ISSN 1650-6553 Nr 219
Turbulence Intensity in Complex Environments and its Influence on Small Wind Turbines
Nicole Carpman
Copyright © Nicole Carpman and the Department of Earth Sciences, Uppsala University.
Printed at the Department of Earth Sciences Geotryckeriet, Uppsala University, Uppsala, 2011
A BSTRACT
The market of wind power as a sustainable energy source is growing, both on large and small scale. Conventional large scale wind turbines normally operate in uniform areas where expected wind speeds and turbulence characteristics are well investigated and the constructional design of the wind turbines is regulated by standard classes for different
external conditions. Small scale wind turbines (SWT), on the other hand, are sometimes placed in more complex environments where the turbulence conditions are rougher. A larger amount of turbulence will generate a larger amount of fatigue loadings on the construction, increasing the risk of breakdown. It is therefore of major concern to perform more measurements and further investigate the turbulence characteristics in complex environments and the effect that these will have on small wind turbine construction. Thus, turbulence is measured with sonic anemometers at two sites with complex environments; at an urban site above a rooftop in a medium sized city (Uppsala, Sweden) and above a forest in Norunda (outside Uppsala) at two heights, near the treetops (33 ) defined as complex and further up (97 ) defined as more uniform. The turbulence data is analyzed and the results are compared to the normal turbulence model (NTM) as it is defined for the standard SWT classes by the International Electrotechnical Commission in the International standard 61400‐2: Design requirements for small wind turbines (IEC, 2006). Measurements of 10 minute standard deviations of
longitudinal wind speed ( ) and turbulence intensity ( ) are reported, as well as the distributions of and of 10 minute mean wind speeds ( ) for the different sites and stabilities. The results show that the NTM represents the turbulence at 97 height above the forest only for light wind speeds, smaller than 10 / , but underestimates the turbulence for higher wind speeds. It should also be noted that the data is scattered and contain a number of occasions with extreme values of and . For wind speeds higher than 10 / the number of observations is limited but the majority of the observations are more extreme than the NTM. At the complex sites (near the treetops and the rooftop) the NTM clearly underestimates both the magnitude and rate of change of with increasing wind speed, although the
observed wind speeds close to these rough surfaces are low so the conclusions are limited.
Average at 97 height is 19 %, compared to 41 % close above forest and 43 % above rooftop. Mean values of above forest are generally 10 % lower during stable conditions ( ⁄ 0.05 while above rooftop, the wind material is sparse and 95 % of the observations had stable stratification so no dependence on stability can be seen. From these results it can be concluded that the turbulence characteristics close above treetops is similar to those above rooftop, but that the NTM, as it is defined for the standard SWT classes, is not valid in these complex and urban terrains and need to be modified to correctly estimate the turbulence intensities, and consequently also the loadings, affecting small wind turbines located at these kinds of sites.
Key words: turbulence intensity, complex, uniform, urban, small wind turbines, IEC standard
classes, normal turbulence model
R EFERAT
Marknaden för vindkraft som en förnyelsebar energikälla växer snabbt, både stor‐ och småskaligt. Traditionella storskaliga vindkraftverk placeras normalt på homogena platser där vindklimatet och turbulensens karaktär är ganska väl kartlagda och konstruktionsstandarden regleras av standardklasser utifrån olika externa förhållanden. Små vindkraftverk (SWT) å andra sidan placeras ofta i mer komplex eller urban miljö där turbulensen är mer intensiv. En större andel turbulens genererar större utmattningslaster på konstruktionen vilket ökar risken att vindturbinen går sönder. Det är därför av stor vikt att utföra fler mätningar och ytterligare undersöka turbulensen i komplexa miljöer och vilken effekt den kommer ha på de små vindkraftverkens konstruktion. Med anledning av detta så har turbulensdata analyserats från mätningar med sonicanemometrar. Dels på en urban plats, ovanför ett hustak i en medelstor stad (Uppsala, Sverige). Dels vanför en skog i Norunda (utanför Uppsala) på två höjder, nära trädtopparna (33 m) som anses komplex och högre upp (97 m) som anes mer homogen.
Resultaten är jämförda med den normala turbulensmodellen (NTM) så som den definieras för standard SWT klasserna av International Electrotechnical Commission i International standard 61400‐2: Design requirements for small wind turbines (IEC, 2006). Mätningar av 10 minuters standardavvikelse av den longitudinella vindhastigheten ( ) och turbulensintensiteten ( ) redovisas, liksom fördelningen av och 10 minuters medelvinden ( ) för olika stabilitet för de olika mätplatserna. Resultaten visar att NTM är representativ på 97 höjd endast för låga vindhastigheter, under 10 m/s, medan modellen underskattar turbulensen för högre
vindhastigheter. Det bör också noteras att spridningen är stor i data och att extrema värden av och uppmätts vid flertalet tillfällen. För vindhastigheter över 10 m/s så är antalet mätvärden begränsade, men majoriteten av mätvärdena är högre än NTM. På de komplexa mätplatserna (nära trädtopparna och ovan hustaket) så underskattar NTM avsevärt både storleken av och dess förändring med ökad vindhastighet på de komplexa platserna (nära trädtopparna och ovan hustaket). Dock är de observerade vindhastigheterna låga såhär nära de skrovliga ytorna så slutsatserna är begränsade. På 97 höjd är medelvärdet av 19 %, jämfört med 41 % nära trädtopparna och 43 % ovan hustak. De är generellt 10 % lägre under stabila förhållanden ( ⁄ 0.05 över skog, medan ovan hustak där vindmaterialet är
begränsat och 95 % av observationerna var stabilt skiktade så ses inte något
stabilitetsberoende. Från dessa resultat kan slutsatserna dras att turbulensens karaktär nära trädtoppar liknar den ovan hustak, men att NTM, så som den definieras för standard SWT klasserna, inte gäller vid dessa komplexa och urbana platser och behöver modifieras för att korrekt uppskatta turbulensintensiteterna och därmed också de laster som påverkar små vindkraftverk placerade på den här typen av platser.
Nyckelord: turbulensintensitet, komplex, homogen, urban, små vindkraftverk, IEC standard klasser, normal turbulensmodell
T ABLE OF C ONTENTS
ABSTRACT ... III REFERAT ... IV
1 INTRODUCTION... 1
1.1 BACKGROUND ... 1
1.2 OBJECTIVES ... 2
2 THEORY ... 3
2.1 METEOROLOGY ... 3
2.1.1 The Planetary Boundary Layer ... 3
2.1.2 Turbulence Characteristics ... 5
2.1.3 Dynamic and Thermal Instability ... 6
2.1.4 TKE – Turbulent Kinetic Energy ... 7
2.1.5 Turbulence Characteristics in Uniform and Complex Environments ... 7
2.2 STATISTICAL TOOLS AND PARAMETERS ... 11
2.2.1 Vertical Fluxes and Stress ... 13
2.2.2 Stability Parameter ... 13
2.3 SMALL WIND TURBINES ... 14
2.3.1 Wind Turbines in General ... 14
2.3.2 Construction ... 14
2.3.3 Aerodynamics ... 16
2.3.4 Wind energy ... 17
2.4 IEC SMALL WIND TURBINE CLASSES ... 17
2.4.1 Normal Wind Conditions ... 18
2.4.2 Extreme Wind Conditions ... 19
3 MEASUREMENTS ... 20
3.1 SITES ... 20
3.1.1 Norunda ... 20
3.1.2 Earth Sciences Center, Uppsala University ... 20
3.2 INSTRUMENTATION ... 21
3.3 DATA ... 21
4 METHOD ... 22
4.1 CALCULATIONS AND MODIFICATIONS OF DATA ... 22
4.1.1 Wind Direction ... 22
4.1.2 Rotation of Coordinate Axes ... 22
4.1.3 Mean Values ... 22
4.1.4 Standard Deviations and Covariance Terms ... 23
4.1.5 Detection of Errors in the Data ... 23
4.1.6 Turbulence Intensity ... 24
4.1.7 Stability Parameter ... 24
5 RESULTS ... 25
5.1 STANDARD DEVIATION OF WIND SPEED ... 25
5.2 OBSERVATIONS OF TURBULENCE INTENSITY ... 28
5.4 DISTRIBUTION OF TURBULENCE INTENSITY ... 30
5.5 DISTRIBUTION OF WIND SPEEDS ... 30
5.7 AVERAGE TURBULENCE INTENSITY ... 32
5.8 STABILITY DISTRIBUTION ... 32
5.10 CUMULATIVE DISTRIBUTION OF TURBULENCE INTENSITY AND STABILITY ... 34
6 DISCUSSION AND CONCLUSIONS ... 37
6.1 VALIDATION OF THE NTM ... 37
6.1.1 Uniform Site ... 37
6.1.2 Complex Sites ... 37
6.2 STABILITY DEPENDENCE ... 38
6.3 CONCLUSIONS ... 39
7 ACKNOWLEDGEMENTS ... 40
8 REFERENCES ... 41 APPENDIX A SYMBOLS AND DESCRIPTIONS ... I APPENDIX B ... III APPENDIX C PERCENTILE VALUES FROM A NORMAL DISTRIBUTION ... IV
1 I NTRODUCTION
The demand for a more sustainable energy supply is constantly growing. Hydro power, wave power and wind power are only a few examples of natural sources of energy. This growing use of new energy sources leads to a demand for new technical solutions. The market for wind turbines is growing fast. In Sweden, almost 2 % of the total electricity production nowadays comes from wind power.
Most wind turbines are of large scale, designed to yield as much energy as possible in a cost‐efficient way. These large wind turbines are preferably placed at sites where the wind speed capacity is high. Normally, this means sites with a uniform environment with a flat terrain and a long undisturbed upwind fetch. At these kinds of sites, the knowledge about the characteristics of the lower part of the atmosphere, i.e. the boundary layer, are extensive when it comes to parameters like annual and seasonal average wind speed and turbulence characteristics. But as the demand for environmentally friendly energy production grows, there is also an increased interest in small scale wind turbines located in more complex environment and at lower height with high turbulence levels but lower wind speeds. This includes areas where mountains affect the wind pattern, or above forests as well as in urban areas close to buildings.
Small wind turbines (SWT) have a rotor sweep area smaller than 200 , which yields a rotor diameter of less than 16 . They are designed to be placed e.g. near farms or on the roofs of buildings in a city. But in these urban, or in other ways complex, environments the boundary layer flow acts rather differently compared to the flow in uniform environments. For example, wind speeds are normally lower in irregular terrain, but in return the turbulence rate is much larger due to the larger production of turbulent kinetic energy near the rougher surface and in the presence of varying obstacles. This changes the constructional design requirements of the wind turbines. For example, the wind turbines have to withstand a larger amount of fatigue loadings. If the SWTs are not designed for these new, rougher conditions they might break down and falling pieces may act as projectiles and cause severe accidents and material damage due to their nearness to buildings and people.
1.1 B
ACKGROUNDThe International Electrotechnical Commission (IEC) is a worldwide organization that works with questions concerning standardization in the electrical and electronic fields (IEC, 2006).
The organization discusses and formulates new standards for a variety of products, one example being small wind turbines. It is a collaboration between all interested national electrotechnical committees where every committee can have a representative in the discussions preceding the formulation and publishing of new standards. The IEC publications are thus in agreement with the overall international opinion and are meant to be used as recommendations for international use.
The IEC International standard number 61400‐2: Design requirements for small wind turbines (2006), contains four standard SWT classes defined by a few basic parameters. These classes are formulated to describe the characteristic external conditions of many different sites. The basic parameters are defined in terms of wind speed and turbulence parameters and are used in the wind and turbulence models described in the standard, such as the Normal
Turbulence Model (NTM). This description of external conditions was originally developed for a uniform environment, typical for larger wind turbines, and may therefore need to be modified in the case of small wind turbines located in complex environment.
Since 2009, Maintenance Team 2 of IEC’s Technical Committee 88 is working to revise this standard, and in liaison with IEA Wind1 Task 27, to introduce consumer labeling for small wind turbines. The intention of the labeling initiative is to define a globally standardized product label for small wind turbines and minimum requirements for a testing process which are said to benefit the entire wind sector (IEA Wind, 2011).
One problem when investigating the currently used standards is that urban terrain observations are hard to find since it is such a new field of interest. Meteorological investigations of the planetary boundary layer often try to avoid urban sites and the wind power researchers usually find the economic benefits from placing wind turbines in urban terrain too small to invest in such measurements. It is therefore of interest to investigate whether the characteristics of wind measurements from other complex environments, for example above forests, where much more data is available, can be used as a frame of reference also for urban environments.
1.2 O
BJECTIVESTo support the above described investigations concerning SWTs in IEC and IEA, this report aims to analyze high frequency turbulence measurements from sites in complex environments and compare the results to the Normal Turbulence Model (NTM), as it is defined for the standard SWT classes by the IEC (2006).
Therefore, measurements performed on top of the roof of a building in an urban environment are compared to existing data from above a forest at two heights. The
environment close to the treetops is considered to be complex and very rough, while further up, the environment can be considered to be more uniform.
The results are then compared to the NTM to see whether this model provide a correct representation of the turbulence characteristics of complex environments. The model is also compared to the more uniform environment. Because of the lack of measurements in urban terrain, it is of interest to investigate whether turbulence characteristics at other complex sites can be used in a model, with some kind of modification, to describe turbulence characteristics at urban sites.
The results of the study are planned to be used as an informative annex of the coming IEC International Standard 61400‐2 Ed. 3.
As a background, boundary layer flow characteristics are presented as well as a description of flow over plant or tree canopies and flow over cubical obstacles. Also, the constructional and aerodynamic properties of wind turbines are presented. Methods used to analyze high frequency turbulence data are described. A table of symbol descriptions and
abbreviations is presented in Appendix A.
1 The IEA Wind agreement is also known as the Implementing Agreement for Co‐Operation in The Research, Developement and Deployment of Wind Energy Systems functions within a framework created by the International Energy Agency, IEA (IEA Wind, 2011). IEA is an organization which works to ensure reliable, affordable and clean energy for its 28 member countries and beyond (IEA, 2011).
2 T HEORY
2.1 M
ETEOROLOGYTo be able to describe the external conditions that a wind turbine is exposed to, knowledge about how the wind field behaves in different environments and during varying meteorological conditions is important.
The initiator to all atmospheric motions is the irregular surface heating from the
absorption of solar radiation. The absorbed energy is transferred into the atmosphere mainly by thermal or turbulent exchange processes near the surface. These give rise to air
temperature differences which in turn yield pressure differences. Therefore, due to the constant strive for balance in the atmosphere, air movements are initiated. These winds transport kinetic energy which can be extracted by the wind turbines. Unfortunately, the winds are not constant, they are often gusty and hit the wind turbine from different directions.
This behavior is due to turbulence and is a large contributor to fatigue loads on the turbines.
Air that flows over any surface is decelerated near the surface due to viscous and frictional forces. A vertical wind velocity gradient is thus created which generates turbulence.
A turbulent air flow consists of totally stochastic air motions, characterized by rapid variations in wind speed and direction. These motions consist of whirls of varying sizes and they
effectively transport both energy and matter throughout the boundary layer. The planetary boundary layer (PBL) is always turbulent (Högström & Smedman, 1989) even though the degree of turbulence varies with time and is affected by the structure of the surface elements as well as the vertical temperature and humidity distribution, i.e. the thermal stability. Above the PBL is the Ekman‐layer where the wind field turns and adapts to the free atmosphere above where the turbulence can be ignored and the wind is governed by the pressure gradients.
The following sections will give a description of the characteristics of the lower parts of the atmosphere, mainly the planetary boundary layer. A comparison of turbulence
characteristics is made between uniform and complex environments and statistical tools needed to analyze turbulence data are presented.
2.1.1 THE PLANETARY BOUNDARY LAYER
The atmosphere contains a number of layers that behave different when it comes to wind conditions and turbulence characteristics. They interact in different ways with the surface and have varying depth depending on meteorological conditions that are changing with time.
The planetary boundary layer (PBL) is the part of the atmosphere closest to the surface, except for a very thin laminar layer, in which the flow field is strongly influenced by the interaction with the surface. A significant part of the energy exchange between the
atmosphere and the surface of the earth occurs in this layer through the turbulent transports of momentum, heat and humidity, which are due to shear forces and thermal instabilities (discussed in Chapter 2.1.3).
Shear forces arise in the presence of wind gradients. The wind velocity profile in the PBL has a logarithmic form due the friction at the, more or less, rough underlying surface. All surfaces have some degree of aerodynamic roughness exerting a frictional force on the air above it. In the first few millimeters, closest to the surface, this interaction is called molecular viscosity. Every fluid has a viscosity, , which is a measure of the internal friction between the
fluid elements. Viscosity acts to resist the tendency to flow and forces the fluid particles to move with the same speed as the surface that they are in contact with (Holton, 2004). This force is called shearing stress, , and is defined as viscous force per unit area. It is ultimately responsible for the deceleration near the surface so that the mean wind speed reaches zero near the ground, which gives rise to a large wind velocity gradient.
The roughness of a surface depends on the sizes and distribution of the so called
roughness elements. The roughness elements can have the size of gravel to the size of trees or houses and be distributed far away from each other or very dense. The disturbed air volume in between the roughness elements is called a canopy layer. It may refer to both crop fields, forests and urban areas. In this layer, the vertical wind profile takes an exponential form but it is completely dependent on the geometry of the roughness elements and cannot be generally described.
The top of the roughness elements are at height . If there is a mix of different roughness elements this height is the mean value . The height where the roughness elements appear as a uniform rough surface, instead of a number of individual roughness elements, is denoted
. Above , a relation for the increase of mean wind speed as a function of height can be obtained by integrating the wind speed gradient (Equation 2.1). This general relation, called the logarithmic wind law, is valid above the roughness elements during neutral stratification (Equation 2.2).
2.1
ln 2.2
where is the frictional velocity, 0.4 is the von Kármán constant, is the displacement height and is the roughness length.
The frictional velocity is a characteristic velocity that relates shear between layers of flow (defined in Chapter 2.2.1). The roughness length is a measure of the surface roughness.
It is defined as the height at which the extrapolated logarithmic wind law reaches zero, typically in the order of 10 % of (Högström & Smedman, 1989). This so called zeroplane is displaced vertically at the presence of roughness elements, so that the flow behaves as if there were a physical boundary at height (as described by Rotach (1991)) so that, theoretically,
0. Above a canopy, the zeroplane will rather denote an inflection point, which will cause turbulence production, as will be described in Chapter 2.1.5.1.
The planetary boundary layer can have a depth of a couple of tens of meters up to a couple of kilometers depending on the stability (described in Chapter 2.1.2). This layer can be divided into a number of sublayers depending on the structure of the surface, i.e. the
roughness elements (Figure 1). In an urban environment the layer interacting with the surface is called the urban boundary layer (UBL) (Oke, 1988). It consists of a mixed layer (ML), an inertial sublayer (IS) and a surface layer (SL) as seen in Figure 1. The surface layer, which is the lower part, is divided into a roughness sublayer (RS) and an urban canopy layer (UCL). The urban canopy layer has a vertical extent of 0 and encloses the air in between the roughness elements (Rotach, 1991). The roughness sublayer starts at the top of the UCL and
extends to ( ).
Figure 1. Schematic illustration of the different layers of the planetary boundary layer above an urban
area. The urban boundary layer (UBL) is divided into a mixed layer (ML), inertial sublayer (IS) and surface layer (SL), which in turn is divided into a roughness sublayer (RS) and an urban canopy layer (UCL). Also illustrated are the vertical wind speed profiles, , and its difference between rural and urban areas (Fernando, 2010).
2.1.2 TURBULENCE CHARACTERISTICS
The planetary boundary layer is always characterized with some degree of turbulence.
Turbulence is defined as a continuous, three dimensional flow that is non linear and contains whirls of different sizes. A fully developed turbulent flow is completely irregular and random and the turbulent eddies effectively transport both energy and matter (momentum, heat and humidity etc.) over time and length scales of varying sizes (Högström & Smedman, 1989).
The whirls are not static, they are constantly breaking down through the cascade process which describes how larger turbulent eddies are scaling down by transferring their kinetic energy to smaller and smaller eddies until viscosity dissipate the eddies into heat. The dissipation is proportional to the radius of the eddy by 1 r⁄ , which means that the smaller turbulent eddies are breaking down turbulent energy much more effectively than larger ones (Högström & Smedman, 1989).
A flow converts from being laminar to being turbulent when the ratio between inertial forces and viscous forces reaches a certain value (Högström & Smedman, 1989). This ratio is called Reynolds number given by Equation 2.3. Turbulence occurs at high enough Reynolds numbers, that is, when the inertial forces of the flow are large while the viscous forces are small so that turbulent eddies cannot be prevented from occurring.
2.3
is defined with the air density , scale representative wind speed and length (defined in Chapter 2.2.2), and the viscosity of the fluid .
2.1.3 DYNAMIC AND THERMAL INSTABILITY
Turbulence arises because of dynamic and thermal instabilities. Dynamical instability is primarily due to wind shear. Turbulence through wind shear arises in the boundary between air volumes with different velocity, so that ⁄ 0. It can be either between the surface of the earth and the air flow above it, as described earlier, between flows at different heights with different wind speeds, or in the wakes behind obstacles where the wind speed is locally reduced.
All obstacles cause deflection of the flow of the air. An obstacle can have different density, it can be solid, like a building, or less dense, like a forest but it will always affect the flow. In the wake of an obstacle, the wind speed is locally reduced, compared to the mean flow, generating a wind gradient. This wind gradient creates shear stress that will produce turbulence. Especially in complex environments this is an important source to turbulence. The flow around buildings has fairly complex characteristics and the amount of turbulence in an urban environment is higher than in more uniform sites like a crop field. A more detailed description of flow characteristics for uniform and urban sites will be found in Chapter 2.1.5.
Thermal instability is a result of the solar heating of the surface or by cooling of the surface due to emitted long‐wave radiation. When a surface is heated the air above it is also heated. When the air parcel is warmer than the air surrounding it, the air parcel starts to lift due to buoyancy forces. These thermal bubbles, also referred to as convection, create turbulence as they rise through the atmosphere (Stull, 1988).
The stability, i.e. the stratification, of the atmosphere depends on the potential
temperature gradient ⁄ , where denotes the potential temperature. If the atmosphere is stably stratified, the temperature increases with height so that the temperature gradient is positive ( ⁄ 0). Since the density of cold air is higher than that of warmer air, the buoyancy forces are negative and therefore oppose vertical motion so that no spontaneous convection occurs. This is normal conditions during nighttime or during winter when the solar radiation is small so that there is a net loss of energy at the surface which then becomes cooler than the air above it. Warm air that is advected over a cold surface will also generate a stable stratification. In stable stratification all thermally induced turbulence is dampened. Only shear production of turbulence is present.
For an unstably stratified atmosphere the temperature gradient is negative ( ⁄ 0) so that the air closest to the ground is warmer, and thus have a lower density than the surrounding air, resulting in positive buoyancy forces that will make the air parcel start lifting.
In an unstable atmosphere, even a small vertical displacement of an air parcel would make the air keep on rising until the air surrounding it is warmer. This convection might be due to irregular heating of the surface by the solar radiation. If some obstacle forces the air to be lifted it is called forced convection. Both results in thermal production of turbulent eddies in addition to the shear production. The turbulent eddies in an unstable boundary layer can reach a significant vertical extent.
In a neutral, or near neutral, atmosphere the air is well mixed so that the vertical
potential temperature gradient is close to zero, hence the buoyancy force will be close to zero.
This can be due to high wind speeds and a cloudy sky that prevent any significant temperature gradient to occur. High wind speeds also mean high wind shear at the surface resulting in a significant production of turbulence.
2.1.4 TKE – TURBULENT KINETIC ENERGY
Since the planetary boundary layer is always turbulent there must be a continuous production of turbulent kinetic energy (TKE) to oppose the cascade process.
The budget equation for turbulent kinetic energy describes how TKE is produced, redistributed and destructed. As described by Rotach (1991) and Högström & Smedman (1989), it states
i) Shear production ‐ the rate of production of TKE by the mean wind shear
ii) Buoyancy production ‐ the rate of production of TKE in unstable stratification due to convective processes (or vice versa destruction of TKE in stable stratification due to buoyancy when kinetic energy is transferred into potential energy)
iii) Pressure transport ‐ the redistribution of TKE performed by pressure perturbations (turbulent energy from convection is transferred from the vertical component to the horizontal components)
iv) Turbulent transport ‐ the vertical turbulent transport of TKE
v) Dissipation ‐ how TKE is dissipated into heat through the viscosity in the end of the cascade process.
Depending on the structure of the wind and temperature profiles, i.e. the stratification of the atmosphere, the importance of shear induced versus convective TKE production varies significantly. This dependence is given by the flux Richardson number which is the ratio of the buoyancy term (ii) divided by the shear generated turbulence term (i) in the TKE budget equation (AMS Glossary, 2000). A comparison of the two processes shows that shear induced turbulence is most important in a neutral stratification while in stable stratification the shear induced turbulence is dampened by buoyancy forces so that the turbulence starts to decay (Rotach, 1991). In an unstable atmosphere the convection is strong and the shear induced turbulence becomes more and more unimportant. When a flow becomes turbulent the wind shear ⁄ is automatically reduced.
2.1.5 TURBULENCE CHARACTERISTICS IN UNIFORM AND COMPLEX ENVIRONMENTS Meteorological studies of air flow and turbulence characteristics in the planetary boundary layer are commonly performed at sites with flat and homogenous environments. A lot of information is therefore available from the numerous measurements carried out at uniform tree or plant canopies. But the flow and turbulence characteristics at uniform sites deviate essentially from those at complex and urban sites, as will be described in the following sections.
2.1.5.1 Uniform Tree or Plant Canopies
Flow and turbulence characteristics in and above uniform tree or plant canopies are widely investigated for meteorological purposes. The studies have been performed in varying kinds of plant canopies such as crop fields, e.g. wheat, corn or other cereals, as well as forests of various height and density complemented with numerous wind tunnel experiments.
A plant canopy has a more or less complex structure of roughness elements such as stems, branches, leaves, needles and seeds referred to as canopy elements, contributing to the roughness of the surface. In a plant canopy the roughness density may be defined as the total frontal area of canopy elements per unit ground area affecting a air volume (Finnigan, 2000).
Earlier, canopy turbulence was thought of as a superposition of general boundary layer turbulence and energetic small‐scale eddies produced in the wakes of the canopy elements.
But this is true only in very sparse canopies where the turbulence is a result of wake effects from individual plants. Now, decades of surveys show that canopy turbulence is dominated by organized structures of large scale eddies. These dominating energy‐containing turbulent structures have horizontal length scales in the order of the canopy height and vertically about /3. They are found to transfer a vast majority of the momentum and other scalars both within the roughness sublayer and above (Finnigan, 2000).
It is found that gusts of higher wind speed, that rapidly move downward from the inertial sublayer, are affecting the entire roughness sublayer. In the case of uniformly distributed, non rigid roughness elements, as in crop fields or forests, these downward moving so called sweeps are able to penetrate the canopy. This results in a displacement of the zeroplane so that it lay well within the canopy, commonly at 3/4 of the mean canopy height (Rotach, 1991).
In and above plant and tree canopies, the vertical profile of wind speed is shown to increase exponentially within the canopy. At the zeroplane there is an inflection point above which the velocity profile takes the standard boundary layer logarithmic form (as given by Equation 2.2). The inflection point is characteristic for such canopy roughness layers (Finnigan, 2000). Here the shear stress has its maximum, affecting the characteristics of the turbulent flow and the turbulent kinetic energy production. Below the canopy top there is a peak in the wake production implemented by the canopy elements.
Coherent structures
Roughness sublayer turbulence is better described from the patterns typically seen in a so called plane mixing layer than in the inertial sublayer, as discussed by Finnigan (2000). A mixing layer is obtained by initially letting two airstreams of different velocity be separated by a splitter plate at 0. At the trailing edge of the plate ( 0), the two airstreams mix and become turbulent. The velocity field is found to have an inflection point at 0, which is the level of maximum shear between the two initial air streams resulting in a peak in the shear production of TKE at this level. It is also the level where the velocity variances and shear stress reaches its maximum value (discussed in more detail in Chapter 2.2).
In this kind of mixing layer the organized structures arise from instabilities supposedly created when high‐wind speed gusts sweep down and increase the shear at the inflection point. The initiated small perturbations evolve into waves that are growing rapidly until they eventually break down into small‐scale turbulence (known as Kelvin‐Helmholtz waves). First, they form complex but organized patterns of transverse rollers connected by twinned regions of intense plane strain. The initial vorticity is amplified and the rollers merge together, forming irregularly spaced energy‐containing rollers in the streamwise direction. After a while, these rollers break down forming fully developed turbulence. This is what is seen in field studies as well.
TKE transfer
A turbulent wind field in the roughness sublayer always undergoes a conversion of energy through the cascade process from large to small eddies, as discussed earlier. But in canopy layers there are processes that let the energy take shortcuts through the eddy cascade.
Generally, energy of the mean flow (MKE) is transferred into organized structures and viscous dissipation transfer turbulent kinetic energy (TKE) of the high frequency eddies into
heat. Additionally, the turbulent wind field flow is exposed to aerodynamic drag forces
absorbing momentum from all eddies of scales larger than the canopy elements, i.e. the scales of seeds, leaves or branches and so on. The aerodynamic drag is the sum of the dominating pressure drag force and the smaller, but still considerable, viscous drag force.
Work against pressure drag converts MKE into fine‐scale TKE called wake kinetic energy (WKE). Work against the viscous component converts MKE directly into heat bypassing a large part of the eddy cascade (Finnigan, 2000). The waving of the canopy elements also contribute to the production of turbulent eddies by temporarily storing MKE as potential energy and thereafter release it as TKE (Raupach, 1981).
Production, transport and dissipation of turbulent kinetic energy above canopies are given by modifying the TKE budget equation (presented in Chapter 2.1.4). To fully describe the area‐
averaged wind field in and above a canopy it must include a shear production term, a wake production term, a dispersive transport term, the correlation of plant motion to pressure drag and the correlation of plant motion to viscous drag.
Turbulence intensity
The intensity of turbulence, , (defined in Chapter 2.2) in and above canopies is studied in various field and wind tunnel experiments. Measurements of standard deviations of horizontal and vertical velocity fluctuations, , (defined in Chapter 2.2) show that these variables are very scattered within canopies (Finnigan, 2000). The scatter is due to effects from the structure of the canopy as well as pressure gradients and turbulence characteristics above the canopy (Seginer et al., 1976). Other factors that play a crucial role to the amount turbulence are changes in mean wind speed, which affect the magnitude of the turbulence intensity, and thermal stability, which has a dampening effect on the turbulent eddies. Generally, velocity standard deviations are found to increase with height within and above the canopy, with maximum increasing rate in the upper part of the foliage.
Due to the normalization with mean wind speed, turbulence intensity is found to slowly increase with height within the canopy with a maximum in the upper part of the canopy. If the canopy density is vertically constant, then so is the turbulence intensity. This confirms the dependence on canopy density and that the fluctuations are larger in the presence of wakes behind the canopy elements.
Above the canopy top, decreases with height and is always lower than within the canopy. Maximum values range between 50 80 % in forest while for plant canopies like corn and wheat maximum is smaller, about 20 80 % (Baldocchi & Meyers, 1987).
2.1.5.2 Urban and Complex Environments
The turbulence characteristics of a flow in an urban canopy layer (UCL) are dependent on the high roughness lengths and the inhomogeneous surface. Also thermal effects are different compared to plant or tree canopies, changing the stability distribution. The stratifications in cities are mostly near neutral due to extensive mixing and do not play a very important role either to enhance or dampen the turbulence (Yersel & Goble, 1986).
A built area consists of randomly distributed roughness elements which all together form what is called an urban canopy. A typical medium sized city contains an inhomogeneous mix of houses and residential buildings, gardens and trees, separated by roads and possibly rivers positioned with inconsistent geometry. These elements of varying heights, shapes and densities therefore affect the atmospheric flow in complex ways.
Flow around a single obstacle
The randomness of the roughness elements makes it almost impossible to give a general description of how the flow will behave at a specific site within the canopy. Not even strong computers and well developed numeric computational models can fully describe the three‐
dimensional flow characteristics of such complex environments. For less complex installations, on the other hand, large eddy simulation (LES) models are shown to be able to simulate the average flow in quite good alignment with field study results (Shah & Ferziger, 1997).
The streamlines of a shear flow around a single three dimensional cubic obstacle is described in detail by Shah & Ferziger (1997). According to their LES simulations, and in agreement with other field studies, the oncoming flow is separated ahead of the obstacle, forming a commonly seen horizontal horse‐shoe shaped vortex (i.e. three‐dimensional pattern of whirls). The separation point is at a distance of one obstacle height ahead of the obstacle and the vortex is advected by the mean flow, converging again at 1.6 obstacle heights behind the obstacle. The vortex is wrapped around the cube and widens downstream of the obstacle simultaneously as its center is lifting from the surface. At the boundaries of the horse‐shoe vortex, regions with significant mixing are found, caused by strong vertical motions; upwash (on the inner boundary) and downwash (on the outer boundary). The breaking up of the horse‐shoe vortex, far behind the obstacle, contributes to the background TKE in the roughness sublayer.
On the sides of the obstacle, enclosed by the horse‐shoe vortex, are regions of flow that oppose the mean flow. Here the viscous drag is small and negative. Fluid enters this region from the sides instead of from the direction of the mean flow. This kind of reversed circulation is also found, momentarily, directly behind the obstacle where a vertical vortex is formed, shaped like an arch, with two separated “feet” of strong circulation on the ground. The
locations of these ground‐based circulations are dependent on the angle of attack of the mean flow. In the vertical, the arch vortex has its center in alignment with the top surface of the obstacle (as sketched up by Becker, Lienhart & Durst (2002)).
The frontal top border of the obstacle is affecting the flow significantly. Here, the streamlines of the mean flow are curved above the top surface and a region of reversed circulation is formed, which separates the mean flow from the obstacle.
It should be noted that the flow streamline characteristics described, are only the averaged representation of this kind of flow. Although coherent structures of these types are found in the flow pattern, they are not periodic nor have the same sizes or strengths so that instantaneous pictures are highly intermittent (Shah & Ferziger, 1997).
Complex terrain
The LES simulations, mentioned above, show an example on how complex air flows across single obstacles can be. Expanding this to cases with numerous obstacles of varying character, like an urban area, the flow patterns are highly complex and vary significantly depending on the direction of the oncoming flow, as discussed by for example (Heath, Walsche, & Watson, 2007). At any site, within a complex area, the surface area that influences a measurement, called the source area, varies significantly with mean flow direction and measuring height. This variability also makes it difficult to define a general zeroplane displacement height or a
roughness length for a certain measuring point.
The mean roughness length of a city can vary between 0.5 to 4.5 although it is somewhat misleading to give a single value of in such an inhomogeneous area (Yersel &
Goble, 1986).
Turbulence intensity
Turbulence intensity is found to decrease with height above an urban area as a consequence of the increase of mean wind speed with height while the standard deviation of wind speed is found to be nearly constant with height above rough surfaces (for example by Mulhearn &
Finnigan (1978)). A minimum in wind speed is found at the top of the roughness elements which, by definition, result in a maximum in turbulence intensity.
Turbulence intensity is also observed to increase with increasing roughness length, due to the large mechanical production of TKE. Also, horizontal velocity variances are found in a larger span in complex environments. They are both considerably larger in complex environments resulting in larger turbulence intensity (Rotach, 1991)
2.2 S
TATISTICALT
OOLS ANDP
ARAMETERSTurbulence can be detected in a time series of high frequency measurements as rapid deviations from a larger scale mean value in the signal (an example of this can be seen in Chapter 4.1.2). These fluctuations can be seen in parameters like temperature and both horizontal and vertical wind speeds. To be able to describe such irregularly behaving phenomena some statistical analyzing tools are needed.
Standard procedure when analyzing turbulence data is to transform the horizontal wind vector in the geographical coordinate system , into a rotated coordinate system that aligns with the mean wind direction during every averaging period. The mean wind direction is given by tan as shown in Figure 2. The new components are given by
cos 2.4
Now the new rotated components and will describe the longitudinal and lateral wind velocities , . In a wind turbine system the longitudinal component is directed along the hub and the lateral component is perpendicular to the hub. From here on and will refer to these rotated variables.
A first step to analyze measured turbulent variables is to use Reynolds averaging where the variables are separated into a slowly varying mean part and a rapidly varying turbulent part , so that the total field variable is describes as
2.5 From this definition follows that 0. The arithmetic mean value is calculated using Equation 2.6 where is number of elements in each averaging period.
1 2.6 1
From the turbulent part of the flow one can form variance and covariance terms describing turbulent fluxes and stress (see Chapter 2.2.1). The variance describes the dispersion of the measurements around a mean value, which also can be expressed as the standard deviation from the mean, defined as the square root of the variance (Equation 2.7). This quantity can therefore be used as a measure of the intensity of turbulence (Stull, 1988).
1 2.7
The covariance is calculated according to Equation 2.8 and can be interpreted as a measure of how much two variables vary together.
1 1
2.8
Turbulence intensity, , is often defined as the standard deviation of longitudinal wind speed, , normalized with the mean wind speed, (Equation 2.9).
2.9
Figure 2. Principal of an axes rotation (From Sahlée, 2009)
2.2.1 VERTICAL FLUXES AND STRESS
As mentioned earlier, turbulent eddies transport quantities like momentum and heat through the atmosphere. This transport is called flux and is physically described with covariance terms.
Heat flux can be described as the rate that air of different temperature is transported vertically. Similarly, momentum flux can be described as the rate that air of different speed is transported vertically (Stull, 1988).
where is the longitudinal wind speed deviation, is the vertical wind speed deviation and is the air temperature deviation.
Turbulent momentum flux has the same effect as a shearing stress. Stress can be described as a force that, when applied to a body, will cause deformation (Stull, 1988). In the turbulent boundary layer two types of stresses are of interest, the turbulent shearing stress and the viscous shear stress. The turbulent shearing stress is that given by the turbulent momentum flux and can be described as . The turbulent momentum flux is also used to define the friction velocity since it describes the frictional force between the surface and the air.
2.10
2.2.2 STABILITY PARAMETER
The stratification of the boundary layer can be determined with the parameter (Monin Obukhovs length) which can be read as the height where the turbulent forcing from thermal and shear processes are in balance. is constant with height but vary with stability in the surface layer and can therefore be used as a stability parameter (Högström & Smedman, 1989)
is defined as
2.11
where is the friction velocity, is the mean air temperature in Kelvin, 9.82 ⁄ the gravitational acceleration and 0.4 von Karmáns constant and is the kinematic heat flux.
Normalizing the measuring height above ground, , with gives the dimensionless stability parameter ⁄ where
0 0
0
In reality, neutral conditions are extremely rare. Instead, near neutral conditions are defined with a small span so that ⁄ 0 for near neutral conditions.
2.3 S
MALLW
INDT
URBINES2.3.1 WIND TURBINES IN GENERAL
Conventional large scale wind turbines are normally placed in wind farms at sites with high wind energy potential, either on land or offshore, but often some distance away from where the energy supply is needed. The harvested energy is therefore often transported long distances which is quite inefficient. Small wind turbines on the other hand, can be placed directly near a farm, alongside of manufactory buildings or on rooftops and therefore yield energy where it is needed. But some of these locations provide different external conditions and therefore demand new design requirements of the turbines.
The principle of a wind turbine is to convert the energy in the wind into electrical energy by retarding the wind using rotors that are driving a generator which in turn generates electrical energy. The most common large scale wind turbine construction is the three bladed horizontal axis wind turbine with a rotor diameter of about 100 and a hub height in the same scale. This constructional principle is also found for small wind turbines.
Small wind turbines have a rotor sweep area of less than 200 (IEC, 2006) which corresponds to a rotor diameter of maximum 16 . The hub height for these small wind turbines often spans between 10 – 40 depending on where they will be mounted.
Wind energy production is constantly expanding with the installation of new and more efficient wind turbines. During the year 2009, wind energy accounted for 2.49 TWh in Sweden which amount to 1.9 % of the total electricity production (Energimyndigheten, 2010). The total number of wind turbines was 1359 by the end of 2009. Of these are 1288 95 % land‐
based while 71 wind turbines are located offshore2. In Sweden, the largest land‐based wind park consists of 48 wind turbines. According to an estimation done within IEA Wind Task 27, small wind turbines in Sweden 2009 produced about 2 GWh
2.3.2 CONSTRUCTION
A small wind turbine that is built to operate in urban environment has some requirements. It has to be technically reliable during long turn operation in turbulent conditions, the noise emissions have to be minimized so that it does not disturb the neighborhood and vibrations has to be as small as possible to minimize the structure‐borne sound and the strain on the construction. Additionally, the esthetic appearance has to be taken into consideration (van Bussel & Mertens, 2005).
Wind turbines can be designed in various ways which will affect their performance, aerodynamics and efficiency. One way to categorize them is according to the orientation of the axis of rotation.
Horizontal axis wind turbine (HAWT)
Vertical axis wind turbine (VAWT)
Horizontal axis wind turbines (HAWTs) consist of a tower with a nacelle on top which is the housing of mechanical and electrical components. On the nacelle, propeller type rotor blades are attached with a hub in the center of rotation. The basic components contained in the
2 New publications show that the number of wind turbines in Sweden now exceeds 1500 and the wind energy production during 2010 will be more than 3 TWh (Energimyndigheten, 2010), but the potential is still much larger and Sweden should be able to reach 30 TWh wind power by the year 2020.
nacelle are a rotor shaft and bearings, a generator and often, but not always, a gear system and a rotor brake mechanism. A yaw system used to turn the axis of rotation into the mean wind connects the nacelle to the tower. Power cables running through the tower transports the electricity which may pass through power electronics and/or a transformer before entering the power distribution grid.
HAWTs have a high efficiency and demand a small amount of material. They are normally located at homogenous sites with high wind speeds and operate with a tip speed that is several times faster than the prevailing wind speed. The HAWT is designed to operate with the axis of rotation turned into the mean wind direction, otherwise it loses much of its efficiency.
This design is therefore not very convenient in complex environments with gusty winds and rapid wind direction changes.
Vertical axis wind turbines (VAWTs) consist of curved or straight rotor blades which rotate around a central column that is mounted to the ground. The rotor diameter is measured as the horizontal distance between the blades. All mechanical and electrical components are placed on the ground, which makes maintenance more convenient. No tower is needed, which has economic benefits but with the disadvantage that it is therefore operating closer to the ground where wind speeds are lower and the shear in the vertical wind profile is larger.
The VAWT have a lower efficiency compared to the HAWT in smooth wind conditions (van Bussel & Mertens, 2005). On the other hand, it is insensitive to wind direction because of its symmetry and is therefore preferable in complex environments where turbulence is high and wind direction changes are rapid. The drawbacks of the VAWT include operation with lower tip speed so that the loading on the rotor blades is larger generating a higher torque that put strain on the construction. There is also a high cyclic aerodynamic loading on the blades due to the 360 degree rotation with respect to the wind direction (Scheurich, 2009). Still, VAWTs are found to be more convenient in complex terrain.
A control system controlling the rotor brake mechanism can be built into the wind turbines. It is coupled to a wind speed measuring instrument (anemometer) and controls for which wind speeds the turbine will be operating. When the wind speed is high enough to overcome the internal friction in the drive train, the brake is loosened and the blades start rotating. This so‐called cut‐in wind speed is normally about 2 – 4 / for small wind turbines.
The generator is dimensioned for a certain maximum wind speed, which is the wind speed when maximum energy is produced. Above this wind speed, the wind turbine will still operate but the power production will be constant. At really high wind speeds the brake system kicks in and the turbine is turned off to prevent it from breaking down. This cut‐out wind speed is approximately 25 / .
The blades of the wind turbines are preferably made of a light but strong material with a low rotational inertia and thus a quick acceleration so that the tip speed ratio3 can be
maintained nearly constant, even in gusty conditions. The larger the blades, the more important it is to keep the blade weight under control.
All wind turbines are a source of noise emissions of different character and intensity and at different frequencies that is spread in the nearby area. The rotation of the blades through the air gives rise to a sweeping sound and in some constructions the cogwheels in the gearbox emits a humming noise that is amplified through the tower of the wind turbine. The noise level decreases with distance due to geometrical spreading, weather effects and dampening effects
3 ratio between tip speed and wind speed
by vegetation or buildings as well as the atmosphere itself. The effect of the latter on sound propagation is dependent on atmospheric stability and wind direction. But the noises can also be minimized by installing damping systems that produce counter vibrations. One problem is that modern wind turbines change their rotational speed depending on the wind speed, producing noise at varying frequencies. Older versions of the damping systems only produce certain counter frequencies but modifications of these damping systems are under
development. The new versions detect the varying frequencies of the sound and produces negative, dampening vibrations at those frequencies (Fraunhofer‐Gesellschaft, 2008).
2.3.3 AERODYNAMICS
The rotor blades of wind turbines are typically airfoil shaped, using the same airfoil design as in airplane wings or helicopter rotors. Airfoils are streamline‐shaped with a thicker leading edge that gets thinner towards the sharp trailing edge. The curvature of the airfoil can either be symmetric or asymmetric. The airfoil design will create an aerodynamic force that can be divided into two components.
1) A drag force in the direction of the flow 2) A lift force perpendicular to the flow
Wind turbines can either be drag driven or lift driven. Drag driven rotors are pushed around by the wind. The drag force opposes the motion of an object through a fluid and can be seen as the friction exerted by the fluid. The drag force is perpendicular to the area facing the wind so that a larger frontal area will generate a larger drag force. A larger angle of attack will also generate a larger drag force. Since the rotor blades are moving in the same direction as the wind they are bound to rotate with maximum tip speed given by the prevailing wind speed.
Drag driven rotors also demand a larger amount of material. They therefore become less economic and less efficient compared to the lift driven rotors (Mertens, 2002).
Lift driven rotors consist of air‐foiled shaped blades. When the rotor is exposed to the wind the air flow will be divided into two air streams at the leading edge, one that is flowing above the upper surface and one that is flowing beneath the lower surface. Both streams will be deflected, the upper stream tube will be compressed while the lower stream tube area will be increased. Flow speed will increase above the airfoil, due to the law of conservation of mass, and therefore decrease underneath the airfoil. Thus a pressure difference will arise between the two stream tubes according to Bernoulli's principle, which states that a faster flow speed will generate a lower pressure and a slower wind speed will generate a higher pressure. The pressure difference results in an aerodynamic lift force, perpendicular to the direction of the flow, which will make the rotor blade turn in the direction of rotation. Lift driven rotors operate at tip speeds higher than the wind speed and are therefore much more efficient than drag driven rotors. If the blades are not helically twisted they will suffer from oscillations in the aerodynamic loading which results in vibrations and material fatigue (Scheurich, 2009).
One of the most appropriate design choices for application on rooftops is the lift driven VAWT, for example the Darrieus turbine. Even though this kind of wind turbine has a lower efficiency in undisturbed air flows with low turbulence it has the advantage of running smoothly in turbulent flows with rapid wind direction changes (van Bussel & Mertens, 2005).