Introduction 11
In order to serve both objectives, the wake model will only look at the interaction of steady wakes.
More complex modelling such as wake meandering of multiple wakes does not lend itself to be validated by lidar due to the latter’s limited spatial and temporal resolution when it comes to scanning large sectors within a wind farm.
The two objectives are addressed in reverse order, beginning with the application of lidar to wake measurements from Chapters 2 to 5. The new wake model is then described in Chapters 6 and 7.
Finally, Chapter 8 gives an account with respect to the objectives and the achievements. These chapters are briefly outlined in the following paragraphs. s
Chapter 2
The present research started when knowledge and experience of wind speed measurements in the wake of a wind turbine with lidars was still limited. To fill this gap, Chapter 2 deals with a lidar simulator which enables testing of measurement strategies and estimation of their error in a virtual environment. The chapter also introduces basic concepts applied in the following chapters for lidar measurements in wakes.
Chapter 3
Wake meandering has often been studied with lidar measurements. In fact, the centre position of the wind deficit can be identified from horizontal or vertical scans of the wake. However, it is not always possible to achieve a sufficient repetition rate of the scanning trajectory. The journal article "Application of staring lidars to study the dynamics of wind turbine wakes" (Trabucchi et al., 2015b) included in this chapter suggests how a sufficient repetition rate can be achieved with an atypical approach and it also shows how insight about wake meandering can be gained from these measurements.
Chapter 4
In Chapter 3 lidar measurements along a fixed direction were analysed in the frequency domain, assuming that the spectral characteristics of the wind could be measured with lidar measurements along a direction. This assumption is verified in the paper "Study of wake meandering by means of fixed point lidar measurements: Spectral analysis of line of sight wind component" (Trabucchi et al., 2015a) included here. In the publication, the results of the full-field experiment of Chapter 3 are confirmed on the one hand by virtual measurements synthesised with the lidar simulator introduced in Chapter 2 and on the other hand by new offshore measurements.
Chapter 5
While the two previous chapters are focused on measurements of the wake meandering, the research of this chapter aims to study 10 min averaged wake profiles obtained from lidar measurements.
The work is reported here in the form of the paper "Nacelle-based Lidar Measurements for the Calibration of a Wake Model at Different Offshore Operating Conditions" (Trabucchi et al., 2017b).
This work describes the experimental setup of the lidar measurements and the methodology applied to calculate the profiles of the wind speed deficit used in the calibration of an analytical wake model.
12 1.3. OBJECTIVES AND STRUCTURE OF THE THESIS
Chapter 6
As explained in Section 1.2.2, most engineering wake models are not suitable for dealing with multiple wakes directly because they solve a two-dimensional, axisymmetric flow. This chapter introduces a three-dimensional model which is applicable also to non-axisymmetric, single or multiple wakes. The development and evaluation of the model are explained by the paper entitled
"3-D shear-layer model for the simulation of multiple wind turbine wakes: description and first assessment" Trabucchi et al., 2017a which is the last paper incorporated into the thesis.
Chapter 7
In this chapter, the 3-D shear-layer model introduced in Chapter 6 is further developed to include the previously excluded induction zone into the domain of the model. Furthermore, Chapter 7 closes the circle between the two main objectives of the thesis comparing the new wake model with the lidar measurements of Chapter 5.
Chapter 8
This chapter closes the thesis with a twofold conclusion: On the one hand, it compares the objective with the achievements. On the other hand, it deals with two questions that are hidden behind the main objectives of the present research:
1. How to deal with the limitations of lidar technology when being applied to wake measurements?
2. How far is it possible to conveniently improve the physics of engineering wake models?
Chapter 2
Lidar simulations for the design of wake measurement campaigns
2.1 Introduction
Doppler wind lidars cannot measure the wind vector at a specific point of interest as wind vanes, cup and sonic anemometers. They measure the component of the wind vector parallel to their pointing direction as a weighted average over a thin (tens of centimetres), but long volume (ten to hundred or more metres) illuminated by their laser.
Nevertheless, they can be implemented for wake measurements. In fact, they can retrieve the wind vector over large surfaces in a relatively short time interval. In the most optimistic scenario, three simultaneous lidar measurements with linearly independent pointing directions and intersecting at – or being representative of – the same point in space are available and can be combined to reconstruct the wind vector. If such configuration cannot be implemented, a wind field reconstruction method based on reasonable assumptions on the wind field (e.g. horizontal homogeneity of wind speed and wind direction, or negligible influence of the vertical flow on the radial wind speed measurements) is applied to estimate the wind vector at the point of interest.
During full-field measurements, it is not easy to identify all the environmental variables defining the actual atmospheric conditions. Hence, it is not always possible to define an accurate model corresponding to the actual situation and, for this reason, also the estimation of the lidar volume average effects might be a cumbersome task.
Lidar simulations provide a practicable alternative to full-field experiments for the verification of the wind field reconstruction methodologies. Lidar measurements are simulated in a well-known wind field and the results of the wind vector reconstruction method are compared to the original wind field which is a perfect reference.
Lidar simulations have been used often in the past, for instance, to investigate the performances of wind lidars (Frehlich, 1996) and to assess the accuracy of turbulence measurements with lidars (Banakh et al., 2005). Lidar simulators have been developed for wind energy applications too, e.g. in order to support the development of scanning strategies for predictive wind turbine control (Raach
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