Product sum superposition

[prith-gs]

Hello,

I was wondering if I can add the product sum superposition model to the list of wake combination models in FLORIS and I have a doubt.

For example, let's take the linear sum superposition method and the product sum superposition method.
let's assume three turbines T1, T2 and T3 and I'm calculating the velocity at a location downstream of the three turbines.
FLS is given by

The above equation works regardless of whether the wake deficit is normalized (unit-less) or absolute velocity deficit (m/s).

if the wake deficit is normalized then to get the effective velocity, we need to use

if the wake deficit is not normalized, then we need to use

Similarly, the product sum superposition is given by

Now, unlike the Linear sum, Sum of squares or Maximum wake deficit methods, the above equation for the product sum only works when the deficits are normalized. To calculate the cummulative effect of wake from the upstream turbines, the individual wake deficits should be passed as Normalized wake deficits and not absolute deficits.

Now, I see in the solver, the wake combination model is called with two inputs: wake field and velocity_deficit*u_initial_sorted

Through velocity_deficit*u_initial_sorted, the wake deficit is passed as absolute deficits. As I explained before this works for all the three wake combination models used in FLORIS but unfortunately won't work for the product sum.

If I have to add the product sum superposition model, how would I go about this?

Looking forward to your response.

Thanks,
Pritheesh

[misi9170]

Hi Pritheesh,

To add another combination model and pass other arguments in, you'll need to modify the function call in the sequential_solver. This will break the operation of existing combination models (max, FLS, SOFS), so you'll need to add the new arguments to those combination models (even if they aren't used). Possibly, you can just pass in the freestream velocity so that you can normalize the deficits inside the combination model.

Does that make sense?

Misha

[prith-gs]

Hi @misi9170

I have been playing around with this.
What I have done now, instead of adding the pdt sum to the list of wake superposition models in NREL FLORIS, I have modified the max model and adjusted the sequential solver so that it works with pdt sum. This is a WIP.

First change:

I removed the freestream velocity (u_initial_sorted) from the wake_field calculation here.
So that the cumulative wake deficits (wake_field) will now be normalized which is what we need for the product sum.

Before edit,

wake_field = model_manager.combination_model.function(
                                  wake_field,
                                  velocity_deficit * flow_field.u_initial_sorted
                              )

After edit,

wake_field = model_manager.combination_model.function(
                                  wake_field,
                                  velocity_deficit
                              )

Second change:

Since the reference velocity was removed from the wake_field, this needs to included at a later part of the solver where the freestream velocity is adjusted for wake effects.

Before edit,
flow_field.u_sorted = flow_field.u_initial_sorted - wake_field

After edit,
flow_field.u_sorted = flow_field.u_initial_sorted - wake_field* flow_field.u_initial_sorted

Third change:

I have replaced the max model with the following piece of code.

def function(self, wake_field: np.ndarray, velocity_field: np.ndarray):
    """
    Combines the base flow field with the velocity deficits
    using a hybrid method:
    - Linear sum when no existing deficit is present.
    - Product of complements when a deficit already exists.

    Args:
          wake_field (np.ndarray): Cumulative wake deficit field.
          velocity_field (np.ndarray): Wake deficit field from the 'i'th turbine.

    Returns:
        np.ndarray: Updated deficit field.
    """
    fls = wake_field + velocity_field
    pdt = 1.0 - (1.0 - wake_field) * (1.0 - velocity_field)
    
    is_zero = velocity_field == 0.0
    is_nonzero = velocity_field > 0.0

    return is_zero * fls + is_nonzero * pdt

The wake_field and velocity_field are initialized with zeros. So, when adding the wake effect of the first turbine I use linear sum, when there's an already existing wake then I use the product sum. The numbers I'm getting seems to make sense.

Here's a sample calculation comparing the 4 different wake superposition models for a simple three turbine setup.

I'm curious to know what you guys think about this implementation.

Looking forward to your response.

Best,
Pritheesh

[misi9170]

Hi Pritheesh,

Thanks for diving into this and sharing your progress! This all sounds very reasonable to me. The changes you are suggesting for wake_field (and, subsequently, flow_field.u_sorted) look fine in principle, and it's nice to see the results you are getting seem to be working out well.

I'm also very happy to set up a short meeting if you'd like to discuss further. You can find my email address here. No pressure, of course, if you'd rather simply keep the discussion here on Github!

Cheers,
Misha

[prith-gs]

Hi Misha,

I will send an email to you to further discuss on this. Thanks!

Hi Pritheesh,

To add another combination model and pass other arguments in, you'll need to modify the function call in the sequential_solver. This will break the operation of existing combination models (max, FLS, SOFS), so you'll need to add the new arguments to those combination models (even if they aren't used). Possibly, you can just pass in the freestream velocity so that you can normalize the deficits inside the combination model.

Does that make sense?

Misha

To respond to your earlier message on how this will break the operation of the existing combination models. I believe with the modified version it still works on the solver level. I'm not sure if there are other areas in the code such as flow visualization etc. where this needs to be modified if product sum needs to be part of FLORIS.

Best,
Pritheesh