Table of Contents ........................................................................................................................................ Importing plot .................................................................................................................... Horizontal axis wind turbine ................................................................................................. Question 1 ......................................................................................................................... Question 2 ......................................................................................................................... Vertical axis wind turbine ..................................................................................................... Question 3 ......................................................................................................................... Question 4 ......................................................................................................................... Kite-based turbine ............................................................................................................... Question 5 ......................................................................................................................... Question 6 ......................................................................................................................... Question 7 ......................................................................................................................... clear close all
Importing plot % grabit('Capture.PNG') addpath('C:\Users\Pedro\Dropbox\ITA\DTU_Wind_Energy\05 - Wind Energy Technology\Quiz\Preparation\grabit') Data = load('Darrieus.mat'); DarrieusP = Data.Darrieus; Darrieus = fit(DarrieusP(:,1),DarrieusP(:,2),'linearinterp');
Data = load('Fast_HAWT.mat'); Fast_HAWTP = Data.Fast_HAWT; Fast_HAWT = fit(Fast_HAWTP(:,1),Fast_HAWTP(:,2),'linearinterp');
Data = load('Old_wind_mill.mat'); Old_wind_millP = Data.Old_wind_mill; Old_wind_mill = fit(Old_wind_millP(:,1),Old_wind_millP(:,2),'linearinterp');
Data = load('Savonius.mat'); SavoniusP = Data.Savonius;
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Savonius = fit(SavoniusP(:,1),SavoniusP(:,2),'linearinterp');
Data = load('Slow_HAWT.mat'); Slow_HAWTP = Data.Slow_HAWT; Slow_HAWT = fit(Slow_HAWTP(:,1),Slow_HAWTP(:,2),'linearinterp');
figure hold all plot(Darrieus,DarrieusP(:,1),DarrieusP(:,2),'*') plot(Fast_HAWT,Fast_HAWTP(:,1),Fast_HAWTP(:,2),'*'); plot(Old_wind_mill,Old_wind_millP(:,1),Old_wind_millP(:,2),'*'); plot(Savonius,SavoniusP(:,1),SavoniusP(:,2),'*'); plot(Slow_HAWT,Slow_HAWTP(:,1),Slow_HAWTP(:,2),'*'); grid legend(' ','Darrieus',' ','Fast HAWT',' ','Old wind mill',' ','Savonius',' ','Slow HAWT','Location','best') xlabel('Tip Speed Ration') ylabel('Power Coeff. C_P')
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Horizontal axis wind turbine rho = 1.225; % kgm3 V = 10; % m/s P_MW = 5; P = P_MW*1e6;
Question 1 What is the required rotor radius (blade length) of a fast-running horizontal-axis wind turbine (m)? Cpmax_FHAWT = max(Fast_HAWT(0:0.1:7)) R_FHAWT = sqrt(P/(1/2*rho*pi*V^3*Cpmax_FHAWT))
Cpmax_FHAWT = 0.4556
R_FHAWT =
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75.5178
Question 2 What is the required rotor radius (blade length) of a slow-running horizontal-axis wind turbine with a rotor of multiple blades (m)? Cpmax_SHAWT = max(Slow_HAWT(0:0.1:7)) R_SHAWT = sqrt(P/(1/2*rho*pi*V^3*Cpmax_SHAWT))
Cpmax_SHAWT = 0.3040
R_SHAWT = 92.4510
Vertical axis wind turbine Question 3 What is the required swept area of a Darrieus wind turbine (m2)? Cpmax_Darrieus = max(Darrieus(0:0.1:7)) A_Darrieus = P/(1/2*rho*V^3*Cpmax_Darrieus)
Cpmax_Darrieus = 0.3819
A_Darrieus = 2.1376e+04
Question 4
What is the length of a blade of this Darrieus wind turbine assuming that t R_Darrieus = sqrt(A_Darrieus/pi) L_Darrieus = R_Darrieus*pi
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R_Darrieus = 82.4868
L_Darrieus = 259.1398
Kite-based turbine Question 5 What is the required area of the kite Akite if the lift coefficient is CL=1 and the glide ratio is 5 ( in m2)? Cl = 1; G = 5; Akite_G5 = P/(1/2*rho*V^3*4/27*Cl*G^2)
Akite_G5 = 2.2041e+03
Question 6 What is the required area of the kite Akite if the lift coefficient is CL=1 and the glide ratio is 5 ( in m2)? G = 10; Akite_G10 = P/(1/2*rho*V^3*4/27*Cl*G^2)
Akite_G10 = 551.0204
Question 7 What is the required length of a straight and rigid beam that vibrates with an amplitude of 10m in a plane perpendicular to the mean wind speed of 10m/s if you assume that the power coefficient is CP=0.1 and the machine must extract 5MW ( in m)? Cp_vib = 0.1; Amp = 10;
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A = P/(1/2*rho*V^3*Cp_vib) L_beam = A/(Amp)
A = 8.1633e+04
L_beam = 8.1633e+03
Published with MATLAB® R2016a
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