
Next, S(f) is factored by an eigenvalue decomposition:
K(t) is Fourier transformed:
![Page 7: Generation of Synthetic Turbulence in Arbitrary Domains Lasse Gilling and Søren R. K. Nielsen Department of Civil Engineering, Aalborg University, Denmark.](https://reader033.fdocuments.us/reader033/viewer/2022052509/56649cec5503460f949b8d79/html5/thumbnails/7.jpg)
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Method 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
• H(f) contains spectral information• dW(f) contains random amplitudes and
phases
![Page 8: Generation of Synthetic Turbulence in Arbitrary Domains Lasse Gilling and Søren R. K. Nielsen Department of Civil Engineering, Aalborg University, Denmark.](https://reader033.fdocuments.us/reader033/viewer/2022052509/56649cec5503460f949b8d79/html5/thumbnails/8.jpg)
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Comparison 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
Present method:• Generates
incompressible turbulence
• Uses 1D FFT
• Points can be placed freely and move in time
• Number of entries
Nt: Number of time steps, N,M: Number of points in rotor plane, M >> N
![Page 9: Generation of Synthetic Turbulence in Arbitrary Domains Lasse Gilling and Søren R. K. Nielsen Department of Civil Engineering, Aalborg University, Denmark.](https://reader033.fdocuments.us/reader033/viewer/2022052509/56649cec5503460f949b8d79/html5/thumbnails/9.jpg)
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Example 1
• Generate turbulence along a single rotating blade
![Page 10: Generation of Synthetic Turbulence in Arbitrary Domains Lasse Gilling and Søren R. K. Nielsen Department of Civil Engineering, Aalborg University, Denmark.](https://reader033.fdocuments.us/reader033/viewer/2022052509/56649cec5503460f949b8d79/html5/thumbnails/10.jpg)
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Example 2
• Generate turbulence as in the figure
• 8×8 points in a 1×1m2 area (in the rotorplane)
• 512 time steps• Diameter: 80 m
• Required RAM: 72MB
• Generate the same field with Mann: 4.3GB
![Page 11: Generation of Synthetic Turbulence in Arbitrary Domains Lasse Gilling and Søren R. K. Nielsen Department of Civil Engineering, Aalborg University, Denmark.](https://reader033.fdocuments.us/reader033/viewer/2022052509/56649cec5503460f949b8d79/html5/thumbnails/11.jpg)
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Conclusions
• Proposed method can generate synthetic turbulence• Correct spatial correlation• Correct spectra• Incompressible field
• Lower memory requirement allows finer resolution in rotor area and time
![Page 12: Generation of Synthetic Turbulence in Arbitrary Domains Lasse Gilling and Søren R. K. Nielsen Department of Civil Engineering, Aalborg University, Denmark.](https://reader033.fdocuments.us/reader033/viewer/2022052509/56649cec5503460f949b8d79/html5/thumbnails/12.jpg)
Generation of Synthetic Turbulence in Arbitrary Domains
Lasse Gilling and Søren R. K. NielsenDepartment of Civil Engineering, Aalborg University, Denmark
Niels N. SørensenNational Laboratory for Sustainable Energy, Risø-DTU, Denmark