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Generation of Synthetic Turbulence in Arbitrary Domains

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.

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Generation of Synthetic Turbulence in Arbitrary Domains

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  1. 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

  2. Generation of Synthetic Turbulence in Arbitrary Domains – Outline • Motivation • Description of the method • Comparison with the Mann and Sandia methods • Examples • Conclusions

  3. 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

  4. Method for Generating the Turbulence • Introduce cross-covariance tensor • Collectcorrelation information for all points • Fouriertransform and factorization • Introduce random phases and amplitudes and FFT Connell (1982): Ra(r) and Rl(r) given by von Karman (1948) They are also denoted f(r) and g(r)

  5. Method for Generating the Turbulence • Introduce cross-covariance tensor • Collectcorrelation information for all points • Fouriertransform and factorization • Introducerandomphases and amplitudes and FFT

  6. Method for Generating the Turbulence • Introduce cross-covariance tensor • Collectcorrelation information for all points • Fouriertransform and factorization • Introducerandomphases and amplitudes and FFT K(t)is Fourier transformed: Next, S(f)is factored by an eigenvalue decomposition:

  7. Method for Generating the Turbulence • Introduce cross-covariance tensor • Collectcorrelation information for all points • Fouriertransform and factorization • Introducerandomphases and amplitudes and FFT • H(f)contains spectral information • dW(f) contains random amplitudes and phases

  8. Comparisonwith the Mann and SandiaMethods • 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

  9. Example 1 • Generate turbulence along a single rotating blade

  10. 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

  11. 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

  12. 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

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