## Forum

# Power coefficient calculations

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Quote from David on 8. March 2023, 13:47Hi Brecht,

in my Phd Thesis from page 44 onwards you find some more info regarding the effect of wake discretization.

Best,

David

Hi Brecht,

in my Phd Thesis from page 44 onwards you find some more info regarding the effect of wake discretization.

Best,

David

Quote from Brecht T on 8. March 2023, 18:27Hello David,

I’m sorry to bother you again, but I have some additional questions:

- In your thesis, how did you make the graph (Graph Cp-TSR.png) as normally for a simulation you have to choose a particular TSR and then perform the simulation? Did you do each simulation apart (per TSR) and then make a graph by yourself by f.e. Excel? Or is it possible in QBlade as well?
- I’m currently investigating the effect of the number of blades on the power coefficient. I performed an analysis for a straight-bladed rotor with variating number of blades (1 to 7 blades). Everything looked OK until I did the 6-bladed rotor simulation (Power coefficient for rotor with different number of blades.png) as the power coefficient diverged again after a certain amount of time (similar for the 7-bladed rotor). I then discovered that I can’t use the TSR of 4 (as concluded for the 3-bladed rotor to be the maximum power coefficient at TSR of 4) for the other rotors. I than performed already another simulation to compare a 7-bladed rotor (TSR=2.5) with a 3-bladed rotor (TSR=4) and got a result that is a bit surprising, namely that the power coefficient of the 7-bladed rotor is higher than that one of the 3-bladed rotor (Power coefficient for 3-bladed and 7-bladed rotor.png). According to general literature, it should be vice versa.
I fully understand if you are not able to respond directly. Thanks in advance!

Kind regards,

Brecht

Hello David,

I’m sorry to bother you again, but I have some additional questions:

- In your thesis, how did you make the graph (Graph Cp-TSR.png) as normally for a simulation you have to choose a particular TSR and then perform the simulation? Did you do each simulation apart (per TSR) and then make a graph by yourself by f.e. Excel? Or is it possible in QBlade as well?
- I’m currently investigating the effect of the number of blades on the power coefficient. I performed an analysis for a straight-bladed rotor with variating number of blades (1 to 7 blades). Everything looked OK until I did the 6-bladed rotor simulation (Power coefficient for rotor with different number of blades.png) as the power coefficient diverged again after a certain amount of time (similar for the 7-bladed rotor). I then discovered that I can’t use the TSR of 4 (as concluded for the 3-bladed rotor to be the maximum power coefficient at TSR of 4) for the other rotors. I than performed already another simulation to compare a 7-bladed rotor (TSR=2.5) with a 3-bladed rotor (TSR=4) and got a result that is a bit surprising, namely that the power coefficient of the 7-bladed rotor is higher than that one of the 3-bladed rotor (Power coefficient for 3-bladed and 7-bladed rotor.png). According to general literature, it should be vice versa.

I fully understand if you are not able to respond directly. Thanks in advance!

Kind regards,

Brecht

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Quote from David on 13. March 2023, 20:59Hi Brecht,

you are correct that “Cp-TSR” graph that you mentioned above is a combination of data from multiple simulations.

Regarding your simulations:

I think that your sims are not fully converged yet. Usually you should run for at least 20 full rotations to have a converged Cp when the rotor is under such a large load. Finding good wake parameters for the 7-blade rotor can be a bit tricky.

Also you could think about activating the dynamic stall model (Gormont-Berg) which will have a larger effect at lower TSR’s.

There is also the Reynolds-number effect, at the lower TSR RE will be lower so the airfoils will be less efficient – this is probably not reflected in your setup.

What does the literature show as a difference between the 3- and 7-bladed rotor?

BR,

David

Hi Brecht,

you are correct that “Cp-TSR” graph that you mentioned above is a combination of data from multiple simulations.

Regarding your simulations:

I think that your sims are not fully converged yet. Usually you should run for at least 20 full rotations to have a converged Cp when the rotor is under such a large load. Finding good wake parameters for the 7-blade rotor can be a bit tricky.

Also you could think about activating the dynamic stall model (Gormont-Berg) which will have a larger effect at lower TSR’s.

There is also the Reynolds-number effect, at the lower TSR RE will be lower so the airfoils will be less efficient – this is probably not reflected in your setup.

What does the literature show as a difference between the 3- and 7-bladed rotor?

BR,

David

Quote from Brecht T on 15. March 2023, 09:51Hello dr. David,

In most cases literature compares 2, 3 and 4 bladed rotors (Power coefficient 2, 3 and 4 bladed rotor.png, source: Aerodynamic design and performance parameters of a lift-type vertical axis wind turbine: A comprehensive review)

Some other observations in the paper:

- It was concluded the Reynolds number should be kept high as possible and this suggests the number of blades should be small as feasibly possible [78]
- Shiono et al. indicate the reduced efficiency is due to detrimental interference between the blades and increases with the number of blades utilised and is supported by wind tunnel tests performed by Li et al. [92].
- A qualitative analysis by Sun et al. [94] showed the blade vortex shedding frequency increases as the number of blades is increased and especially at low TSRs.
I would consequently expect that for a larger amount of blades (4, 5, 6 and 7) the power coefficient would be even lower than that for a 3 bladed rotor.

Kind regards

Brecht Timmerman

Hello dr. David,

In most cases literature compares 2, 3 and 4 bladed rotors (Power coefficient 2, 3 and 4 bladed rotor.png, source: Aerodynamic design and performance parameters of a lift-type vertical axis wind turbine: A comprehensive review)

Some other observations in the paper:

- It was concluded the Reynolds number should be kept high as possible and this suggests the number of blades should be small as feasibly possible [78]
- Shiono et al. indicate the reduced efficiency is due to detrimental interference between the blades and increases with the number of blades utilised and is supported by wind tunnel tests performed by Li et al. [92].
- A qualitative analysis by Sun et al. [94] showed the blade vortex shedding frequency increases as the number of blades is increased and especially at low TSRs.

I would consequently expect that for a larger amount of blades (4, 5, 6 and 7) the power coefficient would be even lower than that for a 3 bladed rotor.

Kind regards

Brecht Timmerman

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Quote from David on 15. March 2023, 11:23Hi Brecht,

I think the graph that you attached is not valid for your simulations, since it is generated for rotors with constant solidity.

In your simulations you dont have a constant rotor solidity since you are not adjusting the chord length when increasing the number of blades.

If you look at the attached graph, from the same paper, you can see that changing the solidity also has an effect on the CP, so in your sims your are mixing up both effects and its not easy to say which one (change in solidity vs. change in blade number) is dominant in influencing CP.

In fact your 7 blade rotor has a solidity of ~3.5 which is pretty close to the optimum if oyu look at the graph below…

Best,

David

Hi Brecht,

I think the graph that you attached is not valid for your simulations, since it is generated for rotors with constant solidity.

In your simulations you dont have a constant rotor solidity since you are not adjusting the chord length when increasing the number of blades.

If you look at the attached graph, from the same paper, you can see that changing the solidity also has an effect on the CP, so in your sims your are mixing up both effects and its not easy to say which one (change in solidity vs. change in blade number) is dominant in influencing CP.

In fact your 7 blade rotor has a solidity of ~3.5 which is pretty close to the optimum if oyu look at the graph below…

Best,

David

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Quote from Brecht T on 15. March 2023, 16:48Hello Dr. David,

Thanks a lot for your response! I will take this into account.

Kind regards,

Brecht

Hello Dr. David,

Thanks a lot for your response! I will take this into account.

Kind regards,

Brecht

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