floris.core.wake_velocity.empirical_gauss

floris.core.wake_velocity.empirical_gauss#

Functions

awc_added_wake_mixing(awc_mode_i, ...)

empirical_gauss_model_wake_width(x, ...)

rCalt(wind_veer, sigma_y, sigma_z, y, y_i, ...)

sigmoid_integral(x[, center, width])

Classes

EmpiricalGaussVelocityDeficit([...])

The Empirical Gauss velocity model has a Gaussian profile (see [4] and [6]) throughout and expands in a (smoothed) piecewise linear fashion.
class floris.core.wake_velocity.empirical_gauss.EmpiricalGaussVelocityDeficit(wake_expansion_rates=NOTHING, breakpoints_D=NOTHING, sigma_0_D=0.28, smoothing_length_D=2.0, mixing_gain_velocity=2.0, awc_mode='baseline', awc_wake_exp=1.2, awc_wake_denominator=400)[source]#

The Empirical Gauss velocity model has a Gaussian profile (see [4] and [6]) throughout and expands in a (smoothed) piecewise linear fashion.

parameter_dictionary (dict): Model-specific parameters.

Default values are used when a parameter is not included in parameter_dictionary. Possible key-value pairs include:

  • wake_expansion_rates (list): List of expansion rates for the Gaussian wake width. Must be of length 1 or greater.

  • breakpoints_D (list): List of downstream locations, specified in terms of rotor diameters, where the expansion rates go into effect. Must be one element shorter than wake_expansion_rates. May be empty.

  • sigma_0_D (float): Initial width of the Gaussian wake at the turbine location, specified as a multiplier of the rotor diameter.

  • smoothing_length_D (float): Distance over which the corners in the piece-wise linear wake expansion rate are smoothed (specified as a multiplier of the rotor diameter).

  • mixing_gain_deflection (float): Gain to set the increase in wake expansion due to wake-induced mixing.

References:
[1] (1,2,3)

Majid Bastankhah and Fernando Porté-Agel. Experimental and theoretical study of wind turbine wakes in yawed conditions. Journal of Fluid Mechanics, 806:506–541, 2016.

[2] (1,2,3)

Jennifer King, Paul Fleming, Ryan King, and Luis A. Martinez-Tossas. Controls-oriented model to capture secondary effects of wake steering. Submitted to Wind Energy Science, 2019.

Parameters:

  • wake_expansion_rates (list)

  • breakpoints_D (list)

  • sigma_0_D (float)

  • smoothing_length_D (float)

  • mixing_gain_velocity (float)

  • awc_mode (str)

  • awc_wake_exp (float)

  • awc_wake_denominator (float)

wake_expansion_rates: list#
breakpoints_D: list#
sigma_0_D: float#
smoothing_length_D: float#
mixing_gain_velocity: float#
awc_mode: str#
awc_wake_exp: float#
awc_wake_denominator: float#
prepare_function(grid, flow_field)[source]#
Return type:

Dict[str, Any]

Parameters:
function(x_i, y_i, z_i, axial_induction_i, deflection_field_y_i, deflection_field_z_i, yaw_angle_i, tilt_angle_i, mixing_i, ct_i, hub_height_i, rotor_diameter_i, *, x, y, z, wind_veer)[source]#

Calculates the velocity deficits in the wake.

Return type:

None

Parameters:

  • x_i (ndarray)

  • y_i (ndarray)

  • z_i (ndarray)

  • axial_induction_i (ndarray)

  • deflection_field_y_i (ndarray)

  • deflection_field_z_i (ndarray)

  • yaw_angle_i (ndarray)

  • tilt_angle_i (ndarray)

  • mixing_i (ndarray)

  • ct_i (ndarray)

  • hub_height_i (float)

  • rotor_diameter_i (ndarray)

  • x (ndarray)

  • y (ndarray)

  • z (ndarray)

  • wind_veer (float)

Args:
x_i (np.array): Streamwise direction grid coordinates of

the ith turbine (m).

y_i (np.array): Cross stream direction grid coordinates of

the ith turbine (m).

z_i (np.array): Vertical direction grid coordinates of

the ith turbine (m) [not used].

axial_induction_i (np.array): Axial induction factor of the

ith turbine (-) [not used].

deflection_field_y_i (np.array): Horizontal wake deflections

due to the ith turbine's yaw misalignment (m).

deflection_field_z_i (np.array): Vertical wake deflections

due to the ith turbine's tilt angle (m).

yaw_angle_i (np.array): Yaw angle of the ith turbine (deg). tilt_angle_i (np.array): Tilt angle of the ith turbine

(deg).

mixing_i (np.array): The wake-induced mixing term for the

ith turbine.

ct_i (np.array): Thrust coefficient for the ith turbine (-). hub_height_i (float): Hub height for the ith turbine (m). rotor_diameter_i (np.array): Rotor diameter for the ith

turbine (m).

x (np.array): Streamwise direction grid coordinates of the

flow field domain (m).

y (np.array): Cross stream direction grid coordinates of the

flow field domain (m).

z (np.array): Vertical direction grid coordinates of the

flow field domain (m).

wind_veer (np.array): Wind veer (deg).

Returns:

np.array: Velocity deficits (-).

floris.core.wake_velocity.empirical_gauss.rCalt(wind_veer, sigma_y, sigma_z, y, y_i, delta_y, delta_z, z, HH, Ct, yaw, tilt, D, sigma_y0, sigma_z0)[source]#
floris.core.wake_velocity.empirical_gauss.sigmoid_integral(x, center=0, width=1)[source]#
floris.core.wake_velocity.empirical_gauss.empirical_gauss_model_wake_width(x, wake_expansion_rates, breakpoints, sigma_0, smoothing_length, mixing_final)[source]#
floris.core.wake_velocity.empirical_gauss.awc_added_wake_mixing(awc_mode_i, awc_amplitude_i, awc_frequency_i, awc_wake_exp, awc_wake_denominator)[source]#