Spatial integration effect on velocity spectrum: Towards an interpretation of the − 11/3 power law observed in the spectra of turbine outputs

To improve the turbine operational life, the interaction between flow properties and turbine performance needs to be elucidated. We then propose to examine the physical origin of the power-law scaling in the inertial range of turbine power outputs by experimentally exploring the spectral content of a 1:20 scaled model of a three-bladed horizontal-axis turbine positioned in a 3D turbulent flow. First, measurements confirm that the turbine power frequency spectra exhibit a power law decay proportional to −11/3 in the inertial range. Knowing that the turbine power fluctuations are linearly dependent on the incoming velocity fluctuations, PIV measurements are carried out to study the effect of the spatially integrated velocity onto its resulted spectrum. It is demonstrated that in inhomogeneous anisotropic turbulent flow, the velocity spectrum of its spatial average along N direction(s) has an inertial slope of −5/3 − 2N/3. This information is used to physically interpret the power-law scaling in the inertial range of the turbine power spectra. The previously observed f−11/3 scaling results from a 2D-spatial average velocity field coupled with a spectral average over blades. This physical explanation confirms previous works in which a transfer function was developed between incoming turbulence and the turbine power outputs.