floris.core.wake_deflection.empirical_gauss

floris.core.wake_deflection.empirical_gauss#

Functions

yaw_added_wake_mixing(axial_induction_i, ...)

Classes

EmpiricalGaussVelocityDeflection([...])

The Empirical Gauss deflection model is based on the form of previous the Gauss deflection model (see [4] and [6]) but simplifies the formulation for simpler tuning and more independence from the velocity deficit model.
class floris.core.wake_deflection.empirical_gauss.EmpiricalGaussVelocityDeflection(horizontal_deflection_gain_D=3.0, vertical_deflection_gain_D=-1, deflection_rate=22, mixing_gain_deflection=0.0, yaw_added_mixing_gain=0.0)[source]#

The Empirical Gauss deflection model is based on the form of previous the Gauss deflection model (see [4] and [6]) but simplifies the formulation for simpler tuning and more independence from the velocity deficit model.

parameter_dictionary (dict): Model-specific parameters.

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

  • horizontal_deflection_gain_D (float): Gain for the maximum (y-direction) deflection achieved far downstream of a yawed turbine.

  • vertical_deflection_gain_D (float): Gain for the maximum vertical (z-direction) deflection achieved at a far downstream location due to rotor tilt. Specifying as -1 will mean that vertical deflections due to tilt match horizontal deflections due to yaw.

  • deflection_rate (float): Rate at which the deflected wake center approaches its maximum deflection.

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

  • yaw_added_mixing_gain (float): Sets the contribution of turbine yaw misalignment to the mixing in that turbine's wake (similar to yaw-added recovery).

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:

  • horizontal_deflection_gain_D (float)

  • vertical_deflection_gain_D (float)

  • deflection_rate (float)

  • mixing_gain_deflection (float)

  • yaw_added_mixing_gain (float)

horizontal_deflection_gain_D: float#
vertical_deflection_gain_D: float#
deflection_rate: float#
mixing_gain_deflection: float#
yaw_added_mixing_gain: float#
prepare_function(grid, flow_field)[source]#
Return type:

Dict[str, Any]

Parameters:
function(x_i, y_i, yaw_i, tilt_i, mixing_i, ct_i, rotor_diameter_i, *, x)[source]#

Calculates the deflection field of the wake.

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) [not used].

yaw_i (np.array): Yaw angle of the ith turbine (deg). tilt_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 (-). 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).

Returns:

np.array: Deflection field for the wake.

Parameters:

  • x_i (ndarray)

  • y_i (ndarray)

  • yaw_i (ndarray)

  • tilt_i (ndarray)

  • mixing_i (ndarray)

  • ct_i (ndarray)

  • rotor_diameter_i (float)

  • x (ndarray)

floris.core.wake_deflection.empirical_gauss.yaw_added_wake_mixing(axial_induction_i, yaw_angle_i, downstream_distance_D_i, yaw_added_mixing_gain)[source]#