• Author / Uploaded
• Pedro Galvani

• Categories
• Turbina
• Movimiento (física)
• Dinámica (Mecánica)
• Cantidades fisicas
• Mecanica clasica

Citation preview

Table of Contents ........................................................................................................................................ 1D Momentum theory .......................................................................................................... Question 01 ........................................................................................................................ Question 02 ........................................................................................................................ Question 03 ........................................................................................................................ Question 04 ........................................................................................................................ Question 05 ........................................................................................................................ Rotational theory and velocity triangle at r=40m ...................................................................... Question 06 ........................................................................................................................ Question 07 ........................................................................................................................ Question 08 ........................................................................................................................ Question 09 ........................................................................................................................ Question 09 ........................................................................................................................

1 1 1 1 3 3 4 4 4 6 6 8 9

close all clear rho = 1.225; % kgm3 V0 = 8; % m/s In question 2.- 10., it is assumed that the rotor runs with optimum induction. In question 6.- 10. we'll consider a blade section at r=40m from the rotor centre at a rotational speed of 10 rpm. Here the cord length is c=3m and the blade twist is ?=4?.

1D Momentum theory Question 01 The wind speed after the wake expansion is measured to be 4m/s. What is the axial induction factor? u1 = 4; a_u4 = (-u1/V0 + 1)/2

a_u4 = 0.2500

Question 02 What would the flow velocity through the rotor be if it was run with optimal induction? Give the result in m/s.

1

dCp_da = @(a)4*(1-a).*(1-3*a); [a_opt,fval,exitflag,output] = fzero(dCp_da,0); hold all a_plot = -1:0.1:2; plot(a_plot,dCp_da(a_plot)) plot(a_opt,fval,'*') xlabel('a') ylabel('dCp/da') grid a_opt Cp_opt = 4*a_opt*(1-a_opt)^2 u = (1-a_opt)*V0

a_opt = 0.3333

Cp_opt = 0.5926

u = 5.3333

2

Question 03

What rotor radius (and thus approximate blade length) should the turbine ha P = 1.5e6; R_1p5MW = sqrt(P/(1/2*rho*pi*V0^3*Cp_opt))

R_1p5MW = 50.6879

Question 04 Assume now a rotor diameter of 2r=116m. What is the thrust force on the rotor in kN? CT = 4*a_opt*(1-a_opt) A_116 = pi*116^2/4; T_kN = 1/2*rho*A_116*V0^2*CT*1e-3

CT =

3

0.8889

T_kN = 368.2472

Question 05 What is the main limitation of 1D momentum theory? The consideration of optimal induction.

Rotational theory and velocity triangle at r=40m Question 06 Which values of a and a? correspond to optimum operation at r=40m? (choose the right option) Hint: Use the equations 1) to 4) to calculate x and then a and a?. Keep in mind that the value of a should be within the interval 0