Turbulence and Wind Energy

Claudia Brunner

The Earth is on track to warm 2.7°C by the end of the century [1]. Decarbonising global energy generation is one of the greatest challenges facing humanity and requires both scientific discovery and technological innovation. Using the unique facilities at the Max Planck Institute for Dynamics and Self-Organisation, we combine laboratory experiments and field measurements to optimise wind energy from the blade scale to the farm scale.

We focus on the following three topics:

Wakes and turbine-turbine interactions in wind farms. In wind farms, the wakes of upstream turbines reduce the performance of downstream ones. We study the re-energising of the wake region through turbulent entrainment of momentum and the resulting interactions with downstream turbines.

The unsteady aerodynamics of wind turbine blades. Atmospheric turbulence leads to rapidly fluctuating loads on turbine blades, which impede performance predictions and cause mechanical failure. We study the underlying time-resolved flow physics and further our understanding of non-stationary flows.

Novel sensing technology for atmospheric turbulence. Atmospheric turbulence is notoriously difficult to study because conventional sensors are fragile, costly and lack spatial resolution. Based on novel sensing technology, we develop a durable high-resolution sensor for use in harsh atmospheric conditions.

In addition to our fluid dynamics research, we conduct public policy research on the following topic:

The representation of wind energy in techno-economic models. As wind energy deployment increases, so does public opposition to it. We investigate the effect of non-monetary factors like public acceptance on wind energy deployment in techno-economic models.

The fundamental challenge in the study of wind turbines lies in the large separation of scales, which is represented by the Reynolds number Re=UL/ν. Here, U is a characteristic velocity of the flow, L is a characteristic length scale and ν is the kinematic viscosity of air.

For example, the turbine Reynolds number ReD=UD/ν, which is based on the turbine diameter D and the mean free-stream velocity U, describes the size of the turbine relative to the surrounding flow. Modern wind turbines are among the largest machines ever built, spanning diameters of up to 220 m. Turbine Reynolds numbers up to ReD=1.5 ×108 are possible and even larger designs are being considered. High Reynolds numbers are thus a defining feature of real-world wind turbines. State-of-the-art numerical simulations are nowhere near capable of resolving the full range of scales encountered in wind farms. This makes field measurements of the flows around real wind turbines crucial, but fully characterising atmospheric turbulence down to its smallest scales requires durable sensors with sub-millimeter resolution. Atmospheric flows are heterogeneous in space and time, so that elucidating the underlying flow physics through field measurements alone is challenging. A combination of field studies and laboratory experiments is therefore necessary. However, small-scale experiments only replicate the true flow physics if dynamic similarity with real-world conditions is achieved. This requires that all non-dimensional parameters are matched to full-scale flows. That includes the turbine Reynolds number as well as a non-dimensional time scale, for example the tip speed ratio TSR=ωR/U, which describes the velocity of the turbine rotation relative to the incoming flow. Here, ω is the rotational velocity of the turbine and R is its radius. It is impossible to match both non-dimensional parameters in a conventional atmospheric-pressure wind tunnel because the use of a scaled-down model lowers the Reynolds number. The only way to increase the Reynolds number is then to increase the flow velocity, but this lowers the tip speed ratio. Unfeasibly high rotation rates are then needed to maintain realistic tip speed ratios.

To overcome this limitation, we conduct our research in the Variable Density Turbulence Tunnel (VDTT) at our institute [2]. It uses compressed gas to achieve high Reynolds numbers at low velocities. Pressurizing the gas inside increases its density and thus the Reynolds number of the flow without altering the velocity. Using a gas with a lower dynamic viscosity than air, for example SF6, additionally increases the Reynolds number. The tip speed ratio remains unaffected. By combining high-resolution field measurements and pressurized wind tunnel experiments we uncover the fundamental fluid dynamics of wind turbines.


Wakes of upstream turbines interfere with downstream turbines.

Wind turbines are often grouped together in wind farms that cover large areas of land and sea. Due to the close spacing, wakes from upstream turbines influence downstream turbines, thereby reducing their power output. Current wind farm designs are informed by simple wake models, which are known to not capture the complex flow phenomena involved [3]. Even improved simulations providing insight into farm-scale flows, like Large-Eddy Simulations, must parameterize the turbines and their wakes to remain computationally tractable. Our lack of understanding of the underlying flow physics limits the accuracy of the parameterizations therein. We know that 1) a wind farm flow is more than a simple superposition of many individual turbine flows and 2) the local meteorological conditions intricately affect turbine- and farm-scale flows [4]. In our group, we study the fundamental fluid dynamics associated with wind turbine wakes and turbine-turbine interactions with the aim of optimising the efficacy of wind farms.

Wind farm performance depends on the transport and redistribution of momentum from the turbulent atmospheric flow to the wind turbines [5]. Turbine fatigue loading depends on the length scales and intensity of turbulent fluctuations in the inflow. The turbulence is characterised by the turbulence Reynolds number Reλ=urmsλ/ν, based on the turbulent velocity fluctuations and the Taylor scale λ. While the turbine Reynolds number ReD describes the mean flow at the turbine, Reλ gives the strength of turbulent fluctuations a free-standing turbine may encounter. Typical large-scale fluctuations are around a hundred meters in diameter and carry velocity fluctuations of around 1 m/s. Turbulence Reynolds numbers are commonly around Reλ=10000. The Variable Density Turbulence Tunnel (VDTT) at the MPI-DS, which uses sulphur hexaflouride (SF6) at up to 19 bar as the working fluid, is the only wind tunnel capable of matching both ReD and Reλ to real conditions. We are using the VDTT to conduct the first ever laboratory studies of the interaction of two wind turbines at full dynamic similarity to real wind turbines.

[1] IPCC, 2021: Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change [Masson-Delmotte, V., P. Zhai, A. Pirani et al. (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 2391 pp.

[2] Bodenschatz, E., Bewley, G. P., Nobach, H., Sinhuber, M. and Xu, H. (2014). “Variable density turbulence tunnel facility” Rev. Sci. Instrum. 85, 093908

[3] Porté-Agel, F., Bastankhah, M. and Shamsoddin, S. (2020): Wind-turbine and wind-farm flows: a review Bound.-Layer Meteorol. 174, 1-59

[4] Meneveau, C. (2019): Big wind power: seven questions for turbulence research J. Turbul. 20 (1), 2-20.

[5] Milan, P., Wächter, M. and Peinke, J. (2013): Turbulent character of wind energy, Phys. Rev. Lett. 110, 138701.

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