Wind Profiles Quiz

Importing data................................................................................................................................1 Question 01....................................................................................................................................1 Question 02....................................................................................................................................1 Question 03....................................................................................................................................2 Question 04....................................................................................................................................3 Question 05....................................................................................................................................4 Question 06 and 07........................................................................................................................5 Question 08....................................................................................................................................6 clear close all

Importing data Import_data = 1; if Import_data currentFolder = pwd; raw_data = xlsread([currentFolder '\Preparation_data\WindprofileMOOC.xls']); U = raw_data(:,2:8); dir = raw_data(:,9:11); time_hr = raw_data(:,12); U_h = [10 40 60 80 100 116 160]; dir_h = [10 60 100]; end

Question 01 From the table look up, estimate the roughness length that is relevant for the wind profile at the mast location. Hint: Use Fig. 1 to guide you. z0 = 0.03; % Farmland with very fewbuildings/trees

Question 02 The friction velocity is a measure of the momentum transport from the free atmosphere to the boundary layer. Assuming that the stability effect is small at 10m, use the table value of z0 to derive the variation of the friction velocity u? over the 18 hours in the data file by means of Eq.(1). Make a plot of u? as a function of time (use Excel, Matlab, or another computer program).

k = 0.4; z = 10; u_fric_h10 = U(:,find(U_h == z))*k/log(z/z0); % % % % %

z = 60; u_fric_h60 = U(:,find(U_h == z))*k/log(z/z0); hold all plot(time_hr,u_fric_h60,'--*') legend('10 m','60 m')

plot(time_hr,u_fric_h10,'--*') xlabel('Time [hour]') ylabel('u_* Friction velocity [m/s]') grid

Question 03 The logarithmic wind profile with the stability correction is given in Eq.(2). Use the time varying u? that you just derived and a constant value of z0 to derive the diurnal variation of the stability correction parameter ?. Use the wind speed measurements at 60m and make a plot of ? as a function of time.

z = 60; psi = -U(:,find(U_h == z))*k./u_fric_h10 + log(z/z0); figure plot(time_hr,psi,'--*') xlabel('Time [hour]') ylabel('\psi stability correction parameter') grid

Question 04 Use the measured wind speed at and to derive the roughness length from the logarithmic wind pro?le without accounting for the stability correction, . The roughness length characterizes the upwind landscape and is thus constant. Hint: Write the logarithmic wind pro?le expression for the wind speed at both and and express as ; then eliminate , and solve for the roughness length. Calculate it for every instance in the time series and plot as a function of time. z1 = 10; z2 = 40; z0_Q4 = exp((log(z1)./U(:,find(U_h == z1)) - log(z2)./U(:,find(U_h == z2)))/(1/z2 + 1/z1));

figure plot(time_hr,z0_Q4,'--*') xlabel('Time [hour]') ylabel('Z_0 Roughness length [m]') grid

% syms z0_sym % vpasolve((log(z1) - log(z0_sym))./U(2,find(U_h == z1)) == (log(z2) log(z0_sym))./U(2,find(U_h == z2)))

Question 05 Make plots of the wind direction at 10m and 100m as a function of time and find the difference. z1 = 10; z2 = 100; figure hold all plot(time_hr,dir(:,find(dir_h == z1)),'--*') plot(time_hr,dir(:,find(dir_h == z2)),'--*')

legend('10 m','100 m') xlabel('Time [hour]') ylabel('Wind direction [m]') grid

Question 06 and 07 Assume that the energy production of a wind turbine is proportional to the cube of the wind speed. Consider you have a 10m tall wind turbine and calculate the wind speed cubed for that height. Plot the values as a function of time. % Now consider you have a 160m tall wind turbine and repeat the tasks given in question number 6. z1 = 10; z2 = 160; figure hold all plot(time_hr,U(:,find(U_h == z1)).^3,'--*') plot(time_hr,U(:,find(U_h == z2)).^3,'--*')

legend('10 m','160 m') xlabel('Time [hour]') ylabel('Wind speed cube [m3/s3]') grid

Question 08 cube_diff = U(:,find(U_h == z2)).^3 ./ U(:,find(U_h == z1)).^3; [~, nmax] = max(cube_diff); figure hold all plot(time_hr,cube_diff,'--*') plot(time_hr(nmax),cube_diff(nmax),'o') text(time_hr(nmax)+0.5,cube_diff(nmax),num2str(time_hr(nmax))) xlabel('Time [hour]') ylabel('Wind speed cube diference (160m / 10m) [m3/s3]') grid

cube_diff = U(:,find(U_h == z2)).^3 - U(:,find(U_h == z1)).^3;

[~, nmax] = max(cube_diff); figure hold all plot(time_hr,cube_diff,'--*') plot(time_hr(nmax),cube_diff(nmax),'o') text(time_hr(nmax)+0.5,cube_diff(nmax),num2str(time_hr(nmax))) xlabel('Time [hour]') ylabel('Wind speed cube diference (160m - 10m) [m3/s3]') grid

Published with MATLAB® R2016a

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