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Power coefficient calculations

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Hello,

I’m currently comparing the power coefficients of a blade with several helical angles (from straight to twisted 180°). I have done this for a rotor with a single blade (Single_bladed_rotor.png) and a rotor with three blades (Triple_bladed_rotor). My results are however a bit weird, as I receive the same power coefficient for each blade.

Does someone know what I’m doing wrong?

Kind regards,

Brecht Timmerman

 

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Hi Brecht,

the DMST algorithm evaluates the different blade stations over the turbine height as aerodynamically independent. So what the DMST algorithm “sees” at every height position of the turbine is three (or a single) blade – so the integrated performance at each height is the same just that the azimuthal positions of the blade stations are slightly shifted. So for the integral values such as Cp, Ct etc. you wont see a difference. Only the azimuthal variables, such as the torque distribution over the azimuthal rotor angle are affected by this (for instance visible as a reduction in torque “ripple” for larger helical twist angles).

If you run simulations with the free wake method in the time domain the different blade stations wont be treated as independent as the free wake vorticity and the bound blade vorticity is causing some aerodynamic interaction.

BR,

David

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Brecht T

Hello,

Thanks a lot for your fast respond David.

So I tried a simulation for straight-bladed VAWT (Straight.png) for a wind speed of 10 m/s (file is to large to include). I tried several timesteps (0.02, 0.05, 0.1, 0.2, 0.5) to know which one is a good trade-off between fast but accurate simulation of the power coefficient (Power coefficient_straight.png) . I reasoned as follows: the smaller the timestep, the more the power coefficient converged to its most accurate value. I concluded that a timestep of 0.1 represents a good trade-off choice.

However, when I tried this ‘method’ again for a helical-bladed (180° twisted) VAWT (Helical_180.png) for a wind speed of 10 m/s for several timesteps (0.03, 0.05, 0.1), I obtain exceptional results (file is to large to include). These values do not converge at all, they even diverge to values of more than 1 (Power coefficient_helical_180.png).

Do you have an explanation for this? Do I something wrong

Kind regards,

Brecht

 

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Hi Brecht,

without looking at your settings I can already see that this issue (large Cp & divergence of the wake) is probably coming from you vortex wake settings. Try testing with a different vortex core radius. Another reason could be that your rpm is too high so that the wake cannot concet downstream due to the high induction and then vortex interaction causes the divergence.

BR,

David

Dear David,

You can find my wake settings in attachement. You can find the file here as well.

Thanks a lot already for spending your time to help me!

Kind regards,

Brecht

 

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Hi Brecht,

try setting the “Initial Wake Core Radius” parameter to 1.0. Increasing this parameter causes the vortex core radius to be larger when a vortex element is released from the trailing edge and this effectively dampens the wake self induction.

Best,

David

Brecht T has reacted to this post.
Brecht T

Hello David,

In attachement you can see the results with an Initial Wake Core Radius of 1 for different time steps (0.1, 0.05, 0.03 and 0.01 (0.01 only partially because to time excessive)). The values are already closer, however the timestep 0.01 differs still quite significantly.

I have two questions:

Are my simulations reliable and compliant?

Gives a smaller timestep always a more accurate result?

Thanks already!

Kind regards,

Brecht

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Two additional questions:

  • Which time step do you recommend to use while comparing power outputs and power coeficients of different VAWTs designs?
  • Is the power coefficient at the end of a simulation (in this case about 32 s) ‘the’ power coefficient of the turbine?

Hi Brecht,

without going into too much detail here, also since I’m lacking the time to look at your sims in detail:

Talking about “absolute” timsteps (in seconds) can be confusing because the required timestep depends on the rotor rpm which usually is a function of turbine size. This is why, when talking about required discretization, the timestep should be normalized by rpm, resulting in the azimuthal rotor increment per timestep, in degrees. In general for HAWT’s and VAWT’s a timestep that is equivalent of 2°-5° of azimuthal rotor increment is sufficiently fine (often even 10° azimuthal discretization yield good results). You should try to “tune” your wake setting to such a timestep. When running simulations at multiple rpm’s you can tune your wake settings to the timestep at the largest rpm and then you can use this as a constant timestep (and wake settings) for all other simulations at lower rpm’s (even though sims at the lower rpms then have a much finer discretization and take longer than if you would individually tune those).

Regarding your second question: When the wake settings are sensible then the converged CP value at the end of a sim should be the CP at that operating state. How long such a convergence takes is different (again depends on rpm) but usually 20-30 simulated rotor revolutions should be enough for the CP to converge (the required revolutions can be significantly lower if you are simulating at a very low TSR).

Best,

David

Brecht T has reacted to this post.
Brecht T

Hi David,

Thanks a lot for your explanation!

Kind regards,

Brecht

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A simulation of the Lillgrund windfram in QBlade, using the Dynamic Wake Meandering Model