Aerodynamic calculation of loads and dynamic behavior of wind ...

it is obvious that the power output of a wind turbine is a function of the power
coefficient, the air density, the rotor area and the wind velocity. The power
coefficient varies with the tip speed ratio (see Chapter 3) and describes the fraction of
the power in the wind that may be converted into mechanical work. Although several
attempts have been made in order to increase its value, a maximum limit of 0.593
cannot be exceeded, as will be proven later on. As for the air density, its variations
are essentially negligible. Thus, major changes in the power output can only be
achieved by two means: either by increasing the swept area of the rotor, or by
locating the wind turbines on sites with higher wind speeds. More specifically, a
doubling of the rotor diameter leads to a four-time increase in power output. The
influence of the wind speed is, of course, more pronounced with a doubling of wind
speed leading to an eight-fold increase in power. This fact has led to today’s
enormous rotor diameters of 60m and tower heights of more than 100m, in order to
take advantage of the increase of wind speed with height (see Chapter 2). Both these
characteristics of modern wind turbines, despite the remarkable addition to the
efficiency, encumber the tower with all the greater wind loads. The blades, the tower
and finally the foundation of a wind turbine are exposed to even more significant
forces and moments as the wind speed and rotor diameters increase. Furthermore,
these loads are of a dynamic nature, that is, they vary with time and spatial distance,
an aspect that renders their calculation a rather complex procedure. This complexity
is based on two different factors: Firstly, the wind variations are impossible to predict
and calculate using any kind of deterministic methods. The mean wind speed is
subject to changes from one point to another, let alone the wind turbulence, which is
a continuously varying parameter, which can only be approached by means of
stochastic analysis. Secondly, the aerodynamic characteristics of the rotor follow their
own, rather complicated physical laws. The less the simplistic assumptions made
regarding these rules, the more one has to indulge into the subject in order to reach an
adequate knowledge level.
1.2 Thesis’s objective
The aim of this thesis is to offer a concise description of the phenomenon of
airflow passing through the rotor of a modern horizontal-axis wind turbine, as well as
an algorithm with the utilization of which the dimensioning of the tower can be
achieved. In chapters 2, 3 the above-mentioned complex concepts are analyzed with
the simpler language possible. Additionally, chapter 2 describes the way a stochastic
wind field can be digitally simulated, while chapter 3 provides the means by which
the aerodynamic theory of the rotating rotor exposed to airflow can be
computationally approached. In chapter 4 the reader shall find some information
regarding the algorithm produced in this thesis, in the MATLAB environment, for
both the simulation of the wind velocity field and the calculation of the loads exerted
on the rotor and, consequently on the top of the tower. In the 5 th chapter of this thesis
the results of the program’s execution are demonstrated. These results are obtained
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