Generalized Dynamic Wake Theory and Implementation

Wind & Water AeroDyn Development
1

This topic is dedicated to the discussion of GDW theory and implementation.

2

Hi,

I’ve noticed that I often get unstable results for average wind speeds at 9 m/s, and I have to re-run these cases with equilibrium inflow. Perhaps the cutoff for the switch to equilibrium should be raised from 8 m/s to 9 m/s until the problem with the dynamic wake at low speeds gets fixed.

Regards

3

Hi Scott,

You’re welcome to do this yourself in line 5442 in AeroSubs.f90

IF (DYNINFL .AND. UBar / ConvFact <= 8.0) THEN

by changing 8.0 to 9.0 or any number you prefer. This essentially forces it to run in BEM mode, which you are doing manually now. So it may be easier to just do it manually if you don’t want to recompile.

The next version of AeroDyn will have a more elegant correction (vortex ring correction) to this problem. We’re currently testing the stability of the algorithms. Until then we’re stuck with this implementation.

cheers,
Pat

4

Thank you for the reply Pat. I probably stick to manual re-runs unless it becomes a burden. Good luck with the new algorithms; I hope that it makes for interesting work.

5

Hi Pat,

Just writing to let you that I couldn’t take it any longer so I made the code change you suggested and it works fine. No more wasted runs, no more manual re-runs.

Regards,

6

Hi everyone,

I have a question about the GDW model, because I’m implementing such a model.

In the “AeroDyn Theory Manual”, at pg.18 there is expression 88.

Now, my question is: do the signs of the quantities in this expression refer to the figure 12?
So for a WT operating in a standard idealized condition, being the induced flow opposite to the incoming flow direction,
the total inflow velocity is equal to the difference between the inflow due to free-stream wind and the induced flow?

Is this correct?

Thanks

Marco

7

Hi Marco,

We do have some inconsistencies in the signs for GDW, i.e. sometimes Aerodyn follows the helicopter conventions, and sometimes the wind turbine conventions, but in the end via double minus signs things work out just fine. We have in the plans to take care of that and make nomenclature uniform, in fact in Peters’s model the sign convention can take care of all situations from helicopter to wind turbine states.
Figure 12 is confusing, and we are planning on replacing that as well, I have produced another figure in a work I did for the lab in the past that is meant to replace it.
Aerodyn assumes lamda_m<0 and lamda_f>0.

The more generic Peters’s model assumes those quantities positive when pointed towards incoming flow (upwdind).
So in turbine state, lambda_f<0 and lambda_m>0 (both assumed positive when pointed towards incoming flow).

Hope that helps,
Rick

8

Hi Rick,

yes your answer helps and I think I understood Aerodyn’s convention.

thanks

Marco

9

Hi everyone,

I have a question about the GDW (Generalized Dynamic Wake) model implemented within Aerodyn.

In the manual It is stated that the initial values of induced flow are obtained from the BEM routine. Then, the software switches on the GDW model, by using
the BEM solution as initial value for the differential equations, which define the GDW modelling.
Now, clearly you need to project the BEM solution on to the expansion shape functions and the azimuthal modes in order to calculate the initial values in the
appropriate reference.

My question is: when projecting the BEM solution, do you consider the inflow value upon a certain blade element as distributed over the respective annular surface
or is it considered as distributed only over the part of the rotor occupied by the blades (as it is done for the thrust, when calculating the pressure coefficients for
the GDW model)?

Thanks,

Marco

10

Marco,

The initial value for the GDW is the average of the BEM solution, and the average is over the blade radius.

Khanh

11

Hi Khanh,

thanks for the reply; I understand that you consider the average over the radius, but this value is considered as
constant also over the azimuth? i.e. do you consider the initial value of induced flow to be different from zero only on the first harmonic (m=0)?

I have some questions about the GDW as described within the Aerodyn Theory Manual. Sorry if I’m picky or sometime not precise, but I’m try to
implement the same model and I need to use the correct expressions.

  1. In expressions 92,93 (pg.19), the azimuthal coordinate is left as an independent variable. Shouldn’t it refer to the azimuthal coordinate of the considered blade?
    What I mean is, the sine and cosine should not be calculate as sin(mψ_q) and cos(mψ_q)? Where “q” refers to the blade identification number.

  2. In the same expressions you are considering a summation to approximate the integral of the lift distribution multiplied by the shape function over the dimensionless blade’s length.
    Why the term “∆r”, approximating the infinitesimal variation of the radius “dr”, is not present in the expression? Are you assuming an uniform aerodynamic mesh? Because, if the mesh is not
    uniform, even though the radial coordinate is dimensionless and varies between zero and one, I thought you had to consider this term in the approximated numeric integration.

  3. By comparing expressions 92-93 and the same terms as expressed in Peters (1991,Correlation of measured induced velocities with a finite-state wake model), I found a difference, which can be important.
    In Peters, they consider the thrust per unit span (in N/m) and then they non-dimensionalize it. In the manual, the resultant thrust (in N) of a certain blade element is considered and then non-dimensionalized. If you compare
    these two non-dimensionalizations, you have that in the manual the thrust per unit span is equal to the elements’ thrusts divided by the blade’s length (indeed, in your expression the R term at the denominator
    has an exponent 4 instead of 3, as in Peters). Clearly, this is dimensionally correct, but it yields different results, because Peters thrust per unit span is equal to the element’s thrust divided by its radial width.
    Can you try to clarify this? Probably I misunderstood something, but I do not see what it is.

Thanks in advance,

Marco

12

Hi Khanh,

with regard to questions 2 and 3 in my last post, you can ignore them. I redid all of the calculations again and I found why
I was obtaining different results. Sorry!!

Question 1 still stands.

Regards

Marco

13

Marco,

The initial condition of the GDW model requires the inflow value (calculated with BEM in this case) at a rotor azimuth (or at one instance in time). Thus, there is no need for the azimuth-averaged value.

Regarding question (1), you are correct. The variable ψ in Eqs. [92] and [93] in the Theory Manual should be corrected to ψ_q to be consistent with the outer summation of q, from 1 to B, B being the blade number.

Thanks,

Khanh

14

Hi Everyone,

I have been doing some work to compare CFD models of rotor dynamics with dynamic wake models. When using the GDW model, I found that the radial distribution of inflow factor was not fine enough to make an accurate comparison. I was wondering how to include more radial mode shapes in the calculation.
I found the following parameter arrays which are used in the creation of the gamma matrix:
MRvector = (/ 0, 0, 1, 1, 2, 3 /)
NJVector = (/ 1, 3, 2, 4, 3, 4 /)
However, I’m not sure of the logic for assigning these arrays; could anyone give any tips for this?
Also, is the reason for the current choice of number of mode shapes governed by the speed of calculation, stability, or both?

Thanks

James