Trying to design Wind Turbine Blades

[jonagad]

Homework Statement

Blade Element Momentum

Relevant Equations

Reynolds numer:
Re=((V)*(ρ)*(c))/μ
Where:
V:wind velocity
ρ: density
c: chord
μ: Dynamic viscosity

Hello, I'm trying to follow the instructions from the book "Aerodynamics of Wind Turbines"-Martin O.L. Hansen, to design a blade, the method it's the BEM accounting for the tip loss (Prandtl) and Glauert corrections, but I can't get it right, for the Cl (lift coefficient) and Cd (drag coefficient) I need the Reynolds number, but in order to calculate de Re, I need the chord, how can I give a value to the chord?

 

[Arjan82]

You need to assume a chord distribution. See what comes out and if not feasible / desirable, choose another chord distribution. That's the design iteration loop.

 

[Arjan82]

Ps: it is usually referred to as BEMT (Blade Element Momentum Theory), not to be confused with BEM (Boundary Element Method)

 

[jonagad]

You need to assume a chord distribution. See what comes out and if not feasible / desirable, choose another chord distribution. That's the design iteration loop.

Ohh, I see, that´s exactly what I was doubting, thank you for responding, i will do that.

This is what I have, if you want to check it out:
Data:
a: Axial Induction factor
a´: Angular induction factor
Both a and a´ usually are =0 initially.
Then it´s an iterative process

U_1=	5.17	m/s
Ω=	25	rpm	2.61799388	rad/s
R=	1.25	m
B=	3
a_c=	0.2

Results:

Airfoil	S823	S823	S823	S822	S822	S822	S822	S822
No	1	2	3	4	5	6	7	8
Section	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9
a=	0.199999	0.199999	0.199999	0.199999	0.199999	0.199999	0.199999	0.199999
a´=	0	0	0	0	0	0	0	0
r=	0.25	0.375	0.5	0.625	0.75	0.875	1	1.125
λ_r=	0.12659545	0.18989317	0.2531909	0.31648862	0.37978635	0.44308407	0.50638179	0.56967952
tanφ=	6.31935041	4.21290027	3.1596752	2.52774016	2.10645014	1.80552869	1.5798376	1.40430009
φ=	1.41385359	1.33774321	1.26428219	1.19407991	1.1275664	1.0649987	1.00648169	0.95199662
f=	6.0746591	3.59724868	2.35999667	1.61311558	1.10696468	0.73487167	0.44381043	0.2046056
F=	0.9985355	0.98255507	0.93980034	0.87228856	0.78552425	0.68158749	0.55655264	0.39350817
α(°)=	8.9	8.9	8.9	9.3	9.3	9.3	9.3	9.3
α(rad)=	0.1553343	0.1553343	0.1553343	0.16231562	0.16231562	0.16231562	0.16231562	0.16231562
θ_p=	1.25851929	1.18240891	1.10894789	1.03176429	0.96525078	0.90268308	0.84416607	0.789681
C_l	1.2	1.2	1.2	1	1	1	1	1
C_d	0.018	0.018	0.018	0.01	0.01	0.01	0.01	0.01
C_n	0.20533788	0.29465239	0.37924554	0.37716791	0.43789323	0.49325323	0.5432864	0.5882036
C_t	1.18243831	1.1634019	1.13863814	0.92619888	0.8990826	0.86994325	0.83960699	0.80877471
supposed chord=	0.3	0.3	0.3	0.3	0.3	0.3	0.3	0.3
σ=	0.5729578	0.38197186	0.2864789	0.22918312	0.19098593	0.16370223	0.14323945	0.12732395
K=	33.1200113	33.0575543	31.4502953	34.9023254	30.6607275	25.838245	20.42407	13.9456387
a (if≤a_c)=	0.03113324	0.0311939	0.0328404	0.0294965	0.03371461	0.04026049	0.05148252	0.07724609
a (if>a_c)=	-0.01483998	0.02854777	0.02992187	0.02711849	0.03064657	0.03596828	0.04468398	0.06296168
a´=	-11.1285299	1.01283376	0.43191772	0.21631925	0.164224	0.14056692	0.1357714	0.16071096
dF_N=	0.5850977	0.43256206	0.57787566	0.60832726	0.74183354	0.87908453	1.01370567	1.11762702
dQ=	3.36928547	1.70792275	1.73500068	1.49384935	1.523133	1.55042807	1.56660348	1.53672719
dr=	0.25	0.125	0.125	0.125	0.125	0.125	0.125	0.125
U_rel=	5.07136957	5.14789674	5.24466267	5.39587492	5.53005839	5.67206174	5.80366212	5.85659519
dF_T=	4.49238063	1.51815355	1.15666712	0.79671965	0.676948	0.59063926	0.52220116	0.45532658
dF_L=	1.13977548	0.58721677	0.60950029	0.53762728	0.56469895	0.5940725	0.62195905	0.6333561
dF_D=	0.01709663	0.00880825	0.0091425	0.00537627	0.00564699	0.00594072	0.00621959	0.00633356

 

[jonagad]

Of course, thank you

Ps: it is usually referred to as BEMT (Blade Element Momentum Theory), not to be confused with BEM (Boundary Element Method)