floris.core.turbine.unified_momentum_model

Functions

UMM_rotor_axial_induction(Cts, yaw_angles)	Computes the axial induction of a yawed rotor given the yaw-aligned thrust coefficient and yaw angles using the yawed actuator disk model developed at MIT as described in Heck et al. 2023.
UMM_rotor_velocity_yaw_correction(Cts, ...)	Computes adjusted rotor wind speeds given the yaw-aligned thrust coefficient, yaw angles, and axial induction values using the yawed actuator disk model developed at MIT as described in Heck et al. 2023.
adaptivefixedpointiteration([max_iter, ...])	Class decorator which adds a __call__ method to the class which performs fixed-point iteration.
fixedpointiteration([max_iter, tolerance, ...])	Class decorator which adds a __call__ method to the class which performs fixed-point iteration.

Classes

FixedPointIterationCompatible(*args, **kwargs)
FixedPointIterationResult(converged, niter, ...)
Heck([v4_correction])	Solves the iterative momentum equation for an actuator disk model.
LimitedHeck()	Solves the limiting case when v_4 << u_4.
MomentumSolution(Ctprime, yaw, an, u4, v4, ...)	Stores the results of the Unified Momentum model solution.
UnifiedMomentumModelTurbine()	Turbine operation model as described by Heck et al. (2023).

floris.core.turbine.unified_momentum_model.UMM_rotor_axial_induction(Cts, yaw_angles)

Computes the axial induction of a yawed rotor given the yaw-aligned thrust coefficient and yaw angles using the yawed actuator disk model developed at MIT as described in Heck et al. 2023. Assumes the modified thrust coefficient, C_T', is invariant to yaw misalignment angle.

Uses form of C_T' from Eq. (19) of Calaf et al., 2010, https://doi.org/10.1063/1.3291077

Return type:

ndarray[tuple[int, ...], dtype[float64]]

Parameters:

• Cts (ndarray[tuple[int, ...], dtype[float64]])

• yaw_angles (ndarray[tuple[int, ...], dtype[float64]])

Args

Cts (NDArrayFloat): Yaw-aligned thrust coefficient(s). yaw_angles (NDArrayFloat): Rotor yaw angle(s) in degrees.

Returns: NDArrayFloat: Axial induction factor(s) of the yawed rotor.

floris.core.turbine.unified_momentum_model.UMM_rotor_velocity_yaw_correction(Cts, yaw_angles, axial_inductions, rotor_effective_velocities)

Computes adjusted rotor wind speeds given the yaw-aligned thrust coefficient, yaw angles, and axial induction values using the yawed actuator disk model developed at MIT as described in Heck et al. 2023. Assumes the modified thrust coefficient, C_T', is invariant to yaw misalignment angle.

Return type:

ndarray[tuple[int, ...], dtype[float64]]

Parameters:

• Cts (ndarray[tuple[int, ...], dtype[float64]])

• yaw_angles (ndarray[tuple[int, ...], dtype[float64]])

• axial_inductions (ndarray[tuple[int, ...], dtype[float64]])

• rotor_effective_velocities (ndarray[tuple[int, ...], dtype[float64]])

Args

Cts (NDArrayFloat): Yaw-aligned thrust coefficient(s). yaw_angles (NDArrayFloat): Rotor yaw angle(s) in degrees. axial_induction (NDArrayFloat): Rotor axial induction(s); this should follow the MIT model yaw dependent derivation and probably gotten from UMM_rotor_axial_induction. rotor_effective_velocities (NDArrayFloat) rotor effective wind speed(s) at the rotor.

Returns: NDArrayFloat: corrected rotor effective wind speed(s) of the yawed rotor.

class floris.core.turbine.unified_momentum_model.FixedPointIterationCompatible(*args, **kwargs)

residual(*args, **kwargs)

Return type:

Tuple[Union[Buffer, _SupportsArray[dtype[Any]], _NestedSequence[_SupportsArray[dtype[Any]]], bool, int, float, complex, str, bytes, _NestedSequence[bool | int | float | complex | str | bytes]]]

initial_guess(*args, **kwargs)

Return type:

Tuple[Union[Buffer, _SupportsArray[dtype[Any]], _NestedSequence[_SupportsArray[dtype[Any]]], bool, int, float, complex, str, bytes, _NestedSequence[bool | int | float | complex | str | bytes]]]

class floris.core.turbine.unified_momentum_model.FixedPointIterationResult(converged, niter, relax, max_resid, x)

Parameters:

• converged (bool)

• niter (int)

• relax (float)

• max_resid (float)

• x (Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes])

converged: bool

niter: int

relax: float

max_resid: float

x: Union[Buffer, _SupportsArray[dtype[Any]], _NestedSequence[_SupportsArray[dtype[Any]]], bool, int, float, complex, str, bytes, _NestedSequence[bool | int | float | complex | str | bytes]]

floris.core.turbine.unified_momentum_model.fixedpointiteration(max_iter=100, tolerance=1e-06, relaxation=0.0)

Class decorator which adds a __call__ method to the class which performs fixed-point iteration.

Return type:

FixedPointIterationCompatible

Parameters:

• max_iter (int)

• tolerance (float)

• relaxation (float)

Args:

max_iter (int): Maximum number of iterations (default: 100) tolerance (float): Convergence criteria (default: 1e-6) relaxation (float): Relaxation factor between 0 and 1 (default: 0.0)

The class must contain 2 mandatory methods and 3 optional method:

mandatory: initial_guess(self, *args, **kwargs) residual(self, x, *args, **kwargs)

optional: pre_process(self, *args, **kwargs) # Optional post_process(self, result:FixedPointIterationResult) # Optional callback(self, x) # Optional

floris.core.turbine.unified_momentum_model.adaptivefixedpointiteration(max_iter=100, tolerance=1e-06, relaxations=[0.0])

Class decorator which adds a __call__ method to the class which performs fixed-point iteration. Same as fixedpointiteration, but takes a list of relaxation factors, and iterates over all of them in order until convergence is reached.

Return type:

Callable

Parameters:

• max_iter (int)

• tolerance (float)

• relaxations (List[float])

class floris.core.turbine.unified_momentum_model.UnifiedMomentumModelTurbine

Turbine operation model as described by Heck et al. (2023).

power(velocities, air_density, yaw_angles, average_method='cubic-mean', cubature_weights=None, **kwargs)

Return type:

None

Parameters:

• power_thrust_table (dict)

• velocities (ndarray[tuple[int, ...], dtype[float64]])

• air_density (float)

• yaw_angles (ndarray[tuple[int, ...], dtype[float64]])

• average_method (str)

• cubature_weights (ndarray[tuple[int, ...], dtype[float64]] | None)

thrust_coefficient(velocities, air_density, yaw_angles, average_method='cubic-mean', cubature_weights=None, **kwargs)

Return type:

None

Parameters:

• power_thrust_table (dict)

• velocities (ndarray[tuple[int, ...], dtype[float64]])

• air_density (float)

• yaw_angles (ndarray[tuple[int, ...], dtype[float64]])

• average_method (str)

• cubature_weights (ndarray[tuple[int, ...], dtype[float64]] | None)

axial_induction(velocities, air_density, yaw_angles, average_method='cubic-mean', cubature_weights=None, **kwargs)

Parameters:

• power_thrust_table (dict)

• velocities (ndarray[tuple[int, ...], dtype[float64]])

• air_density (float)

• yaw_angles (ndarray[tuple[int, ...], dtype[float64]])

• average_method (str)

• cubature_weights (ndarray[tuple[int, ...], dtype[float64]] | None)

class floris.core.turbine.unified_momentum_model.MomentumSolution(Ctprime, yaw, an, u4, v4, x0, dp, dp_NL=0.0, niter=1, converged=True, beta=0.0)

Stores the results of the Unified Momentum model solution.

Parameters:

• Ctprime (float)

• yaw (float)

• an (float | ndarray[tuple[int, ...], dtype[float64]])

• u4 (float | ndarray[tuple[int, ...], dtype[float64]])

• v4 (float | ndarray[tuple[int, ...], dtype[float64]])

• x0 (float | ndarray[tuple[int, ...], dtype[float64]])

• dp (float | ndarray[tuple[int, ...], dtype[float64]])

• dp_NL (float | ndarray[tuple[int, ...], dtype[float64]] | None)

• niter (int | None)

• converged (bool | None)

• beta (float | None)

Ctprime: float

yaw: float

an: Union[float, ndarray[tuple[int, ...], dtype[float64]]]

u4: Union[float, ndarray[tuple[int, ...], dtype[float64]]]

v4: Union[float, ndarray[tuple[int, ...], dtype[float64]]]

x0: Union[float, ndarray[tuple[int, ...], dtype[float64]]]

dp: Union[float, ndarray[tuple[int, ...], dtype[float64]]]

dp_NL: Union[float, ndarray[tuple[int, ...], dtype[float64]], None] = 0.0

niter: Optional[int] = 1

converged: Optional[bool] = True

beta: Optional[float] = 0.0

property Ct

Returns the thrust coefficient Ct.

property Cp

Returns the power coefficient Cp.

class floris.core.turbine.unified_momentum_model.LimitedHeck

Solves the limiting case when v_4 << u_4. (Eq. 2.19, 2.20). Also takes Numpy array arguments.

class floris.core.turbine.unified_momentum_model.Heck(v4_correction=1.0)

Solves the iterative momentum equation for an actuator disk model.

Parameters:

v4_correction (float)

initial_guess(Ctprime, yaw)

residual(x, Ctprime, yaw)

Residual function of yawed-actuator disk model in Eq. 2.15.

Return type:

ndarray

Parameters:

• x (ndarray)

• Ctprime (float)

• yaw (float)

Args:

x (np.ndarray): (a, u4, v4) Ctprime (float): Rotor thrust coefficient. yaw (float): Rotor yaw angle (radians).

Returns:

np.ndarray: residuals of induction and outlet velocities.

post_process(result, Ctprime, yaw)

Parameters:

• Ctprime (float)

• yaw (float)