# Deflection Models

The deflection models calculate the deflection of the wake due to yaw-misalignment, sheared inflow etc.

Note, this is one of the four effects of skew inflow that is handled in PyWake, see here.

The deflection models take as input the downwind and crosswind distances between the source wind turbines and the destination wind turbines/sites and calculate a new set of deflected downwind and crosswind distances. This type of model is important for simulations where the turbine experiences a change in angle between the incoming flow and the rotor, for example in active yaw control or wake steering optimization.

In PyWake, there are three different wake deflection models:

Install PyWake if needed

[1]:

# Install PyWake if needed
try:
import py_wake
except ModuleNotFoundError:
!pip install git+https://gitlab.windenergy.dtu.dk/TOPFARM/PyWake.git


First we create a simple function to plot the different deflection models available in PyWake.

[2]:

import numpy as np
import matplotlib.pyplot as plt

# import and setup site and windTurbines
import py_wake
from py_wake import BastankhahGaussian
from py_wake.examples.data.iea37._iea37 import IEA37Site, IEA37_WindTurbines
from py_wake.examples.data.hornsrev1 import V80

site = IEA37Site(16)
x, y = [0, 400, 800], [0, 0, 0]
windTurbines = V80()
D = windTurbines.diameter()

[3]:

def plot_deflection(deflectionModel):

wfm = BastankhahGaussian(site, windTurbines, deflectionModel=deflectionModel)

yaw = [-20,20,0]
D = windTurbines.diameter()

plt.figure(figsize=(14,4))
fm = wfm(x, y, yaw=yaw, tilt=0, wd=270, ws=10).flow_map()
fm.plot_wake_map(normalize_with=D)
center_line = fm.min_WS_eff()
plt.plot(center_line.x/D, center_line/D,'--k')
plt.grid()


## JimenezWakeDeflection

The JimenezWakeDeflection model is implemented according to Jiménez, Á., Crespo, A. and Migoya, E. (2010), Application of a LES technique to characterize the wake deflection of a wind turbine in yaw. Wind Energ., 13: 559-572. doi:10.1002/we.380.

It is the most common wake deflection model used in PyWake and has proved to result in a decent representation of the skewed inflow behind the turbine rotor. In the study, the authors carried out a Large Eddy Simulation (LES) to characterize the turbulence behind a wind turbine given the wake deflection created by different yaw angle and thrust coefficient settings.

[4]:

from py_wake.deflection_models import JimenezWakeDeflection
plt.figure()
plot_deflection(JimenezWakeDeflection())
plt.xlabel('x [m]')
plt.ylabel('y [m]')

/builds/TOPFARM/PyWake/py_wake/deficit_models/gaussian.py:127: UserWarning: The BastankhahGaussian model is not representative of the setup used in the literature. For this, use py_wake.literature.gaussian_models.Bastankhah_PorteAgel_2014 instead
DeprecatedModel.__init__(self, 'py_wake.literature.gaussian_models.Bastankhah_PorteAgel_2014')

[4]:

Text(0, 0.5, 'y [m]')

<Figure size 640x480 with 0 Axes>


[5]:

from py_wake.deflection_models import FugaDeflection
plt.figure()
plt.xlabel('x [m]')
plt.ylabel('y [m]')

/builds/TOPFARM/PyWake/py_wake/deficit_models/gaussian.py:127: UserWarning: The BastankhahGaussian model is not representative of the setup used in the literature. For this, use py_wake.literature.gaussian_models.Bastankhah_PorteAgel_2014 instead
DeprecatedModel.__init__(self, 'py_wake.literature.gaussian_models.Bastankhah_PorteAgel_2014')

[5]:

Text(0, 0.5, 'y [m]')

<Figure size 640x480 with 0 Axes>


## GCLHillDeflection

Deflection model based on Hill’s ring vortex theory.

Implemented according to: Larsen, G. C., Ott, S., Liew, J., van der Laan, M. P., Simon, E., R.Thorsen, G., & Jacobs, P. (2020). Yaw induced wake deflection - a full-scale validation study. Journal of Physics - Conference Series, 1618, [062047]. https://doi.org/10.1088/1742-6596/1618/6/062047.

Note, this model uses the wake centerline deficit magnitude to calculate the deflection. Hence non-gaussian-shaped wake deficit models as well as deficit models with improper near wake fields, e.g. NOJDeficit, BastankhahGaussianDeficit, NiayifarGaussianDeficit, should be avoided.

As default the model uses the WakeDeficitModel specified for the WindFarmModel to calculate the magnitude of the deficit, but a separate model can be specified.

[6]:

from py_wake.deflection_models import GCLHillDeflection
plt.figure()
plot_deflection(GCLHillDeflection())
plt.xlabel('x [m]')
plt.ylabel('y [m]')

/builds/TOPFARM/PyWake/py_wake/deficit_models/gaussian.py:127: UserWarning: The BastankhahGaussian model is not representative of the setup used in the literature. For this, use py_wake.literature.gaussian_models.Bastankhah_PorteAgel_2014 instead
DeprecatedModel.__init__(self, 'py_wake.literature.gaussian_models.Bastankhah_PorteAgel_2014')

[6]:

Text(0, 0.5, 'y [m]')

<Figure size 640x480 with 0 Axes>


## You can also implement your own deflection models

Deficit models must subclass DeficitModel and thus must implement the calc_deflection method and a class variable, args4deflection specifying the arguments required by its calc_deflection method.

class DeflectionModel(ABC):
args4deflection = ["ct_ilk"]

@abstractmethod
def calc_deflection(self, dw_ijl, hcw_ijl, **kwargs):
"""Calculate deflection

This method must be overridden by subclass

Arguments required by this method must be added to the class list
args4deflection

See documentation of EngineeringWindFarmModel for a list of available input arguments

Returns
-------
dw_ijlk : array_like
downwind distance from source wind turbine(i) to destination wind turbine/site (j)
for all wind direction (l) and wind speed (k)
hcw_ijlk : array_like
horizontal crosswind distance from source wind turbine(i) to destination wind turbine/site (j)
for all wind direction (l) and wind speed (k)
"""

[7]:

from py_wake.deflection_models import DeflectionModel
from numpy import newaxis as na
from py_wake import BastankhahGaussian

class MyDeflectionModel(DeflectionModel):

def calc_deflection(self, dw_ijlk, hcw_ijlk, **_):
hcw_ijlk =hcw_ijlk + .1*dw_ijlk       # deflect 1/10 of the downstream distance
dh_ijlk =np.zeros_like(hcw_ijlk)      # no vertical deflection
return dw_ijlk, hcw_ijlk, dh_ijlk

iea_my_deflection = BastankhahGaussian(site, windTurbines, deflectionModel=MyDeflectionModel())

plt.figure(figsize=(10,4))
iea_my_deflection(x=[0], y=[0], wd=270, ws=10).flow_map().plot_wake_map(normalize_with=D)
plt.xlabel('x/D')
plt.ylabel('y/D');

/builds/TOPFARM/PyWake/py_wake/deficit_models/gaussian.py:127: UserWarning: The BastankhahGaussian model is not representative of the setup used in the literature. For this, use py_wake.literature.gaussian_models.Bastankhah_PorteAgel_2014 instead
DeprecatedModel.__init__(self, 'py_wake.literature.gaussian_models.Bastankhah_PorteAgel_2014')