Vertical Axis Wind Turbine Design Questions

[lanew]

Hello All,

I'm currently in the process of designing a numerical model for a vertical axis wind turbine, more specifically, a straight blade giromill. I'm currently having trouble because depending on the variables I choose, I can produce more power than available from the wind.

My Calculations are based off the following diagrams:
http://imageshack.us/photo/my-images/851/selection002y.png/
http://imageshack.us/photo/my-images/31/selection003r.png/

I can post the code (MATLAB), but I'm sure no one wants to sift through that, but here's my design methodology:

User Defined Variables:
Airfoil (NACA00XX)
Wind Speed, U
Tip Speed Ratio, \lambda
Chord, c
Radius, R
Number of Blades, N
Change in Azimuthal Position, d\theta
Swept Area, A

From these variables, I have a loop that iterates \theta, the azimuthal position, and calculated the following variables each time:

Chord Velocity
V_c=U(\lambda+\cos(\theta)

Normal Velocity
V_n=U\sin(\theta)

Angle of Attack
\alpha=\arctan\left(\frac{V_n}{V_c}\right)

Relative Wind Speed
W=\sqrt{V_c^2+V_n^2}

Coefficient of Lift and Drag
Calculated using XFoil

Tangential Force Coefficient
C_t=C_l\sin(\alpha)-C_d\cos(\alpha)

Normal Force Coefficient
C_n=C_l\cos(\alpha)+C_d\sin(\alpha)

Tangential Force
F_t=\frac{C_t \rho c h W^2}{2}

Normal Force
F_n=\frac{C_n \rho c h W^2}{2}

As I said, the above variables are calculated for every \theta_i. Once the loop is finished, the following variables are calculated:

Average Tangential Force
\bar{F}_t=\frac{1}{2\pi}\int_{i=0}^{2\pi} F_t(\theta) \mathrm{d}\theta
Numerical Approximation
\bar{F}_t=\frac{1}{n}\sum_{i=1}^n F_t

Total Torque
T=N\bar{F}_tR

Total Power
P=T\omega

I have checked the numbers individually, and my \alpha's range from 0-13^{\circ}, C_l and C_d range from -1.8-1.8, C_t from 0-0.34, and C_n from 0-1.22.

For some reason, if I choose parameters such as:

NACA0015
U=4.5\,m/s
\lambda=5
c=0.5\,m
R=1.0\,m
h=10\,m
N=3

I get a power output of:
P=10\,kW

However, I don't believe I should be getting more than:
P_{max}=\frac{\rho AU^3}{2}

Can someone please help me? I'm pulling my hair out here. If the code would actually help, let me know and I can try and post it.

Thanks So Much.

 

[RandomGuy88]

I am unfamiliar with this type of device. Could you post a picture of what you are working on? What is the tip speed ratio and swept area?

I do have a question about your use of xfoil. In order to get a Cd I assume you are running it in viscous mode. What Reynolds number are you inputting? Because if your Reynolds number is really low, which I imagine it will be at least during part of the rotation cycle if U=4.5m/s, then Xfoil will likely have problems at the high angles of attack.

 

[lanew]

Certainly, here is a picture of the general idea:
http://www.manufacturer.com/upload/product/6414997/Vertical+Axis+Wind+Turbine+Generator_0_detail.jpg . The swept area has been fixed at A=20\,m^2. I need to optimize the dimensions given this area.

As I mentioned, I don't think my AoA is too high, it maxes out at about \alpha=13^{\circ} (depending on the Tip Speed Ratio). Does this seem too high for low Reynolds?

I've been using Tip Speed Ratios of \lambda=3 to \lambda=5 for initial testing. This results in relative velocities of W=9 to W=18 when \lambda=3, and W=18 to W=27 when \lambda=5.

My Reynolds number \left(Re=\frac{Wc}{\nu}\right) for \lambda=3 ranges from Re=5.1e5 to Re=7.6e5.

Thanks so much for taking the time to reply. I appreciate it.