On the scaling of wind turbine rotors

Abstract

Abstract. This article formulates laws for scaling wind turbine rotors. Although the analysis is general, the article primarily focuses on subscaling, i.e. on the design of a smaller size model mimicking a full-scale machine. The present study considers both the steady-state and transient response cases, including the effects of aerodynamic, elastic, inertial and gravitational forces. The analysis reveals the changes to physical characteristics induced by a generic change of scale, indicates which characteristics can be matched faithfully by a sub-scaled model, and states the conditions that must be fulfilled for desired matchings to hold. Based on the scaling laws formulated here, two different strategies to design scaled rotors are considered: in the first strategy the scaled model is simply geometrically zoomed from the reference full-scale one, while in the second strategy the scaled rotor is completely redesigned in order to match desired characteristics of the full-scale machine. The two strategies are discussed and compared, highlighting their respective advantages and disadvantages. The comparison considers the scaling of a reference 10-MW wind turbine of about 180 m of diameter down to three different sizes of 54, 27 and 2.8 m. Simulation results indicate that, with the proper choices, several key performance indicators can be accurately matched even by models characterized by significant scaling factors.

Wind tunnel testing of wake steering with dynamic wind direction changes

“…Given a set of ambient wind conditions, the FLORIS model computes the steady-state flow within a wind farm and, in turn, the power output of the individual turbines (Doekemeijer et al, 2019). The present results were obtained with the MATLAB implementation available online (Doekemeijer and Storm, 2018), using the selfSimilar velocity deficit, the rans deflection, the wake model of Bastankhah and Porté-Agel (2016), the quadraticRotorVelocity wake combination, and the crespoHernandez added turbulence (Crespo and Hernández, 1996). To improve accuracy at the cost of a slightly increased computational effort, the power of a turbine is computed by integrating the flow at the rotor disk using P = 1/2ρ A V 3 C P dA (where ρ is air density, V the local wind speed, and A the rotor disk area), instead of the original implementation based on the rotor-average wind speed.…”

“…The ambient wind field in the model is horizontally sheared to match the wind tunnel inflow. The model was tuned based on wake measurements of one isolated G1 turbine, as discussed in Campagnolo et al (2019), obtaining the parameters reported in Table 1; notice that, having been tuned with ad hoc measurements, the values of these parameters differ from the ones provided by Bastankhah and Porté-Agel (2016) and Crespo and Hernández (1996). The wind speed at y = 0 was set to 5.25 m s −1 , while the turbulence intensity was set to 6.1 %.…”

How realistic are the wakes of scaled wind turbine models?

“…Quantities referred to the scaled model are indicated with the subscript (•) M , while quantities referred to the full-scale physical system with the subscript (•) P . Scaling is defined by two parameters (Bottasso and Campagnolo, 2020;Canet et al, 2020): the length scale factor n l = l M /l P , where l is a characteristic length (for example the rotor radius R), and the time compression ratio n t = t M /t P , where t is time. In the present case n l = 1/162.1 and n t = 1/82.5.…”

“…-Detailed flow measurements are possible with a plethora of devices, from standard pressure and hot-wire probes, to PIV (Meinhart, 1999) and scanning lidars (van Dooren et al, 2017), whereas measurements of comparable accuracy are today hardly possible at full scale. Additionally, time flows faster in a scaled experiment than at full scale (Bottasso and Campagnolo, 2020;Canet et al, 2020;Campagnolo et al, 2020), which means that a large informational content can be accumulated over relatively short periods of time. small-scale model blade compared to a full-scale machine implies very different aerodynamic characteristics of the airfoils, which in turn drive a number of specific design choices of the scaled model (Bottasso and Campagnolo, 2020;Canet et al, 2020).…”

“…Additionally, time flows faster in a scaled experiment than at full scale (Bottasso and Campagnolo, 2020;Canet et al, 2020;Campagnolo et al, 2020), which means that a large informational content can be accumulated over relatively short periods of time. small-scale model blade compared to a full-scale machine implies very different aerodynamic characteristics of the airfoils, which in turn drive a number of specific design choices of the scaled model (Bottasso and Campagnolo, 2020;Canet et al, 2020). Notwithstanding the differences caused by the chord-based Reynolds mismatch, it is relatively easy -as shown more in detail later on-to match the main processes taking place in the outer shell of the near wake, as well as the ones that govern its breakdown and the characteristics of the far wake.…”