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Gaussian wake models have 2 errors that do not align with theory
This doesn't fit the typical issue template since it is just comparing code with theory. I will do my best to justify everything with references.
The first reference is the research paper that the Gaussian wake model is based off of:
Bastankhah, Majid, and Fernando Porté-Agel.
"Experimental and theoretical study of wind turbine wakes in yawed conditions."
Journal of Fluid Mechanics 806 (2016): 506-541.
which may be accessed publicly here. The main equations I am looking at are Eq. (6.4) $$\frac{u_R}{u_\infty} = \frac{C_T \cos \gamma}{2 ( 1 - \sqrt{1-C_T \cos \gamma} )}$$
and Eq. (6.16) $$\frac{x_0}{D} = \frac{\cos \gamma (1+\sqrt{1-C_T})}{\sqrt{2} [ 4 \alpha I + 2 \beta (1-\sqrt{1-C_T})]}$$
I am specifically referencing the code within the following files:
floris/simulation/wake_velocity/gauss.py
(herein referred to as wake_velocity) and
floris/simulation/wake_deflection/gauss.py
(herein referred to as wake_deflection)
Error 1 in wake_velocity
The first error occurs in wake_velocity, with respect to Eq. (6.4) where $u_R$ is calculated on line 87.
uR=u_initial*ct_i/ ( 2.0* (1-np.sqrt(1-ct_i) ) )
This equation does not match up with Eq. (6.4), and it should be
There is another difference that I found between the code and the theory.
The reference paper is also the :
Bastankhah, Majid, and Fernando Porté-Agel.
"Experimental and theoretical study of wind turbine wakes in yawed conditions."
Journal of Fluid Mechanics 806 (2016): 506-541.
In order to determine the potential core area at x=0, we should refer to the content in page 530.
And according to the formulas (6.4) and (6.7) given in reference paper:
While determining the wake expansion in near wake zone, the linear ramp from 0 to 1, from the start of the near wake to the start of the far wake is calculated as:
Furthermore, @RyanDunn729, in wake_velocity line 102, I think the formula for $x_0$ is correct, because it is not finished, $x_0$ is calculated via line 102 and line 103.
Gaussian wake models have 2 errors that do not align with theory
This doesn't fit the typical issue template since it is just comparing code with theory. I will do my best to justify everything with references.
The first reference is the research paper that the Gaussian wake model is based off of:
which may be accessed publicly here. The main equations I am looking at are Eq. (6.4)
$$\frac{u_R}{u_\infty} = \frac{C_T \cos \gamma}{2 ( 1 - \sqrt{1-C_T \cos \gamma} )}$$
$$\frac{x_0}{D} = \frac{\cos \gamma (1+\sqrt{1-C_T})}{\sqrt{2} [ 4 \alpha I + 2 \beta (1-\sqrt{1-C_T})]}$$
and Eq. (6.16)
I am specifically referencing the code within the following files:
(herein referred to as wake_velocity) and
(herein referred to as wake_deflection)
Error 1 in wake_velocity
The first error occurs in wake_velocity, with respect to Eq. (6.4) where$u_R$ is calculated on line 87.
This equation does not match up with Eq. (6.4), and it should be
(note that cosine is multiplied in the numerator)
For additional verification, I also noticed that in wake_deflection lines 150-156,$u_R$ is calculated by
further confirming the inconsistency with theory.
Error 2 in wake_deflection
The first error occurs in wake_deflection, with respect to Eq. (6.16) where$x_0$ is calculated on lines 160-166.
This equation does not match up with Eq. (6.16), and it should be
(note that cosine is removed within the square root)
For additional verification, I also noticed that in wake_velocity line 102,$x_0$ is calculated by
further confirming the inconsistency with theory.
Floris version
v3.4 (latest)
I installed by
Before submitting I made sure to git pull and it appears this has not yet been spotted.
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