Nico Reinke

The turbulent nature of the atmospheric boundary layer and its impact on the wind energy conversion process

Wind turbines operate in the atmospheric boundary layer, where they are exposed to turbulent atmospheric flows. As the response time of wind turbines is typically in the range of seconds, they are affected by the small-scale intermittent properties of turbulent wind. Consequently, basic features that are known for small-scale homogeneous isotropic turbulence, in particular the well-known intermittency problem, have an important impact on the wind energy conversion process. We report on basic research results concerning the small-scale intermittent properties of atmospheric flows and their impact on the wind energy conversion process. The analysis of wind data shows strong intermittent statistics of wind fluctuations. To achieve numerical modeling, a data-driven superposition model is proposed. For the experimental reproduction and adjustment of intermittent flows, the so-called active grid setup is presented. Its ability to generate reproducible properties of atmospheric flows on the smaller scales of lab...

Multi-scale generation of turbulence with fractal grids and an active grid

Turbulence plays an important role in our everyday life, yet it is still not well understood. Wind tunnel experiments can help to develop generalized descriptions of turbulent flows. However, creating turbulent flows with suitable characteristics for various experiments is still challenging. In this work, fractal and active grids were used to generate multi-scale turbulent flows. Using hot-wire measurements we investigated the influence of different boundary conditions, bar sizes and solidity for fractal grids. We found that the evolution of the flow generated by a fractal grid does not depend on the considered boundary conditions. An alternative to these rigid structured grids is an active grid, which allows for a dynamical generation of flow fields with comparable properties. Experiments were conducted with an active grid in which the distribution of the local solidity was actively changed. A transition between classical and fractal grid type decaying turbulence depending on the active grid excitation protocol was observed. We conclude that the distribution of the local solidity of these grids has a strong influence on the evolution of the generated turbulent flow.

Wind Energy and the Turbulent Nature of the Atmospheric Boundary Layer

The challenge of developing a sustainable and renewable energy supply within the next decades requires collaborative eorts as well as new concepts in the elds of science and engineering. Here we give an overview on the impact of small-scale properties of atmospheric turbulence on the wind energy conversion process. Special emphasis is given to the noisy and intermittent structure of turbulence and its outcome for wind energy conversion and utilization. Experimental, theoretical, analytical, and numerical concepts and methods are presented. In particular we report on new aspects resulting from the combination of basic research, especially in the eld of turbulence and complex stochastic systems, with engineering applications.

On universal features of the turbulent cascade in terms of non-equilibrium thermodynamics

Features of the turbulent cascade are investigated for various datasets from three different turbulent flows. The analysis is focused on the question as to whether developed turbulent flows show universal small scale features. To answer this question, 2-point statistics and joint multi-scale statistics of longitudinal velocity increments are analysed. Evidence of the Markov property for the turbulent cascade is shown, which corresponds to a 3-point closure that reduces the joint multi-scale statistics to simple conditional probability density functions (cPDF). The cPDF are described by the Fokker-Planck equation in scale and its Kramers-Moyal coefficients (KMCs). KMCs are obtained by a self-consistent optimisation procedure from the measured data and result in a Fokker-Planck equation for each dataset. The knowledge of these stochastic cascade equations enables to make use of the concepts of non-equilibrium thermodynamics and thus to determine the entropy production along individual cascade trajectories. In addition to this new concept, it is shown that the local entropy production is nearly perfectly balanced for all datasets by the integral fluctuation theorem (IFT). Thus the validity of the IFT can be taken as a new law of the turbulent cascade and at the same time independently confirms that the physics of the turbulent cascade is a memoryless Markov process in scale. IFT is taken as a new tool to prove the optimal functional form of the Fokker-Planck equations and subsequently to investigate the question of universality of small scale turbulence. The results of our analysis show that the turbulent cascade contains universal and non-universal features. We identify small scale intermittency as a universality breaking feature. We conclude that specific turbulent flows have their own particular multi-scale cascade, with other words their own stochastic fingerprint.

Stochastic Analysis of a Fractal Grid Wake

We analyze a turbulent flow field generated by a fractal grid, with respect to spatial scale and different downstream positions. 2- and N-point statistics are used for the analysis. 2-point statistics are done by a spectrogram, which shows the spectral energy density in scale r and in distance to the grid x. The loglog-derivative in scale of the spectrogram is calculated and illustrates different scaling regions of the energy cascade. A complete characterization of the turbulent cascade is done by N-point statistic in terms of its stochastic process evolving in scale. This analysis is done in scale r at three characteristic downstream positions. The results of 2- and N-point statistic are interpreted and compared with each other, which provide a deeper understanding of the fractal grid wake.

Application of an Integral Fluctuation Theorem to Turbulent Flows

There is a long lasting discussion on universal properties of turbulence. The following questions arise: do turbulent properties change with the Reynolds number, or are they even dependent on the large scale properties of turbulence? An important feature would be that turbulence could be taken as universal below some scales. In this case, even for turbulent flows which are generated on a large scale by different processes, the same subgrid models can be used, an important aspect for numerical simulations. For large eddy simulations, it is essential to know the connections between larger scales and the unresolved subgrid turbulence. From this aspect it is important to get a profound understanding of the turbulent cascade, relating turbulent structures on different scales. Rigorous results on the turbulent cascade are still missing.

The Langevin Approach: A Simple Stochastic Method for Complex Phenomena

We describe a simple stochastic method, so-called Langevin approach, which enables one to extract evolution equations of stochastic variables from a set of measurements. Our method is parameter free and it is based on the nonlinear Langevin equation. Moreover, it can be applied not only to processes in time, but also to processes in scale, given that the data available shows ergodicity. This chapter introduces the mathematical foundations of this Langevin approach and describes how to implement it numerically. In addition, we present an application of the method to a turbulent velocity field measured in laboratory, retrieving the corresponding energy cascade and comparing with the results from a computer fluid dynamics (CFD) simulation of that experiment. Finally, we describe extensions of the method for time series reconstruction and applications to other fields such as finance, medicine, geophysics and renewable energies.