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
%matplotlib inline
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 sharpy.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
We define our parameters:
[4]:
# Mathematical constants
deg2rad = np.pi/180.
# Case
case = 'rotor'
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 information in the excel file:
[6]:
op_params = {}
op_params['rotation_velocity'] = rotation_velocity
op_params['pitch_deg'] = pitch_deg
op_params['wsp'] = WSP
op_params['dt'] = dt
geom_params = {}
geom_params['chord_panels'] = chord_panels
geom_params['tol_remove_points'] = 1e-8
geom_params['n_points_camber'] = 100
geom_params['h5_cross_sec_prop'] = None
geom_params['m_distribution'] = 'uniform'
options = {}
options['camber_effect_on_twist'] = False
options['user_defined_m_distribution_type'] = None
options['include_polars'] = False
options['separate_blades'] = False
excel_description = {}
excel_description['excel_file_name'] = 'source/type04_db_nrel5mw_oc3_v06.xlsx'
excel_description['excel_sheet_parameters'] = 'parameters'
excel_description['excel_sheet_structural_blade'] = 'structural_blade'
excel_description['excel_sheet_discretization_blade'] = 'discretization_blade'
excel_description['excel_sheet_aero_blade'] = 'aero_blade'
excel_description['excel_sheet_airfoil_info'] = 'airfoil_info'
excel_description['excel_sheet_airfoil_chord'] = 'airfoil_coord'
rotor, hub_nodes = template_wt.rotor_from_excel_type03(op_params,
geom_params,
excel_description,
options)
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 29 by node 0
WARNING: Replacing node 58 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',
'StaticCoupled',
'BeamPlot',
'AerogridPlot',
'SaveData']
else:
SimInfo.solvers['SHARPy']['flow'] = ['BeamLoader',
'AerogridLoader',
'StaticCoupled',
'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['AerogridLoader']['wake_shape_generator'] = 'HelicoidalWake'
SimInfo.solvers['AerogridLoader']['wake_shape_generator_input'] = {'u_inf': WSP,
'u_inf_direction': SimInfo.solvers['SteadyVelocityField']['u_inf_direction'],
'rotation_velocity': rotation_velocity*np.array([0., 0., 1.]),
'dt': dt,
'dphi1': dphi,
'ndphi1': mstar,
'r': 1.,
'dphimax': 10*deg2rad}
SimInfo.solvers['StaticCoupled']['structural_solver'] = 'RigidDynamicPrescribedStep'
SimInfo.solvers['StaticCoupled']['structural_solver_settings'] = SimInfo.solvers['RigidDynamicPrescribedStep']
SimInfo.solvers['StaticCoupled']['aero_solver'] = 'StaticUvlm'
SimInfo.solvers['StaticCoupled']['aero_solver_settings'] = SimInfo.solvers['StaticUvlm']
SimInfo.solvers['StaticCoupled']['tolerance'] = 1e-8
SimInfo.solvers['StaticCoupled']['n_load_steps'] = 0
SimInfo.solvers['StaticCoupled']['relaxation_factor'] = 0.
SimInfo.solvers['StaticUvlm']['num_cores'] = 8
SimInfo.solvers['StaticUvlm']['velocity_field_generator'] = 'SteadyVelocityField'
SimInfo.solvers['StaticUvlm']['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_blade_pitch_v2
The version and commit hash are: v1.2.1-546-g05602d1f-05602d1f
SHARPy output folder set
./output//rotor/
Generating an instance of BeamLoader
Generating an instance of AerogridLoader
Variable shear_direction has no assigned value in the settings file.
will default to the value: [1. 0. 0.]
Variable shear_exp has no assigned value in the settings file.
will default to the value: 0.0
Variable h_ref has no assigned value in the settings file.
will default to the value: 1.0
Variable h_corr has no assigned value in the settings file.
will default to the value: 1.0
The aerodynamic grid contains 3 surfaces
Surface 0, M=8, N=26
Wake 0, M=450, N=26
Surface 1, M=8, N=26
Wake 1, M=450, N=26
Surface 2, M=8, N=26
Wake 2, M=450, N=26
In total: 624 bound panels
In total: 35100 wake panels
Total number of panels = 35724
Generating an instance of StaticCoupled
Generating an instance of RigidDynamicPrescribedStep
Generating an instance of StaticUvlm
|=====|=====|============|==========|==========|==========|==========|==========|==========|
|iter |step | log10(res) | Fx | Fy | Fz | Mx | My | Mz |
|=====|=====|============|==========|==========|==========|==========|==========|==========|
| 0 | 0 | 0.00000 | -0.0000 | 0.0000 |21927.8250| 0.0000 | -0.0000 |5962997.5361|
| 1 | 0 | -inf | -0.0000 | 0.0000 |21927.8250| 0.0000 | -0.0000 |5962997.5361|
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
|=======|========|======|==============|==============|==============|==============|==============|
| ts | t | iter | struc ratio | iter time | residual vel | FoR_vel(x) | FoR_vel(z) |
|=======|========|======|==============|==============|==============|==============|==============|
| 1 | 0.0551 | 1 | 0.001471 | 11.072773 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 2 | 0.1102 | 1 | 0.001529 | 11.094774 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 3 | 0.1653 | 1 | 0.001487 | 11.017530 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 4 | 0.2204 | 1 | 0.001487 | 11.053551 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 5 | 0.2755 | 1 | 0.001495 | 10.972424 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 6 | 0.3306 | 1 | 0.001496 | 10.951425 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 7 | 0.3857 | 1 | 0.001492 | 11.018625 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 8 | 0.4408 | 1 | 0.001476 | 11.044770 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 9 | 0.4959 | 1 | 0.001478 | 11.122489 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 10 | 0.5510 | 1 | 0.001500 | 10.997606 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 11 | 0.6061 | 1 | 0.001481 | 11.076450 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 12 | 0.6612 | 1 | 0.001513 | 10.976762 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 13 | 0.7163 | 1 | 0.001489 | 11.056770 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 14 | 0.7713 | 1 | 0.001473 | 11.147662 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 15 | 0.8264 | 1 | 0.001485 | 11.047932 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 16 | 0.8815 | 1 | 0.001500 | 10.984375 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 17 | 0.9366 | 1 | 0.001492 | 10.999334 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 18 | 0.9917 | 1 | 0.001492 | 11.036468 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 19 | 1.0468 | 1 | 0.001490 | 10.989860 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 20 | 1.1019 | 1 | 0.001487 | 10.981977 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 21 | 1.1570 | 1 | 0.001480 | 11.026050 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 22 | 1.2121 | 1 | 0.001501 | 10.964416 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 23 | 1.2672 | 1 | 0.001483 | 11.061231 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 24 | 1.3223 | 1 | 0.001502 | 11.026285 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 25 | 1.3774 | 1 | 0.001497 | 10.937541 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 26 | 1.4325 | 1 | 0.001464 | 11.216671 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 27 | 1.4876 | 1 | 0.001489 | 11.077631 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 28 | 1.5427 | 1 | 0.001487 | 11.029765 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 29 | 1.5978 | 1 | 0.001484 | 11.057365 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 30 | 1.6529 | 1 | 0.001499 | 10.988523 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 31 | 1.7080 | 1 | 0.001480 | 11.082585 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 32 | 1.7631 | 1 | 0.001493 | 11.026814 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 33 | 1.8182 | 1 | 0.001500 | 10.964227 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 34 | 1.8733 | 1 | 0.001496 | 11.070894 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 35 | 1.9284 | 1 | 0.001499 | 10.991359 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 36 | 1.9835 | 1 | 0.001493 | 10.956692 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 37 | 2.0386 | 1 | 0.001489 | 11.022953 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 38 | 2.0937 | 1 | 0.001493 | 11.002933 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 39 | 2.1488 | 1 | 0.001494 | 10.971854 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 40 | 2.2039 | 1 | 0.001499 | 10.956611 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 41 | 2.2590 | 1 | 0.001484 | 11.020658 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 42 | 2.3140 | 1 | 0.001484 | 11.016274 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 43 | 2.3691 | 1 | 0.001490 | 11.171444 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 44 | 2.4242 | 1 | 0.001496 | 10.975332 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 45 | 2.4793 | 1 | 0.001479 | 11.094840 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 46 | 2.5344 | 1 | 0.001484 | 11.060059 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 47 | 2.5895 | 1 | 0.001329 | 12.309849 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 48 | 2.6446 | 1 | 0.001455 | 11.269876 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 49 | 2.6997 | 1 | 0.001489 | 11.076657 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 50 | 2.7548 | 1 | 0.001496 | 10.998456 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 51 | 2.8099 | 1 | 0.001471 | 11.215534 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 52 | 2.8650 | 1 | 0.001494 | 10.981076 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 53 | 2.9201 | 1 | 0.001476 | 11.089418 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 54 | 2.9752 | 1 | 0.001482 | 10.973016 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 55 | 3.0303 | 1 | 0.001469 | 11.115966 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 56 | 3.0854 | 1 | 0.001458 | 11.172810 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 57 | 3.1405 | 1 | 0.001496 | 10.984580 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 58 | 3.1956 | 1 | 0.001451 | 11.196615 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 59 | 3.2507 | 1 | 0.001498 | 10.961545 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 60 | 3.3058 | 1 | 0.001492 | 11.053819 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 61 | 3.3609 | 1 | 0.001492 | 11.066293 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 62 | 3.4160 | 1 | 0.001489 | 11.025009 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 63 | 3.4711 | 1 | 0.001485 | 10.999920 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 64 | 3.5262 | 1 | 0.001505 | 10.973439 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 65 | 3.5813 | 1 | 0.001495 | 10.981763 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 66 | 3.6364 | 1 | 0.001481 | 10.997240 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 67 | 3.6915 | 1 | 0.001489 | 11.030007 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 68 | 3.7466 | 1 | 0.001487 | 10.977346 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 69 | 3.8017 | 1 | 0.001490 | 11.086072 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 70 | 3.8567 | 1 | 0.001478 | 11.027897 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 71 | 3.9118 | 1 | 0.001492 | 10.997195 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 72 | 3.9669 | 1 | 0.001476 | 11.129629 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 73 | 4.0220 | 1 | 0.001491 | 10.996616 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 74 | 4.0771 | 1 | 0.001513 | 10.996785 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 75 | 4.1322 | 1 | 0.001487 | 11.010984 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 76 | 4.1873 | 1 | 0.001504 | 10.960333 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 77 | 4.2424 | 1 | 0.001483 | 11.062480 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 78 | 4.2975 | 1 | 0.001502 | 10.999189 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 79 | 4.3526 | 1 | 0.001504 | 10.989805 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 80 | 4.4077 | 1 | 0.001499 | 10.986292 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 81 | 4.4628 | 1 | 0.001471 | 11.064248 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 82 | 4.5179 | 1 | 0.001478 | 11.030763 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 83 | 4.5730 | 1 | 0.001423 | 11.418318 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 84 | 4.6281 | 1 | 0.001513 | 10.934981 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 85 | 4.6832 | 1 | 0.001477 | 10.947891 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 86 | 4.7383 | 1 | 0.001449 | 11.337449 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 87 | 4.7934 | 1 | 0.001446 | 11.356113 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 88 | 4.8485 | 1 | 0.001493 | 11.006986 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 89 | 4.9036 | 1 | 0.001508 | 10.995290 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 90 | 4.9587 | 1 | 0.001519 | 10.961908 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 91 | 5.0138 | 1 | 0.001511 | 11.004637 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 92 | 5.0689 | 1 | 0.001493 | 11.060139 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 93 | 5.1240 | 1 | 0.001475 | 11.108975 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 94 | 5.1791 | 1 | 0.001501 | 10.946505 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 95 | 5.2342 | 1 | 0.001504 | 10.936386 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 96 | 5.2893 | 1 | 0.001486 | 10.994701 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 97 | 5.3444 | 1 | 0.001483 | 11.023811 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 98 | 5.3994 | 1 | 0.001494 | 10.979126 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 99 | 5.4545 | 1 | 0.001481 | 11.163518 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 100 | 5.5096 | 1 | 0.001479 | 11.047313 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 101 | 5.5647 | 1 | 0.001473 | 11.060119 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 102 | 5.6198 | 1 | 0.001486 | 11.053105 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 103 | 5.6749 | 1 | 0.001486 | 11.092742 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 104 | 5.7300 | 1 | 0.001477 | 11.137425 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 105 | 5.7851 | 1 | 0.001491 | 11.010371 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 106 | 5.8402 | 1 | 0.001496 | 10.990369 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 107 | 5.8953 | 1 | 0.001473 | 11.243003 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 108 | 5.9504 | 1 | 0.001388 | 11.929604 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 109 | 6.0055 | 1 | 0.001458 | 11.222341 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 110 | 6.0606 | 1 | 0.001499 | 11.021925 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 111 | 6.1157 | 1 | 0.001489 | 10.988726 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 112 | 6.1708 | 1 | 0.001464 | 11.127002 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 113 | 6.2259 | 1 | 0.001490 | 10.982098 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 114 | 6.2810 | 1 | 0.001490 | 11.058744 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 115 | 6.3361 | 1 | 0.001501 | 11.036917 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 116 | 6.3912 | 1 | 0.001487 | 11.093127 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 117 | 6.4463 | 1 | 0.001511 | 10.986041 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 118 | 6.5014 | 1 | 0.001473 | 11.067499 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 119 | 6.5565 | 1 | 0.001495 | 10.978576 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 120 | 6.6116 | 1 | 0.001497 | 11.027401 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 121 | 6.6667 | 1 | 0.001487 | 11.056618 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 122 | 6.7218 | 1 | 0.001492 | 10.946566 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 123 | 6.7769 | 1 | 0.001492 | 10.977270 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 124 | 6.8320 | 1 | 0.001466 | 11.212596 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 125 | 6.8871 | 1 | 0.001493 | 10.996106 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 126 | 6.9421 | 1 | 0.001480 | 11.018607 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 127 | 6.9972 | 1 | 0.001509 | 10.976320 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 128 | 7.0523 | 1 | 0.001329 | 12.417034 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 129 | 7.1074 | 1 | 0.001510 | 10.938081 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 130 | 7.1625 | 1 | 0.001496 | 10.964072 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 131 | 7.2176 | 1 | 0.001497 | 11.006588 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 132 | 7.2727 | 1 | 0.001493 | 11.018465 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 133 | 7.3278 | 1 | 0.001493 | 11.030553 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 134 | 7.3829 | 1 | 0.001490 | 11.034491 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 135 | 7.4380 | 1 | 0.001493 | 10.942718 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 136 | 7.4931 | 1 | 0.001485 | 11.063141 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 137 | 7.5482 | 1 | 0.001490 | 10.940797 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 138 | 7.6033 | 1 | 0.001496 | 11.094267 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 139 | 7.6584 | 1 | 0.001476 | 11.092305 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 140 | 7.7135 | 1 | 0.001489 | 10.999871 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 141 | 7.7686 | 1 | 0.001486 | 10.969563 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 142 | 7.8237 | 1 | 0.001485 | 11.045270 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 143 | 7.8788 | 1 | 0.001493 | 10.999192 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 144 | 7.9339 | 1 | 0.001498 | 11.051950 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 145 | 7.9890 | 1 | 0.001489 | 11.134410 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 146 | 8.0441 | 1 | 0.001474 | 11.101941 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 147 | 8.0992 | 1 | 0.001480 | 11.063681 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 148 | 8.1543 | 1 | 0.001486 | 10.946801 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 149 | 8.2094 | 1 | 0.001484 | 11.076774 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 150 | 8.2645 | 1 | 0.001480 | 11.143664 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 151 | 8.3196 | 1 | 0.001509 | 10.947056 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 152 | 8.3747 | 1 | 0.001447 | 11.226169 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 153 | 8.4298 | 1 | 0.001479 | 11.063754 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 154 | 8.4848 | 1 | 0.001484 | 10.961506 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 155 | 8.5399 | 1 | 0.001497 | 11.050401 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 156 | 8.5950 | 1 | 0.001503 | 11.018204 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 157 | 8.6501 | 1 | 0.001472 | 11.145519 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 158 | 8.7052 | 1 | 0.001486 | 11.037257 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 159 | 8.7603 | 1 | 0.001492 | 11.036405 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 160 | 8.8154 | 1 | 0.001480 | 11.015381 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 161 | 8.8705 | 1 | 0.001498 | 10.979052 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 162 | 8.9256 | 1 | 0.001496 | 11.051611 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 163 | 8.9807 | 1 | 0.001486 | 11.052557 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 164 | 9.0358 | 1 | 0.001491 | 11.034617 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 165 | 9.0909 | 1 | 0.001488 | 11.049273 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 166 | 9.1460 | 1 | 0.001491 | 11.085268 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 167 | 9.2011 | 1 | 0.001503 | 10.958939 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 168 | 9.2562 | 1 | 0.001497 | 11.062020 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 169 | 9.3113 | 1 | 0.001518 | 10.996845 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 170 | 9.3664 | 1 | 0.001470 | 11.209611 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 171 | 9.4215 | 1 | 0.001477 | 11.023668 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 172 | 9.4766 | 1 | 0.001481 | 11.090508 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 173 | 9.5317 | 1 | 0.001512 | 10.958598 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 174 | 9.5868 | 1 | 0.001472 | 11.093911 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 175 | 9.6419 | 1 | 0.001495 | 11.022321 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 176 | 9.6970 | 1 | 0.001497 | 10.963686 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 177 | 9.7521 | 1 | 0.001495 | 11.014677 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 178 | 9.8072 | 1 | 0.001494 | 10.971079 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 179 | 9.8623 | 1 | 0.001478 | 11.075295 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 180 | 9.9174 | 1 | 0.001492 | 10.967837 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 181 | 9.9725 | 1 | 0.001502 | 11.002055 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 182 |10.0275 | 1 | 0.001478 | 11.256881 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 183 |10.0826 | 1 | 0.001503 | 10.965836 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 184 |10.1377 | 1 | 0.001492 | 11.003513 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 185 |10.1928 | 1 | 0.001499 | 11.033890 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 186 |10.2479 | 1 | 0.001477 | 11.086396 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 187 |10.3030 | 1 | 0.001494 | 11.022237 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 188 |10.3581 | 1 | 0.001488 | 11.065405 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 189 |10.4132 | 1 | 0.001479 | 11.172747 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 190 |10.4683 | 1 | 0.001488 | 11.135500 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 191 |10.5234 | 1 | 0.001485 | 10.995766 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 192 |10.5785 | 1 | 0.001494 | 10.953639 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 193 |10.6336 | 1 | 0.001492 | 11.006385 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 194 |10.6887 | 1 | 0.001384 | 11.898180 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 195 |10.7438 | 1 | 0.001505 | 10.971906 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 196 |10.7989 | 1 | 0.001506 | 10.982670 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 197 |10.8540 | 1 | 0.001324 | 12.325860 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 198 |10.9091 | 1 | 0.001502 | 11.026861 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 199 |10.9642 | 1 | 0.001505 | 10.987199 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 200 |11.0193 | 1 | 0.001488 | 11.061289 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 201 |11.0744 | 1 | 0.001489 | 11.049199 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 202 |11.1295 | 1 | 0.001501 | 10.973437 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 203 |11.1846 | 1 | 0.001500 | 10.937448 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 204 |11.2397 | 1 | 0.001499 | 10.940185 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 205 |11.2948 | 1 | 0.001506 | 10.956871 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 206 |11.3499 | 1 | 0.001496 | 10.959225 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 207 |11.4050 | 1 | 0.001380 | 11.911324 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 208 |11.4601 | 1 | 0.001505 | 10.983367 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 209 |11.5152 | 1 | 0.001483 | 11.116040 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 210 |11.5702 | 1 | 0.001499 | 10.946843 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 211 |11.6253 | 1 | 0.001495 | 11.007702 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 212 |11.6804 | 1 | 0.001484 | 11.036537 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 213 |11.7355 | 1 | 0.001501 | 10.962850 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 214 |11.7906 | 1 | 0.001458 | 11.231765 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 215 |11.8457 | 1 | 0.001500 | 10.974388 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 216 |11.9008 | 1 | 0.001502 | 10.971881 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 217 |11.9559 | 1 | 0.001484 | 11.094227 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 218 |12.0110 | 1 | 0.001465 | 11.285769 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 219 |12.0661 | 1 | 0.001472 | 11.138884 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 220 |12.1212 | 1 | 0.001462 | 11.085258 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 221 |12.1763 | 1 | 0.001506 | 10.962956 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 222 |12.2314 | 1 | 0.001481 | 11.063845 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 223 |12.2865 | 1 | 0.001490 | 10.940562 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 224 |12.3416 | 1 | 0.001487 | 11.074080 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 225 |12.3967 | 1 | 0.001500 | 10.966088 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 226 |12.4518 | 1 | 0.001503 | 10.940730 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 227 |12.5069 | 1 | 0.001500 | 10.983767 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 228 |12.5620 | 1 | 0.001495 | 11.087621 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 229 |12.6171 | 1 | 0.001491 | 11.030768 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 230 |12.6722 | 1 | 0.001501 | 10.986019 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 231 |12.7273 | 1 | 0.001471 | 11.210606 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 232 |12.7824 | 1 | 0.001496 | 10.989540 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 233 |12.8375 | 1 | 0.001479 | 10.991125 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 234 |12.8926 | 1 | 0.001484 | 10.997315 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 235 |12.9477 | 1 | 0.001495 | 10.981242 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 236 |13.0028 | 1 | 0.001494 | 11.034151 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 237 |13.0579 | 1 | 0.001521 | 11.393696 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 238 |13.1129 | 1 | 0.001483 | 11.187673 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 239 |13.1680 | 1 | 0.001476 | 11.165030 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 240 |13.2231 | 1 | 0.001461 | 11.121420 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 241 |13.2782 | 1 | 0.001497 | 11.077922 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 242 |13.3333 | 1 | 0.001472 | 11.274707 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 243 |13.3884 | 1 | 0.001477 | 11.087600 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 244 |13.4435 | 1 | 0.001469 | 11.061153 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 245 |13.4986 | 1 | 0.001449 | 11.292755 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 246 |13.5537 | 1 | 0.001495 | 11.001245 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 247 |13.6088 | 1 | 0.001493 | 11.024726 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 248 |13.6639 | 1 | 0.001480 | 10.968597 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 249 |13.7190 | 1 | 0.001478 | 11.008988 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 250 |13.7741 | 1 | 0.001464 | 11.120604 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 251 |13.8292 | 1 | 0.001494 | 10.976703 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 252 |13.8843 | 1 | 0.001464 | 11.173856 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 253 |13.9394 | 1 | 0.001478 | 11.182188 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 254 |13.9945 | 1 | 0.001474 | 11.138903 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 255 |14.0496 | 1 | 0.001498 | 10.998538 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 256 |14.1047 | 1 | 0.001490 | 10.959735 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 257 |14.1598 | 1 | 0.001497 | 11.015843 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 258 |14.2149 | 1 | 0.001442 | 11.296236 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 259 |14.2700 | 1 | 0.001470 | 11.035043 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 260 |14.3251 | 1 | 0.001499 | 11.025067 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 261 |14.3802 | 1 | 0.001483 | 11.032883 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 262 |14.4353 | 1 | 0.001450 | 11.225693 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 263 |14.4904 | 1 | 0.001490 | 11.049877 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 264 |14.5455 | 1 | 0.001500 | 10.961913 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 265 |14.6006 | 1 | 0.001468 | 11.227395 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 266 |14.6556 | 1 | 0.001500 | 10.950821 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 267 |14.7107 | 1 | 0.001496 | 11.034819 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 268 |14.7658 | 1 | 0.001478 | 11.039118 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 269 |14.8209 | 1 | 0.001480 | 11.054862 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 270 |14.8760 | 1 | 0.001499 | 10.966170 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 271 |14.9311 | 1 | 0.001492 | 11.013549 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 272 |14.9862 | 1 | 0.001487 | 11.063011 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 273 |15.0413 | 1 | 0.001494 | 11.025787 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 274 |15.0964 | 1 | 0.001492 | 11.056323 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 275 |15.1515 | 1 | 0.001502 | 11.017958 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 276 |15.2066 | 1 | 0.001498 | 10.993303 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 277 |15.2617 | 1 | 0.001492 | 11.045624 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 278 |15.3168 | 1 | 0.001488 | 11.001706 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 279 |15.3719 | 1 | 0.001501 | 11.019076 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 280 |15.4270 | 1 | 0.001482 | 10.980229 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 281 |15.4821 | 1 | 0.001500 | 10.990641 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 282 |15.5372 | 1 | 0.001482 | 11.039660 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 283 |15.5923 | 1 | 0.001506 | 10.960431 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 284 |15.6474 | 1 | 0.001483 | 11.035762 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 285 |15.7025 | 1 | 0.001483 | 10.972536 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 286 |15.7576 | 1 | 0.001497 | 11.078446 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 287 |15.8127 | 1 | 0.001494 | 11.003910 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 288 |15.8678 | 1 | 0.001524 | 10.954572 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 289 |15.9229 | 1 | 0.001468 | 11.170064 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 290 |15.9780 | 1 | 0.001466 | 11.078832 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 291 |16.0331 | 1 | 0.001500 | 10.965774 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 292 |16.0882 | 1 | 0.001492 | 10.988034 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 293 |16.1433 | 1 | 0.001498 | 11.034559 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 294 |16.1983 | 1 | 0.001485 | 10.967131 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 295 |16.2534 | 1 | 0.001480 | 11.102506 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 296 |16.3085 | 1 | 0.001504 | 10.998471 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 297 |16.3636 | 1 | 0.001499 | 10.959420 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 298 |16.4187 | 1 | 0.001483 | 11.099791 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 299 |16.4738 | 1 | 0.001493 | 10.974991 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 300 |16.5289 | 1 | 0.001487 | 10.989717 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 301 |16.5840 | 1 | 0.001484 | 11.069229 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 302 |16.6391 | 1 | 0.001503 | 10.985806 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 303 |16.6942 | 1 | 0.001496 | 11.041107 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 304 |16.7493 | 1 | 0.001487 | 10.991144 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 305 |16.8044 | 1 | 0.001492 | 11.005035 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 306 |16.8595 | 1 | 0.001488 | 11.087163 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 307 |16.9146 | 1 | 0.001491 | 11.002862 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 308 |16.9697 | 1 | 0.001519 | 11.018252 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 309 |17.0248 | 1 | 0.001489 | 11.030986 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 310 |17.0799 | 1 | 0.001509 | 11.001859 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 311 |17.1350 | 1 | 0.001492 | 11.019300 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 312 |17.1901 | 1 | 0.001488 | 11.036436 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 313 |17.2452 | 1 | 0.001493 | 11.046922 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 314 |17.3003 | 1 | 0.001485 | 10.976898 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 315 |17.3554 | 1 | 0.001497 | 10.941875 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 316 |17.4105 | 1 | 0.001497 | 11.056621 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 317 |17.4656 | 1 | 0.001471 | 11.117604 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 318 |17.5207 | 1 | 0.001469 | 11.168160 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 319 |17.5758 | 1 | 0.001476 | 11.020628 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 320 |17.6309 | 1 | 0.001490 | 11.020211 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 321 |17.6860 | 1 | 0.001488 | 11.010496 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 322 |17.7410 | 1 | 0.001475 | 11.125369 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 323 |17.7961 | 1 | 0.001494 | 10.955690 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 324 |17.8512 | 1 | 0.001493 | 11.078510 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 325 |17.9063 | 1 | 0.001362 | 12.022863 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 326 |17.9614 | 1 | 0.001489 | 11.021870 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 327 |18.0165 | 1 | 0.001463 | 11.139775 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 328 |18.0716 | 1 | 0.001475 | 11.015395 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 329 |18.1267 | 1 | 0.001475 | 10.995628 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 330 |18.1818 | 1 | 0.001490 | 11.037015 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 331 |18.2369 | 1 | 0.001489 | 10.994272 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 332 |18.2920 | 1 | 0.001485 | 11.023925 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 333 |18.3471 | 1 | 0.001465 | 11.131615 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 334 |18.4022 | 1 | 0.001481 | 10.996215 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 335 |18.4573 | 1 | 0.001493 | 11.042847 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 336 |18.5124 | 1 | 0.001493 | 11.153712 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 337 |18.5675 | 1 | 0.001497 | 10.981005 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 338 |18.6226 | 1 | 0.001490 | 10.993124 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 339 |18.6777 | 1 | 0.001498 | 10.970379 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 340 |18.7328 | 1 | 0.001492 | 10.992345 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 341 |18.7879 | 1 | 0.001492 | 10.998224 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 342 |18.8430 | 1 | 0.001523 | 10.982035 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 343 |18.8981 | 1 | 0.001485 | 11.054384 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 344 |18.9532 | 1 | 0.001486 | 11.027520 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 345 |19.0083 | 1 | 0.001482 | 11.016985 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 346 |19.0634 | 1 | 0.001484 | 11.169659 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 347 |19.1185 | 1 | 0.001476 | 11.164135 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 348 |19.1736 | 1 | 0.001499 | 10.963815 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 349 |19.2287 | 1 | 0.001481 | 11.041115 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 350 |19.2837 | 1 | 0.001478 | 11.025983 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 351 |19.3388 | 1 | 0.001504 | 10.984140 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 352 |19.3939 | 1 | 0.001478 | 11.033161 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 353 |19.4490 | 1 | 0.001490 | 11.040692 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 354 |19.5041 | 1 | 0.001479 | 11.018249 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 355 |19.5592 | 1 | 0.001471 | 10.995813 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 356 |19.6143 | 1 | 0.001478 | 11.009744 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 357 |19.6694 | 1 | 0.001489 | 11.012060 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 358 |19.7245 | 1 | 0.001487 | 11.043458 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 359 |19.7796 | 1 | 0.001492 | 10.996924 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 360 |19.8347 | 1 | 0.001486 | 10.997914 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 361 |19.8898 | 1 | 0.001462 | 11.193126 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 362 |19.9449 | 1 | 0.001476 | 11.131790 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 363 |20.0000 | 1 | 0.001456 | 11.255347 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 364 |20.0551 | 1 | 0.001443 | 11.262457 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 365 |20.1102 | 1 | 0.001442 | 11.282331 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 366 |20.1653 | 1 | 0.001460 | 11.133270 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 367 |20.2204 | 1 | 0.001461 | 11.137590 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 368 |20.2755 | 1 | 0.001458 | 11.279287 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 369 |20.3306 | 1 | 0.001473 | 11.155934 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 370 |20.3857 | 1 | 0.001480 | 11.140440 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 371 |20.4408 | 1 | 0.001464 | 11.196868 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 372 |20.4959 | 1 | 0.001473 | 11.196430 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 373 |20.5510 | 1 | 0.001467 | 11.166742 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 374 |20.6061 | 1 | 0.001488 | 11.095840 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 375 |20.6612 | 1 | 0.001456 | 11.119288 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 376 |20.7163 | 1 | 0.001514 | 10.997535 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 377 |20.7713 | 1 | 0.001500 | 10.973636 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 378 |20.8264 | 1 | 0.001485 | 11.041631 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 379 |20.8815 | 1 | 0.001474 | 11.054704 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 380 |20.9366 | 1 | 0.001505 | 10.956344 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 381 |20.9917 | 1 | 0.001485 | 11.037928 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 382 |21.0468 | 1 | 0.001494 | 11.004072 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 383 |21.1019 | 1 | 0.001460 | 11.191711 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 384 |21.1570 | 1 | 0.001464 | 11.213192 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 385 |21.2121 | 1 | 0.001297 | 12.715977 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 386 |21.2672 | 1 | 0.001473 | 11.214244 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 387 |21.3223 | 1 | 0.001488 | 11.175076 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 388 |21.3774 | 1 | 0.001477 | 11.140157 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 389 |21.4325 | 1 | 0.001476 | 11.217773 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 390 |21.4876 | 1 | 0.001487 | 11.070076 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 391 |21.5427 | 1 | 0.001476 | 11.079977 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 392 |21.5978 | 1 | 0.001497 | 10.963420 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 393 |21.6529 | 1 | 0.001492 | 10.965270 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 394 |21.7080 | 1 | 0.001499 | 11.031488 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 395 |21.7631 | 1 | 0.001379 | 11.928026 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 396 |21.8182 | 1 | 0.001474 | 11.124487 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 397 |21.8733 | 1 | 0.001482 | 11.037149 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 398 |21.9284 | 1 | 0.001491 | 11.062619 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 399 |21.9835 | 1 | 0.001483 | 11.227740 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 400 |22.0386 | 1 | 0.001460 | 11.253708 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 401 |22.0937 | 1 | 0.001474 | 11.210907 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 402 |22.1488 | 1 | 0.001483 | 11.119041 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 403 |22.2039 | 1 | 0.001490 | 11.014906 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 404 |22.2590 | 1 | 0.001499 | 10.956471 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 405 |22.3140 | 1 | 0.001468 | 11.109550 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 406 |22.3691 | 1 | 0.001490 | 10.982853 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 407 |22.4242 | 1 | 0.001478 | 11.193154 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 408 |22.4793 | 1 | 0.001498 | 11.031459 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 409 |22.5344 | 1 | 0.001508 | 10.978516 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 410 |22.5895 | 1 | 0.001481 | 11.028180 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 411 |22.6446 | 1 | 0.001492 | 11.037275 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 412 |22.6997 | 1 | 0.001483 | 10.967960 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 413 |22.7548 | 1 | 0.001493 | 10.990911 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 414 |22.8099 | 1 | 0.001484 | 11.067482 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 415 |22.8650 | 1 | 0.001486 | 10.987234 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 416 |22.9201 | 1 | 0.001453 | 11.105183 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 417 |22.9752 | 1 | 0.001484 | 11.019325 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 418 |23.0303 | 1 | 0.001489 | 11.033711 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 419 |23.0854 | 1 | 0.001486 | 10.961752 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 420 |23.1405 | 1 | 0.001488 | 11.020402 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 421 |23.1956 | 1 | 0.001485 | 10.985927 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 422 |23.2507 | 1 | 0.001484 | 11.122986 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 423 |23.3058 | 1 | 0.001488 | 11.010117 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 424 |23.3609 | 1 | 0.001494 | 11.027276 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 425 |23.4160 | 1 | 0.001498 | 11.002853 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 426 |23.4711 | 1 | 0.001504 | 10.948009 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 427 |23.5262 | 1 | 0.001537 | 10.965587 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 428 |23.5813 | 1 | 0.001480 | 11.023513 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 429 |23.6364 | 1 | 0.001495 | 11.016430 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 430 |23.6915 | 1 | 0.001498 | 10.990407 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 431 |23.7466 | 1 | 0.001482 | 11.029547 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 432 |23.8017 | 1 | 0.001489 | 11.028503 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 433 |23.8567 | 1 | 0.001494 | 10.994521 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 434 |23.9118 | 1 | 0.001497 | 11.033860 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 435 |23.9669 | 1 | 0.001472 | 11.085127 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 436 |24.0220 | 1 | 0.001519 | 10.940756 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 437 |24.0771 | 1 | 0.001477 | 11.058848 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 438 |24.1322 | 1 | 0.001479 | 11.067911 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 439 |24.1873 | 1 | 0.001488 | 11.029004 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 440 |24.2424 | 1 | 0.001497 | 10.977903 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 441 |24.2975 | 1 | 0.001486 | 11.038936 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 442 |24.3526 | 1 | 0.001492 | 11.042946 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 443 |24.4077 | 1 | 0.001492 | 10.970813 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 444 |24.4628 | 1 | 0.001486 | 11.023437 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 445 |24.5179 | 1 | 0.001504 | 10.981979 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 446 |24.5730 | 1 | 0.001487 | 10.943550 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 447 |24.6281 | 1 | 0.001504 | 10.990585 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 448 |24.6832 | 1 | 0.001488 | 11.020756 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 449 |24.7383 | 1 | 0.001502 | 11.020719 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
| 450 |24.7934 | 1 | 0.001490 | 10.944653 | 0.000000 | 0.000000e+00 | 0.000000e+00 |
...Finished
FINISHED - Elapsed time = 5192.1956986 seconds
FINISHED - CPU process time = 38238.0321676 seconds
Postprocessing
This reads 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]
Now we 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['StaticCoupled']['aero_solver_settings']['rho']
uinf = sharpy_output.settings['StaticCoupled']['aero_solver_settings']['velocity_field_input']['u_inf']
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.data_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 0.52
Ct[-] 0.70 0.70