Add wake deflection to the TurbOPark wake deficit model

[bayc]

Feature or improvement description
This PR includes wake deflection in the TurbOPark wake deficit model. Co-created with @rafmudaf.

Related issue, if one exists
None.

Impacted areas of the software
The TurbOPark wake deficit model and the TurbOPark solver.

Additional supporting information
This introduces another for loop to the TurbOPark solver when yaw angles are non-zero. Hopefully this can be optimized further, but the calculation requires the wake centerline position of upstream turbines, where in the current solver schemes, the wake deflection is calculated for all downstream turbines and the effect of that deflection is stored in the wake velocity fields. Here, I assume the wake centerline to be the amount of deflection calculated by the deflection model.

Test results, if applicable
Need to update the regression tests to include yawed results.

Below are the results of a 2 turbine pair, yawing the first turbine 25 degrees and sweeping the second turbine laterally (y-direction), recording its change in power. Beneath that is the result for a 3 turbine array, yawed first turbine, and sweeping the third turbine. The code to reproduce these results is at the bottom.

import matplotlib.pyplot as plt
import numpy as np

from floris.tools import FlorisInterface

# Initialize FLORIS with the given input file via FlorisInterface.
# For basic usage, FlorisInterface provides a simplified and expressive
# entry point to the simulation routines.
fi_gch = FlorisInterface("inputs/gch.yaml")
fi_turbo = FlorisInterface("inputs/turbopark.yaml")

fi_gch.reinitialize(wind_directions=[270.], wind_speeds=[8.0])
fi_gch.reinitialize(wind_directions=[270.], wind_speeds=[8.0])

# Convert to a simple two turbine layout
y_range = np.arange(-300,300,20.)

x_spacing = 5*126.
nturbs = 2

# Get the base profiles
gch_base = []
turbo_base = []
for y in y_range:
    x_layout = np.array([i*x_spacing for i in range(nturbs)])
    y_layout = np.append(np.array([0.0] * (nturbs - 1)), y)
    fi_gch.reinitialize( layout=( x_layout, y_layout ) )
    fi_turbo.reinitialize( layout=( x_layout, y_layout ) )

    fi_gch.calculate_wake()
    fi_turbo.calculate_wake()

    gch_base.append(fi_gch.get_turbine_powers()[0,0,-1]/1000.)
    turbo_base.append(fi_turbo.get_turbine_powers()[0,0,-1]/1000.)

# Get the yaw profiles
gch_yaw = []
turbo_yaw = []
for y in y_range:
    x_layout = np.array([i*x_spacing for i in range(nturbs)])
    y_layout = np.append(np.array([0.0] * (nturbs - 1)), y)
    fi_gch.reinitialize( layout=( x_layout, y_layout ) )
    fi_turbo.reinitialize( layout=( x_layout, y_layout ) )

    yaw_angles =np.zeros([1,1,nturbs])
    yaw_angles[0,0,0] = 25.

    fi_gch.calculate_wake(yaw_angles = yaw_angles)
    fi_turbo.calculate_wake(yaw_angles = yaw_angles)

    gch_yaw.append(fi_gch.get_turbine_powers()[0,0,-1]/1000.)
    turbo_yaw.append(fi_turbo.get_turbine_powers()[0,0,-1]/1000.)


fig, ax = plt.subplots(1,1)


ax.plot(y_range, gch_base, 'b-',label='gch base')
ax.plot(y_range, turbo_base,'m-', label='turbo base')
ax.grid(True)
ax.legend()


ax.plot(y_range, gch_yaw, 'b--',label='gch yaw')
ax.plot(y_range, turbo_yaw, 'm--',label='turbo yaw')
ax.grid(True)
ax.legend()

plt.show()

[rafmudaf]

This could be simplified to

if not np.all(farm.yaw_angles_sorted):
    for ii in range(i):
        etc
        etc

[rafmudaf]

@bayc I added the yaw reg test case