On the velocity at wind turbine and propeller actuator discs

The first version of the actuator disc momentum theory is more than 100 years old. The extension towards very low rotational speeds with high torque for discs with a constant circulation became available only recently. This theory gives the performance data like the power coefficient and average velocity at the disc. Potential flow calculations have added flow properties like the distribution of this velocity. The present paper addresses the comparison of actuator discs representing propellers and wind turbines, with emphasis on the velocity at the disc. At a low rotational speed, propeller discs have an expanding wake while still energy is put into the wake. The high angular momentum of the wake, due to the high torque, creates a pressure deficit which is supplemented by the pressure added by the disc thrust. This results in a positive energy balance while the wake axial velocity has lowered. In the propeller and wind turbine flow regime the velocity at the disc is 0 for a certain minimum but non-zero rotational speed. At the disc, the distribution of the axial velocity component is non-uniform in all actuator disc flows. However, the distribution of the velocity in the plane containing the axis, the meridian plane, is practically uniform (deviation <0.2 %) for wind turbine disc flows with tip speed ratio λ>5, almost uniform (deviation ≈2 %) for wind turbine disc flows with λ=1 and propeller flows with advance ratio J=π, and non-uniform (deviation 5 %) for the propeller disc flow with wake expansion at J=2π. These differences in uniformity are caused by the different strengths of the singularity in the wake boundary vorticity strength at its leading edge.

On the velocity at wind turbine and propeller actuator discs

The first version of the actuator disc momentum theory is more than 100 years old. The extension towards very low rotational speeds with high torque for discs with a constant circulation, became available only recently. This theory gives the performance data like the power coefficient and average velocity at the disc. Potential flow calculations have added flow properties like the distribution of this velocity. The present paper addresses the comparison of actuator discs representing propellers and wind turbines, with emphasis on the velocity at the disc. At a low rotational speed, propeller discs have an expanding wake while still energy is put into the wake. The high angular momentum of the wake, due to the high torque, creates a pressure deficit which is supplemented by the pressure added by the disc thrust. This results in a positive energy balance while the wake axial velocity has lowered. In the propeller and wind turbine flow regime the velocity at the disc is 0 for a certain minimum but non-zero rotational speed. At the disc, the distribution of the axial velocity component is non-uniform in all flow states. However, the distribution of the velocity in the plane containing the axis, the meridian plane, is practically uniform (deviation approximately 0.2 %) for wind turbine disc flows with tip speed ratio λ > 5, almost uniform (deviation 2 %) for wind turbine disc flows with λ = 1 and propeller flows with advance ratio J = Π, and non-uniform (deviation 5 %) for the propeller disc flow with wake expansion at J = 2 Π. These differences in uniformity are caused by the different strengths of the singularity in the wake boundary vorticity strength at its leading edge.

DIFFERENCES IN THE STABILITY OF THE HEART INTERBEAT RATE DURING WAKE AND SLEEP PERIODS

The Allan (ADEV) and Hadamard (HDEV) deviations are mathematical tools developed in the field of time and frequency metrology to define quantitatively the frequency instabilities of an oscillator; which consist of any unwanted departure from its nominal frequency value over a specified time interval. We use both deviations to analyze the stability of the heart interbeat rate for healthy subjects and patients with congestive heart failure (CHF) during wake and sleep periods. We find that the ADEV and HDEV profiles for the subjects in the CHF group exhibit remarkably different trends between wake and sleep periods, namely, larger dispersion between the results for each member of the group while the results for the healthy subjects show some uniformity across the members of the group. Moreover, we observe that the stability for both groups degrades for low scales during the sleep phase, being more significant for the CHF group. Both ADEV and HDEV statistics reveal that healthy data can be described by more uniform deviation values along several scales, particularly for the wake period, whereas CHF data shows important variations.