generation of synthetic turbulence in arbitrary domains

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

lg@civil.aau.dk

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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

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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

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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)

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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

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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:

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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

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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

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Example 1

• Generate turbulence along a single rotating blade

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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

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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

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

lg@civil.aau.dk