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.