{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Simulation NREL 5MW wind turbine" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%config InlineBackend.figure_format = 'svg'\n", "from IPython.display import Image\n", "url = 'https://raw.githubusercontent.com/ImperialCollegeLondon/sharpy/dev_doc/docs/source/content/example_notebooks/images/turbulence_no_legend.png'\n", "Image(url=url, width=800)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "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." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "OpenFAST: _https://openfast.readthedocs.io_" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "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" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Load the required packages:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Required packages\n", "import numpy as np\n", "import os\n", "import matplotlib.pyplot as plt\n", "\n", "# Required SHARPy modules\n", "import sharpy.sharpy_main\n", "import sharpy.utils.algebra as algebra\n", "import sharpy.utils.generate_cases as gc\n", "import cases.templates.template_wt as template_wt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "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" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "of_rR = np.array([0.20158356, 0.3127131, 0.40794048, 0.5984148, 0.6936519, 0.85238045, 0.899999, 0.95555407, 0.98729974, 1.0])\n", "of_cNdrR = np.array([0.08621394, 0.14687876, 0.19345148, 0.2942731, 0.36003628, 0.43748564, 0.44762507, 0.38839236, 0.29782477, 0.0])\n", "of_cTdrR = np.array([0.048268348, 0.051957503, 0.05304592, 0.052862607, 0.056001827, 0.0536646, 0.050112925, 0.038993906, 0.023664437, 0.0])\n", "\n", "of_ct = 0.69787693\n", "of_cp = 0.48813498" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Create SHARPy case" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Definition of parameters" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# Mathematical constants\n", "deg2rad = np.pi/180.\n", "\n", "# Case\n", "case = 'rotor'\n", "# route = os.path.dirname(os.path.realpath(__file__)) + '/'\n", "route = './'\n", "\n", "# Geometry discretization\n", "chord_panels = np.array([8], dtype=int)\n", "revs_in_wake = 5\n", "\n", "# Operation\n", "rotation_velocity = 12.1*2*np.pi/60\n", "pitch_deg = 0. #degrees\n", "\n", "# Wind\n", "WSP = 12.\n", "air_density = 1.225\n", "\n", "# Simulation\n", "dphi = 4.*deg2rad\n", "revs_to_simulate = 5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Computation of associated parameters" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "dt = dphi/rotation_velocity\n", "time_steps = int(revs_to_simulate*2.*np.pi/dphi)\n", "mstar = int(revs_in_wake*2.*np.pi/dphi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generation of the rotor geometry based on the information in the excel file" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[33mrotor_from_excel_type02 is obsolete! rotor_from_excel_type03 instead!\u001b[0m\n", "\u001b[33mWARNING: The poisson cofficient is assumed equal to 0.3\u001b[0m\n", "\u001b[33mWARNING: Cross-section area is used as shear area\u001b[0m\n", "\u001b[33mWARNING: Using perpendicular axis theorem to compute the inertia around xB\u001b[0m\n", "\u001b[33mWARNING: Replacing node 49 by node 0\u001b[0m\n", "\u001b[33mWARNING: Replacing node 98 by node 0\u001b[0m\n" ] } ], "source": [ "rotor = template_wt.rotor_from_excel_type02(\n", " chord_panels,\n", " rotation_velocity,\n", " pitch_deg,\n", " excel_file_name= 'source/type02_db_NREL5MW_v01.xlsx',\n", " excel_sheet_parameters = 'parameters',\n", " excel_sheet_structural_blade = 'structural_blade',\n", " excel_sheet_discretization_blade = 'discretization_blade',\n", " excel_sheet_aero_blade = 'aero_blade',\n", " excel_sheet_airfoil_info = 'airfoil_info',\n", " excel_sheet_airfoil_coord = 'airfoil_coord',\n", " m_distribution = 'uniform',\n", " n_points_camber = 100,\n", " tol_remove_points = 1e-8,\n", " wsp = WSP,\n", " dt = dt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "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." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "steady simulation? False\n" ] } ], "source": [ "steady_simulation = False\n", "print(\"steady simulation? \", steady_simulation)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "SimInfo = gc.SimulationInformation()\n", "SimInfo.set_default_values()\n", "\n", "if steady_simulation:\n", " SimInfo.solvers['SHARPy']['flow'] = ['BeamLoader',\n", " 'AerogridLoader',\n", " 'StaticCoupledRBM',\n", " 'BeamPlot',\n", " 'AerogridPlot', \n", " 'SaveData'] \n", "else:\n", " SimInfo.solvers['SHARPy']['flow'] = ['BeamLoader',\n", " 'AerogridLoader',\n", " 'StaticCoupledRBM',\n", " 'DynamicCoupled']\n", "SimInfo.solvers['SHARPy']['case'] = case\n", "SimInfo.solvers['SHARPy']['route'] = route\n", "SimInfo.solvers['SHARPy']['write_log'] = True\n", "SimInfo.set_variable_all_dicts('dt', dt)\n", "SimInfo.set_variable_all_dicts('rho', air_density)\n", "\n", "SimInfo.solvers['SteadyVelocityField']['u_inf'] = WSP\n", "SimInfo.solvers['SteadyVelocityField']['u_inf_direction'] = np.array([0., 0., 1.])\n", "SimInfo.set_variable_all_dicts('velocity_field_input', SimInfo.solvers['SteadyVelocityField'])\n", "\n", "SimInfo.solvers['BeamLoader']['unsteady'] = 'on'\n", "\n", "SimInfo.solvers['AerogridLoader']['unsteady'] = 'on'\n", "SimInfo.solvers['AerogridLoader']['mstar'] = mstar\n", "SimInfo.solvers['AerogridLoader']['freestream_dir'] = np.array([0.,0.,0.])\n", "# added helicoidalwake per suggestion:\n", "SimInfo.solvers['AerogridLoader']['wake_shape_generator'] = 'HelicoidalWake'\n", "SimInfo.solvers['AerogridLoader']['wake_shape_generator_input'] = {'u_inf': WSP,\n", " 'u_inf_direction': np.array([0., 0., 1.]),\n", " 'dt': dt,\n", " 'rotation_velocity': rotation_velocity*np.array([0., 0., 1.])}\n", "\n", "\n", "\n", "SimInfo.solvers['StaticCoupledRBM']['structural_solver'] = 'RigidDynamicPrescribedStep'\n", "SimInfo.solvers['StaticCoupledRBM']['structural_solver_settings'] = SimInfo.solvers['RigidDynamicPrescribedStep']\n", "#SimInfo.solvers['StaticCoupledRBM']['aero_solver'] = 'SHWUvlm'\n", "SimInfo.solvers['StaticCoupledRBM']['aero_solver'] = 'StaticUvlm'\n", "SimInfo.solvers['StaticCoupledRBM']['aero_solver_settings'] = SimInfo.solvers['StaticUvlm']\n", "\n", "SimInfo.solvers['StaticCoupledRBM']['tolerance'] = 1e-8\n", "SimInfo.solvers['StaticCoupledRBM']['n_load_steps'] = 0\n", "SimInfo.solvers['StaticCoupledRBM']['relaxation_factor'] = 0.\n", "\n", "#SimInfo.solvers['SHWUvlm']['convection_scheme'] = 2\n", "#SimInfo.solvers['SHWUvlm']['num_cores'] = 8\n", "#SimInfo.solvers['SHWUvlm']['rot_vel'] = rotation_velocity\n", "#SimInfo.solvers['SHWUvlm']['rot_axis'] = np.array([0.,0.,1.])\n", "#SimInfo.solvers['SHWUvlm']['rot_center'] = np.zeros((3),)\n", "#SimInfo.solvers['SHWUvlm']['velocity_field_generator'] = 'SteadyVelocityField'\n", "#SimInfo.solvers['SHWUvlm']['velocity_field_input'] = SimInfo.solvers['SteadyVelocityField']\n", "SimInfo.solvers['StaticUvlm']['horseshoe'] = False\n", "SimInfo.solvers['StaticUvlm']['num_cores'] = 14\n", "SimInfo.solvers['StaticUvlm']['n_rollup'] = 0\n", "SimInfo.solvers['StaticUvlm']['rollup_dt'] = dt\n", "SimInfo.solvers['StaticUvlm']['rollup_aic_refresh'] = 1\n", "SimInfo.solvers['StaticUvlm']['rollup_tolerance'] = 1e-8\n", "SimInfo.solvers['StaticUvlm']['rbm_vel_g'] = np.array([0., 0., 0.,\n", " 0., 0., rotation_velocity])\n", "\n", "\n", "SimInfo.solvers['SaveData']['compress_float'] = True\n", " \n", "# Only used for steady_simulation = False\n", "SimInfo.solvers['StepUvlm']['convection_scheme'] = 3\n", "SimInfo.solvers['StepUvlm']['num_cores'] = 14\n", "SimInfo.solvers['StepUvlm']['velocity_field_generator'] = 'SteadyVelocityField'\n", "SimInfo.solvers['StepUvlm']['velocity_field_input'] = SimInfo.solvers['SteadyVelocityField']\n", "\n", "SimInfo.solvers['DynamicCoupled']['structural_solver'] = 'RigidDynamicPrescribedStep'\n", "SimInfo.solvers['DynamicCoupled']['structural_solver_settings'] = SimInfo.solvers['RigidDynamicPrescribedStep']\n", "SimInfo.solvers['DynamicCoupled']['aero_solver'] = 'StepUvlm'\n", "SimInfo.solvers['DynamicCoupled']['aero_solver_settings'] = SimInfo.solvers['StepUvlm']\n", "SimInfo.solvers['DynamicCoupled']['postprocessors'] = ['BeamPlot', 'AerogridPlot', 'Cleanup', 'SaveData']\n", "SimInfo.solvers['DynamicCoupled']['postprocessors_settings'] = {'BeamPlot': SimInfo.solvers['BeamPlot'],\n", " 'AerogridPlot': SimInfo.solvers['AerogridPlot'],\n", " 'Cleanup': SimInfo.solvers['Cleanup'],\n", " 'SaveData': SimInfo.solvers['SaveData']}\n", "SimInfo.solvers['DynamicCoupled']['minimum_steps'] = 0\n", "SimInfo.solvers['DynamicCoupled']['include_unsteady_force_contribution'] = True\n", "SimInfo.solvers['DynamicCoupled']['relaxation_factor'] = 0.\n", "SimInfo.solvers['DynamicCoupled']['final_relaxation_factor'] = 0.\n", "SimInfo.solvers['DynamicCoupled']['dynamic_relaxation'] = False\n", "SimInfo.solvers['DynamicCoupled']['relaxation_steps'] = 0\n", "\n", "# Define dynamic simulation (used regardless the value of \"steady_simulation\" variable)\n", "SimInfo.define_num_steps(time_steps)\n", "SimInfo.with_forced_vel = True\n", "SimInfo.for_vel = np.zeros((time_steps,6), dtype=float)\n", "SimInfo.for_vel[:,5] = rotation_velocity\n", "SimInfo.for_acc = np.zeros((time_steps,6), dtype=float)\n", "SimInfo.with_dynamic_forces = True\n", "SimInfo.dynamic_forces = np.zeros((time_steps,rotor.StructuralInformation.num_node,6), dtype=float)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generate simulation files" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "gc.clean_test_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n", "rotor.generate_h5_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n", "SimInfo.generate_solver_file()\n", "SimInfo.generate_dyn_file(time_steps)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Run SHARPy case" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "--------------------------------------------------------------------------------\u001b[0m\n", " ###### ## ## ### ######## ######## ## ##\u001b[0m\n", " ## ## ## ## ## ## ## ## ## ## ## ##\u001b[0m\n", " ## ## ## ## ## ## ## ## ## ####\u001b[0m\n", " ###### ######### ## ## ######## ######## ##\u001b[0m\n", " ## ## ## ######### ## ## ## ##\u001b[0m\n", " ## ## ## ## ## ## ## ## ## ##\u001b[0m\n", " ###### ## ## ## ## ## ## ## ##\u001b[0m\n", "--------------------------------------------------------------------------------\u001b[0m\n", "Aeroelastics Lab, Aeronautics Department.\u001b[0m\n", " Copyright (c), Imperial College London.\u001b[0m\n", " All rights reserved.\u001b[0m\n", " License available at https://github.com/imperialcollegelondon/sharpy\u001b[0m\n", "\u001b[36mRunning SHARPy from /home/wm/src/sharpy/docs/source/content/example_notebooks\u001b[0m\n", "\u001b[36mSHARPy being run is in /home/wm/src/sharpy\u001b[0m\n", "\u001b[36mThe branch being run is master\u001b[0m\n", "\u001b[36mThe version and commit hash are: v1.2-2-g6dc2353b-6dc2353b\u001b[0m\n", "\u001b[36mThe available solvers on this session are:\u001b[0m\n", "\u001b[36m_BaseStructural \u001b[0m\n", "\u001b[36mAerogridLoader \u001b[0m\n", "\u001b[36mBeamLoader \u001b[0m\n", "\u001b[36mDynamicCoupled \u001b[0m\n", "\u001b[36mDynamicUVLM \u001b[0m\n", "\u001b[36mLinDynamicSim \u001b[0m\n", "\u001b[36mLinearAssembler \u001b[0m\n", "\u001b[36mModal \u001b[0m\n", "\u001b[36mNoAero \u001b[0m\n", "\u001b[36mNonLinearDynamic \u001b[0m\n", "\u001b[36mNonLinearDynamicCoupledStep \u001b[0m\n", "\u001b[36mNonLinearDynamicMultibody \u001b[0m\n", "\u001b[36mNonLinearDynamicPrescribedStep \u001b[0m\n", "\u001b[36mNonLinearStatic \u001b[0m\n", "\u001b[36mNonLinearStaticMultibody \u001b[0m\n", "\u001b[36mPrescribedUvlm \u001b[0m\n", "\u001b[36mRigidDynamicPrescribedStep \u001b[0m\n", "\u001b[36mStaticCoupled \u001b[0m\n", "\u001b[36mStaticCoupledRBM \u001b[0m\n", "\u001b[36mStaticTrim \u001b[0m\n", "\u001b[36mStaticUvlm \u001b[0m\n", "\u001b[36mStepLinearUVLM \u001b[0m\n", "\u001b[36mStepUvlm \u001b[0m\n", "\u001b[36mTrim \u001b[0m\n", "\u001b[36mAeroForcesCalculator \u001b[0m\n", "\u001b[36mAerogridPlot \u001b[0m\n", "\u001b[36mAsymptoticStability \u001b[0m\n", "\u001b[36mBeamLoads \u001b[0m\n", "\u001b[36mBeamPlot \u001b[0m\n", "\u001b[36mCleanup \u001b[0m\n", "\u001b[36mCreateSnapshot \u001b[0m\n", "\u001b[36mFrequencyResponse \u001b[0m\n", "\u001b[36mLiftDistribution \u001b[0m\n", "\u001b[36mPickleData \u001b[0m\n", "\u001b[36mPlotFlowField \u001b[0m\n", "\u001b[36mSaveData \u001b[0m\n", "\u001b[36mSaveParametricCase \u001b[0m\n", "\u001b[36mStallCheck \u001b[0m\n", "\u001b[36mUDPout \u001b[0m\n", "\u001b[36mWriteVariablesTime \u001b[0m\n", "\u001b[36mPreSharpy \u001b[0m\n", "\u001b[36mGenerating an instance of BeamLoader\u001b[0m\n", "\u001b[36mGenerating an instance of AerogridLoader\u001b[0m\n", "Variable dphi1 has no assigned value in the settings file.\u001b[0m\n", "\u001b[34m will default to the value: -1.0\u001b[0m\n", "Variable ndphi1 has no assigned value in the settings file.\u001b[0m\n", "\u001b[34m will default to the value: 1\u001b[0m\n", "Variable r has no assigned value in the settings file.\u001b[0m\n", "\u001b[34m will default to the value: 1.0\u001b[0m\n", "Variable dphimax has no assigned value in the settings file.\u001b[0m\n", "\u001b[34m will default to the value: -1.0\u001b[0m\n", "Variable shear_direction has no assigned value in the settings file.\u001b[0m\n", "\u001b[34m will default to the value: [1. 0. 0.]\u001b[0m\n", "Variable shear_exp has no assigned value in the settings file.\u001b[0m\n", "\u001b[34m will default to the value: 0.0\u001b[0m\n", "Variable h_ref has no assigned value in the settings file.\u001b[0m\n", "\u001b[34m will default to the value: 1.0\u001b[0m\n", "Variable h_corr has no assigned value in the settings file.\u001b[0m\n", "\u001b[34m will default to the value: 1.0\u001b[0m\n", "\u001b[34mThe aerodynamic grid contains 3 surfaces\u001b[0m\n", "\u001b[34m Surface 0, M=8, N=48\u001b[0m\n", " Wake 0, M=450, N=48\u001b[0m\n", "\u001b[34m Surface 1, M=8, N=48\u001b[0m\n", " Wake 1, M=450, N=48\u001b[0m\n", "\u001b[34m Surface 2, M=8, N=48\u001b[0m\n", " Wake 2, M=450, N=48\u001b[0m\n", " In total: 1152 bound panels\u001b[0m\n", " In total: 64800 wake panels\u001b[0m\n", " Total number of panels = 65952\u001b[0m\n", "\u001b[36mGenerating an instance of StaticCoupledRBM\u001b[0m\n", "\u001b[36mGenerating an instance of RigidDynamicPrescribedStep\u001b[0m\n", "\u001b[36mGenerating an instance of StaticUvlm\u001b[0m\n", "i_step: 0, i_iter: 0\u001b[0m\n", "Resultant forces and moments: (array([-1.69961822e-10, 1.27556632e-10, 8.51720550e+05]), array([1.35041773e-08, 5.00276656e-08, 6.02114324e+06]))\u001b[0m\n", "\u001b[36mGenerating an instance of DynamicCoupled\u001b[0m\n", "\u001b[36mGenerating an instance of RigidDynamicPrescribedStep\u001b[0m\n", "\u001b[36mGenerating an instance of StepUvlm\u001b[0m\n", "\u001b[36mGenerating an instance of BeamPlot\u001b[0m\n", "\u001b[36mGenerating an instance of AerogridPlot\u001b[0m\n", "\u001b[36mGenerating an instance of Cleanup\u001b[0m\n", "\u001b[36mGenerating an instance of SaveData\u001b[0m\n", "Variable save_linear has no assigned value in the settings file.\u001b[0m\n", "\u001b[34m will default to the value: c_bool(False)\u001b[0m\n", "Variable save_linear_uvlm has no assigned value in the settings file.\u001b[0m\n", "\u001b[34m will default to the value: c_bool(False)\u001b[0m\n", "Variable skip_attr has no assigned value in the settings file.\u001b[0m\n", "\u001b[34m 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']]\u001b[0m\n", "Variable format has no assigned value in the settings file.\u001b[0m\n", "\u001b[34m will default to the value: h5\u001b[0m\n", "\u001b[0m\n", "\u001b[0m\n", "\u001b[0m\n", "|=======|========|======|==============|==============|==============|==============|==============|\u001b[0m\n", "| ts | t | iter | struc ratio | iter time | residual vel | FoR_vel(x) | FoR_vel(z) |\u001b[0m\n", "|=======|========|======|==============|==============|==============|==============|==============|\u001b[0m\n", "| 1 | 0.0551 | 1 | 0.000485 | 34.843854 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 2 | 0.1102 | 1 | 0.000410 | 34.761563 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 3 | 0.1653 | 1 | 0.000404 | 34.932218 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 4 | 0.2204 | 1 | 0.000483 | 35.284282 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 5 | 0.2755 | 1 | 0.000406 | 35.083160 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 6 | 0.3306 | 1 | 0.000405 | 35.132987 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 7 | 0.3857 | 1 | 0.000404 | 35.060116 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 8 | 0.4408 | 1 | 0.000488 | 35.029655 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 9 | 0.4959 | 1 | 0.000467 | 36.258882 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 10 | 0.5510 | 1 | 0.000406 | 35.032129 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 11 | 0.6061 | 1 | 0.000481 | 35.362523 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 12 | 0.6612 | 1 | 0.000411 | 34.975506 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 13 | 0.7163 | 1 | 0.000398 | 35.608281 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 14 | 0.7713 | 1 | 0.000402 | 35.100920 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 15 | 0.8264 | 1 | 0.000410 | 35.017352 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 16 | 0.8815 | 1 | 0.000407 | 35.425095 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 17 | 0.9366 | 1 | 0.000462 | 36.604027 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 18 | 0.9917 | 1 | 0.000401 | 35.275673 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 19 | 1.0468 | 1 | 0.000390 | 36.274420 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 20 | 1.1019 | 1 | 0.000399 | 35.564413 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 21 | 1.1570 | 1 | 0.000397 | 35.707034 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 22 | 1.2121 | 1 | 0.000484 | 35.184307 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 23 | 1.2672 | 1 | 0.000393 | 35.890493 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 24 | 1.3223 | 1 | 0.000402 | 35.255084 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 25 | 1.3774 | 1 | 0.000403 | 35.065845 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 26 | 1.4325 | 1 | 0.000404 | 35.190785 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "| 27 | 1.4876 | 1 | 0.000399 | 35.229580 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 28 | 1.5427 | 1 | 0.000403 | 35.334666 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 29 | 1.5978 | 1 | 0.000402 | 35.127491 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 30 | 1.6529 | 1 | 0.000393 | 36.075205 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 31 | 1.7080 | 1 | 0.000399 | 36.461376 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 32 | 1.7631 | 1 | 0.000401 | 36.586069 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 33 | 1.8182 | 1 | 0.000401 | 35.661475 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 34 | 1.8733 | 1 | 0.000479 | 35.590713 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 35 | 1.9284 | 1 | 0.000401 | 35.274358 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 36 | 1.9835 | 1 | 0.000398 | 35.457478 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 37 | 2.0386 | 1 | 0.000493 | 36.019366 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 38 | 2.0937 | 1 | 0.000401 | 35.421036 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 39 | 2.1488 | 1 | 0.000403 | 35.596356 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 40 | 2.2039 | 1 | 0.000480 | 35.415416 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 41 | 2.2590 | 1 | 0.000396 | 36.031187 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 42 | 2.3140 | 1 | 0.000400 | 35.487847 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 43 | 2.3691 | 1 | 0.000415 | 35.585801 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 44 | 2.4242 | 1 | 0.000402 | 35.510973 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 45 | 2.4793 | 1 | 0.000400 | 35.585651 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 46 | 2.5344 | 1 | 0.000401 | 35.422684 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 47 | 2.5895 | 1 | 0.000401 | 35.797867 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 48 | 2.6446 | 1 | 0.000402 | 35.605142 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 49 | 2.6997 | 1 | 0.000403 | 35.564439 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 50 | 2.7548 | 1 | 0.000404 | 35.421701 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 51 | 2.8099 | 1 | 0.000399 | 35.504787 | 0.000000 | 0.000000e+00 | 0.000000e+00 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| 3.4160 | 1 | 0.000406 | 34.949019 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 63 | 3.4711 | 1 | 0.000405 | 34.993716 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 64 | 3.5262 | 1 | 0.000404 | 35.043047 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 65 | 3.5813 | 1 | 0.000487 | 35.074952 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 66 | 3.6364 | 1 | 0.000396 | 35.737198 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 67 | 3.6915 | 1 | 0.000402 | 35.036806 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 68 | 3.7466 | 1 | 0.000403 | 35.025218 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 69 | 3.8017 | 1 | 0.000397 | 35.635562 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 70 | 3.8567 | 1 | 0.000480 | 35.045761 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 71 | 3.9118 | 1 | 0.000405 | 35.053802 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 72 | 3.9669 | 1 | 0.000404 | 35.034261 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 73 | 4.0220 | 1 | 0.000401 | 35.563820 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 74 | 4.0771 | 1 | 0.000409 | 35.004013 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 75 | 4.1322 | 1 | 0.000406 | 34.937238 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 76 | 4.1873 | 1 | 0.000400 | 35.550421 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 77 | 4.2424 | 1 | 0.000402 | 35.059801 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 78 | 4.2975 | 1 | 0.000403 | 35.040280 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 79 | 4.3526 | 1 | 0.000398 | 35.126306 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 80 | 4.4077 | 1 | 0.000404 | 35.013848 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 81 | 4.4628 | 1 | 0.000404 | 34.998984 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 82 | 4.5179 | 1 | 0.000398 | 35.593557 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 83 | 4.5730 | 1 | 0.000404 | 35.024937 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 84 | 4.6281 | 1 | 0.000419 | 35.055118 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 85 | 4.6832 | 1 | 0.000404 | 34.900097 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 86 | 4.7383 | 1 | 0.000393 | 35.614877 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 87 | 4.7934 | 1 | 0.000405 | 34.956673 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 88 | 4.8485 | 1 | 0.000406 | 34.979990 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 89 | 4.9036 | 1 | 0.000402 | 35.015081 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 90 | 4.9587 | 1 | 0.000403 | 35.092176 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 91 | 5.0138 | 1 | 0.000401 | 35.046211 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 92 | 5.0689 | 1 | 0.000401 | 35.046779 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 93 | 5.1240 | 1 | 0.000400 | 35.034448 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 94 | 5.1791 | 1 | 0.000398 | 35.034049 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 95 | 5.2342 | 1 | 0.000406 | 34.988538 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 96 | 5.2893 | 1 | 0.000398 | 35.269648 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 97 | 5.3444 | 1 | 0.000404 | 34.972387 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 98 | 5.3994 | 1 | 0.000403 | 35.014380 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 99 | 5.4545 | 1 | 0.000400 | 35.136493 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 100 | 5.5096 | 1 | 0.000405 | 35.056979 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 101 | 5.5647 | 1 | 0.000479 | 35.102823 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 102 | 5.6198 | 1 | 0.000401 | 35.018139 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 103 | 5.6749 | 1 | 0.000403 | 35.111360 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 104 | 5.7300 | 1 | 0.000406 | 35.048090 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 105 | 5.7851 | 1 | 0.000406 | 34.995252 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "| 106 | 5.8402 | 1 | 0.000476 | 35.000510 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 107 | 5.8953 | 1 | 0.000474 | 35.010273 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 108 | 5.9504 | 1 | 0.000405 | 35.016181 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 109 | 6.0055 | 1 | 0.000478 | 35.545543 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 110 | 6.0606 | 1 | 0.000397 | 35.374309 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 111 | 6.1157 | 1 | 0.000404 | 35.005756 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 112 | 6.1708 | 1 | 0.000492 | 35.024691 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 113 | 6.2259 | 1 | 0.000477 | 35.436690 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 114 | 6.2810 | 1 | 0.000405 | 34.969606 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 115 | 6.3361 | 1 | 0.000404 | 34.944303 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 116 | 6.3912 | 1 | 0.000402 | 35.074717 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 117 | 6.4463 | 1 | 0.000408 | 35.166313 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 118 | 6.5014 | 1 | 0.000399 | 35.048361 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 119 | 6.5565 | 1 | 0.000401 | 35.061432 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 120 | 6.6116 | 1 | 0.000404 | 34.953936 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 121 | 6.6667 | 1 | 0.000481 | 35.107045 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 122 | 6.7218 | 1 | 0.000483 | 35.020663 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 123 | 6.7769 | 1 | 0.000406 | 34.999084 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 124 | 6.8320 | 1 | 0.000403 | 35.041239 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 125 | 6.8871 | 1 | 0.000404 | 34.985621 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 126 | 6.9421 | 1 | 0.000404 | 35.015430 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 127 | 6.9972 | 1 | 0.000486 | 35.004876 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 128 | 7.0523 | 1 | 0.000407 | 34.912113 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 129 | 7.1074 | 1 | 0.000488 | 34.950935 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 130 | 7.1625 | 1 | 0.000408 | 34.916967 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 131 | 7.2176 | 1 | 0.000405 | 35.177190 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 132 | 7.2727 | 1 | 0.000420 | 34.986353 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0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 153 | 8.4298 | 1 | 0.000396 | 35.416597 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 154 | 8.4848 | 1 | 0.000402 | 34.964640 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 155 | 8.5399 | 1 | 0.000403 | 34.995596 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 156 | 8.5950 | 1 | 0.000400 | 34.989531 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 157 | 8.6501 | 1 | 0.000481 | 35.020522 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 158 | 8.7052 | 1 | 0.000402 | 35.049288 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 159 | 8.7603 | 1 | 0.000402 | 34.955673 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 160 | 8.8154 | 1 | 0.000404 | 35.006943 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 161 | 8.8705 | 1 | 0.000405 | 35.156192 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 162 | 8.9256 | 1 | 0.000401 | 34.933962 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 163 | 8.9807 | 1 | 0.000403 | 35.109843 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 164 | 9.0358 | 1 | 0.000485 | 35.075494 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 165 | 9.0909 | 1 | 0.000405 | 34.914076 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 166 | 9.1460 | 1 | 0.000402 | 34.943376 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 167 | 9.2011 | 1 | 0.000404 | 34.936707 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 168 | 9.2562 | 1 | 0.000401 | 35.057687 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 169 | 9.3113 | 1 | 0.000402 | 35.012661 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 170 | 9.3664 | 1 | 0.000403 | 35.066586 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 171 | 9.4215 | 1 | 0.000415 | 35.001301 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 172 | 9.4766 | 1 | 0.000407 | 34.982057 | 0.000000 | 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0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 183 |10.0826 | 1 | 0.000409 | 35.083685 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 184 |10.1377 | 1 | 0.000401 | 35.031384 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "| 185 |10.1928 | 1 | 0.000401 | 35.276806 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 186 |10.2479 | 1 | 0.000403 | 35.021602 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 187 |10.3030 | 1 | 0.000404 | 35.106824 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 188 |10.3581 | 1 | 0.000402 | 35.070060 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 189 |10.4132 | 1 | 0.000486 | 35.054683 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 190 |10.4683 | 1 | 0.000405 | 35.109055 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 191 |10.5234 | 1 | 0.000404 | 35.096072 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 192 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1 | 0.000489 | 35.053995 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 203 |11.1846 | 1 | 0.000405 | 34.992125 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 204 |11.2397 | 1 | 0.000406 | 34.938804 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 205 |11.2948 | 1 | 0.000399 | 35.034143 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 206 |11.3499 | 1 | 0.000407 | 35.044612 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 207 |11.4050 | 1 | 0.000403 | 35.059423 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 208 |11.4601 | 1 | 0.000409 | 34.960622 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 209 |11.5152 | 1 | 0.000400 | 34.938379 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 210 |11.5702 | 1 | 0.000404 | 34.967449 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 211 |11.6253 | 1 | 0.000480 | 35.007166 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 212 |11.6804 | 1 | 0.000406 | 34.908820 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 213 |11.7355 | 1 | 0.000404 | 34.946568 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 214 |11.7906 | 1 | 0.000403 | 34.984994 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 215 |11.8457 | 1 | 0.000409 | 34.961272 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 216 |11.9008 | 1 | 0.000484 | 34.983150 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 217 |11.9559 | 1 | 0.000402 | 35.073425 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 218 |12.0110 | 1 | 0.000401 | 35.008107 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 219 |12.0661 | 1 | 0.000488 | 34.999300 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 220 |12.1212 | 1 | 0.000406 | 35.011400 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 221 |12.1763 | 1 | 0.000406 | 34.975334 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 222 |12.2314 | 1 | 0.000404 | 34.891954 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 223 |12.2865 | 1 | 0.000484 | 34.980813 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 224 |12.3416 | 1 | 0.000408 | 34.958210 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 225 |12.3967 | 1 | 0.000403 | 34.964099 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 226 |12.4518 | 1 | 0.000398 | 35.094358 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 227 |12.5069 | 1 | 0.000407 | 34.902481 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 228 |12.5620 | 1 | 0.000413 | 34.985481 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 229 |12.6171 | 1 | 0.000404 | 34.962867 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 230 |12.6722 | 1 | 0.000402 | 34.978417 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 231 |12.7273 | 1 | 0.000403 | 34.979397 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 232 |12.7824 | 1 | 0.000404 | 34.996452 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0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 253 |13.9394 | 1 | 0.000405 | 34.972141 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 254 |13.9945 | 1 | 0.000403 | 35.057171 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 255 |14.0496 | 1 | 0.000406 | 35.073741 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 256 |14.1047 | 1 | 0.000502 | 35.005126 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 257 |14.1598 | 1 | 0.000480 | 35.280310 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 258 |14.2149 | 1 | 0.000475 | 35.065014 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 259 |14.2700 | 1 | 0.000409 | 34.983943 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 260 |14.3251 | 1 | 0.000405 | 35.069824 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 261 |14.3802 | 1 | 0.000402 | 34.937582 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 262 |14.4353 | 1 | 0.000408 | 34.901083 | 0.000000 | 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0.000484 | 34.909251 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 293 |16.1433 | 1 | 0.000398 | 35.118651 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 294 |16.1983 | 1 | 0.000405 | 34.991492 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 295 |16.2534 | 1 | 0.000405 | 34.897498 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 296 |16.3085 | 1 | 0.000482 | 35.025593 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 297 |16.3636 | 1 | 0.000476 | 34.872443 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 298 |16.4187 | 1 | 0.000405 | 34.971136 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 299 |16.4738 | 1 | 0.000481 | 34.960969 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 300 |16.5289 | 1 | 0.000401 | 34.946343 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 301 |16.5840 | 1 | 0.000468 | 34.955198 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 302 |16.6391 | 1 | 0.000405 | 34.928494 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 303 |16.6942 | 1 | 0.000401 | 35.092693 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 304 |16.7493 | 1 | 0.000400 | 34.966226 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 305 |16.8044 | 1 | 0.000398 | 35.555843 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 306 |16.8595 | 1 | 0.000401 | 34.951204 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 307 |16.9146 | 1 | 0.000401 | 34.979698 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 308 |16.9697 | 1 | 0.000403 | 35.018901 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 309 |17.0248 | 1 | 0.000403 | 34.972950 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 310 |17.0799 | 1 | 0.000402 | 34.957216 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 311 |17.1350 | 1 | 0.000404 | 34.929909 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 312 |17.1901 | 1 | 0.000404 | 34.903014 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0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 333 |18.3471 | 1 | 0.000400 | 34.939845 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 334 |18.4022 | 1 | 0.000404 | 34.885150 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 335 |18.4573 | 1 | 0.000402 | 35.058580 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 336 |18.5124 | 1 | 0.000405 | 34.949995 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 337 |18.5675 | 1 | 0.000403 | 35.219875 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 338 |18.6226 | 1 | 0.000408 | 35.057766 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 339 |18.6777 | 1 | 0.000403 | 35.093494 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 340 |18.7328 | 1 | 0.000404 | 34.980430 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 341 |18.7879 | 1 | 0.000474 | 35.082315 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 342 |18.8430 | 1 | 0.000404 | 34.959996 | 0.000000 | 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|23.2507 | 1 | 0.000406 | 34.907677 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 423 |23.3058 | 1 | 0.000409 | 34.941690 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 424 |23.3609 | 1 | 0.000407 | 34.826514 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 425 |23.4160 | 1 | 0.000402 | 34.967844 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 426 |23.4711 | 1 | 0.000408 | 34.917703 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 427 |23.5262 | 1 | 0.000405 | 34.842577 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 428 |23.5813 | 1 | 0.000400 | 34.999124 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 429 |23.6364 | 1 | 0.000403 | 34.861921 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 430 |23.6915 | 1 | 0.000468 | 34.903638 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 431 |23.7466 | 1 | 0.000403 | 34.974015 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 432 |23.8017 | 1 | 0.000405 | 34.988520 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 433 |23.8567 | 1 | 0.000405 | 34.981791 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 434 |23.9118 | 1 | 0.000475 | 34.915171 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 435 |23.9669 | 1 | 0.000406 | 34.957745 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 436 |24.0220 | 1 | 0.000406 | 35.011116 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 437 |24.0771 | 1 | 0.000399 | 34.940656 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 438 |24.1322 | 1 | 0.000408 | 34.928146 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 439 |24.1873 | 1 | 0.000405 | 34.953401 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 440 |24.2424 | 1 | 0.000403 | 34.899574 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 441 |24.2975 | 1 | 0.000403 | 34.973123 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 442 |24.3526 | 1 | 0.000405 | 34.949872 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 443 |24.4077 | 1 | 0.000404 | 34.958560 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 444 |24.4628 | 1 | 0.000406 | 34.936809 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 445 |24.5179 | 1 | 0.000404 | 34.864200 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 446 |24.5730 | 1 | 0.000404 | 35.068376 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 447 |24.6281 | 1 | 0.000404 | 34.851542 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 448 |24.6832 | 1 | 0.000404 | 34.941544 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 449 |24.7383 | 1 | 0.000408 | 34.975950 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "| 450 |24.7934 | 1 | 0.000408 | 34.957740 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\u001b[0m\n", "\u001b[34m...Finished\u001b[0m\n", "\u001b[36mFINISHED - Elapsed time = 16186.9064006 seconds\u001b[0m\n", "\u001b[36mFINISHED - CPU process time = 193852.8039516 seconds\u001b[0m\n" ] } ], "source": [ "sharpy_output = sharpy.sharpy_main.main(['', SimInfo.solvers['SHARPy']['route'] + SimInfo.solvers['SHARPy']['case'] + '.sharpy'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Postprocessing" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Read the structural and aerodynamic information of the last time step" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "tstep = sharpy_output.structure.timestep_info[-1]\n", "astep = sharpy_output.aero.timestep_info[-1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Separate the structure into blades" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "# Define beams\n", "ielem = 0\n", "nblades = np.max(sharpy_output.structure.beam_number) + 1\n", "nodes_blade = []\n", "first_node = 0\n", "for iblade in range(nblades):\n", " nodes_blade.append(np.zeros((sharpy_output.structure.num_node,), dtype=bool))\n", " while sharpy_output.structure.beam_number[ielem] <= iblade:\n", " ielem += 1\n", " if ielem == sharpy_output.structure.num_elem:\n", " break\n", " nodes_blade[iblade][first_node:sharpy_output.structure.connectivities[ielem-1,1]+1] = True\n", " first_node = sharpy_output.structure.connectivities[ielem-1,1]+1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute the radial position of the nodes and initialise the rest of the variables" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "r = []\n", "c = []\n", "dr = []\n", "forces = []\n", "CN_drR = []\n", "CTan_drR = []\n", "CP_drR = []\n", "nodes_num = []\n", "for iblade in range(nblades):\n", " forces.append(tstep.steady_applied_forces[nodes_blade[iblade]].copy())\n", "\n", " nodes_num.append(np.arange(0, sharpy_output.structure.num_node, 1)[nodes_blade[iblade]])\n", "\n", " r.append(np.linalg.norm(tstep.pos[nodes_blade[iblade], :], axis=1))\n", " dr.append(np.zeros(np.sum(nodes_blade[iblade])))\n", " dr[iblade][0] = 0.5*(r[iblade][1]-r[iblade][0])\n", " dr[iblade][-1] = 0.5 * (r[iblade][-1] - r[iblade][-2])\n", " for inode in range(1,len(r[iblade]) - 1):\n", " dr[iblade][inode] = 0.5*(r[iblade][inode+1] - r[iblade][inode-1])\n", "\n", " CN_drR.append(np.zeros(len(r[iblade])))\n", " c.append(np.zeros(len(r[iblade])))\n", " CTan_drR.append(np.zeros(len(r[iblade])))\n", " CP_drR.append(np.zeros(len(r[iblade])))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Transform the loads computed by SHARPy into out-of-plane and in-plane components" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "rho = sharpy_output.settings['StaticCoupledRBM']['aero_solver_settings']['rho'].value\n", "uinf = sharpy_output.settings['StaticCoupledRBM']['aero_solver_settings']['velocity_field_input']['u_inf'].value\n", "R = np.max(r[0])\n", "Cp = 0\n", "Ct = 0\n", "\n", "global_force_factor = 0.5 * rho * uinf** 2 * np.pi * R**2\n", "global_power_factor = global_force_factor*uinf\n", "for iblade in range(nblades):\n", " for inode in range(len(r[iblade])):\n", " forces[iblade][inode, 0] *= 0. # Discard the spanwise component\n", "\n", " node_global_index = nodes_num[iblade][inode]\n", " ielem = sharpy_output.structure.node_master_elem[node_global_index, 0]\n", " inode_in_elem = sharpy_output.structure.node_master_elem[node_global_index, 1]\n", " CAB = algebra.crv2rotation(tstep.psi[ielem, inode_in_elem, :])\n", "\n", " c[iblade][inode] = sharpy_output.aero.aero_dict['chord'][ielem,inode_in_elem]\n", "\n", " forces_AFoR = np.dot(CAB, forces[iblade][inode, 0:3])\n", "\n", " CN_drR[iblade][inode] = forces_AFoR[2]/dr[iblade][inode]*R / global_force_factor\n", " CTan_drR[iblade][inode] = np.linalg.norm(forces_AFoR[0:2])/dr[iblade][inode]*R / global_force_factor\n", " CP_drR[iblade][inode] = np.linalg.norm(forces_AFoR[0:2])/dr[iblade][inode]*R * r[iblade][inode]*rotation_velocity / global_power_factor\n", "\n", " Cp += np.sum(CP_drR[iblade]*dr[iblade]/R)\n", " Ct += np.sum(CN_drR[iblade]*dr[iblade]/R)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot of the loads along the blade" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, list_plots = plt.subplots(1, 2, figsize=(12, 3))\n", "\n", "list_plots[0].grid()\n", "list_plots[0].set_xlabel(\"r/R [-]\")\n", "list_plots[0].set_ylabel(\"CN/d(r/R) [-]\")\n", "list_plots[0].plot(r[0]/R, CN_drR[0], '-', label='SHARPy')\n", "list_plots[0].plot(of_rR, of_cNdrR, '-', label='OpenFAST')\n", "list_plots[0].legend()\n", "\n", "list_plots[1].grid()\n", "list_plots[1].set_xlabel(\"r/R [-]\")\n", "list_plots[1].set_ylabel(\"CT/d(r/R) [-]\")\n", "list_plots[1].plot(r[0]/R, CTan_drR[0], '-', label='SHARPy')\n", "list_plots[1].plot(of_rR, of_cTdrR, '-', label='OpenFAST')\n", "list_plots[1].legend()\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Print the rotor thrust and power coefficients" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OpenFAST SHARPy\n", "Cp[-] 0.49 0.54\n", "Ct[-] 0.70 0.75\n" ] } ], "source": [ "print(\" OpenFAST SHARPy\")\n", "print(\"Cp[-] %.2f %.2f\" % (of_cp, Cp))\n", "print(\"Ct[-] %.2f %.2f\" % (of_ct, Ct))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.5" } }, "nbformat": 4, "nbformat_minor": 4 }