Simulation NREL 5MW wind turbine¶
[1]:
%config InlineBackend.figure_format = 'svg'
from IPython.display import Image
url = 'https://raw.githubusercontent.com/ImperialCollegeLondon/sharpy/dev_doc/docs/source/content/example_notebooks/images/turbulence_no_legend.png'
Image(url=url, width=800)
[1]:
In this notebook the blade loads on the NREL-5MW reference wind turbine computed with SHARPy and OpenFAST will be compared. However, zero-drag airfoils have been used.
OpenFAST: https://openfast.readthedocs.io
NREL-5MW: Jonkman, J.; Butterfield, S.; Musial, W. and Scott, G.. Definition of a 5-MW Reference Wind Turbine for Offshore System Development, Technical Report, NREL 2009
Load the required packages:
[2]:
# Required packages
import numpy as np
import os
import matplotlib.pyplot as plt
# Required SHARPy modules
import sharpy.sharpy_main
import sharpy.utils.algebra as algebra
import sharpy.utils.generate_cases as gc
import cases.templates.template_wt as template_wt
These are the results from the OpenFAST simulation for comparison: out-of-plane of_cNdrR and in-plane of_cTdrR coefficients along the blade and thrust of_ct and power of_cp rotor coefficients
[3]:
of_rR = np.array([0.20158356, 0.3127131, 0.40794048, 0.5984148, 0.6936519, 0.85238045, 0.899999, 0.95555407, 0.98729974, 1.0])
of_cNdrR = np.array([0.08621394, 0.14687876, 0.19345148, 0.2942731, 0.36003628, 0.43748564, 0.44762507, 0.38839236, 0.29782477, 0.0])
of_cTdrR = np.array([0.048268348, 0.051957503, 0.05304592, 0.052862607, 0.056001827, 0.0536646, 0.050112925, 0.038993906, 0.023664437, 0.0])
of_ct = 0.69787693
of_cp = 0.48813498
Create SHARPy case¶
Definition of parameters
[4]:
# Mathematical constants
deg2rad = np.pi/180.
# Case
case = 'rotor'
# route = os.path.dirname(os.path.realpath(__file__)) + '/'
route = './'
# Geometry discretization
chord_panels = np.array([8], dtype=int)
revs_in_wake = 5
# Operation
rotation_velocity = 12.1*2*np.pi/60
pitch_deg = 0. #degrees
# Wind
WSP = 12.
air_density = 1.225
# Simulation
dphi = 4.*deg2rad
revs_to_simulate = 5
Computation of associated parameters
[5]:
dt = dphi/rotation_velocity
time_steps = int(revs_to_simulate*2.*np.pi/dphi)
mstar = int(revs_in_wake*2.*np.pi/dphi)
Generation of the rotor geometry based on the information in the excel file
[6]:
rotor = template_wt.rotor_from_excel_type02(
chord_panels,
rotation_velocity,
pitch_deg,
excel_file_name= 'source/type02_db_NREL5MW_v01.xlsx',
excel_sheet_parameters = 'parameters',
excel_sheet_structural_blade = 'structural_blade',
excel_sheet_discretization_blade = 'discretization_blade',
excel_sheet_aero_blade = 'aero_blade',
excel_sheet_airfoil_info = 'airfoil_info',
excel_sheet_airfoil_coord = 'airfoil_coord',
m_distribution = 'uniform',
n_points_camber = 100,
tol_remove_points = 1e-8,
wsp = WSP,
dt = dt)
WARNING: The poisson cofficient is assumed equal to 0.3
WARNING: Cross-section area is used as shear area
WARNING: Using perpendicular axis theorem to compute the inertia around xB
WARNING: Replacing node 49 by node 0
WARNING: Replacing node 98 by node 0
Define simulation details. The steady simulation is faster than the dynamic simulation. However, the dynamic simulation includes wake self-induction and provides more accurate results.
[7]:
steady_simulation = False
[8]:
SimInfo = gc.SimulationInformation()
SimInfo.set_default_values()
if steady_simulation:
SimInfo.solvers['SHARPy']['flow'] = ['BeamLoader',
'AerogridLoader',
'StaticCoupledRBM',
'BeamPlot',
'AerogridPlot',
'SaveData']
else:
SimInfo.solvers['SHARPy']['flow'] = ['BeamLoader',
'AerogridLoader',
'StaticCoupledRBM',
'DynamicCoupled']
SimInfo.solvers['SHARPy']['case'] = case
SimInfo.solvers['SHARPy']['route'] = route
SimInfo.solvers['SHARPy']['write_log'] = True
SimInfo.set_variable_all_dicts('dt', dt)
SimInfo.set_variable_all_dicts('rho', air_density)
SimInfo.solvers['SteadyVelocityField']['u_inf'] = WSP
SimInfo.solvers['SteadyVelocityField']['u_inf_direction'] = np.array([0., 0., 1.])
SimInfo.solvers['BeamLoader']['unsteady'] = 'on'
SimInfo.solvers['AerogridLoader']['unsteady'] = 'on'
SimInfo.solvers['AerogridLoader']['mstar'] = mstar
SimInfo.solvers['AerogridLoader']['freestream_dir'] = np.array([0.,0.,0.])
SimInfo.solvers['StaticCoupledRBM']['structural_solver'] = 'RigidDynamicPrescribedStep'
SimInfo.solvers['StaticCoupledRBM']['structural_solver_settings'] = SimInfo.solvers['RigidDynamicPrescribedStep']
SimInfo.solvers['StaticCoupledRBM']['aero_solver'] = 'SHWUvlm'
SimInfo.solvers['StaticCoupledRBM']['aero_solver_settings'] = SimInfo.solvers['SHWUvlm']
SimInfo.solvers['StaticCoupledRBM']['tolerance'] = 1e-8
SimInfo.solvers['StaticCoupledRBM']['n_load_steps'] = 0
SimInfo.solvers['StaticCoupledRBM']['relaxation_factor'] = 0.
SimInfo.solvers['SHWUvlm']['convection_scheme'] = 2
SimInfo.solvers['SHWUvlm']['num_cores'] = 8
SimInfo.solvers['SHWUvlm']['rot_vel'] = rotation_velocity
SimInfo.solvers['SHWUvlm']['rot_axis'] = np.array([0.,0.,1.])
SimInfo.solvers['SHWUvlm']['rot_center'] = np.zeros((3),)
SimInfo.solvers['SHWUvlm']['velocity_field_generator'] = 'SteadyVelocityField'
SimInfo.solvers['SHWUvlm']['velocity_field_input'] = SimInfo.solvers['SteadyVelocityField']
SimInfo.solvers['SaveData']['compress_float'] = True
# Only used for steady_simulation = False
SimInfo.solvers['StepUvlm']['convection_scheme'] = 3
SimInfo.solvers['StepUvlm']['num_cores'] = 8
SimInfo.solvers['StepUvlm']['velocity_field_generator'] = 'SteadyVelocityField'
SimInfo.solvers['StepUvlm']['velocity_field_input'] = SimInfo.solvers['SteadyVelocityField']
SimInfo.solvers['DynamicCoupled']['structural_solver'] = 'RigidDynamicPrescribedStep'
SimInfo.solvers['DynamicCoupled']['structural_solver_settings'] = SimInfo.solvers['RigidDynamicPrescribedStep']
SimInfo.solvers['DynamicCoupled']['aero_solver'] = 'StepUvlm'
SimInfo.solvers['DynamicCoupled']['aero_solver_settings'] = SimInfo.solvers['StepUvlm']
SimInfo.solvers['DynamicCoupled']['postprocessors'] = ['BeamPlot', 'AerogridPlot', 'Cleanup', 'SaveData']
SimInfo.solvers['DynamicCoupled']['postprocessors_settings'] = {'BeamPlot': SimInfo.solvers['BeamPlot'],
'AerogridPlot': SimInfo.solvers['AerogridPlot'],
'Cleanup': SimInfo.solvers['Cleanup'],
'SaveData': SimInfo.solvers['SaveData']}
SimInfo.solvers['DynamicCoupled']['minimum_steps'] = 0
SimInfo.solvers['DynamicCoupled']['include_unsteady_force_contribution'] = True
SimInfo.solvers['DynamicCoupled']['relaxation_factor'] = 0.
SimInfo.solvers['DynamicCoupled']['final_relaxation_factor'] = 0.
SimInfo.solvers['DynamicCoupled']['dynamic_relaxation'] = False
SimInfo.solvers['DynamicCoupled']['relaxation_steps'] = 0
# Define dynamic simulation (used regardless the value of "steady_simulation" variable)
SimInfo.define_num_steps(time_steps)
SimInfo.with_forced_vel = True
SimInfo.for_vel = np.zeros((time_steps,6), dtype=float)
SimInfo.for_vel[:,5] = rotation_velocity
SimInfo.for_acc = np.zeros((time_steps,6), dtype=float)
SimInfo.with_dynamic_forces = True
SimInfo.dynamic_forces = np.zeros((time_steps,rotor.StructuralInformation.num_node,6), dtype=float)
Generate simulation files
[9]:
gc.clean_test_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])
rotor.generate_h5_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])
SimInfo.generate_solver_file()
SimInfo.generate_dyn_file(time_steps)
Run SHARPy case¶
[10]:
sharpy_output = sharpy.sharpy_main.main(['', SimInfo.solvers['SHARPy']['route'] + SimInfo.solvers['SHARPy']['case'] + '.sharpy'])
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Aeroelastics Lab, Aeronautics Department.
Copyright (c), Imperial College London.
All rights reserved.
License available at https://github.com/imperialcollegelondon/sharpy
Running SHARPy from /home/arturo/code/sharpy/docs/source/content/example_notebooks
SHARPy being run is in /home/arturo/code/sharpy
The branch being run is dev_doc
The version and commit hash are: v0.1-1816-g6185d82-6185d82
The available solvers on this session are:
_BaseStructural
AerogridLoader
BeamLoader
DynamicCoupled
DynamicUVLM
LinDynamicSim
LinearAssembler
Modal
NoAero
NonLinearDynamic
NonLinearDynamicCoupledStep
NonLinearDynamicMultibody
NonLinearDynamicPrescribedStep
NonLinearStatic
NonLinearStaticMultibody
PrescribedUvlm
RigidDynamicPrescribedStep
SHWUvlm
StaticCoupled
StaticCoupledRBM
StaticTrim
StaticUvlm
StepLinearUVLM
StepUvlm
Trim
FrequencyResponse
WriteVariablesTime
BeamPlot
LiftDistribution
AeroForcesCalculator
CreateSnapshot
StabilityDerivatives
Cleanup
AsymptoticStability
PickleData
SaveData
StallCheck
BeamLoads
PlotFlowField
AerogridPlot
PreSharpy
Generating an instance of BeamLoader
Generating an instance of AerogridLoader
The aerodynamic grid contains 3 surfaces
Surface 0, M=8, N=48
Wake 0, M=450, N=48
Surface 1, M=8, N=48
Wake 1, M=450, N=48
Surface 2, M=8, N=48
Wake 2, M=450, N=48
In total: 1152 bound panels
In total: 64800 wake panels
Total number of panels = 65952
Generating an instance of StaticCoupledRBM
Generating an instance of RigidDynamicPrescribedStep
Generating an instance of SHWUvlm
i_step: 0, i_iter: 0
i_step: 0, i_iter: 1
Pos res = 0.000000e+00. Psi res = 0.000000e+00.
Pos_dot res = 0.000000e+00. Psi_dot res = 0.000000e+00.
Resultant forces and moments: (array([1.19344329e-02, 4.42818203e-03, 8.51720587e+05]), array([-2.23034084e-02, 8.00768152e-03, 6.02114389e+06]))
Generating an instance of DynamicCoupled
Generating an instance of RigidDynamicPrescribedStep
Generating an instance of StepUvlm
Generating an instance of BeamPlot
Generating an instance of AerogridPlot
Generating an instance of Cleanup
Generating an instance of SaveData
Variable save_linear has no assigned value in the settings file.
will default to the value: c_bool(False)
Variable save_linear_uvlm has no assigned value in the settings file.
will default to the value: c_bool(False)
Variable skip_attr has no assigned value in the settings file.
will default to the value: ['fortran', 'airfoils', 'airfoil_db', 'settings_types', 'ct_dynamic_forces_list', 'ct_gamma_dot_list', 'ct_gamma_list', 'ct_gamma_star_list', 'ct_normals_list', 'ct_u_ext_list', 'ct_u_ext_star_list', 'ct_zeta_dot_list', 'ct_zeta_list', 'ct_zeta_star_list', 'dynamic_input', ['fortran', 'airfoils', 'airfoil_db', 'settings_types', 'ct_dynamic_forces_list', 'ct_forces_list', 'ct_gamma_dot_list', 'ct_gamma_list', 'ct_gamma_star_list', 'ct_normals_list', 'ct_u_ext_list', 'ct_u_ext_star_list', 'ct_zeta_dot_list', 'ct_zeta_list', 'ct_zeta_star_list', 'dynamic_input']]
Variable format has no assigned value in the settings file.
will default to the value: h5
|=======|========|======|==============|==============|==============|==============|==============|
| ts | t | iter | struc ratio | iter time | residual vel | FoR_vel(x) | FoR_vel(z) |
|=======|========|======|==============|==============|==============|==============|==============|
/home/arturo/code/sharpy/sharpy/solvers/dynamiccoupled.py:449: RuntimeWarning: divide by zero encountered in log10
np.log10(self.res_dqdt),
| 1 | 0.0551 | 1 | 0.000689 | 46.721959 | -inf | 0.000000e+00 | 0.000000e+00 |
| 2 | 0.1102 | 1 | 0.000686 | 46.839166 | -inf | 0.000000e+00 | 0.000000e+00 |
| 3 | 0.1653 | 1 | 0.000687 | 46.816562 | -inf | 0.000000e+00 | 0.000000e+00 |
| 4 | 0.2204 | 1 | 0.000666 | 48.386563 | -inf | 0.000000e+00 | 0.000000e+00 |
| 5 | 0.2755 | 1 | 0.000683 | 47.135425 | -inf | 0.000000e+00 | 0.000000e+00 |
| 6 | 0.3306 | 1 | 0.000707 | 46.560263 | -inf | 0.000000e+00 | 0.000000e+00 |
| 7 | 0.3857 | 1 | 0.000697 | 46.562699 | -inf | 0.000000e+00 | 0.000000e+00 |
| 8 | 0.4408 | 1 | 0.000692 | 46.757933 | -inf | 0.000000e+00 | 0.000000e+00 |
| 9 | 0.4959 | 1 | 0.000691 | 46.622405 | -inf | 0.000000e+00 | 0.000000e+00 |
| 10 | 0.5510 | 1 | 0.000700 | 46.480478 | -inf | 0.000000e+00 | 0.000000e+00 |
| 11 | 0.6061 | 1 | 0.000703 | 46.450803 | -inf | 0.000000e+00 | 0.000000e+00 |
| 12 | 0.6612 | 1 | 0.000708 | 46.466538 | -inf | 0.000000e+00 | 0.000000e+00 |
| 13 | 0.7163 | 1 | 0.000576 | 55.899692 | -inf | 0.000000e+00 | 0.000000e+00 |
| 14 | 0.7713 | 1 | 0.000642 | 50.701285 | -inf | 0.000000e+00 | 0.000000e+00 |
| 15 | 0.8264 | 1 | 0.000671 | 47.593583 | -inf | 0.000000e+00 | 0.000000e+00 |
| 16 | 0.8815 | 1 | 0.000699 | 47.287386 | -inf | 0.000000e+00 | 0.000000e+00 |
| 17 | 0.9366 | 1 | 0.000691 | 46.559619 | -inf | 0.000000e+00 | 0.000000e+00 |
| 18 | 0.9917 | 1 | 0.000681 | 46.953868 | -inf | 0.000000e+00 | 0.000000e+00 |
| 19 | 1.0468 | 1 | 0.000693 | 46.526422 | -inf | 0.000000e+00 | 0.000000e+00 |
| 20 | 1.1019 | 1 | 0.000692 | 46.634115 | -inf | 0.000000e+00 | 0.000000e+00 |
| 21 | 1.1570 | 1 | 0.000691 | 46.424641 | -inf | 0.000000e+00 | 0.000000e+00 |
| 22 | 1.2121 | 1 | 0.000684 | 46.882152 | -inf | 0.000000e+00 | 0.000000e+00 |
| 23 | 1.2672 | 1 | 0.000694 | 46.586424 | -inf | 0.000000e+00 | 0.000000e+00 |
| 24 | 1.3223 | 1 | 0.000687 | 46.776280 | -inf | 0.000000e+00 | 0.000000e+00 |
| 25 | 1.3774 | 1 | 0.000692 | 46.704067 | -inf | 0.000000e+00 | 0.000000e+00 |
| 26 | 1.4325 | 1 | 0.000679 | 46.886657 | -inf | 0.000000e+00 | 0.000000e+00 |
| 27 | 1.4876 | 1 | 0.000684 | 46.516365 | -inf | 0.000000e+00 | 0.000000e+00 |
| 28 | 1.5427 | 1 | 0.000682 | 46.684166 | -inf | 0.000000e+00 | 0.000000e+00 |
| 29 | 1.5978 | 1 | 0.000683 | 47.033028 | -inf | 0.000000e+00 | 0.000000e+00 |
| 30 | 1.6529 | 1 | 0.000694 | 46.291923 | -inf | 0.000000e+00 | 0.000000e+00 |
| 31 | 1.7080 | 1 | 0.000687 | 46.680159 | -inf | 0.000000e+00 | 0.000000e+00 |
| 32 | 1.7631 | 1 | 0.000683 | 46.629501 | -inf | 0.000000e+00 | 0.000000e+00 |
| 33 | 1.8182 | 1 | 0.000682 | 46.806173 | -inf | 0.000000e+00 | 0.000000e+00 |
| 34 | 1.8733 | 1 | 0.000687 | 46.757005 | -inf | 0.000000e+00 | 0.000000e+00 |
| 35 | 1.9284 | 1 | 0.000683 | 47.033428 | -inf | 0.000000e+00 | 0.000000e+00 |
| 36 | 1.9835 | 1 | 0.000659 | 48.662729 | -inf | 0.000000e+00 | 0.000000e+00 |
| 37 | 2.0386 | 1 | 0.000659 | 48.571643 | -inf | 0.000000e+00 | 0.000000e+00 |
| 38 | 2.0937 | 1 | 0.000673 | 47.434747 | -inf | 0.000000e+00 | 0.000000e+00 |
| 39 | 2.1488 | 1 | 0.000661 | 48.286789 | -inf | 0.000000e+00 | 0.000000e+00 |
| 40 | 2.2039 | 1 | 0.000679 | 47.779096 | -inf | 0.000000e+00 | 0.000000e+00 |
| 41 | 2.2590 | 1 | 0.000677 | 48.413777 | -inf | 0.000000e+00 | 0.000000e+00 |
| 42 | 2.3140 | 1 | 0.000671 | 47.798777 | -inf | 0.000000e+00 | 0.000000e+00 |
| 43 | 2.3691 | 1 | 0.000710 | 46.501405 | -inf | 0.000000e+00 | 0.000000e+00 |
| 44 | 2.4242 | 1 | 0.000690 | 46.611010 | -inf | 0.000000e+00 | 0.000000e+00 |
| 45 | 2.4793 | 1 | 0.000688 | 46.704990 | -inf | 0.000000e+00 | 0.000000e+00 |
| 46 | 2.5344 | 1 | 0.000728 | 46.796206 | -inf | 0.000000e+00 | 0.000000e+00 |
| 47 | 2.5895 | 1 | 0.000693 | 46.510013 | -inf | 0.000000e+00 | 0.000000e+00 |
| 48 | 2.6446 | 1 | 0.000692 | 46.604489 | -inf | 0.000000e+00 | 0.000000e+00 |
| 49 | 2.6997 | 1 | 0.000693 | 46.648462 | -inf | 0.000000e+00 | 0.000000e+00 |
| 50 | 2.7548 | 1 | 0.000703 | 46.233052 | -inf | 0.000000e+00 | 0.000000e+00 |
| 51 | 2.8099 | 1 | 0.000696 | 46.494563 | -inf | 0.000000e+00 | 0.000000e+00 |
| 52 | 2.8650 | 1 | 0.000689 | 46.427002 | -inf | 0.000000e+00 | 0.000000e+00 |
| 53 | 2.9201 | 1 | 0.000685 | 46.556616 | -inf | 0.000000e+00 | 0.000000e+00 |
| 54 | 2.9752 | 1 | 0.000688 | 46.986618 | -inf | 0.000000e+00 | 0.000000e+00 |
| 55 | 3.0303 | 1 | 0.000685 | 47.021588 | -inf | 0.000000e+00 | 0.000000e+00 |
| 56 | 3.0854 | 1 | 0.000695 | 46.501523 | -inf | 0.000000e+00 | 0.000000e+00 |
| 57 | 3.1405 | 1 | 0.000690 | 46.545832 | -inf | 0.000000e+00 | 0.000000e+00 |
| 58 | 3.1956 | 1 | 0.000688 | 46.394942 | -inf | 0.000000e+00 | 0.000000e+00 |
| 59 | 3.2507 | 1 | 0.000690 | 46.572368 | -inf | 0.000000e+00 | 0.000000e+00 |
| 60 | 3.3058 | 1 | 0.000689 | 46.388416 | -inf | 0.000000e+00 | 0.000000e+00 |
| 61 | 3.3609 | 1 | 0.000674 | 47.326130 | -inf | 0.000000e+00 | 0.000000e+00 |
| 62 | 3.4160 | 1 | 0.000691 | 46.475252 | -inf | 0.000000e+00 | 0.000000e+00 |
| 63 | 3.4711 | 1 | 0.000692 | 46.700463 | -inf | 0.000000e+00 | 0.000000e+00 |
| 64 | 3.5262 | 1 | 0.000684 | 46.761324 | -inf | 0.000000e+00 | 0.000000e+00 |
| 65 | 3.5813 | 1 | 0.000690 | 46.305145 | -inf | 0.000000e+00 | 0.000000e+00 |
| 66 | 3.6364 | 1 | 0.000681 | 47.033500 | -inf | 0.000000e+00 | 0.000000e+00 |
| 67 | 3.6915 | 1 | 0.000690 | 46.707418 | -inf | 0.000000e+00 | 0.000000e+00 |
| 68 | 3.7466 | 1 | 0.000687 | 46.829002 | -inf | 0.000000e+00 | 0.000000e+00 |
| 69 | 3.8017 | 1 | 0.000686 | 46.771566 | -inf | 0.000000e+00 | 0.000000e+00 |
| 70 | 3.8567 | 1 | 0.000687 | 46.798868 | -inf | 0.000000e+00 | 0.000000e+00 |
| 71 | 3.9118 | 1 | 0.000687 | 46.656061 | -inf | 0.000000e+00 | 0.000000e+00 |
| 72 | 3.9669 | 1 | 0.000689 | 46.650955 | -inf | 0.000000e+00 | 0.000000e+00 |
| 73 | 4.0220 | 1 | 0.000689 | 46.676483 | -inf | 0.000000e+00 | 0.000000e+00 |
| 74 | 4.0771 | 1 | 0.000701 | 46.733123 | -inf | 0.000000e+00 | 0.000000e+00 |
| 75 | 4.1322 | 1 | 0.000693 | 46.613006 | -inf | 0.000000e+00 | 0.000000e+00 |
| 76 | 4.1873 | 1 | 0.000691 | 46.569005 | -inf | 0.000000e+00 | 0.000000e+00 |
| 77 | 4.2424 | 1 | 0.000691 | 46.714434 | -inf | 0.000000e+00 | 0.000000e+00 |
| 78 | 4.2975 | 1 | 0.000691 | 46.564491 | -inf | 0.000000e+00 | 0.000000e+00 |
| 79 | 4.3526 | 1 | 0.000691 | 46.293432 | -inf | 0.000000e+00 | 0.000000e+00 |
| 80 | 4.4077 | 1 | 0.000691 | 46.444557 | -inf | 0.000000e+00 | 0.000000e+00 |
| 81 | 4.4628 | 1 | 0.000685 | 46.583821 | -inf | 0.000000e+00 | 0.000000e+00 |
| 82 | 4.5179 | 1 | 0.000692 | 46.464751 | -inf | 0.000000e+00 | 0.000000e+00 |
| 83 | 4.5730 | 1 | 0.000691 | 46.614111 | -inf | 0.000000e+00 | 0.000000e+00 |
| 84 | 4.6281 | 1 | 0.000682 | 47.093682 | -inf | 0.000000e+00 | 0.000000e+00 |
| 85 | 4.6832 | 1 | 0.000668 | 47.848219 | -inf | 0.000000e+00 | 0.000000e+00 |
| 86 | 4.7383 | 1 | 0.000690 | 46.453935 | -inf | 0.000000e+00 | 0.000000e+00 |
| 87 | 4.7934 | 1 | 0.000671 | 47.508853 | -inf | 0.000000e+00 | 0.000000e+00 |
| 88 | 4.8485 | 1 | 0.000704 | 46.453028 | -inf | 0.000000e+00 | 0.000000e+00 |
| 89 | 4.9036 | 1 | 0.000686 | 46.783497 | -inf | 0.000000e+00 | 0.000000e+00 |
| 90 | 4.9587 | 1 | 0.000695 | 46.473095 | -inf | 0.000000e+00 | 0.000000e+00 |
| 91 | 5.0138 | 1 | 0.000699 | 46.384601 | -inf | 0.000000e+00 | 0.000000e+00 |
| 92 | 5.0689 | 1 | 0.000671 | 48.773508 | -inf | 0.000000e+00 | 0.000000e+00 |
| 93 | 5.1240 | 1 | 0.000682 | 46.843241 | -inf | 0.000000e+00 | 0.000000e+00 |
| 94 | 5.1791 | 1 | 0.000691 | 46.690389 | -inf | 0.000000e+00 | 0.000000e+00 |
| 95 | 5.2342 | 1 | 0.000685 | 46.811431 | -inf | 0.000000e+00 | 0.000000e+00 |
| 96 | 5.2893 | 1 | 0.000683 | 46.832472 | -inf | 0.000000e+00 | 0.000000e+00 |
| 97 | 5.3444 | 1 | 0.000690 | 46.410221 | -inf | 0.000000e+00 | 0.000000e+00 |
| 98 | 5.3994 | 1 | 0.000693 | 46.644631 | -inf | 0.000000e+00 | 0.000000e+00 |
| 99 | 5.4545 | 1 | 0.000695 | 46.328560 | -inf | 0.000000e+00 | 0.000000e+00 |
| 100 | 5.5096 | 1 | 0.000693 | 46.709863 | -inf | 0.000000e+00 | 0.000000e+00 |
| 101 | 5.5647 | 1 | 0.000696 | 46.303366 | -inf | 0.000000e+00 | 0.000000e+00 |
| 102 | 5.6198 | 1 | 0.000688 | 46.450453 | -inf | 0.000000e+00 | 0.000000e+00 |
| 103 | 5.6749 | 1 | 0.000704 | 46.611641 | -inf | 0.000000e+00 | 0.000000e+00 |
| 104 | 5.7300 | 1 | 0.000686 | 46.622834 | -inf | 0.000000e+00 | 0.000000e+00 |
| 105 | 5.7851 | 1 | 0.000693 | 46.442312 | -inf | 0.000000e+00 | 0.000000e+00 |
| 106 | 5.8402 | 1 | 0.000697 | 46.894939 | -inf | 0.000000e+00 | 0.000000e+00 |
| 107 | 5.8953 | 1 | 0.000695 | 46.583571 | -inf | 0.000000e+00 | 0.000000e+00 |
| 108 | 5.9504 | 1 | 0.000692 | 46.596199 | -inf | 0.000000e+00 | 0.000000e+00 |
| 109 | 6.0055 | 1 | 0.000689 | 46.675746 | -inf | 0.000000e+00 | 0.000000e+00 |
| 110 | 6.0606 | 1 | 0.000688 | 46.948383 | -inf | 0.000000e+00 | 0.000000e+00 |
| 111 | 6.1157 | 1 | 0.000708 | 46.583486 | -inf | 0.000000e+00 | 0.000000e+00 |
| 112 | 6.1708 | 1 | 0.000687 | 46.777358 | -inf | 0.000000e+00 | 0.000000e+00 |
| 113 | 6.2259 | 1 | 0.000696 | 46.655726 | -inf | 0.000000e+00 | 0.000000e+00 |
| 114 | 6.2810 | 1 | 0.000692 | 46.488556 | -inf | 0.000000e+00 | 0.000000e+00 |
| 115 | 6.3361 | 1 | 0.000687 | 46.641207 | -inf | 0.000000e+00 | 0.000000e+00 |
| 116 | 6.3912 | 1 | 0.000699 | 46.693835 | -inf | 0.000000e+00 | 0.000000e+00 |
| 117 | 6.4463 | 1 | 0.000717 | 47.359647 | -inf | 0.000000e+00 | 0.000000e+00 |
| 118 | 6.5014 | 1 | 0.000689 | 46.684606 | -inf | 0.000000e+00 | 0.000000e+00 |
| 119 | 6.5565 | 1 | 0.000686 | 46.892280 | -inf | 0.000000e+00 | 0.000000e+00 |
| 120 | 6.6116 | 1 | 0.000690 | 46.391236 | -inf | 0.000000e+00 | 0.000000e+00 |
| 121 | 6.6667 | 1 | 0.000687 | 46.619935 | -inf | 0.000000e+00 | 0.000000e+00 |
| 122 | 6.7218 | 1 | 0.000685 | 46.847298 | -inf | 0.000000e+00 | 0.000000e+00 |
| 123 | 6.7769 | 1 | 0.000698 | 46.383369 | -inf | 0.000000e+00 | 0.000000e+00 |
| 124 | 6.8320 | 1 | 0.000690 | 46.623488 | -inf | 0.000000e+00 | 0.000000e+00 |
| 125 | 6.8871 | 1 | 0.000689 | 46.456695 | -inf | 0.000000e+00 | 0.000000e+00 |
| 126 | 6.9421 | 1 | 0.000748 | 46.666541 | -inf | 0.000000e+00 | 0.000000e+00 |
| 127 | 6.9972 | 1 | 0.000695 | 46.393158 | -inf | 0.000000e+00 | 0.000000e+00 |
| 128 | 7.0523 | 1 | 0.000632 | 50.929908 | -inf | 0.000000e+00 | 0.000000e+00 |
| 129 | 7.1074 | 1 | 0.000685 | 47.093784 | -inf | 0.000000e+00 | 0.000000e+00 |
| 130 | 7.1625 | 1 | 0.000688 | 46.682273 | -inf | 0.000000e+00 | 0.000000e+00 |
| 131 | 7.2176 | 1 | 0.000690 | 46.667180 | -inf | 0.000000e+00 | 0.000000e+00 |
| 132 | 7.2727 | 1 | 0.000689 | 46.673738 | -inf | 0.000000e+00 | 0.000000e+00 |
| 133 | 7.3278 | 1 | 0.000690 | 46.813912 | -inf | 0.000000e+00 | 0.000000e+00 |
| 134 | 7.3829 | 1 | 0.000698 | 46.399704 | -inf | 0.000000e+00 | 0.000000e+00 |
| 135 | 7.4380 | 1 | 0.000687 | 46.776766 | -inf | 0.000000e+00 | 0.000000e+00 |
| 136 | 7.4931 | 1 | 0.000687 | 46.979810 | -inf | 0.000000e+00 | 0.000000e+00 |
| 137 | 7.5482 | 1 | 0.000693 | 46.578824 | -inf | 0.000000e+00 | 0.000000e+00 |
| 138 | 7.6033 | 1 | 0.000689 | 46.882381 | -inf | 0.000000e+00 | 0.000000e+00 |
| 139 | 7.6584 | 1 | 0.000676 | 48.142078 | -inf | 0.000000e+00 | 0.000000e+00 |
| 140 | 7.7135 | 1 | 0.000693 | 46.784018 | -inf | 0.000000e+00 | 0.000000e+00 |
| 141 | 7.7686 | 1 | 0.000688 | 46.642419 | -inf | 0.000000e+00 | 0.000000e+00 |
| 142 | 7.8237 | 1 | 0.000689 | 46.662693 | -inf | 0.000000e+00 | 0.000000e+00 |
| 143 | 7.8788 | 1 | 0.000689 | 46.802617 | -inf | 0.000000e+00 | 0.000000e+00 |
| 144 | 7.9339 | 1 | 0.000690 | 46.776085 | -inf | 0.000000e+00 | 0.000000e+00 |
| 145 | 7.9890 | 1 | 0.000701 | 46.875717 | -inf | 0.000000e+00 | 0.000000e+00 |
| 146 | 8.0441 | 1 | 0.000685 | 46.822466 | -inf | 0.000000e+00 | 0.000000e+00 |
| 147 | 8.0992 | 1 | 0.000677 | 47.384767 | -inf | 0.000000e+00 | 0.000000e+00 |
| 148 | 8.1543 | 1 | 0.000675 | 47.679214 | -inf | 0.000000e+00 | 0.000000e+00 |
| 149 | 8.2094 | 1 | 0.000689 | 46.763218 | -inf | 0.000000e+00 | 0.000000e+00 |
| 150 | 8.2645 | 1 | 0.000679 | 46.940251 | -inf | 0.000000e+00 | 0.000000e+00 |
| 151 | 8.3196 | 1 | 0.000686 | 46.627359 | -inf | 0.000000e+00 | 0.000000e+00 |
| 152 | 8.3747 | 1 | 0.000687 | 46.664798 | -inf | 0.000000e+00 | 0.000000e+00 |
| 153 | 8.4298 | 1 | 0.000687 | 46.633910 | -inf | 0.000000e+00 | 0.000000e+00 |
| 154 | 8.4848 | 1 | 0.000679 | 46.877187 | -inf | 0.000000e+00 | 0.000000e+00 |
| 155 | 8.5399 | 1 | 0.000696 | 46.384902 | -inf | 0.000000e+00 | 0.000000e+00 |
| 156 | 8.5950 | 1 | 0.000690 | 46.680191 | -inf | 0.000000e+00 | 0.000000e+00 |
| 157 | 8.6501 | 1 | 0.000690 | 46.595866 | -inf | 0.000000e+00 | 0.000000e+00 |
| 158 | 8.7052 | 1 | 0.000711 | 46.561896 | -inf | 0.000000e+00 | 0.000000e+00 |
| 159 | 8.7603 | 1 | 0.000682 | 46.789459 | -inf | 0.000000e+00 | 0.000000e+00 |
| 160 | 8.8154 | 1 | 0.000712 | 46.585605 | -inf | 0.000000e+00 | 0.000000e+00 |
| 161 | 8.8705 | 1 | 0.000674 | 47.731465 | -inf | 0.000000e+00 | 0.000000e+00 |
| 162 | 8.9256 | 1 | 0.000679 | 47.806239 | -inf | 0.000000e+00 | 0.000000e+00 |
| 163 | 8.9807 | 1 | 0.000687 | 46.597511 | -inf | 0.000000e+00 | 0.000000e+00 |
| 164 | 9.0358 | 1 | 0.000695 | 46.662126 | -inf | 0.000000e+00 | 0.000000e+00 |
| 165 | 9.0909 | 1 | 0.000678 | 47.138759 | -inf | 0.000000e+00 | 0.000000e+00 |
| 166 | 9.1460 | 1 | 0.000687 | 46.654425 | -inf | 0.000000e+00 | 0.000000e+00 |
| 167 | 9.2011 | 1 | 0.000683 | 47.072656 | -inf | 0.000000e+00 | 0.000000e+00 |
| 168 | 9.2562 | 1 | 0.000688 | 46.655192 | -inf | 0.000000e+00 | 0.000000e+00 |
| 169 | 9.3113 | 1 | 0.000683 | 46.990134 | -inf | 0.000000e+00 | 0.000000e+00 |
| 170 | 9.3664 | 1 | 0.000704 | 46.960453 | -inf | 0.000000e+00 | 0.000000e+00 |
| 171 | 9.4215 | 1 | 0.000688 | 46.615369 | -inf | 0.000000e+00 | 0.000000e+00 |
| 172 | 9.4766 | 1 | 0.000686 | 46.761498 | -inf | 0.000000e+00 | 0.000000e+00 |
| 173 | 9.5317 | 1 | 0.000686 | 46.698208 | -inf | 0.000000e+00 | 0.000000e+00 |
| 174 | 9.5868 | 1 | 0.000686 | 46.964062 | -inf | 0.000000e+00 | 0.000000e+00 |
| 175 | 9.6419 | 1 | 0.000693 | 46.608047 | -inf | 0.000000e+00 | 0.000000e+00 |
| 176 | 9.6970 | 1 | 0.000684 | 46.848123 | -inf | 0.000000e+00 | 0.000000e+00 |
| 177 | 9.7521 | 1 | 0.000687 | 46.693659 | -inf | 0.000000e+00 | 0.000000e+00 |
| 178 | 9.8072 | 1 | 0.000682 | 46.766093 | -inf | 0.000000e+00 | 0.000000e+00 |
| 179 | 9.8623 | 1 | 0.000689 | 46.497713 | -inf | 0.000000e+00 | 0.000000e+00 |
| 180 | 9.9174 | 1 | 0.000694 | 46.824867 | -inf | 0.000000e+00 | 0.000000e+00 |
| 181 | 9.9725 | 1 | 0.000686 | 46.686000 | -inf | 0.000000e+00 | 0.000000e+00 |
| 182 |10.0275 | 1 | 0.000687 | 46.847956 | -inf | 0.000000e+00 | 0.000000e+00 |
| 183 |10.0826 | 1 | 0.000696 | 46.639555 | -inf | 0.000000e+00 | 0.000000e+00 |
| 184 |10.1377 | 1 | 0.000694 | 46.582859 | -inf | 0.000000e+00 | 0.000000e+00 |
| 185 |10.1928 | 1 | 0.000692 | 46.696143 | -inf | 0.000000e+00 | 0.000000e+00 |
| 186 |10.2479 | 1 | 0.000688 | 47.038347 | -inf | 0.000000e+00 | 0.000000e+00 |
| 187 |10.3030 | 1 | 0.000662 | 48.575645 | -inf | 0.000000e+00 | 0.000000e+00 |
| 188 |10.3581 | 1 | 0.000662 | 48.531096 | -inf | 0.000000e+00 | 0.000000e+00 |
| 189 |10.4132 | 1 | 0.000674 | 47.867980 | -inf | 0.000000e+00 | 0.000000e+00 |
| 190 |10.4683 | 1 | 0.000683 | 47.185120 | -inf | 0.000000e+00 | 0.000000e+00 |
| 191 |10.5234 | 1 | 0.000680 | 47.472356 | -inf | 0.000000e+00 | 0.000000e+00 |
| 192 |10.5785 | 1 | 0.000671 | 48.044142 | -inf | 0.000000e+00 | 0.000000e+00 |
| 193 |10.6336 | 1 | 0.000679 | 47.648927 | -inf | 0.000000e+00 | 0.000000e+00 |
| 194 |10.6887 | 1 | 0.000669 | 48.052096 | -inf | 0.000000e+00 | 0.000000e+00 |
| 195 |10.7438 | 1 | 0.000672 | 47.870581 | -inf | 0.000000e+00 | 0.000000e+00 |
| 196 |10.7989 | 1 | 0.000688 | 47.670530 | -inf | 0.000000e+00 | 0.000000e+00 |
| 197 |10.8540 | 1 | 0.000669 | 47.552862 | -inf | 0.000000e+00 | 0.000000e+00 |
| 198 |10.9091 | 1 | 0.000668 | 47.895285 | -inf | 0.000000e+00 | 0.000000e+00 |
| 199 |10.9642 | 1 | 0.000677 | 47.475987 | -inf | 0.000000e+00 | 0.000000e+00 |
| 200 |11.0193 | 1 | 0.000689 | 47.705888 | -inf | 0.000000e+00 | 0.000000e+00 |
| 201 |11.0744 | 1 | 0.000677 | 47.488158 | -inf | 0.000000e+00 | 0.000000e+00 |
| 202 |11.1295 | 1 | 0.000712 | 48.576639 | -inf | 0.000000e+00 | 0.000000e+00 |
| 203 |11.1846 | 1 | 0.000673 | 47.734807 | -inf | 0.000000e+00 | 0.000000e+00 |
| 204 |11.2397 | 1 | 0.000670 | 47.568058 | -inf | 0.000000e+00 | 0.000000e+00 |
| 205 |11.2948 | 1 | 0.000663 | 48.250896 | -inf | 0.000000e+00 | 0.000000e+00 |
| 206 |11.3499 | 1 | 0.000670 | 47.559952 | -inf | 0.000000e+00 | 0.000000e+00 |
| 207 |11.4050 | 1 | 0.000670 | 47.573367 | -inf | 0.000000e+00 | 0.000000e+00 |
| 208 |11.4601 | 1 | 0.000687 | 46.850101 | -inf | 0.000000e+00 | 0.000000e+00 |
| 209 |11.5152 | 1 | 0.000685 | 46.660332 | -inf | 0.000000e+00 | 0.000000e+00 |
| 210 |11.5702 | 1 | 0.000685 | 46.485644 | -inf | 0.000000e+00 | 0.000000e+00 |
| 211 |11.6253 | 1 | 0.000687 | 46.798719 | -inf | 0.000000e+00 | 0.000000e+00 |
| 212 |11.6804 | 1 | 0.000688 | 46.841973 | -inf | 0.000000e+00 | 0.000000e+00 |
| 213 |11.7355 | 1 | 0.000685 | 46.615664 | -inf | 0.000000e+00 | 0.000000e+00 |
| 214 |11.7906 | 1 | 0.000685 | 46.819705 | -inf | 0.000000e+00 | 0.000000e+00 |
| 215 |11.8457 | 1 | 0.000695 | 46.534639 | -inf | 0.000000e+00 | 0.000000e+00 |
| 216 |11.9008 | 1 | 0.000687 | 47.054001 | -inf | 0.000000e+00 | 0.000000e+00 |
| 217 |11.9559 | 1 | 0.000685 | 46.458661 | -inf | 0.000000e+00 | 0.000000e+00 |
| 218 |12.0110 | 1 | 0.000685 | 46.475964 | -inf | 0.000000e+00 | 0.000000e+00 |
| 219 |12.0661 | 1 | 0.000681 | 46.980705 | -inf | 0.000000e+00 | 0.000000e+00 |
| 220 |12.1212 | 1 | 0.000683 | 46.885118 | -inf | 0.000000e+00 | 0.000000e+00 |
| 221 |12.1763 | 1 | 0.000690 | 46.385044 | -inf | 0.000000e+00 | 0.000000e+00 |
| 222 |12.2314 | 1 | 0.000687 | 46.472218 | -inf | 0.000000e+00 | 0.000000e+00 |
| 223 |12.2865 | 1 | 0.000711 | 46.681981 | -inf | 0.000000e+00 | 0.000000e+00 |
| 224 |12.3416 | 1 | 0.000686 | 46.755873 | -inf | 0.000000e+00 | 0.000000e+00 |
| 225 |12.3967 | 1 | 0.000684 | 47.479635 | -inf | 0.000000e+00 | 0.000000e+00 |
| 226 |12.4518 | 1 | 0.000697 | 46.237011 | -inf | 0.000000e+00 | 0.000000e+00 |
| 227 |12.5069 | 1 | 0.000681 | 46.954574 | -inf | 0.000000e+00 | 0.000000e+00 |
| 228 |12.5620 | 1 | 0.000665 | 47.804645 | -inf | 0.000000e+00 | 0.000000e+00 |
| 229 |12.6171 | 1 | 0.000683 | 46.649178 | -inf | 0.000000e+00 | 0.000000e+00 |
| 230 |12.6722 | 1 | 0.000619 | 51.822896 | -inf | 0.000000e+00 | 0.000000e+00 |
| 231 |12.7273 | 1 | 0.000691 | 46.453337 | -inf | 0.000000e+00 | 0.000000e+00 |
| 232 |12.7824 | 1 | 0.000688 | 46.512926 | -inf | 0.000000e+00 | 0.000000e+00 |
| 233 |12.8375 | 1 | 0.000693 | 46.372334 | -inf | 0.000000e+00 | 0.000000e+00 |
| 234 |12.8926 | 1 | 0.000691 | 46.443784 | -inf | 0.000000e+00 | 0.000000e+00 |
| 235 |12.9477 | 1 | 0.000685 | 46.595713 | -inf | 0.000000e+00 | 0.000000e+00 |
| 236 |13.0028 | 1 | 0.000685 | 46.675990 | -inf | 0.000000e+00 | 0.000000e+00 |
| 237 |13.0579 | 1 | 0.000673 | 47.477098 | -inf | 0.000000e+00 | 0.000000e+00 |
| 238 |13.1129 | 1 | 0.000685 | 46.907466 | -inf | 0.000000e+00 | 0.000000e+00 |
| 239 |13.1680 | 1 | 0.000679 | 46.745359 | -inf | 0.000000e+00 | 0.000000e+00 |
| 240 |13.2231 | 1 | 0.000667 | 47.812544 | -inf | 0.000000e+00 | 0.000000e+00 |
| 241 |13.2782 | 1 | 0.000676 | 46.828156 | -inf | 0.000000e+00 | 0.000000e+00 |
| 242 |13.3333 | 1 | 0.000674 | 47.228874 | -inf | 0.000000e+00 | 0.000000e+00 |
| 243 |13.3884 | 1 | 0.000675 | 47.213317 | -inf | 0.000000e+00 | 0.000000e+00 |
| 244 |13.4435 | 1 | 0.000685 | 46.946864 | -inf | 0.000000e+00 | 0.000000e+00 |
| 245 |13.4986 | 1 | 0.000686 | 46.518108 | -inf | 0.000000e+00 | 0.000000e+00 |
| 246 |13.5537 | 1 | 0.000683 | 46.918194 | -inf | 0.000000e+00 | 0.000000e+00 |
| 247 |13.6088 | 1 | 0.000681 | 46.772611 | -inf | 0.000000e+00 | 0.000000e+00 |
| 248 |13.6639 | 1 | 0.000681 | 46.738571 | -inf | 0.000000e+00 | 0.000000e+00 |
| 249 |13.7190 | 1 | 0.000701 | 46.844015 | -inf | 0.000000e+00 | 0.000000e+00 |
| 250 |13.7741 | 1 | 0.000692 | 46.682392 | -inf | 0.000000e+00 | 0.000000e+00 |
| 251 |13.8292 | 1 | 0.000684 | 46.749444 | -inf | 0.000000e+00 | 0.000000e+00 |
| 252 |13.8843 | 1 | 0.000690 | 46.676376 | -inf | 0.000000e+00 | 0.000000e+00 |
| 253 |13.9394 | 1 | 0.000688 | 46.902780 | -inf | 0.000000e+00 | 0.000000e+00 |
| 254 |13.9945 | 1 | 0.000700 | 46.342343 | -inf | 0.000000e+00 | 0.000000e+00 |
| 255 |14.0496 | 1 | 0.000676 | 47.290718 | -inf | 0.000000e+00 | 0.000000e+00 |
| 256 |14.1047 | 1 | 0.000690 | 46.483884 | -inf | 0.000000e+00 | 0.000000e+00 |
| 257 |14.1598 | 1 | 0.000687 | 46.475610 | -inf | 0.000000e+00 | 0.000000e+00 |
| 258 |14.2149 | 1 | 0.000697 | 46.243039 | -inf | 0.000000e+00 | 0.000000e+00 |
| 259 |14.2700 | 1 | 0.000691 | 46.327818 | -inf | 0.000000e+00 | 0.000000e+00 |
| 260 |14.3251 | 1 | 0.000684 | 47.023605 | -inf | 0.000000e+00 | 0.000000e+00 |
| 261 |14.3802 | 1 | 0.000684 | 46.992628 | -inf | 0.000000e+00 | 0.000000e+00 |
| 262 |14.4353 | 1 | 0.000689 | 46.655423 | -inf | 0.000000e+00 | 0.000000e+00 |
| 263 |14.4904 | 1 | 0.000687 | 46.780777 | -inf | 0.000000e+00 | 0.000000e+00 |
| 264 |14.5455 | 1 | 0.000687 | 46.914670 | -inf | 0.000000e+00 | 0.000000e+00 |
| 265 |14.6006 | 1 | 0.000688 | 46.680806 | -inf | 0.000000e+00 | 0.000000e+00 |
| 266 |14.6556 | 1 | 0.000678 | 47.492095 | -inf | 0.000000e+00 | 0.000000e+00 |
| 267 |14.7107 | 1 | 0.000688 | 46.786733 | -inf | 0.000000e+00 | 0.000000e+00 |
| 268 |14.7658 | 1 | 0.000680 | 47.164431 | -inf | 0.000000e+00 | 0.000000e+00 |
| 269 |14.8209 | 1 | 0.000708 | 45.651456 | -inf | 0.000000e+00 | 0.000000e+00 |
| 270 |14.8760 | 1 | 0.000684 | 47.118467 | -inf | 0.000000e+00 | 0.000000e+00 |
| 271 |14.9311 | 1 | 0.000686 | 46.986024 | -inf | 0.000000e+00 | 0.000000e+00 |
| 272 |14.9862 | 1 | 0.000705 | 45.811613 | -inf | 0.000000e+00 | 0.000000e+00 |
| 273 |15.0413 | 1 | 0.000701 | 45.809912 | -inf | 0.000000e+00 | 0.000000e+00 |
| 274 |15.0964 | 1 | 0.000698 | 46.075125 | -inf | 0.000000e+00 | 0.000000e+00 |
| 275 |15.1515 | 1 | 0.000697 | 46.349127 | -inf | 0.000000e+00 | 0.000000e+00 |
| 276 |15.2066 | 1 | 0.000707 | 45.612900 | -inf | 0.000000e+00 | 0.000000e+00 |
| 277 |15.2617 | 1 | 0.000699 | 45.962354 | -inf | 0.000000e+00 | 0.000000e+00 |
| 278 |15.3168 | 1 | 0.000703 | 45.854950 | -inf | 0.000000e+00 | 0.000000e+00 |
| 279 |15.3719 | 1 | 0.000688 | 46.591173 | -inf | 0.000000e+00 | 0.000000e+00 |
| 280 |15.4270 | 1 | 0.000691 | 46.439605 | -inf | 0.000000e+00 | 0.000000e+00 |
| 281 |15.4821 | 1 | 0.000700 | 45.609099 | -inf | 0.000000e+00 | 0.000000e+00 |
| 282 |15.5372 | 1 | 0.000705 | 45.473630 | -inf | 0.000000e+00 | 0.000000e+00 |
| 283 |15.5923 | 1 | 0.000704 | 45.499228 | -inf | 0.000000e+00 | 0.000000e+00 |
| 284 |15.6474 | 1 | 0.000707 | 45.474494 | -inf | 0.000000e+00 | 0.000000e+00 |
| 285 |15.7025 | 1 | 0.000690 | 46.229681 | -inf | 0.000000e+00 | 0.000000e+00 |
| 286 |15.7576 | 1 | 0.000699 | 45.890873 | -inf | 0.000000e+00 | 0.000000e+00 |
| 287 |15.8127 | 1 | 0.000693 | 46.117946 | -inf | 0.000000e+00 | 0.000000e+00 |
| 288 |15.8678 | 1 | 0.000698 | 45.995581 | -inf | 0.000000e+00 | 0.000000e+00 |
| 289 |15.9229 | 1 | 0.000707 | 45.766717 | -inf | 0.000000e+00 | 0.000000e+00 |
| 290 |15.9780 | 1 | 0.000726 | 45.936229 | -inf | 0.000000e+00 | 0.000000e+00 |
| 291 |16.0331 | 1 | 0.000709 | 46.439345 | -inf | 0.000000e+00 | 0.000000e+00 |
| 292 |16.0882 | 1 | 0.000690 | 46.546813 | -inf | 0.000000e+00 | 0.000000e+00 |
| 293 |16.1433 | 1 | 0.000693 | 46.523355 | -inf | 0.000000e+00 | 0.000000e+00 |
| 294 |16.1983 | 1 | 0.000709 | 45.438468 | -inf | 0.000000e+00 | 0.000000e+00 |
| 295 |16.2534 | 1 | 0.000698 | 46.057489 | -inf | 0.000000e+00 | 0.000000e+00 |
| 296 |16.3085 | 1 | 0.000692 | 46.396248 | -inf | 0.000000e+00 | 0.000000e+00 |
| 297 |16.3636 | 1 | 0.000671 | 47.804347 | -inf | 0.000000e+00 | 0.000000e+00 |
| 298 |16.4187 | 1 | 0.000700 | 45.745559 | -inf | 0.000000e+00 | 0.000000e+00 |
| 299 |16.4738 | 1 | 0.000695 | 46.054604 | -inf | 0.000000e+00 | 0.000000e+00 |
| 300 |16.5289 | 1 | 0.000705 | 45.744685 | -inf | 0.000000e+00 | 0.000000e+00 |
| 301 |16.5840 | 1 | 0.000698 | 45.782885 | -inf | 0.000000e+00 | 0.000000e+00 |
| 302 |16.6391 | 1 | 0.000694 | 46.331677 | -inf | 0.000000e+00 | 0.000000e+00 |
| 303 |16.6942 | 1 | 0.000693 | 46.501020 | -inf | 0.000000e+00 | 0.000000e+00 |
| 304 |16.7493 | 1 | 0.000697 | 45.868491 | -inf | 0.000000e+00 | 0.000000e+00 |
| 305 |16.8044 | 1 | 0.000699 | 46.378612 | -inf | 0.000000e+00 | 0.000000e+00 |
| 306 |16.8595 | 1 | 0.000695 | 46.308039 | -inf | 0.000000e+00 | 0.000000e+00 |
| 307 |16.9146 | 1 | 0.000691 | 46.526447 | -inf | 0.000000e+00 | 0.000000e+00 |
| 308 |16.9697 | 1 | 0.000696 | 46.122122 | -inf | 0.000000e+00 | 0.000000e+00 |
| 309 |17.0248 | 1 | 0.000684 | 46.856025 | -inf | 0.000000e+00 | 0.000000e+00 |
| 310 |17.0799 | 1 | 0.000701 | 46.113206 | -inf | 0.000000e+00 | 0.000000e+00 |
| 311 |17.1350 | 1 | 0.000692 | 46.398112 | -inf | 0.000000e+00 | 0.000000e+00 |
| 312 |17.1901 | 1 | 0.000767 | 45.619590 | -inf | 0.000000e+00 | 0.000000e+00 |
| 313 |17.2452 | 1 | 0.000675 | 47.797250 | -inf | 0.000000e+00 | 0.000000e+00 |
| 314 |17.3003 | 1 | 0.000685 | 46.677846 | -inf | 0.000000e+00 | 0.000000e+00 |
| 315 |17.3554 | 1 | 0.000689 | 46.488186 | -inf | 0.000000e+00 | 0.000000e+00 |
| 316 |17.4105 | 1 | 0.000711 | 46.798838 | -inf | 0.000000e+00 | 0.000000e+00 |
| 317 |17.4656 | 1 | 0.000690 | 46.569277 | -inf | 0.000000e+00 | 0.000000e+00 |
| 318 |17.5207 | 1 | 0.000695 | 46.209487 | -inf | 0.000000e+00 | 0.000000e+00 |
| 319 |17.5758 | 1 | 0.000698 | 45.909949 | -inf | 0.000000e+00 | 0.000000e+00 |
| 320 |17.6309 | 1 | 0.000679 | 47.280223 | -inf | 0.000000e+00 | 0.000000e+00 |
| 321 |17.6860 | 1 | 0.000696 | 45.957118 | -inf | 0.000000e+00 | 0.000000e+00 |
| 322 |17.7410 | 1 | 0.000689 | 46.661208 | -inf | 0.000000e+00 | 0.000000e+00 |
| 323 |17.7961 | 1 | 0.000689 | 46.485928 | -inf | 0.000000e+00 | 0.000000e+00 |
| 324 |17.8512 | 1 | 0.000702 | 45.910141 | -inf | 0.000000e+00 | 0.000000e+00 |
| 325 |17.9063 | 1 | 0.000698 | 46.091762 | -inf | 0.000000e+00 | 0.000000e+00 |
| 326 |17.9614 | 1 | 0.000697 | 46.191874 | -inf | 0.000000e+00 | 0.000000e+00 |
| 327 |18.0165 | 1 | 0.000697 | 46.020327 | -inf | 0.000000e+00 | 0.000000e+00 |
| 328 |18.0716 | 1 | 0.000683 | 47.056295 | -inf | 0.000000e+00 | 0.000000e+00 |
| 329 |18.1267 | 1 | 0.000679 | 47.225815 | -inf | 0.000000e+00 | 0.000000e+00 |
| 330 |18.1818 | 1 | 0.000687 | 46.711211 | -inf | 0.000000e+00 | 0.000000e+00 |
| 331 |18.2369 | 1 | 0.000683 | 46.838738 | -inf | 0.000000e+00 | 0.000000e+00 |
| 332 |18.2920 | 1 | 0.000690 | 46.530371 | -inf | 0.000000e+00 | 0.000000e+00 |
| 333 |18.3471 | 1 | 0.000682 | 47.151909 | -inf | 0.000000e+00 | 0.000000e+00 |
| 334 |18.4022 | 1 | 0.000705 | 46.465808 | -inf | 0.000000e+00 | 0.000000e+00 |
| 335 |18.4573 | 1 | 0.000698 | 46.918384 | -inf | 0.000000e+00 | 0.000000e+00 |
| 336 |18.5124 | 1 | 0.000680 | 46.982040 | -inf | 0.000000e+00 | 0.000000e+00 |
| 337 |18.5675 | 1 | 0.000688 | 46.834463 | -inf | 0.000000e+00 | 0.000000e+00 |
| 338 |18.6226 | 1 | 0.000685 | 47.082787 | -inf | 0.000000e+00 | 0.000000e+00 |
| 339 |18.6777 | 1 | 0.000667 | 47.776211 | -inf | 0.000000e+00 | 0.000000e+00 |
| 340 |18.7328 | 1 | 0.000694 | 46.342369 | -inf | 0.000000e+00 | 0.000000e+00 |
| 341 |18.7879 | 1 | 0.000679 | 47.334009 | -inf | 0.000000e+00 | 0.000000e+00 |
| 342 |18.8430 | 1 | 0.000676 | 47.224326 | -inf | 0.000000e+00 | 0.000000e+00 |
| 343 |18.8981 | 1 | 0.000681 | 47.006368 | -inf | 0.000000e+00 | 0.000000e+00 |
| 344 |18.9532 | 1 | 0.000682 | 46.777730 | -inf | 0.000000e+00 | 0.000000e+00 |
| 345 |19.0083 | 1 | 0.000694 | 46.232870 | -inf | 0.000000e+00 | 0.000000e+00 |
| 346 |19.0634 | 1 | 0.000692 | 46.253289 | -inf | 0.000000e+00 | 0.000000e+00 |
| 347 |19.1185 | 1 | 0.000693 | 46.055296 | -inf | 0.000000e+00 | 0.000000e+00 |
| 348 |19.1736 | 1 | 0.000687 | 46.546440 | -inf | 0.000000e+00 | 0.000000e+00 |
| 349 |19.2287 | 1 | 0.000685 | 46.769534 | -inf | 0.000000e+00 | 0.000000e+00 |
| 350 |19.2837 | 1 | 0.000698 | 45.705568 | -inf | 0.000000e+00 | 0.000000e+00 |
| 351 |19.3388 | 1 | 0.000699 | 45.612452 | -inf | 0.000000e+00 | 0.000000e+00 |
| 352 |19.3939 | 1 | 0.000689 | 46.311269 | -inf | 0.000000e+00 | 0.000000e+00 |
| 353 |19.4490 | 1 | 0.000704 | 45.581321 | -inf | 0.000000e+00 | 0.000000e+00 |
| 354 |19.5041 | 1 | 0.000692 | 46.268870 | -inf | 0.000000e+00 | 0.000000e+00 |
| 355 |19.5592 | 1 | 0.000695 | 45.857139 | -inf | 0.000000e+00 | 0.000000e+00 |
| 356 |19.6143 | 1 | 0.000672 | 47.383261 | -inf | 0.000000e+00 | 0.000000e+00 |
| 357 |19.6694 | 1 | 0.000697 | 46.039425 | -inf | 0.000000e+00 | 0.000000e+00 |
| 358 |19.7245 | 1 | 0.000673 | 47.209931 | -inf | 0.000000e+00 | 0.000000e+00 |
| 359 |19.7796 | 1 | 0.000693 | 46.166173 | -inf | 0.000000e+00 | 0.000000e+00 |
| 360 |19.8347 | 1 | 0.000689 | 46.307711 | -inf | 0.000000e+00 | 0.000000e+00 |
| 361 |19.8898 | 1 | 0.000690 | 46.204995 | -inf | 0.000000e+00 | 0.000000e+00 |
| 362 |19.9449 | 1 | 0.000707 | 45.873240 | -inf | 0.000000e+00 | 0.000000e+00 |
| 363 |20.0000 | 1 | 0.000702 | 45.896570 | -inf | 0.000000e+00 | 0.000000e+00 |
| 364 |20.0551 | 1 | 0.000703 | 45.762990 | -inf | 0.000000e+00 | 0.000000e+00 |
| 365 |20.1102 | 1 | 0.000689 | 46.398000 | -inf | 0.000000e+00 | 0.000000e+00 |
| 366 |20.1653 | 1 | 0.000698 | 45.893426 | -inf | 0.000000e+00 | 0.000000e+00 |
| 367 |20.2204 | 1 | 0.000690 | 46.226002 | -inf | 0.000000e+00 | 0.000000e+00 |
| 368 |20.2755 | 1 | 0.000694 | 46.151370 | -inf | 0.000000e+00 | 0.000000e+00 |
| 369 |20.3306 | 1 | 0.000688 | 46.556177 | -inf | 0.000000e+00 | 0.000000e+00 |
| 370 |20.3857 | 1 | 0.000707 | 45.573970 | -inf | 0.000000e+00 | 0.000000e+00 |
| 371 |20.4408 | 1 | 0.000693 | 46.446767 | -inf | 0.000000e+00 | 0.000000e+00 |
| 372 |20.4959 | 1 | 0.000694 | 46.152634 | -inf | 0.000000e+00 | 0.000000e+00 |
| 373 |20.5510 | 1 | 0.000696 | 46.155208 | -inf | 0.000000e+00 | 0.000000e+00 |
| 374 |20.6061 | 1 | 0.000705 | 45.472315 | -inf | 0.000000e+00 | 0.000000e+00 |
| 375 |20.6612 | 1 | 0.000676 | 47.016364 | -inf | 0.000000e+00 | 0.000000e+00 |
| 376 |20.7163 | 1 | 0.000700 | 45.441678 | -inf | 0.000000e+00 | 0.000000e+00 |
| 377 |20.7713 | 1 | 0.000705 | 45.608852 | -inf | 0.000000e+00 | 0.000000e+00 |
| 378 |20.8264 | 1 | 0.000693 | 46.611538 | -inf | 0.000000e+00 | 0.000000e+00 |
| 379 |20.8815 | 1 | 0.000701 | 46.255489 | -inf | 0.000000e+00 | 0.000000e+00 |
| 380 |20.9366 | 1 | 0.000688 | 46.646919 | -inf | 0.000000e+00 | 0.000000e+00 |
| 381 |20.9917 | 1 | 0.000585 | 54.423797 | -inf | 0.000000e+00 | 0.000000e+00 |
| 382 |21.0468 | 1 | 0.000667 | 47.716783 | -inf | 0.000000e+00 | 0.000000e+00 |
| 383 |21.1019 | 1 | 0.000700 | 46.025102 | -inf | 0.000000e+00 | 0.000000e+00 |
| 384 |21.1570 | 1 | 0.000699 | 45.861447 | -inf | 0.000000e+00 | 0.000000e+00 |
| 385 |21.2121 | 1 | 0.000698 | 46.278300 | -inf | 0.000000e+00 | 0.000000e+00 |
| 386 |21.2672 | 1 | 0.000699 | 45.952605 | -inf | 0.000000e+00 | 0.000000e+00 |
| 387 |21.3223 | 1 | 0.000704 | 45.592786 | -inf | 0.000000e+00 | 0.000000e+00 |
| 388 |21.3774 | 1 | 0.000689 | 46.150288 | -inf | 0.000000e+00 | 0.000000e+00 |
| 389 |21.4325 | 1 | 0.000697 | 45.931689 | -inf | 0.000000e+00 | 0.000000e+00 |
| 390 |21.4876 | 1 | 0.000697 | 45.977116 | -inf | 0.000000e+00 | 0.000000e+00 |
| 391 |21.5427 | 1 | 0.000690 | 45.976451 | -inf | 0.000000e+00 | 0.000000e+00 |
| 392 |21.5978 | 1 | 0.000690 | 46.597288 | -inf | 0.000000e+00 | 0.000000e+00 |
| 393 |21.6529 | 1 | 0.000681 | 46.697688 | -inf | 0.000000e+00 | 0.000000e+00 |
| 394 |21.7080 | 1 | 0.000696 | 47.318465 | -inf | 0.000000e+00 | 0.000000e+00 |
| 395 |21.7631 | 1 | 0.000699 | 46.267378 | -inf | 0.000000e+00 | 0.000000e+00 |
| 396 |21.8182 | 1 | 0.000689 | 46.555969 | -inf | 0.000000e+00 | 0.000000e+00 |
| 397 |21.8733 | 1 | 0.000679 | 47.319640 | -inf | 0.000000e+00 | 0.000000e+00 |
| 398 |21.9284 | 1 | 0.000671 | 47.558353 | -inf | 0.000000e+00 | 0.000000e+00 |
| 399 |21.9835 | 1 | 0.000689 | 46.302612 | -inf | 0.000000e+00 | 0.000000e+00 |
| 400 |22.0386 | 1 | 0.000667 | 47.758410 | -inf | 0.000000e+00 | 0.000000e+00 |
| 401 |22.0937 | 1 | 0.000687 | 46.813205 | -inf | 0.000000e+00 | 0.000000e+00 |
| 402 |22.1488 | 1 | 0.000689 | 46.336472 | -inf | 0.000000e+00 | 0.000000e+00 |
| 403 |22.2039 | 1 | 0.000707 | 46.668331 | -inf | 0.000000e+00 | 0.000000e+00 |
| 404 |22.2590 | 1 | 0.000688 | 46.649211 | -inf | 0.000000e+00 | 0.000000e+00 |
| 405 |22.3140 | 1 | 0.000691 | 46.482820 | -inf | 0.000000e+00 | 0.000000e+00 |
| 406 |22.3691 | 1 | 0.000681 | 46.947114 | -inf | 0.000000e+00 | 0.000000e+00 |
| 407 |22.4242 | 1 | 0.000689 | 46.618766 | -inf | 0.000000e+00 | 0.000000e+00 |
| 408 |22.4793 | 1 | 0.000680 | 46.817495 | -inf | 0.000000e+00 | 0.000000e+00 |
| 409 |22.5344 | 1 | 0.000686 | 46.703945 | -inf | 0.000000e+00 | 0.000000e+00 |
| 410 |22.5895 | 1 | 0.000675 | 47.620927 | -inf | 0.000000e+00 | 0.000000e+00 |
| 411 |22.6446 | 1 | 0.000689 | 46.717914 | -inf | 0.000000e+00 | 0.000000e+00 |
| 412 |22.6997 | 1 | 0.000674 | 47.499379 | -inf | 0.000000e+00 | 0.000000e+00 |
| 413 |22.7548 | 1 | 0.000683 | 46.991697 | -inf | 0.000000e+00 | 0.000000e+00 |
| 414 |22.8099 | 1 | 0.000844 | 47.362969 | -inf | 0.000000e+00 | 0.000000e+00 |
| 415 |22.8650 | 1 | 0.000681 | 47.379998 | -inf | 0.000000e+00 | 0.000000e+00 |
| 416 |22.9201 | 1 | 0.000688 | 46.840415 | -inf | 0.000000e+00 | 0.000000e+00 |
| 417 |22.9752 | 1 | 0.000696 | 46.394910 | -inf | 0.000000e+00 | 0.000000e+00 |
| 418 |23.0303 | 1 | 0.000680 | 47.481963 | -inf | 0.000000e+00 | 0.000000e+00 |
| 419 |23.0854 | 1 | 0.000677 | 47.425381 | -inf | 0.000000e+00 | 0.000000e+00 |
| 420 |23.1405 | 1 | 0.000675 | 47.313570 | -inf | 0.000000e+00 | 0.000000e+00 |
| 421 |23.1956 | 1 | 0.000680 | 47.051804 | -inf | 0.000000e+00 | 0.000000e+00 |
| 422 |23.2507 | 1 | 0.000692 | 46.392776 | -inf | 0.000000e+00 | 0.000000e+00 |
| 423 |23.3058 | 1 | 0.000700 | 46.097488 | -inf | 0.000000e+00 | 0.000000e+00 |
| 424 |23.3609 | 1 | 0.000704 | 45.675144 | -inf | 0.000000e+00 | 0.000000e+00 |
| 425 |23.4160 | 1 | 0.000678 | 47.188528 | -inf | 0.000000e+00 | 0.000000e+00 |
| 426 |23.4711 | 1 | 0.000674 | 47.721276 | -inf | 0.000000e+00 | 0.000000e+00 |
| 427 |23.5262 | 1 | 0.000679 | 47.517682 | -inf | 0.000000e+00 | 0.000000e+00 |
| 428 |23.5813 | 1 | 0.000699 | 47.314847 | -inf | 0.000000e+00 | 0.000000e+00 |
| 429 |23.6364 | 1 | 0.000677 | 46.942705 | -inf | 0.000000e+00 | 0.000000e+00 |
| 430 |23.6915 | 1 | 0.000685 | 46.500190 | -inf | 0.000000e+00 | 0.000000e+00 |
| 431 |23.7466 | 1 | 0.000690 | 46.497821 | -inf | 0.000000e+00 | 0.000000e+00 |
| 432 |23.8017 | 1 | 0.000681 | 46.785045 | -inf | 0.000000e+00 | 0.000000e+00 |
| 433 |23.8567 | 1 | 0.000695 | 45.813771 | -inf | 0.000000e+00 | 0.000000e+00 |
| 434 |23.9118 | 1 | 0.000710 | 45.188591 | -inf | 0.000000e+00 | 0.000000e+00 |
| 435 |23.9669 | 1 | 0.000692 | 46.043509 | -inf | 0.000000e+00 | 0.000000e+00 |
| 436 |24.0220 | 1 | 0.000703 | 45.755100 | -inf | 0.000000e+00 | 0.000000e+00 |
| 437 |24.0771 | 1 | 0.000696 | 45.757484 | -inf | 0.000000e+00 | 0.000000e+00 |
| 438 |24.1322 | 1 | 0.000683 | 46.637429 | -inf | 0.000000e+00 | 0.000000e+00 |
| 439 |24.1873 | 1 | 0.000688 | 46.360789 | -inf | 0.000000e+00 | 0.000000e+00 |
| 440 |24.2424 | 1 | 0.000691 | 46.138279 | -inf | 0.000000e+00 | 0.000000e+00 |
| 441 |24.2975 | 1 | 0.000697 | 46.142083 | -inf | 0.000000e+00 | 0.000000e+00 |
| 442 |24.3526 | 1 | 0.000699 | 46.033069 | -inf | 0.000000e+00 | 0.000000e+00 |
| 443 |24.4077 | 1 | 0.000685 | 46.517459 | -inf | 0.000000e+00 | 0.000000e+00 |
| 444 |24.4628 | 1 | 0.000699 | 45.831956 | -inf | 0.000000e+00 | 0.000000e+00 |
| 445 |24.5179 | 1 | 0.000683 | 47.009859 | -inf | 0.000000e+00 | 0.000000e+00 |
| 446 |24.5730 | 1 | 0.000703 | 46.299859 | -inf | 0.000000e+00 | 0.000000e+00 |
| 447 |24.6281 | 1 | 0.000684 | 46.631679 | -inf | 0.000000e+00 | 0.000000e+00 |
| 448 |24.6832 | 1 | 0.000696 | 46.171868 | -inf | 0.000000e+00 | 0.000000e+00 |
| 449 |24.7383 | 1 | 0.000704 | 45.749519 | -inf | 0.000000e+00 | 0.000000e+00 |
| 450 |24.7934 | 1 | 0.000673 | 47.822073 | -inf | 0.000000e+00 | 0.000000e+00 |
...Finished
FINISHED - Elapsed time = 21435.5371006 seconds
FINISHED - CPU process time = 165060.5815336 seconds
Postprocessing¶
Read the structural and aerodynamic information of the last time step
[11]:
tstep = sharpy_output.structure.timestep_info[-1]
astep = sharpy_output.aero.timestep_info[-1]
Separate the structure into blades
[12]:
# Define beams
ielem = 0
nblades = np.max(sharpy_output.structure.beam_number) + 1
nodes_blade = []
first_node = 0
for iblade in range(nblades):
nodes_blade.append(np.zeros((sharpy_output.structure.num_node,), dtype=bool))
while sharpy_output.structure.beam_number[ielem] <= iblade:
ielem += 1
if ielem == sharpy_output.structure.num_elem:
break
nodes_blade[iblade][first_node:sharpy_output.structure.connectivities[ielem-1,1]+1] = True
first_node = sharpy_output.structure.connectivities[ielem-1,1]+1
Compute the radial position of the nodes and initialise the rest of the variables
[13]:
r = []
c = []
dr = []
forces = []
CN_drR = []
CTan_drR = []
CP_drR = []
nodes_num = []
for iblade in range(nblades):
forces.append(tstep.steady_applied_forces[nodes_blade[iblade]].copy())
nodes_num.append(np.arange(0, sharpy_output.structure.num_node, 1)[nodes_blade[iblade]])
r.append(np.linalg.norm(tstep.pos[nodes_blade[iblade], :], axis=1))
dr.append(np.zeros(np.sum(nodes_blade[iblade])))
dr[iblade][0] = 0.5*(r[iblade][1]-r[iblade][0])
dr[iblade][-1] = 0.5 * (r[iblade][-1] - r[iblade][-2])
for inode in range(1,len(r[iblade]) - 1):
dr[iblade][inode] = 0.5*(r[iblade][inode+1] - r[iblade][inode-1])
CN_drR.append(np.zeros(len(r[iblade])))
c.append(np.zeros(len(r[iblade])))
CTan_drR.append(np.zeros(len(r[iblade])))
CP_drR.append(np.zeros(len(r[iblade])))
Transform the loads computed by SHARPy into out-of-plane and in-plane components
[14]:
rho = sharpy_output.settings['StaticCoupledRBM']['aero_solver_settings']['rho'].value
uinf = sharpy_output.settings['StaticCoupledRBM']['aero_solver_settings']['velocity_field_input']['u_inf'].value
R = np.max(r[0])
Cp = 0
Ct = 0
global_force_factor = 0.5 * rho * uinf** 2 * np.pi * R**2
global_power_factor = global_force_factor*uinf
for iblade in range(nblades):
for inode in range(len(r[iblade])):
forces[iblade][inode, 0] *= 0. # Discard the spanwise component
node_global_index = nodes_num[iblade][inode]
ielem = sharpy_output.structure.node_master_elem[node_global_index, 0]
inode_in_elem = sharpy_output.structure.node_master_elem[node_global_index, 1]
CAB = algebra.crv2rotation(tstep.psi[ielem, inode_in_elem, :])
c[iblade][inode] = sharpy_output.aero.aero_dict['chord'][ielem,inode_in_elem]
forces_AFoR = np.dot(CAB, forces[iblade][inode, 0:3])
CN_drR[iblade][inode] = forces_AFoR[2]/dr[iblade][inode]*R / global_force_factor
CTan_drR[iblade][inode] = np.linalg.norm(forces_AFoR[0:2])/dr[iblade][inode]*R / global_force_factor
CP_drR[iblade][inode] = np.linalg.norm(forces_AFoR[0:2])/dr[iblade][inode]*R * r[iblade][inode]*rotation_velocity / global_power_factor
Cp += np.sum(CP_drR[iblade]*dr[iblade]/R)
Ct += np.sum(CN_drR[iblade]*dr[iblade]/R)
Results¶
Plot of the loads along the blade
[15]:
fig, list_plots = plt.subplots(1, 2, figsize=(12, 3))
list_plots[0].grid()
list_plots[0].set_xlabel("r/R [-]")
list_plots[0].set_ylabel("CN/d(r/R) [-]")
list_plots[0].plot(r[0]/R, CN_drR[0], '-', label='SHARPy')
list_plots[0].plot(of_rR, of_cNdrR, '-', label='OpenFAST')
list_plots[0].legend()
list_plots[1].grid()
list_plots[1].set_xlabel("r/R [-]")
list_plots[1].set_ylabel("CT/d(r/R) [-]")
list_plots[1].plot(r[0]/R, CTan_drR[0], '-', label='SHARPy')
list_plots[1].plot(of_rR, of_cTdrR, '-', label='OpenFAST')
list_plots[1].legend()
plt.show()
Print the rotor thrust and power coefficients
[16]:
print(" OpenFAST SHARPy")
print("Cp[-] %.2f %.2f" % (of_cp, Cp))
print("Ct[-] %.2f %.2f" % (of_ct, Ct))
OpenFAST SHARPy
Cp[-] 0.49 0.55
Ct[-] 0.70 0.76