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# XFoil Analysis – Angle of attack range

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Dear Dr. David,

You can perform the XFoil Analysis for different Reynolds numbers. Then, you can extrapolate this to a 360° characteristic. Next, for the vertical axis mode you can choose for the different blade sections a certain Reynolds number you have performed in the XFoil Analysis (see Reynolds number blade.png). I choose this Reynolds number by the formula according to Wikipedia: Re = Vc/ν, where V is the flight speed, c is the chord length, and ν is the kinematic viscosity of the fluid in which the airfoil operates, which is 1.460×10−5 m2/s for the atmosphere at sea level (https://en.wikipedia.org/wiki/Reynolds_number#:~:text=The%20Reynolds%20number%20is%20the,the%20interior%20of%20a%20pipe.)

For a VAWT with a turbine radius of R = 25 m, a chord length of c = 2.5 m, a tip speed ratio of TSR = 3.33, a rotational speed of RPM = 15 rpm and a wind speed of v_w = 12 m/s,  this comes down to a Reynolds number of about 6.7 * 10^6 (Re = (v_w*TSR*c)/ν  or Re = (R*RPM*(2Pi/60)*c)/ν ). So I use this value for the blade section and a continue with the simulation.

So here are my questions:

• If I however want to perform a simulation with the same VAWT but a turbine radius of R = 40 m, I reason that I have to change the Reynolds value at the blade section to about 8 * 10^6. Is this reasoning correct? Consequently, I assume the Reynolds  number experienced by the blade strut as half of the Reynolds number of the blade as this Reynolds number changes along the length of the strut. Is this correct?
• I already tried to perform some simulations from the situation described above. When I perform a Rotor DMS simulation (for a wind speed of 12 m/s), I get the result that the highest power coefficient is reached for a TSR of 4 (see Power coefficient.png). When I use this TSR in the full simulation mode of QBlade (see Simulation mode TSR = 4.png), I get a lower power coefficient as compared to the situation of  a TSR = 3.33 (see Simulation mode TSR = 3.33.png). This last situation (with TSR = 3.33) is also the first value of the TSR you get advised from QBlade if you change the wind speed to 12 m/s (see Simulation mode wind speed.png). Is the Rotor DMS simulation then wrong by assuming that the highest power coefficient is reached for a TSR of 4? And consequently, do I have to use the TSR of 3.33 to get the highest power coefficient when performing in the full simulation mode?

I know these are some quite specific questions, but you can really make me happy by answering them. Thank you in advance!

Kind regards,

Brecht Timmerman

Hi Brecht,

while the BEM method for HAWT simulation is physically sound and generates results that are very much comparable to free vortex wake simulations the DMS method for VAWT has several issues and its results often deviate quite a bit from reality. So you cannot directly compare its results with the free wake simulations in the tim domain. The DMS generally gives a good first idea of the VAWT performance, but not much more.

Regarding the Reynolds numbers: you can actually read the current operational RE number from QBlade simulations. What you can also do it to define a multi Reynolds number blade design. For a multi RE number blade design the polar data is always interpolated across the range of RE numbers to use the correct RE number polar data during the simulation. Especially for VAWT who operate under varying RE this can make a difference!

BR,

David

Hello Dr. David,

Concerning the Reynolds numbers, where can you read the current operational Re number then?
And for the multi Reynols number blade design, I think this is only possible for the strut design (see Reynolds number strut.png) and not for the blades itself (see Reynolds number blade.png) for a VAWT?

Kind regards,

Brecht

Dear Dr. David,

Concerning the first question, I think I know the answer. The Reynolds number can be seen in the Graph view of the Simulation mode.

Regarding the second question, I always thought that the Reynolds number you used for the Airfoil Analysis Module is the Reynolds number you used for all consequent simulations (as you have to select a certain polar in the Rotor Blade Design)  . But I now think this is not true for the Turbine Simulation mode.

During filling in the parameters for the Turbine Simulation mode, the TSR changes when filling in a certain windspeed. Is this TSR then corresponding to the TSR for the highest power coefficient (after the simulation has converged) at that windspeed?

Kind regards,

Brecht

Hi Brecht,

if a blade design is carried outr with a “multi-polar” definition, then the polar data is interpolated during the simulation from the Reynolds number range of polars that is defined for a particular section of the blade. If a “single polar” blade is defined the simulations then only the polar data from the assigned polars is used without any interpolation.

the TSR in the dialog is the TSR thats evaluated from the combination of windspeed and rotational speed. When a parameter (RPM, TSR or windspeed) is changed the remaining parameter (TSR or RPM) are automatically updated as they are interdependent.

BR,

David 