An Investigation of the Blade
Designs of Wind Turbines
Research question: How Does the Angle of Attack, Chord Length and Serrated Trailing Edge of
Wind Turbine Blades Affect the Efficiency?
Physics: Extended Essay
Word Count: 3998
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*Received A* IB Physics HL Extended Essay - An Investigation of the Blade Designs of Wind, High school final essays of Physics
IB Extended Essay Physics. This essay is about the efficiency of wind turbines and their blades. It discusses the different factors of the turbine blades such as angle of attack, chord length, etc. Several experiments were completed with methods and raw data. I received an A for this extended essay. It may not be similar to your essay topic, but it will still give you a general idea of how to logically structure your essay. Three different experiments done in the essay will also give you an idea of what you should do in your physics essay. There are methods and raw data tables included as well so it is much easier to understand. Hope this helps! :)
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An Investigation of the Blade
Designs of Wind Turbines
Research question: How Does the Angle of Attack, Chord Length and Serrated Trailing Edge of Wind Turbine Blades Affect the Efficiency? Physics: Extended Essay Word Count: 3998
Table of Contents
- Introduction
- Theoretical Background
- Experimental Investigations
- Experiment 1: Angle of Attack
- Analysis
- Experiment 2: Chord Length
- Analysis
- Experiment 3: Trailing Edge
- Analysis
- Experiment 1: Angle of Attack
- Evaluation
- Conclusion
- References
- Appendices
- Appendix
- 1.1 A raw data table of experiment
- 1.2 Processed data table of experiment
- Appendix
- 2.1 Raw data tables of experiment
- 2.2 Processed data table of experiment
- Appendix
- 3.1 A raw data table of experiment
- 3.2 A processed data table of experiment
- 3.3 An quadratic graph of experiment
- Appendix
20 years. This means that a possible increase in efficiency may result in an increase in the profit of owners as they will be able to sell a bigger amount of electricity. This makes it a more attractive proposition to those considering investing in this technology. The efficiency can be increased by changing the geometrical characteristics of blades or adding some parts since aerodynamics on blades contain complex variables and there are still new technologies in development. Efficiency also takes an important role considering the challenges wind turbines face when getting recycled. As mentioned, most wind turbines have the lifespan of 20 years. After their life span, wind turbines stop their operations and are disassembled. The issue is that the composite materials that wind turbine blades are made out of such as fiberglass are considered as materials that are hard to recycle. Most of the used wind turbine blades nowadays often wind up in the landfill. Efficiency is an important factor because it governs the total amount of green energy produced before waste occurs. In this Extended Essay, I will investigate multiple ways of maximizing the efficiency of wind turbines in terms of the blade design.
Theoretical Background
The common wind turbines that will be discussed in this Essay have three propeller-like blades that function similar to airplane wings. These wind turbine blades spin when the wind blows and allow generators to convert mechanical energy into electrical energy. Then, why do they spin when the wind blows? There are two popular theories that explain why wind turbine blades spin: Newton’s third law of motion and Bernoulli’s principle (Hall, 2021). Before contrasting Newton and Bernoulli, it is important to consider fluid mechanics. When gas flows over an object or an object moves through a gas, the molecules of gas can move freely. Because of their movement, the velocity associated with the gas varies at different places near the object. Fig 1. A diagram showing how Newton’s third law of motion applies to a blade (self-drawn) Newton continues from this point, referencing his third law of motion, there are aerodynamic forces acting on the blades because the turning flow of the gas created by the variation of
Simply, this equation explains that the total energy per unit volume before always equals the total energy per unit volume after. When applied to explain why wind turbines spin, this equation implies that an increase in velocity leads to a decrease in air pressure. Leading to a decrease in the air pressure above the blades, the air pressure under the blades remains the same. As previously noted, resolving the forces shows us that high pressure always moves towards low pressure, air below the blades tends to move upward toward the low-pressure air. Then, the blades are ‘lifted’ upward (Afework, 2018). Despite their different perspectives on lift provided by Newton and Bernoulli, recent studies explain that their understandings are both correct. Even though they seem to have different understandings on the causes of aerodynamic forces, they are both explaining what is going on around the blades. Summing up, there are two major aerodynamic forces acting on the blades: Lift and Drag force. Fig 3. A diagram showing the directions of forces in respect to the airflow (self-drawn)
Lift, the force central to this research, is an upward force perpendicular to the direction of airflow. Due to its direction, lift force directly opposes the weight of blades and some of drag. Drag force is parallel to the airflow so the two forces are always perpendicular to each other and this characteristic makes wind turbines rotate when lift is greater than drag. Lift force(L) can be mathematically written as (Hall, 2021):
ρ · 𝑣 2 2
(Equation 2) ρ represents the density of the air, and v is the relative velocity, with A being the surface area of the blades over which the air flows. Cl represents the lift coefficient, a variable that is determined by geometric characteristics of blades such as the thickness, roundness, attack angle and camber. In this Extended Essay, this complex variable will remain constant as the factors that determine the coefficient will also be constant. Drag force is an aerodynamic and mechanical force that opposes an object’s motion through the air as it is parallel to the airflow. The formula of drag force is:
𝑝·𝑣^2 2
(Equation 3) Cd represents the drag coefficient, also determined by the geometrical characteristics of each blade. This will not be discussed in this essay as it will also be constant throughout the experiments.
Trailing edge is the name of the rearward end of wind turbine blades. As shown in Figure 5, the trailing edge is where the two separated winds rejoin each other. Its characteristic is that it is sharp, not rounded. This is to reduce additional drag that is created when blades have rounded edges. Fig 6. A diagram showing how wingtip vortices are formed and how lift induced drag is formed by downwash effect (AeroGuard Flight Training Center, 2020) In order to understand the occurrence of lift-induced drag, it is necessary to know what the wing tip vortices are. Wing tip vortices are rotating air left behind a blade due to its lift. These vortices occur mostly at the tip and trailing edge of the blade due to the pressure difference of each side. Wing tip vortices push the trailing edge downward which is called downwash effect. As a result, the trailing edge is inclined downward. As lift is always perpendicular to the airflow and as the blade is tilted, the lift vector is also tilted rearward. The rearward component of the tilted lift vector is lift-induced drag. The equation of lift-induced drag is:
𝑖
𝐿 2 1 2 ·𝑝·𝑣 2 ·π·𝑏 2 (Equation 4)
The variables are all previously defined other than 𝑏, the wingspan of the blades which is the measurement of the length from tip to tip. There are two main designs that prevent the increase in drag due to the lift-induced drag: serrated trailing edge and wingtip device. Fig 7. A diagram showing the serrated trailing edge of wind turbine blades (self-drawn) These two designs allow blades to have less downwash effect on themselves by reducing the magnitude of wing tip vortices. Serrated trailing edge shown in Figure 7 prevents vortex shedding arising from the bottom side of the blade by cutting them down. This reduces lift-induced drag and also the noise created by the rotation of blades.
Experimental Investigations
Experiment 1: Angle of Attack
The first experiment of the investigation considers the best angle of attack for wind turbine blades. Angle of attack of blades is an important geometrical factor that determines the lift, drag and lift-induced drag force as this variable is proportional to lift and drag coefficient. When the angle is 0 degree, both the lift and drag will nearly be 0 as the wind will smoothly pass the blades. When the angle is 90 degrees, there will be an extremely higher drag than lift since drag is always parallel to the airflow. With these understandings, I expect that blades in 40 to 50 degree will maximize the lift generated and consequently, the overall output of the turbine. Fig 8. An Image showing the setup of Experiment 1 (photo and self-drawn)
In order to conduct the first experiment, firstly, digital scales (max 2kg) must be turned on. Then, those lego stands need to be glued on the digital scales so that it does not move due to drag force. At this step, the setup must be the same as Figure 8. Then, the initial mass of the lego stand and the 3D printed blade section must be measured for later calculations. After that, using the wind source (Dyson hair dryer with 3 speed levels, measured with an anemometer to be a max of 24.3 ms-1), the angle of attack must be adjusted using a protractor. A variable of Experiment 1 is the angle of attack which is an independent variable. The wind turbine blades will be attached to the lego stand and be controlled by using a protractor. Then, they will be held in that angle by tightening the each side of the stand. There are two dependent variables which are wind speed from the source and the distance between the source and blades. In Experiment 1, they are set up to be 24.3 ms-1^ and 25 cm.
Fig 9: A graph showing the relationship between the lift force and angle of attack As shown in Figure 9, the lift force of the blade section linearly increased from 0 to 40 degrees. Then, the maximum lift force was measured at 40.8 degrees and it started to decrease exponentially as the angle got wider. The linear section shows a directly proportional relationship with a gradient of m = 0.031 ± 0.0007 and an intercept of c = -0.003 ± 0.006. The correlation of the best fit graph is 0. which represents that variables have a strong relationship to each other as it is near 1. A linear graph was plotted from 0 degree to 40 degree because the lift force measurements showed a linear relationship with the change of angle. After the maximum value at 40 degree, the line was not plotted as the value decreased abnormally between 40 and 50 degree. The data
shows that it has an exponential relationship as angle gets wider. To sum up, in Experiment 1, it can be concluded that the best angle of attack for wind turbine blades is between 40 to 50 degrees. 40° as an angle of attack will be used throughout Experiment 2 and 3 as setting the angle constant helps to find the ideal value of other experiments and thus, to find the ideal design of wind turbine blades.
In order to conduct the second experiment, three blades in the same size must be attached to the rotor. Then, the rotor must be attached to the wind turbine kit. Positive and negative cables should be connected to the voltmeter (max 19.99V) to measure the values. When the measurement is done, the wind speed must be changed using the windsource (floor fan with 3 speed levels, measured with an anemometer to be 12.4, 16.2 and 20.6 ms-1). After gathering all measurements in 3 different wind speeds, the blades in the rotor must be replaced with other blades in different sizes (27, 32, 37, 42 and 47 mm). After that, repeat the same procedure again and gather measurements. There are 3 blades for a single size. As there are in total 5 different sizes, 15 blades are required for Experiment 2. The length of the cables connected to the voltmeter is not an important factor to consider. However, in this experiment, 15 cm cables were used. A variable in Experiment 2 is the chord length of wind turbine blades. This is also an independent variable which will be measured in 5 different sizes. Each blade will have a 5mm difference enabling the data to be precise but also wide range. There are two dependent variables which are wind speed from the source and the distance between the source and blades. In Experiment 2, the wind speeds are set up to be 12.4, 16.2 and 20.6 ms-1. The distance will be set up to be 40 cm.
a. Analysis
As previously noted, the raw data and processed data tables for Experiment 2 can be found in Appendix 2.1 and 2.2. Fig 11: graph showing the relationship between voltage outcome and chord length in three different wind speed levels As shown in Figure 11, increase in chord length linearly increases the voltage generated by the wind turbine. As the wind speed increased, the wind turbine tended to spin faster and generate higher voltage. The slope of the wind speed 1 graph is 0.05980 Vmm-1. The slope of wind speed 2 is 0. Vmm-1^ and that of wind speed 3 is 0.05440 Vmm-1. The correlations of 3 experiments are 0.9923, 0.9965 and 0.9954.