Heterogeneous flow¶

The best way to run foxes calculations on heterogeneous background flow fields is by providing them in netCDF format. They should contain the following coordinates:

• A state coordinate, e.g. Time (expected by default) or state, or similar

• A height coordinate, e.g. height (expected by default) or h, or similar

• A y coordinate, e.g. UTMY (expected by default) or y, or similar

• A x coordinate, e.g. UTMX (expected by default) or x, or similar

The file may contain any kind of foxes variables as data fields, e.g.:

• Wind speed data, e.g. WS (expected by default, if claimed as output variable), ws or similar

• Wind direction data, e.g. WD (expected by default, if claimed as output variable), wd or similar

• Turbulence intensity data, e.g. TI (expected by default, if claimed as output variable), ti or similar

• Air density data, e.g. RHO (expected by default, if claimed as output variable), rho or similar

All data must depend on the state coordinate, and may depend on the others.

These are the required imports for this example:

In [1]:

%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np

import foxes
import foxes.variables as FV

One very simple example for netCDF type data is provided in the static data, under the name wind_rotation.nc. It contains two states, two heights, and simple 2 x 2 horizontal data that describes identical wind speeds at all four corner points associated with different wind direction values. It can be loaded as follows:

In [2]:

states = foxes.input.states.FieldDataNC(
    data_source="wind_rotation.nc",
    states_coord="state",
    x_coord="x",
    y_coord="y",
    h_coord="h",
    time_format=None,
    output_vars=[FV.WS, FV.WD, FV.TI, FV.RHO],
    var2ncvar={FV.WS: "ws", FV.WD: "wd"},
    fixed_vars={FV.RHO: 1.225, FV.TI: 0.1},
    load_mode="preload",
    bounds_error=False,
)

Note that it is recommended that the states object should be created outside the DaskRunner when working with NetCFD input.

Now back to our example. Let’s place a simple 3 x 3 grid wind farm inside the data domain, which is a rectangle between (0, 0) and (2500, 2500):

In [3]:

farm = foxes.WindFarm()
foxes.input.farm_layout.add_grid(
    farm,
    xy_base=np.array([500.0, 500.0]),
    step_vectors=np.array([[500.0, 0], [0, 500.0]]),
    steps=(3, 3),
    turbine_models=["NREL5MW"],
    verbosity=0,
)

The streamline following wakes are realized by selecting a wake frame that is an instance of foxes.models.wake_frames.Streamlines, e.g. the model streamlines_100 in the model book. This model has a streamline step size of 100 m:

In [4]:

algo = foxes.algorithms.Downwind(
    farm,
    states,
    rotor_model="grid16",
    wake_models=["Jensen_linear_k007"],
    wake_frame="streamlines_100",
    verbosity=0,
)

We run the algorithm, once explicitely for calculating the wind farm data, and once implicitely when creating horizontal flow plots:

In [5]:

farm_results = algo.calc_farm()

fr = farm_results.to_dataframe()
print(fr[[FV.WD, FV.AMB_REWS, FV.REWS, FV.AMB_P, FV.P]])

o = foxes.output.FlowPlots2D(algo, farm_results)
for fig in o.gen_states_fig_xy(
    FV.WS,
    resolution=10,
    figsize=(8, 8),
    quiver_pars=dict(angles="xy", scale_units="xy", scale=0.07),
    quiver_n=15,
    xmin=0,
    xmax=2500,
    ymin=0,
    ymax=2500,
):
    plt.show()
    plt.close(fig)

Selecting 'DefaultEngine(n_procs=16, chunk_size_states=None, chunk_size_points=None)'
DefaultEngine: Selecting engine 'single'
SingleChunkEngine: Calculating 2 states for 9 turbines
SingleChunkEngine: Running single chunk calculation for 2 states
                       WD  AMB_REWS      REWS        AMB_P            P
state turbine
0     0        201.161371  7.491089  7.491089  1474.211367  1474.211367
      1        208.049066  7.673386  7.673386  1580.523022  1580.523022
      2        214.528483  7.960601  7.960601  1748.171047  1748.171047
      3        218.247780  6.867297  6.867297  1127.597810  1127.597810
      4        222.303121  7.283373  7.283373  1352.715530  1352.715530
      5        225.904246  7.731909  7.731909  1614.607085  1614.607085
      6        236.756149  6.932726  6.932726  1156.958672  1156.958672
      7        237.144203  7.375640  7.375640  1406.547918  1406.547918
      8        237.488279  7.818854  7.818854  1665.347000  1665.347000
1     0         20.313664  6.703701  6.703701  1054.871543  1054.871543
      1         26.262006  6.995899  6.995899  1185.898485  1185.898485
      2         31.680276  7.357075  7.357075  1396.122949  1396.122949
      3         44.542681  5.352448  5.352448   521.748653   521.748653
      4         47.452899  5.960030  5.960030   724.421405   724.421405
      5         49.819769  6.580130  6.580130   998.581195   998.581195
      6         75.465593  5.352662  5.352662   521.621921   521.621921
      7         72.555045  5.960214  5.960214   724.363478   724.363478
      8         70.187742  6.580285  6.580285   998.552663   998.552663
DefaultEngine: Selecting engine 'process'
ProcessEngine: Calculating data at 63001 points for 2 states
ProcessEngine: Computing 32 chunks using 16 processes

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