# Measurements of High-Frequency Atmospheric Turbulence and Its Impact on the Boundary Layer of Wind Turbine Blades

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Measurements

**length**, which is usually more than 100 times larger than the diameter of a hot-wire, influences the spatially resolution.

## 3. Analysis

- ${\theta}_{2}>{\theta}_{1}$
- The surface is colder than the fluid and the gradient becomes $\partial \theta /\partial z>0$ and therefore, $Ri>0$. Heat is transported by conduction only, and a convection flow does not occur. In this case, the stratification is strong, and turbulence gets damped. The boundary condition is stable for $Ri>0$.
- ${\theta}_{2}={\theta}_{1}$
- The temperature gradient is zero and therefore, $Ri=0$. There is no temperature gradient and therefore, no conduction nor convection. This condition is called neutral.
- ${\theta}_{2}<{\theta}_{1}$
- The surface is warmer than the fluid and the gradient becomes $\partial \theta /\partial z<0$ and therefore, $Ri<0$. Heat is transported by conduction and by convection from the surface to the fluid. The convection results in a vertical, upward component of the flow that interacts with the horizontal velocity component. This leads to the production of turbulence in the boundary layer and therefore, is called unstable.

## 4. Results

- (1)
- 19 October 2010, 8:44 a.m.
- (2)
- 19 October 2010, 8:54 a.m.
- (3)
- 19 October 2010, 8:55 a.m.
- (4)
- 19 October 2010, 8:57 a.m.

#### 4.1. Time Development of a Sample Time Series

#### 4.2. Occurrence Probabilities

#### 4.3. Confidence Considerations

## 5. Impact on Boundary Layer Transition on a Wind Turbine Blade

**low-frequency cut-off**for aerodynamic important turbulence can be given by a simple argument to estimate an

**upper**frequency ${f}^{\u2605}$ for a boundary layer (BL) responding to an oscillating outer flow. Stokes [29], pp 191 ff, showed that this outer flow (with $\omega $) is damped out by viscosity according to $U={u}_{0}\xb7{e}^{-ky}\xb7cos(\omega t-ky)$ with $k=\sqrt{\omega /2\nu}$, $\nu $ being the kinematic viscosity and U being the main flow in the x-direction, with y being perpendicular to that. Now, if we introduce a Stokes boundary layer thickness by ${\delta}_{S}=2\pi /k$, we get ${f}^{\u2605}=4\pi \nu /{\delta}^{2}\approx 200\phantom{\rule{0.277778em}{0ex}}Hz$. Here, we have set ${\delta}_{S}$ to an approximate value of 1 mm, a typical value for laminar boundary layers on airfoils at Reynolds numbers of several million. Therefore, this high-frequency, non-Gaussian regime may play an important role in triggering the TS-type of (blade) boundary layer instability on the pathway towards fully developed turbulence.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Locations of onshore (Kaiser–Wilhelm–Koog) and offshore (FINO3 platform) test sites, 80 km west of the island of Sylt. ©FEZ FH Kiel GmbH, Graphics: Bastian Barton.

**Figure 4.**Shape parameters for all collected measurements. Colors represent locations: offshore, onshore with wind coming from land or sea side. The symbols represent the velocity classes for the wind speed. Measurements with $max\left({s}_{p}^{2}\right)<2$ are shown in grey. For reasons of comparison, Taylor’s and Kolmogorov’s time scales are given in 5 msec and 0.05 msec, respectively. The sensor’s resolution goes down to approximately 0.3 msec only.

**Table 1.**Summary of selected Atmospheric Boundary Layer (ABL) stability cases: wind speeds (${v}_{W}$) and turbulence intensities ($Ti$) from cup anemometers, $Ri$ numbers and estimated ABL states.

Date & Time | Location | ${\mathit{v}}_{\mathit{W}}$ (m/s) | Ti (%) | Ri (-) | Boundary Layer State | |
---|---|---|---|---|---|---|

21 October 2010, 7:56 a.m. | Offshore | 06.6 | 08.2 | −0.54 | Unstable | |

28 April 2008, 9:35 a.m. | Onshore | 06.1 | 11.9 | −0.15 | Unstable | |

19 October 2010, 8:57 a.m. | Offshore | 10.8 | 02.2 | −0.13 | Unstable | * |

19 October 2010, 8:44 a.m. | Offshore | 10.2 | 03.1 | −0.12 | Unstable | * |

19 August 2010, 8:13 a.m. | Offshore | 12.7 | 02.8 | −0.06 | Unstable | |

25 March 2008, 2:55 p.m. | Onshore | 11.3 | 10.8 | −0.03 | Unstable | * |

29 March 2008, 11:44 a.m. | Onshore | 15.3 | 10.6 | −0.01 | Neutral | |

30 March 2008, 6:04 p.m. | Onshore | 15.7 | 05.6 | 00.00 | Neutral | * |

28 April 2008, 2:20 p.m. | Onshore | 05.8 | 02.1 | 00.01 | Neutral | * |

1 May 2008, 2:55 a.m. | Onshore | 06.0 | 06.0 | 00.10 | Stable | |

12 April 2008, 7:24 p.m. | Onshore | 05.2 | 11.0 | 00.28 | Stable |

**Table 2.**Development of Time Series on October 19. Potential temperatures ($\theta $), wind speeds (${v}_{W}$) and turbulence intensities ($Ti$) from cup anemometers, $Ri$ numbers, and estimated ABL states.

Time | ${\mathit{\theta}}_{\mathit{air}}$ (K) | ${\mathit{\theta}}_{\mathit{gnd}}$ (K) | ${\mathit{v}}_{\mathit{W}}$ (m/s) | Ti (%) | Ri (-) | Boundary Layer State | ${\mathit{s}}_{\mathit{p}}^{2}\ne 0$ |
---|---|---|---|---|---|---|---|

8:44 a.m. | 283.6 | 286.8 | 10.2 | 03.1 | −0.12 | Unstable | * |

8:45 a.m. | 283.5 | 286.8 | 10.2 | 03.9 | −0.13 | Unstable | |

8:47 a.m. | 283.4 | 286.8 | 10.0 | 07.5 | −0.14 | Unstable | |

8:49 a.m. | 283.4 | 286.8 | 10.1 | 07.3 | −0.13 | Unstable | |

8:50 a.m. | 283.5 | 286.8 | 09.3 | 06.7 | −0.16 | Unstable | |

8:52 a.m. | 283.5 | 286.8 | 11.2 | 06.0 | −0.11 | Unstable | |

8:54 a.m. | 283.5 | 286.8 | 10.8 | 07.7 | −0.11 | Unstable | * |

8:55 a.m. | 283.2 | 286.8 | 11.2 | 04.2 | −0.12 | Unstable | * |

8:57 a.m. | 283.1 | 286.8 | 10.8 | 02.2 | −0.13 | Unstable | * |

**Table 3.**Correlation of the occurrence probability of a high shape factor to boundary layer state for all 119 measurements.

Boundary Layer State | ||||
---|---|---|---|---|

Unstable | Neutral | Stable | Total | |

All | 84.0 | 23.0 | 12.0 | 119.0 |

Offshore | 65.0 | 00.0 | 00.0 | 065.0 |

Onshore | 19.0 | 23.0 | 12.0 | 054.0 |

All ${\mathit{s}}_{\mathit{p}}^{\mathbf{2}}\ne \mathbf{0}$ | 07.0 | 04.0 | 00.0 | 011.0 |

Probability (%) | 08.3 | 17.4 | 00.0 | 009.2 |

Offshore ${\mathit{s}}_{\mathit{p}}^{\mathbf{2}}\ne \mathbf{0}$ | 04.0 | 00.0 | 00.0 | 004.0 |

Probability (%) | 06.2 | -/- | -/- | 0-/- |

Onshore ${\mathit{s}}_{\mathit{p}}^{\mathbf{2}}\ne \mathbf{0}$ | 03.0 | 04.0 | 00.0 | 007.0 |

Probability (%) | 15.8 | 17.4 | 00.0 | 0-/- |

**Table 4.**Error estimation for the occurrence of non-Gaussian turbulence for onshore stable conditions.

Hypotheses: | |
---|---|

${H}_{0}$ | Occurrence probability is ${\Phi}_{0}=0.167$ in stable conditions |

${H}_{1}$ | Occurrence probability is ${\Phi}_{1}<{\Phi}_{0}$ in stable conditions |

Error Type I | |

Number of samples | 12 |

Occurrence probability | ${\Phi}_{0}=0.167$ |

Expected occurrences | ${E}_{0}=2.00$ |

Variance | ${V}_{0}=1.67$ |

Acceptance region for ${H}_{0}$ | {1…12} |

Rejection region for ${H}_{0}$ | {0} |

Probability of error | 11.2% |

**Table 5.**Error estimation for the occurrence of non-Gaussian turbulence for the onshore

**unstable/neutral**conditions.

Hypotheses: | ||
---|---|---|

${H}_{0}$ | Occurrence probability is ${\Phi}_{0}=0.062$ in unstable/neutral conditions | |

${H}_{1}$ | Occurrence probability is ${\Phi}_{1}>{\Phi}_{0}$ in unstable/neutral conditions | |

Error Type I | Error Type II | |

Number of samples | 42 | |

Occurrence probability | ${\Phi}_{0}=0.062$ | ${\Phi}_{1}=0.167$ |

Expected occurrences | ${E}_{0}=2.58$ | ${E}_{1}=7.00$ |

Variance | ${V}_{0}=2.43$ | ${V}_{1}=5.83$ |

Acceptance region for ${H}_{0}$ | {0…4} | |

Rejection region for ${H}_{0}$ | {5…42} | |

Probability of error | 11.4% | 14.9% |

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**MDPI and ACS Style**

Schaffarczyk, A.P.; Jeromin, A.
Measurements of High-Frequency Atmospheric Turbulence and Its Impact on the Boundary Layer of Wind Turbine Blades. *Appl. Sci.* **2018**, *8*, 1417.
https://doi.org/10.3390/app8091417

**AMA Style**

Schaffarczyk AP, Jeromin A.
Measurements of High-Frequency Atmospheric Turbulence and Its Impact on the Boundary Layer of Wind Turbine Blades. *Applied Sciences*. 2018; 8(9):1417.
https://doi.org/10.3390/app8091417

**Chicago/Turabian Style**

Schaffarczyk, Alois Peter, and Andreas Jeromin.
2018. "Measurements of High-Frequency Atmospheric Turbulence and Its Impact on the Boundary Layer of Wind Turbine Blades" *Applied Sciences* 8, no. 9: 1417.
https://doi.org/10.3390/app8091417