def sequential_solver(farm: Farm, flow_field: FlowField, grid: TurbineGrid, model_manager: WakeModelManager) -> None:
# Algorithm
# For each turbine, calculate its effect on every downstream turbine.
# For the current turbine, we are calculating the deficit that it adds to downstream turbines.
# Integrate this into the main data structure.
# Move on to the next turbine.
# <<interface>>
deflection_model_args = model_manager.deflection_model.prepare_function(grid, flow_field)
deficit_model_args = model_manager.velocity_model.prepare_function(grid, flow_field)
# This is u_wake
wake_field = np.zeros_like(flow_field.u_initial_sorted)
v_wake = np.zeros_like(flow_field.v_initial_sorted)
w_wake = np.zeros_like(flow_field.w_initial_sorted)
turbine_turbulence_intensity = flow_field.turbulence_intensity * np.ones((flow_field.n_wind_directions, flow_field.n_wind_speeds, farm.n_turbines, 1, 1))
ambient_turbulence_intensity = flow_field.turbulence_intensity
# Calculate the velocity deficit sequentially from upstream to downstream turbines
for i in range(grid.n_turbines):
# Get the current turbine quantities
x_i = np.mean(grid.x_sorted[:, :, i:i+1], axis=(3, 4))
x_i = x_i[:, :, :, None, None]
y_i = np.mean(grid.y_sorted[:, :, i:i+1], axis=(3, 4))
y_i = y_i[:, :, :, None, None]
z_i = np.mean(grid.z_sorted[:, :, i:i+1], axis=(3, 4))
z_i = z_i[:, :, :, None, None]
u_i = flow_field.u_sorted[:, :, i:i+1]
v_i = flow_field.v_sorted[:, :, i:i+1]
ct_i = Ct(
velocities=flow_field.u_sorted,
yaw_angle=farm.yaw_angles_sorted,
fCt=farm.turbine_fCts,
turbine_type_map=farm.turbine_type_map_sorted,
ix_filter=[i],
)
ct_i = ct_i[:, :, 0:1, None, None] # Since we are filtering for the i'th turbine in the Ct function, get the first index here (0:1)
axial_induction_i = axial_induction(
velocities=flow_field.u_sorted,
yaw_angle=farm.yaw_angles_sorted,
fCt=farm.turbine_fCts,
turbine_type_map=farm.turbine_type_map_sorted,
ix_filter=[i],
)
axial_induction_i = axial_induction_i[:, :, 0:1, None, None] # Since we are filtering for the i'th turbine in the axial induction function, get the first index here (0:1)
turbulence_intensity_i = turbine_turbulence_intensity[:, :, i:i+1]
yaw_angle_i = farm.yaw_angles_sorted[:, :, i:i+1, None, None]
hub_height_i = farm.hub_heights_sorted[: ,:, i:i+1, None, None]
rotor_diameter_i = farm.rotor_diameters_sorted[: ,:, i:i+1, None, None]
TSR_i = farm.TSRs_sorted[: ,:, i:i+1, None, None]
effective_yaw_i = np.zeros_like(yaw_angle_i)
effective_yaw_i += yaw_angle_i
if model_manager.enable_secondary_steering:
added_yaw = wake_added_yaw(
u_i,
v_i,
flow_field.u_initial_sorted,
grid.y_sorted[:, :, i:i+1] - y_i,
grid.z_sorted[:, :, i:i+1],
rotor_diameter_i,
hub_height_i,
ct_i,
TSR_i,
axial_induction_i
)
effective_yaw_i += added_yaw
# Model calculations
# NOTE: exponential
deflection_field = model_manager.deflection_model.function(
x_i,
y_i,
effective_yaw_i,
turbulence_intensity_i,
ct_i,
rotor_diameter_i,
**deflection_model_args
)
if model_manager.enable_transverse_velocities:
v_wake, w_wake = calculate_transverse_velocity(
u_i,
flow_field.u_initial_sorted,
grid.x_sorted - x_i,
grid.y_sorted - y_i,
grid.z_sorted,
rotor_diameter_i,
hub_height_i,
yaw_angle_i,
ct_i,
TSR_i,
axial_induction_i
)
if model_manager.enable_yaw_added_recovery:
I_mixing = yaw_added_turbulence_mixing(
u_i,
turbulence_intensity_i,
v_i,
flow_field.w_sorted[:, :, i:i+1],
v_wake[:, :, i:i+1],
w_wake[:, :, i:i+1],
)
gch_gain = 2
turbine_turbulence_intensity[:, :, i:i+1] = turbulence_intensity_i + gch_gain * I_mixing
# NOTE: exponential
velocity_deficit = model_manager.velocity_model.function(
x_i,
y_i,
z_i,
axial_induction_i,
deflection_field,
yaw_angle_i,
turbulence_intensity_i,
ct_i,
hub_height_i,
rotor_diameter_i,
**deficit_model_args
)
wake_field = model_manager.combination_model.function(
wake_field,
velocity_deficit * flow_field.u_initial_sorted
)
wake_added_turbulence_intensity = model_manager.turbulence_model.function(
ambient_turbulence_intensity,
grid.x_sorted,
x_i,
rotor_diameter_i,
axial_induction_i
)
# Calculate wake overlap for wake-added turbulence (WAT)
area_overlap = np.sum(velocity_deficit * flow_field.u_initial_sorted > 0.05, axis=(3, 4)) / (grid.grid_resolution * grid.grid_resolution)
area_overlap = area_overlap[:, :, :, None, None]
# Modify wake added turbulence by wake area overlap
downstream_influence_length = 15 * rotor_diameter_i
ti_added = (
area_overlap
* np.nan_to_num(wake_added_turbulence_intensity, posinf=0.0)
* np.array(grid.x_sorted > x_i)
* np.array(np.abs(y_i - grid.y_sorted) < 2 * rotor_diameter_i)
* np.array(grid.x_sorted <= downstream_influence_length + x_i)
)
# Combine turbine TIs with WAT
turbine_turbulence_intensity = np.maximum( np.sqrt( ti_added ** 2 + ambient_turbulence_intensity ** 2 ) , turbine_turbulence_intensity )
flow_field.u_sorted = flow_field.u_initial_sorted - wake_field
flow_field.v_sorted += v_wake
flow_field.w_sorted += w_wake
flow_field.turbulence_intensity_field = np.mean(turbine_turbulence_intensity, axis=(3,4))
flow_field.turbulence_intensity_field = flow_field.turbulence_intensity_field[:,:,:,None,None]
def full_flow_cc_solver(farm: Farm, flow_field: FlowField, flow_field_grid: FlowFieldGrid, model_manager: WakeModelManager) -> None:
# Get the flow quantities and turbine performance
turbine_grid_farm = copy.deepcopy(farm)
turbine_grid_flow_field = copy.deepcopy(flow_field)
turbine_grid_farm.construct_turbine_map()
turbine_grid_farm.construct_turbine_fCts()
turbine_grid_farm.construct_turbine_fCps()
turbine_grid_farm.construct_turbine_power_interps()
turbine_grid_farm.construct_hub_heights()
turbine_grid_farm.construct_rotor_diameters()
turbine_grid_farm.construct_turbine_TSRs()
turbine_grid_farm.construc_turbine_pPs()
turbine_grid_farm.construct_coordinates()
turbine_grid = TurbineGrid(
turbine_coordinates=turbine_grid_farm.coordinates,
reference_turbine_diameter=turbine_grid_farm.rotor_diameters_sorted,
wind_directions=turbine_grid_flow_field.wind_directions,
wind_speeds=turbine_grid_flow_field.wind_speeds,
grid_resolution=3,
)
turbine_grid_farm.expand_farm_properties(
turbine_grid_flow_field.n_wind_directions, turbine_grid_flow_field.n_wind_speeds, turbine_grid.sorted_coord_indices
)
turbine_grid_flow_field.initialize_velocity_field(turbine_grid)
turbine_grid_farm.initialize(turbine_grid.sorted_indices)
cc_solver(turbine_grid_farm, turbine_grid_flow_field, turbine_grid, model_manager)
### Referring to the quantities from above, calculate the wake in the full grid
# Use full flow_field here to use the full grid in the wake models
deflection_model_args = model_manager.deflection_model.prepare_function(flow_field_grid, flow_field)
deficit_model_args = model_manager.velocity_model.prepare_function(flow_field_grid, flow_field)
v_wake = np.zeros_like(flow_field.v_initial_sorted)
w_wake = np.zeros_like(flow_field.w_initial_sorted)
turb_u_wake = np.zeros_like(flow_field.u_initial_sorted)
shape = (farm.n_turbines,) + np.shape(flow_field.u_initial_sorted)
Ctmp = np.zeros((shape))
# Calculate the velocity deficit sequentially from upstream to downstream turbines
for i in range(flow_field_grid.n_turbines):
# Get the current turbine quantities
x_i = np.mean(turbine_grid.x_sorted[:, :, i:i+1], axis=(3, 4))
x_i = x_i[:, :, :, None, None]
y_i = np.mean(turbine_grid.y_sorted[:, :, i:i+1], axis=(3, 4))
y_i = y_i[:, :, :, None, None]
z_i = np.mean(turbine_grid.z_sorted[:, :, i:i+1], axis=(3, 4))
z_i = z_i[:, :, :, None, None]
u_i = turbine_grid_flow_field.u_sorted[:, :, i:i+1]
v_i = turbine_grid_flow_field.v_sorted[:, :, i:i+1]
turb_avg_vels = average_velocity(turbine_grid_flow_field.u_sorted)
turb_Cts = Ct(
velocities=turb_avg_vels,
yaw_angle=turbine_grid_farm.yaw_angles_sorted,
fCt=turbine_grid_farm.turbine_fCts,
turbine_type_map=turbine_grid_farm.turbine_type_map_sorted,
)
turb_Cts = turb_Cts[:, :, :, None, None]
axial_induction_i = axial_induction(
velocities=turbine_grid_flow_field.u_sorted,
yaw_angle=turbine_grid_farm.yaw_angles_sorted,
fCt=turbine_grid_farm.turbine_fCts,
turbine_type_map=turbine_grid_farm.turbine_type_map_sorted,
ix_filter=[i],
)
axial_induction_i = axial_induction_i[:, :, :, None, None]
turbulence_intensity_i = turbine_grid_flow_field.turbulence_intensity_field[:, :, i:i+1]
yaw_angle_i = turbine_grid_farm.yaw_angles_sorted[:, :, i:i+1, None, None]
hub_height_i = turbine_grid_farm.hub_heights_sorted[: ,:, i:i+1, None, None]
rotor_diameter_i = turbine_grid_farm.rotor_diameters_sorted[: ,:, i:i+1, None, None]
TSR_i = turbine_grid_farm.TSRs_sorted[: ,:, i:i+1, None, None]
effective_yaw_i = np.zeros_like(yaw_angle_i)
effective_yaw_i += yaw_angle_i
if model_manager.enable_secondary_steering:
added_yaw = wake_added_yaw(
u_i,
v_i,
turbine_grid_flow_field.u_initial_sorted,
turbine_grid.y_sorted[:, :, i:i+1] - y_i,
turbine_grid.z_sorted[:, :, i:i+1],
rotor_diameter_i,
hub_height_i,
turb_Cts[:, :, i:i+1],
TSR_i,
axial_induction_i,
scale=2.0
)
effective_yaw_i += added_yaw
# Model calculations
# NOTE: exponential
deflection_field = model_manager.deflection_model.function(
x_i,
y_i,
effective_yaw_i,
turbulence_intensity_i,
turb_Cts[:, :, i:i+1],
rotor_diameter_i,
**deflection_model_args
)
if model_manager.enable_transverse_velocities:
v_wake, w_wake = calculate_transverse_velocity(
u_i,
flow_field.u_initial_sorted,
flow_field_grid.x_sorted - x_i,
flow_field_grid.y_sorted - y_i,
flow_field_grid.z_sorted,
rotor_diameter_i,
hub_height_i,
yaw_angle_i,
turb_Cts[:, :, i:i+1],
TSR_i,
axial_induction_i,
scale=2.0
)
# NOTE: exponential
turb_u_wake, Ctmp = model_manager.velocity_model.function(
i,
x_i,
y_i,
z_i,
u_i,
deflection_field,
yaw_angle_i,
turbine_grid_flow_field.turbulence_intensity_field,
turb_Cts,
turbine_grid_farm.rotor_diameters_sorted[:, :, :, None, None],
turb_u_wake,
Ctmp,
**deficit_model_args
)
flow_field.v_sorted += v_wake
flow_field.w_sorted += w_wake
flow_field.u_sorted = flow_field.u_initial_sorted - turb_u_wake
def cc_solver(farm: Farm, flow_field: FlowField, grid: TurbineGrid, model_manager: WakeModelManager) -> None:
# <<interface>>
deflection_model_args = model_manager.deflection_model.prepare_function(grid, flow_field)
deficit_model_args = model_manager.velocity_model.prepare_function(grid, flow_field)
# This is u_wake
v_wake = np.zeros_like(flow_field.v_initial_sorted)
w_wake = np.zeros_like(flow_field.w_initial_sorted)
turb_u_wake = np.zeros_like(flow_field.u_initial_sorted)
turb_inflow_field = copy.deepcopy(flow_field.u_initial_sorted)
turbine_turbulence_intensity = flow_field.turbulence_intensity * np.ones((flow_field.n_wind_directions, flow_field.n_wind_speeds, farm.n_turbines, 1, 1))
ambient_turbulence_intensity = flow_field.turbulence_intensity
shape = (farm.n_turbines,) + np.shape(flow_field.u_initial_sorted)
Ctmp = np.zeros((shape))
# Ctmp = np.zeros((len(x_coord), len(wd), len(ws), len(x_coord), y_ngrid, z_ngrid))
sigma_i = np.zeros((shape))
# sigma_i = np.zeros((len(x_coord), len(wd), len(ws), len(x_coord), y_ngrid, z_ngrid))
# Calculate the velocity deficit sequentially from upstream to downstream turbines
for i in range(grid.n_turbines):
# Get the current turbine quantities
x_i = np.mean(grid.x_sorted[:, :, i:i+1], axis=(3, 4))
x_i = x_i[:, :, :, None, None]
y_i = np.mean(grid.y_sorted[:, :, i:i+1], axis=(3, 4))
y_i = y_i[:, :, :, None, None]
z_i = np.mean(grid.z_sorted[:, :, i:i+1], axis=(3, 4))
z_i = z_i[:, :, :, None, None]
mask2 = np.array(grid.x_sorted < x_i + 0.01) * np.array(grid.x_sorted > x_i - 0.01) * np.array(grid.y_sorted < y_i + 0.51*126.0) * np.array(grid.y_sorted > y_i - 0.51*126.0)
# mask2 = np.logical_and(np.logical_and(np.logical_and(grid.x_sorted < x_i + 0.01, grid.x_sorted > x_i - 0.01), grid.y_sorted < y_i + 0.51*126.0), grid.y_sorted > y_i - 0.51*126.0)
turb_inflow_field = turb_inflow_field * ~mask2 + (flow_field.u_initial_sorted - turb_u_wake) * mask2
turb_avg_vels = average_velocity(turb_inflow_field)
turb_Cts = Ct(
turb_avg_vels,
farm.yaw_angles_sorted,
farm.turbine_fCts,
turbine_type_map=farm.turbine_type_map_sorted,
)
turb_Cts = turb_Cts[:, :, :, None, None]
turb_aIs = axial_induction(
turb_avg_vels,
farm.yaw_angles_sorted,
farm.turbine_fCts,
turbine_type_map=farm.turbine_type_map_sorted,
ix_filter=[i],
)
turb_aIs = turb_aIs[:, :, :, None, None]
u_i = turb_inflow_field[:, :, i:i+1]
v_i = flow_field.v_sorted[:, :, i:i+1]
axial_induction_i = axial_induction(
velocities=flow_field.u_sorted,
yaw_angle=farm.yaw_angles_sorted,
fCt=farm.turbine_fCts,
turbine_type_map=farm.turbine_type_map_sorted,
ix_filter=[i],
)
axial_induction_i = axial_induction_i[:, :, :, None, None]
turbulence_intensity_i = turbine_turbulence_intensity[:, :, i:i+1]
yaw_angle_i = farm.yaw_angles_sorted[:, :, i:i+1, None, None]
hub_height_i = farm.hub_heights_sorted[: ,:, i:i+1, None, None]
rotor_diameter_i = farm.rotor_diameters_sorted[: ,:, i:i+1, None, None]
TSR_i = farm.TSRs_sorted[: ,:, i:i+1, None, None]
effective_yaw_i = np.zeros_like(yaw_angle_i)
effective_yaw_i += yaw_angle_i
if model_manager.enable_secondary_steering:
added_yaw = wake_added_yaw(
u_i,
v_i,
flow_field.u_initial_sorted,
grid.y_sorted[:, :, i:i+1] - y_i,
grid.z_sorted[:, :, i:i+1],
rotor_diameter_i,
hub_height_i,
turb_Cts[:, :, i:i+1],
TSR_i,
axial_induction_i,
scale=2.0,
)
effective_yaw_i += added_yaw
# Model calculations
# NOTE: exponential
deflection_field = model_manager.deflection_model.function(
x_i,
y_i,
effective_yaw_i,
turbulence_intensity_i,
turb_Cts[:, :, i:i+1],
rotor_diameter_i,
**deflection_model_args
)
if model_manager.enable_transverse_velocities:
v_wake, w_wake = calculate_transverse_velocity(
u_i,
flow_field.u_initial_sorted,
grid.x_sorted - x_i,
grid.y_sorted - y_i,
grid.z_sorted,
rotor_diameter_i,
hub_height_i,
yaw_angle_i,
turb_Cts[:, :, i:i+1],
TSR_i,
axial_induction_i,
scale=2.0
)
if model_manager.enable_yaw_added_recovery:
I_mixing = yaw_added_turbulence_mixing(
u_i,
turbulence_intensity_i,
v_i,
flow_field.w_sorted[:, :, i:i+1],
v_wake[:, :, i:i+1],
w_wake[:, :, i:i+1],
)
gch_gain = 1.0
turbine_turbulence_intensity[:, :, i:i+1] = turbulence_intensity_i + gch_gain * I_mixing
turb_u_wake, Ctmp = model_manager.velocity_model.function(
i,
x_i,
y_i,
z_i,
u_i,
deflection_field,
yaw_angle_i,
turbine_turbulence_intensity,
turb_Cts,
farm.rotor_diameters_sorted[:, :, :, None, None],
turb_u_wake,
Ctmp,
**deficit_model_args
)
wake_added_turbulence_intensity = model_manager.turbulence_model.function(
ambient_turbulence_intensity,
grid.x_sorted,
x_i,
rotor_diameter_i,
turb_aIs
)
# Calculate wake overlap for wake-added turbulence (WAT)
area_overlap = 1 - np.sum(turb_u_wake <= 0.05, axis=(3, 4)) / (grid.grid_resolution * grid.grid_resolution)
area_overlap = area_overlap[:, :, :, None, None]
# Modify wake added turbulence by wake area overlap
downstream_influence_length = 15 * rotor_diameter_i
ti_added = (
area_overlap
* np.nan_to_num(wake_added_turbulence_intensity, posinf=0.0)
* np.array(grid.x_sorted > x_i)
* np.array(np.abs(y_i - grid.y_sorted) < 2 * rotor_diameter_i)
* np.array(grid.x_sorted <= downstream_influence_length + x_i)
)
# Combine turbine TIs with WAT
turbine_turbulence_intensity = np.maximum( np.sqrt( ti_added ** 2 + ambient_turbulence_intensity ** 2 ) , turbine_turbulence_intensity )
flow_field.v_sorted += v_wake
flow_field.w_sorted += w_wake
flow_field.u_sorted = turb_inflow_field
flow_field.turbulence_intensity_field = np.mean(turbine_turbulence_intensity, axis=(3,4))
flow_field.turbulence_intensity_field = flow_field.turbulence_intensity_field[:,:,:,None,None]