Wind Energy Handbook. Michael Barton Graham

Чтение книги онлайн.

СКАЧАТЬ for strong winds or gales to develop around the time of the spring and autumn equinoxes. Tropical regions also experience seasonal phenomena, such as monsoons and tropical storms, that affect the wind climate. Indeed, the extreme winds associated with tropical storms may significantly influence the design of wind turbines intended to survive in these locations.

      Although a Weibull distribution gives a good representation of the wind regime at many sites, this is not always the case. For example, some sites showing distinctly different wind climates in summer and winter can be represented quite well by a double‐peaked ‘bi‐Weibull’ distribution, with different scale factors and shape factors in the two seasons, i.e.

      (2.5)

      Certain parts of California are good examples of this.

2.5 Synoptic and diurnal variations

      On shorter timescales than the seasonal changes described in Section 2.4, wind speed variations are somewhat more random and less predictable. Nevertheless, these variations contain definite patterns. The frequency content of these variations typically peaks at around four days or so. These are the ‘synoptic’ variations, which are associated with large‐scale weather patterns, such as areas of high and low pressure and associated weather fronts as they move across the earth's surface. Coriolis forces induce a circular motion of the air as it tries to move from high‐ to low‐pressure regions. These coherent large‐scale atmospheric circulation patterns may typically take a few days to pass over a given point, although they may occasionally ‘stick’ in one place for longer before finally moving on or dissipating.

      Following the frequency spectrum to still higher frequencies, many locations will show a distinct diurnal peak, at a frequency of 24 hours. This is usually driven by local thermal effects. Intense heating in the daytime may cause large convection cells in the atmosphere, which die down at night. This process is described in more detail in Section 2.6 because it also contributes significantly to turbulence, on timescales representative of the size of the convection cells. Land and sea breezes, caused by differential heating and cooling between land and sea, also contribute significantly to the diurnal peak. The daily direction reversal of these winds would be seen as a 12‐hour peak in the spectrum of wind speed magnitude.

2.6 Turbulence

      2.6.1 The nature of turbulence

Turbulence refers to fluctuations in wind speed on a relatively fast timescale, typically less than about 10 minutes. In other words, it corresponds to the highest frequency spectral peak in Figure 2.1. It is useful to think of the wind as consisting of a mean wind speed determined by the seasonal, synoptic, and diurnal effects described previously, which varies on a timescale of one to several hours, with turbulent fluctuations superimposed. These turbulent fluctuations then have a zero mean when averaged over about 10 minutes. This description is a useful one as long as the ‘spectral gap’ as illustrated in Figure 2.1 is reasonably distinct.

      Turbulence is generated mainly from two causes: ‘friction’ with the earth's surface, which can be thought of as extending as far as flow disturbances caused by such topographical features as hills and mountains, and thermal effects, which can cause air masses to move vertically as a result of variations of temperature and hence in the density of the air. Often these two effects are interconnected, such as when a mass of air flows over a mountain range and is forced up into cooler regions where it is no longer in thermal equilibrium with its surroundings.

      Turbulence is clearly a complex process and one that cannot be represented simply in terms of deterministic equations. Clearly it does obey certain physical laws, such as those describing the conservation of mass, momentum, and energy. However, to describe turbulence using these laws it is necessary to take account of temperature, pressure, density, and humidity as well as the motion of the air itself in three dimensions. It is then possible to formulate a set of differential equations describing the process, and in principle the progress of the turbulence can be predicted by integrating these equations forward in time starting from certain initial conditions and subject to certain boundary conditions. In practice of course, the process can be described as ‘chaotic’ in that small differences in initial conditions or boundary conditions may result in large differences in the predictions after a relatively short time. For this reason it is generally more useful to develop descriptions of turbulence in terms of its statistical properties.

      There are many statistical descriptors of turbulence that may be useful, depending on the application. These range from simple turbulence intensities and gust factors to detailed descriptions of the way in which the three components of turbulence vary in space and time as a function of frequency.

      The turbulence intensity is a measure of the overall level of turbulence. It is defined as

      (2.6)

      where σ is the standard deviation of wind speed variations about the mean wind speed , usually defined over 10 minutes or an hour. Turbulent wind speed variations can be considered to be roughly Gaussian, meaning that the speed variations are normally distributed, with standard deviation σ, about the mean wind speed . However, the tails of the distribution may be significantly non‐Gaussian, so this approximation is not reliable for estimating, say, the probability of a large gust within a certain period.

      The turbulence intensity clearly depends on the roughness of the ground surface and the height above the surface. However, it also depends on topographical features, such as hills or mountains, especially when they lie upwind, as well as more local features, such as trees or buildings. It also depends on the thermal behaviour of the atmosphere: for example, if the air near to the ground warms up on a sunny day, it may become buoyant enough to rise up through the atmosphere, causing a pattern of convection cells that are experienced as large‐scale turbulent eddies.

Clearly as the height above ground increases, the effects of all these processes that are driven by interactions at the earth's surface become weaker. Above a certain height, the air flow can be considered largely free of surface influences. Here it can be considered to be driven by large‐scale synoptic pressure differences and the rotation of the earth. This air flow is known as the geostrophic wind. At lower altitudes, the effect of the earth's surface can be felt. This part of the atmosphere is known as the boundary layer. The properties of the boundary layer are important in understanding the turbulence experienced by wind turbines.

2.6.2 The boundary layer

      The principal effects governing the properties of the boundary layer are the strength of the geostrophic wind, the surface roughness, Coriolis effects due to the earth's rotation, and thermal effects.

      The СКАЧАТЬ