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

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

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 3

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 4 Connell (1982): R a (r) and R l (r) given by von Karman (1948) They are also denoted f(r) and g(r)

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 5

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 6 Next, S(f) is factored by an eigenvalue decomposition: K(t) is Fourier transformed:

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 7 H(f) contains spectral information dW(f) contains random amplitudes and phases

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 8 Present method: Generates 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

Example 1 9 Generate turbulence along a single rotating blade

Example 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

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 11

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