Generation of Synthetic Turbulence in Arbitrary Domains Lasse

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

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 crosscovariance 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) given by von Karman (1948) They are also denoted f(r) and g(r) 4

Method for Generating the Turbulence • • Introduce crosscovariance 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 crosscovariance tensor Collect correlation information for all points Fourier transform and factorization Introduce random phases and amplitudes and FFT K(t) is Fourier transformed: Next, S(f) is factored by an eigenvalue decomposition: 6

Method for Generating the Turbulence • • Introduce crosscovariance tensor Collect correlation information for all points Fourier transform and factorization Introduce random phases and amplitudes and FFT • • H(f) contains spectral information d. W(f) contains random amplitudes and phases 7

Comparison with the Mann and Sandia Methods Sandia method: • Can be modified to generate incompressible turbulence Present method: • Generates incompressible turbulence Mann method: • Generates incompressible turbulence • Uses 1 D FFT • Uses 3 D FFT • Points can be clustered in rotor plane • Points can be placed freely and move in time • Points are required to be placed equidistant in a 3 D Cartesian grid • Number of entries Nt: Number of time steps, N, M: Number of points in rotor plane, M >> N 8

Example 1 • Generate turbulence along a single rotating blade 9

Example 2 • Generate turbulence as in the figure • • • 8× 8 points in a 1× 1 m 2 area (in the rotorplane) 512 time steps Diameter: 80 m • Required RAM: 72 MB • Generate the same field with Mann: 4. 3 GB 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 lg@civil. aau. dk