3 results
Enhanced recovery caused by nonlinear dynamics in the wake of a floating offshore wind turbine
- Thomas Messmer, Michael Hölling, Joachim Peinke
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- Journal:
- Journal of Fluid Mechanics / Volume 984 / 10 April 2024
- Published online by Cambridge University Press:
- 16 April 2024, A66
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An experimental study in a wind tunnel is presented to explore the wake of a floating wind turbine subjected to harmonic side-to-side and fore–aft motions under laminar inflow conditions. The wake recovery is analysed as a function of the frequency of motion $f_p$, expressed by the rotor-based Strouhal number, $St = f_p D / U_{\infty }$ ($D$ is the rotor diameter, $U_{\infty }$ the inflow wind speed). Our findings indicate that both directions of motion accelerate the transition to the far-wake compared with the fixed turbine. The experimental outcomes confirm the computational fluid dynamics results of Li et al. (J. Fluid Mech., vol. 934, 2022, p. A29) showing that sideways motions lead to faster wake recovery, especially for $St \in [0.2, 0.6]$. Additionally, we find that fore–aft motions also lead to better recovery for $St \in [0.3, 0.9]$. The recovery is closely linked to nonlinear spatiotemporal dynamics found in the shear layer region of the wake. For both directions of motion and $St \in [0.2, 0.55]$, the noisy wake dynamics lock in to the frequency of the motion. In this synchronised-like state, sideways motions result in large coherent structures of meandering, and fore–aft movements induce coherent pulsing of the wake. For fore–aft motion and $St \in [0.55, 0.9]$, the wake shows a more complex quasiperiodic dynamic, namely, a self-generated meandering mode emerges, which interacts nonlinearly with the excitation frequency $St$, as evidenced by the occurrence of mixing components. The coherent structures grow nonlinearly, enhance wake mixing and accelerate the transition to the far-wake, which, once reached, exhibits universal behaviour.
Insights into the periodic gust response of airfoils
- Nathaniel J. Wei, Johannes Kissing, Tom T. B. Wester, Sebastian Wegt, Klaus Schiffmann, Suad Jakirlic, Michael Hölling, Joachim Peinke, Cameron Tropea
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- Journal:
- Journal of Fluid Mechanics / Volume 876 / 10 October 2019
- Published online by Cambridge University Press:
- 31 July 2019, pp. 237-263
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The unsteady lift response of an airfoil in a sinusoidal gust has in the past been modelled by two different transfer functions: the first-order Sears function and the second-order Atassi function. Previous studies have shown that the Sears function holds in experiments, but recently Cordes et al. (J. Fluid Mech., vol. 811, 2017) reported experimental data that corresponded to the Atassi function rather than the Sears function. In order to clarify the observed discrepancy, the specific differences between these models are isolated analytically. To this end, data and analysis are confined to unloaded airfoils. These differences are related to physical gust parameters, and gusts with these parameters are then produced in wind-tunnel experiments using an active-grid gust generator. Measurements of the unsteady gust loads on an airfoil in the wind tunnel at Reynolds numbers ($Re_{c}$) of $2.0\times 10^{5}$ and $2.6\times 10^{5}$ and reduced frequencies between $0.09$ and $0.42$ confirm that the Sears and Atassi functions differ only in convention: the additional gust component of the Atassi problem can be scaled so that the Atassi function collapses onto the Sears function. These experiments, complemented by numerical simulations of the set-up, validate both models across a range of gust parameters. Finally, the influence of boundary-layer turbulence and the turbulent wake of the gust generator on experimental convergence with model predictions is investigated. These results serve to clarify the conditions under which the Sears and Atassi functions can be applied, and demonstrate that the Sears function can effectively model unsteady forces even when significant fluctuations in the streamwise velocity are present.
On universal features of the turbulent cascade in terms of non-equilibrium thermodynamics
- Nico Reinke, André Fuchs, Daniel Nickelsen, Joachim Peinke
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- Journal:
- Journal of Fluid Mechanics / Volume 848 / 10 August 2018
- Published online by Cambridge University Press:
- 05 June 2018, pp. 117-153
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Features of the turbulent cascade are investigated for various datasets from three different turbulent flows, namely free jets as well as wake flows of a regular grid and a cylinder. The analysis is focused on the question as to whether fully developed turbulent flows show universal small-scale features. Two approaches are used to answer this question. First, two-point statistics, namely structure functions of longitudinal velocity increments, and, second, joint multiscale statistics of these velocity increments are analysed. The joint multiscale characterisation encompasses the whole cascade in one joint probability density function. On the basis of the datasets, evidence of the Markov property for the turbulent cascade is shown, which corresponds to a three-point closure that reduces the joint multiscale statistics to simple conditional probability density functions (cPDFs). The cPDFs are described by the Fokker–Planck equation in scale and its Kramers–Moyal coefficients (KMCs). The KMCs are obtained by a self-consistent optimisation procedure from the measured data and result in a Fokker–Planck equation for each dataset. Knowledge of these stochastic cascade equations enables one 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. The 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 in the datasets. 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 multiscale cascades, in other words, their own stochastic fingerprints.