Investigating the Impact of Blade Size on Vertical Axis Wind Turbine Efficiency

Introduction

A Wind Energy Converter, commonly called a Wind Turbine is a device that works by converting the abundant kinetic energy from the wind, firstly into rotational kinetic energy and then thus electrical energy, that can be supplied to the population through the use of a power grid around Australia. The wind speed plays a large role in the energy available for conversion. When in the planning stages of producing a wind farm, to assess the economic viability of a wind turbine, it is crucial to know the expected power, energy and efficiency output produced (Bird, 2007).

Thus, for the basis for the experiment, power, energy and efficiency output will be calculated.

Research Question

How does the size of each blade on a Vertical Axis Wind Turbine (VAWT) effect the overall efficiency produced by the Turbine?

Aim

To investigate the impact of the total efficiency of the Turbine when the blades are altered to different sizes when the wind speed and angle of curvature is kept constant and the charge produced is measured.

Hypothesis

It was hypothesised that if the blades of a Vertical Axis Wind Turbine were altered to have more surface area for each blade set, it would produce more mechanical energy compared to the smaller blades in the experiment. This higher surface area would not only produce a greater mechanical power but would also be more efficient. Thus, by having more energy and a higher standard of efficiency it would be better for mankind. Better to say that it could be produced by means of generating electricity for the home or something more effect means of harnising.

Theory

Wind Turbines can be formed into a variety of sizes and shapes that can rotate about either a horizontal or vertical axis (VAWT or HAWT). However, as per German physicist, Albert Betz determined in 1919, the maximum theoretical efficiency a Wind Turbine can produce is 16/27 (59.3%) (Raneng, 2007). This has been found through the implementation of using Betz Law or Betz Limit:

This is described by

Continuity Equation

m=pA_1 v_1:pSν=pA_2 v_2

Power and Work Equation

v=1/2⋅(v_1+v_2 )

Coefficient and Performance Equation

P_wind=1/2⋅p⋅S⋅v_1^3

Where:

v_1 = speed in front of the rotor (m/s)

v_2 = speed downstream (m/s)

S = cross sectional area (m^2)

P = Fluid density (kg/m^3)

“No more than 59.3% of the of the energy carried by the wind can be extracted by a Wind Turbine” (Raneng, 2007). This value is called the power coefficient, and it can be defined as:

C_(p_max )

This value is specific to each Turbine, and thus cannot operate at this maximum limit as it is a function of that the turbine is operating in.

To calculate the efficiency of the turbine, the power (output) and Power (input) must be calculated. To find the power (output), the current and voltage produced by the blades must be multiplied together. This would give the power in Watts. With this found Betz power and performance equation can be used: P_wind=1/2⋅p⋅S⋅v_1^3 , this will produce the power produced by the wind in Watts.

A wind turbine on its own does no useful work. It just spins in the wind. To produce electricity, it has to be coupled with a generator. The generator changes energy from the wind into electrical energy. The spinning part of the generator, turned by the wind turbine, moves coil of wire past magnets to create electricity flow in the wire. Electricity and magnetism are very closely linked. When electricity flows along a wire, it produces magnetism too. the opposite is also true – when a magnet moves near a wire (or a wire moves near a magnet), it causes electricity to flow along the wire.

To understand the process of generating a current. Electromagnetic induction must first be understood. In essence, there are two key laws that help describe electromagnetic induction, these being:

• Faraday’s Law: This law is one of the basic laws of electromagnetism. Physicist Michael Faraday investigated the factors that influence the magnitude of the Electromotive Force inducted. His law “relates the rate of change of magnetic flux through a loop to the magnitude of the electro-motive force induced in the loop” (Khan academy, 2017).
• Lenz’s Law is a current produced by an induced emf moves in a direction so that its magnetic field opposes the original change in flux (Giancoli, 200. This law looks at the significance of conservation of energy being applied to electromagnetic induction. The law states that “the direction is always such that it will oppose the change in flux which is produced” (Khan Academy, 2017).

Lez’s law details the direction the current will flow, while faradays Law tells us the “magnitude of the EMF produced” (Khan Academy, 2017).

Variables and Parameters:

The independent variable is time (t). The dependant variables voltage and current. The controlled variables are the source of the wind the distance the hairdryer is from the blades, blade and hairdryer height, environmental factors (temperature, wind, humidity,), equipment used.

Limitations and approximations

The approximations in this experiment are the expected values (displayed further in the assignment). another approximation on the experiment is the angle the blades are set to. The same angle will not be consistent throughout the whole experiment thus estimation arises.

The data is limited due to how the resistance wasn’t controlled; this would result in the voltage being effect. More accurate result could have been achieved if the voltage and current were not measuring at the same time through the galvenometre.

Method

Beginning the experiment, equipment and materials must be gathered in order to create the Wind Turbine and to begin experimenting. The equipment that should be used in this experiment are as follows, Retort Stand with clamp, model Pierre generator, Hub, cardboard, super glue, scissors or cutting device, wooden skewers, anemometor connected to the GLX Xplorer or galvenometre that plugs into a computer, alligator clamps, software system called PASCO Capstone must be installed into the computer, hairdryer and ruler. Secondly, the blade sets should be made; this was done by measuring 2 by 3 inch (5.08cm by 7.62cm), 1 by 1.5 inch (2.54cm by 3.81cm) and 3 by 4 inch (7.62cm by 10.16cm) cardboard pieces with a ruler and cutting them out with a pair of scissors.

These cardboard pieces are modelled into having a slight curvature. However, this curve must be the same for each blade produced; a protractor may be helpful for this. Following this, the skewers should be cut into 2-inch long stans. This will act as the prop that will support the weight of the blade as it spins. The skewers must be positioned in the middle of the skinniest part of the blade with exactly 1 inch of excess skewer sticking out for it to be clamped on the hub (as see in the photo above). These skewers would then be glued to the cardboard piece thus creating a blade (allow 24 hours to fully let the glue set). Now with the blades complete, a retort stand must be used in order to have a stable consistent source of air flow; the source being a hairdryer plugged into the wall. the hairdryer is at a fixed position through the use of a clamp attached to the retort stand.

The wind speed can be measured by using an anemometor plugged into either a GLX Xplorer or a galvenometre plugged into a computer with PASCO Capstone online. With the wind speed measured it is now appropriate to attach the blades to the plastic hub. However, the blades cannot be placed at any random spot, the blades must be placed horizontally from each other. Once attached, a model Pierre generator will now be able to slot into a 2mm wide cavity underneath the hub. To complete the experiment, another retort stand, and clamp must be used with positioning and placement of the turbine. With the blades attached to the hub which is attached to the model Pierre generator, the piece can be slotted into the clamp, which is positioned 30cm away from the hairdryer. This generator has cords running down connected with various alligator clamps that feed into the animonitor that is connected to the PASCO capstone on the computer. Finally, the hairdryer on level three of power is now blowing wind hitting the blades causing them to spin horizontally creating electricity.

Results and Analysis

To find the efficiency of the blade set, the power of the wind must be found using Betz equation. However, to find S in Betz equation, we must find the Sweep area, πr^2

For Small Blade Set:

Let r = .0895m

S=πr^2

= π(.0895)^2

= .02516m^2

Uncertainty calculation:

For Medium Blade Set:

Let r = .1016 m

S=πr^2

= π(.1016)^2

.0324m^2

For Large Blade Set:

Let r = .127m

S=πr^2

= π〖.127〗^2

.0506m^2

Thus, knowing the sweep area, Betz equation can be implemented to its full extent:

p_wind=1/2×p×S×v_1^3

Where:

v_1 = speed in front of the rotor (m/s)

S = cross sectional area (m^2)

P = Fluid density (kg/m^3)

The uncertainty calculation:

This is how the uncertainty could be calculated; however, this uncertainty calculation is limited due to the fact limitations in the experiment arose i.e. the size of sensor measuring wind speed to the size of the hairdryer

(Δ_P/p)^2=(Δs/s)^2+(Δv/v)^2

(Δ_P/p)^2=(.0005/.02516)^2+ (.05/7.807)^2

Δ_P= .147 Watts

p_(wind for small blades)= 7.063 ± .147 Watts

For Medium Blade set:

P = 1.060 kg/m^3 as per 60 degrees

S = .0324m^2 ± .0005m^2

v= 7.807m/s ± .05m/s

Thus:

p_wind= 1/2×1.18×.0324×〖7.807〗^3

p_wind= 9.095 Watts

The uncertainty calculation:

This is how the uncertainty could be calculated; however, this uncertainty calculation is limited due to the fact limitations in the experiment arose i.e. the size of sensor measuring wind speed to the size of the hairdryer

(Δ_P/p)^2=(Δs/s)^2+(Δv/v)^2

(Δ_P/p)^2=(.0005/.0324)^2+ (.05/7.807)^2

Δ_P= .1519 Watts

p_(wind for Medium sized blades )= 9.095± .1519 Watts

For Large Blade set:

p= 1.060 kg/m^3 as per 60 degrees

S = .0506m^2 ± .0005m^2

v= 7.807m/s ± .05m/s

Thus:

p_wind = 1/2×1.18×.0506×〖7.807〗^3

= 14.20 Watts

The uncertainty calculation:

This is how the uncertainty could be calculated; however, this uncertainty calculation is limited due to the fact limitations in the experiment arose i.e. the size of sensor measuring wind speed to the size of the hairdryer

(Δ_P/p)^2=(Δs/s)^2+(Δv/v)^2

(Δ_P/p)^2=(.0005/.0506)^2+ (.05/7.807)^2

Δ_P= .1502 Watts

p_(wind for Large Blades )= 12.76± .1672 Watts

Now knowing the power input for each blade set all that is needed is to find the power input. This is done by multiplying the amount of current produced by the voltage produced.

For Big Blade Set:

Efficiency= (power (output))/(Power (input)) x 100

Efficiency= .0001898/14.20 x 100

Efficiency= .00133%

For Medium Blade Set:

Efficiency= (power (output))/(Power (input)) x 100

Efficiency= (.000302 )/(9.095 ) x 100

Efficiency= .00332%

For Small Blade Set:

Efficiency= (power (output))/(Power (input)) x 100

Efficiency= (.000505 )/( 7.063 ) x 100

Efficiency= .00714%

A second calculation could be done to compare the turbine to the potential power of the wind. This is done by multiplying the theoretical maximum efficiency a wind turbine can produce by the power of the wind. This would give a new power input. Then all that is need is to implement the efficiency equation displayed above. This would give the following:

Small Blade Set

Data based on table 8:

Calculating power of the wind:

p_wind=1/2×p×S×v_1^3×C_(p_max )

p_wind= 7.063×59.3%

p_wind= 4.18 Watts

Substituting into the efficiency equation. Power output in table 8

Efficiency= (power (output))/(Power (input)) x 100

Efficiency= (.000505 )/( 4.18 ) x 100

Efficiency= .012%

The theoretical maximum efficiency of the small blade turbine is .12%

Medium Blade Set

Data based on table 8:

Calculating power of the wind:

p_wind=1/2×p×S×v_1^3×C_(p_max )

p_wind= 9.909 ×59.3%

p_wind= 5.39 Watts

Substituting into the efficiency equation. Power output in table 8:

Efficiency= (power (output))/(Power (input)) x 100

Efficiency= (.000302 )/( 5.39 ) x 100

Efficiency= .005%

The theoretical maximum efficiency of the small blade turbine is .0.005%

Large Blade Set

Calculating power of the wind:

p_wind=1/2×p×S×v_1^3×C_(p_max )

p_wind= 14.2 ×59.3%

p_wind= 8.4206 Watts

Substituting into the efficiency equation. Power output in table 8:

Efficiency= (power (output))/(Power (input)) x 100

Efficiency= (.0001898 )/( 8.4206 ) x 100

Efficiency= .0022%

The theoretical maximum efficiency of the small blade turbine is .0.0022%

Conclusion

The investigation demonstrated the significant impact of blade size on VAWT efficiency. Larger blades resulted in improved energy conversion and higher turbine efficiency, aligning with the hypothesis. These findings underscore the importance of blade design optimization in maximizing wind energy utilization. Further research could explore additional factors influencing wind turbine efficiency and investigate practical applications of the study's findings in wind energy technology.