Rationale behind frozen wake assumption

Wind & Water Computer-Aided Engineering Software Tools
1

Hi Team,

I’ve seen several topics on the forum advocating the use of frozen wake modelling during the linearisation process for control design. From Jason Jonkman’s thesis the justification is given as:

“This gives a more accurate linearization for heavily loaded rotors”.

Is anyone able to explain this in more detail?

It seems to me that using dynamic wake would be the most accurate, followed by frozen wake and finally equilibrium wake.

Best regards,

Avi

2

Dear Avi,

Although states associated with the dynamic wake are not included in a linearized model based on frozen wake, linearization with frozen wake is a better approximation of the linearization one would obtain with dynamic wake than one would obtain with equilibrium wake. As shown in the following forum topic: Gain Scheduling - #10 by Jason.Jonkman (particularly Ville’s post dated Nov 25, 2010), the sensitivity of power to pitch with equilibrium wake shows a similar trend to that of frozen wake, but (inaccurately) shows a loss of control authority—whereby the sensitivity is near zero—at rated conditions. As such, the use of frozen wake in the linearization process is recommended.

Linearization with frozen wake is now a standard feature of the linearization capability of FAST v8 with AeroDyn v15.

I hope that helps.

Best regards,

3

Hi Jason,

Thanks for that reply, I now realise my mistake. I was incorrectly assuming that it was possible to include the aerodynamic states in the linearisation, in which case dynamic wake would be most preferable. In the absence of this ability I agree that that frozen wake better represents dynamic wake and equilibrium wake is unsuitable.

Regards,

Avi

4

Dear Jonkman,

Do I always have to use frozen wake assumption whenever i want to linearize turbine model in between the cut-in and cut-out velocities? Or Frozen wake assumtion is only used for the linearization process above the rated wind speeds (for higly loaded rotors).

Yours Sincerely.

Mustafa.

5

Dear Mustafa,

We recommend to enable frozen wake during a linearization analysis in general. However, I would expect frozen wake to have the most significant effect near rated conditions.

Best regards,