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Vertical Axis Wind Turbine Design Questions

  1. Nov 11, 2011 #1
    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, [itex]U[/itex]
    Tip Speed Ratio, [itex]\lambda[/itex]
    Chord, [itex]c[/itex]
    Radius, [itex]R[/itex]
    Number of Blades, [itex]N[/itex]
    Change in Azimuthal Position, [itex]d\theta[/itex]
    Swept Area, [itex]A[/itex]

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

    Chord Velocity
    [itex]V_c=U(\lambda+\cos(\theta)[/itex]

    Normal Velocity
    [itex]V_n=U\sin(\theta)[/itex]

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

    Relative Wind Speed
    [itex]W=\sqrt{V_c^2+V_n^2}[/itex]

    Coefficient of Lift and Drag
    Calculated using XFoil

    Tangential Force Coefficient
    [itex]C_t=C_l\sin(\alpha)-C_d\cos(\alpha)[/itex]

    Normal Force Coefficient
    [itex]C_n=C_l\cos(\alpha)+C_d\sin(\alpha)[/itex]

    Tangential Force
    [itex]F_t=\frac{C_t \rho c h W^2}{2}[/itex]

    Normal Force
    [itex]F_n=\frac{C_n \rho c h W^2}{2}[/itex]

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

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

    Total Torque
    [itex]T=N\bar{F}_tR[/itex]

    Total Power
    [itex]P=T\omega[/itex]

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

    For some reason, if I choose parameters such as:

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

    I get a power output of:
    [itex]P=10\,kW[/itex]

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

    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.
     
  2. jcsd
  3. Nov 11, 2011 #2
    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.
     
  4. Nov 12, 2011 #3
    Certainly, here is a picture of the general idea:
    http://www.manufacturer.com/upload/product/6414997/Vertical+Axis+Wind+Turbine+Generator_0_detail.jpg [Broken]. The swept area has been fixed at [itex]A=20\,m^2[/itex]. 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 [itex]\alpha=13^{\circ}[/itex] (depending on the Tip Speed Ratio). Does this seem too high for low Reynolds?

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

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

    Thanks so much for taking the time to reply. I appreciate it.
     
    Last edited by a moderator: May 5, 2017
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