From 3b095b25985fb3c3f75dd9bda2752fa51eeaa892 Mon Sep 17 00:00:00 2001 From: Brantegger Georg Date: Thu, 9 Feb 2023 15:01:10 +0100 Subject: [PATCH] updated steady state test for the pipeline and visualization of the pressure surge --- .../Druckrohrleitung_test_steady_state.ipynb | 244 +++++++++++++----- .../Druckstoß Visualisierung.ipynb | 40 +-- 2 files changed, 194 insertions(+), 90 deletions(-) diff --git a/Druckrohrleitung/Druckrohrleitung_test_steady_state.ipynb b/Druckrohrleitung/Druckrohrleitung_test_steady_state.ipynb index 084444c..15cecdb 100644 --- a/Druckrohrleitung/Druckrohrleitung_test_steady_state.ipynb +++ b/Druckrohrleitung/Druckrohrleitung_test_steady_state.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": null, + "execution_count": 66, "metadata": {}, "outputs": [], "source": [ @@ -22,7 +22,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 67, "metadata": {}, "outputs": [], "source": [ @@ -80,9 +80,34 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 68, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The pipeline has the following attributes: \n", + "----------------------------- \n", + "Length = 1013.0 m \n", + "Diameter = 0.9 m \n", + "Hydraulic head = 105.0 m \n", + "Number of segments = 50 \n", + "Number of nodes = 51 \n", + "Length per segments = 20.26 m \n", + "Pipeline angle = 0.104 rad \n", + "Pipeline angle = 5.95° \n", + "Darcy friction factor = 0.014 \n", + "Density of liquid = 1000.0 kg/m³ \n", + "Pressure wave vel. = 500.0 m/s \n", + "Simulation timestep = 0.04052 s \n", + "----------------------------- \n", + "Velocity and pressure distribution are vectors and are accessible via the \n", + " get_current_velocity_distribution() and get_current_pressure_distribution() methods of the pipeline object. \n", + " See also get_lowest_XXX_per_node() and get_highest_XXX_per_node() methods.\n" + ] + } + ], "source": [ "# create objects\n", "\n", @@ -93,12 +118,14 @@ "# pipeline\n", "pipe = Druckrohrleitung_class(Pip_length,Pip_dia,Pip_head,Pip_n_seg,Pip_f_D,Pip_pw_vel,Pip_dt,pUnit_conv,rho)\n", "pipe.set_steady_state(flux_init,reservoir.get_current_pressure())\n", - "pipe.get_info()\n" + "pipe.get_info()\n", + "\n", + "p_0 = pipe.get_initial_pressure_distribution()" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 69, "metadata": {}, "outputs": [], "source": [ @@ -106,9 +133,13 @@ "\n", "level_vec = np.zeros_like(t_vec)\n", "level_vec[0] = reservoir.get_current_level()\n", + "volume_vec = np.zeros_like(t_vec) \n", + "volume_vec[0] = reservoir.get_current_volume()\n", + "\n", "\n", "# prepare the vectors in which the pressure and velocity distribution in the pipeline from the previous timestep are stored\n", "v_old = pipe.get_current_velocity_distribution()\n", + "Q_old = pipe.get_current_flux_distribution()\n", "p_old = pipe.get_current_pressure_distribution()\n", "\n", "# prepare the vectors in which the temporal evolution of the boundary conditions are stored\n", @@ -116,51 +147,104 @@ " # through the time evolution of the reservoir respectively \n", " # the pressure at the turbine and the velocity at the reservoir are calculated from the method of characteristics\n", "v_boundary_res = np.zeros_like(t_vec)\n", - "v_boundary_tur = np.zeros_like(t_vec)\n", + "v_boundary_tur = np.full_like(t_vec,v_old[-1])\n", "p_boundary_res = np.zeros_like(t_vec)\n", "p_boundary_tur = np.zeros_like(t_vec)\n", + "Q_boundary_res = np.zeros_like(t_vec)\n", + "Q_boundary_tur = np.zeros_like(t_vec)\n", "\n", "# set the boundary conditions for the first timestep\n", "v_boundary_res[0] = v_old[0]\n", - "v_boundary_tur[0] = v_old[-1] \n", "p_boundary_res[0] = p_old[0]\n", + "Q_boundary_res[0] = Q_old[0]\n", "p_boundary_tur[0] = p_old[-1]\n", - "\n", - "v_boundary_tur[:np.argmin(np.abs(t_vec-100))] = v_old[-1] \n", - "v_boundary_tur[np.argmin(np.abs(t_vec-100)):] = 0\n", - "\n" + "Q_boundary_tur[0] = Q_old[-1]\n" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 70, "metadata": {}, "outputs": [], "source": [ "%matplotlib qt5\n", - "fig1,axs1 = plt.subplots(2,1)\n", + "# create a figure and subplots to display the velocity and pressure distribution across the pipeline in each pipeline step\n", + "fig1,axs1 = plt.subplots(3,1)\n", + "fig1.suptitle(str(0) +' s / '+str(round(t_vec[-1],2)) + ' s' )\n", "axs1[0].set_title('Pressure distribution in pipeline')\n", "axs1[0].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", - "axs1[0].set_ylabel(r'$p$ [mWS]')\n", - "axs1[0].set_ylim([0.9*np.min(pressure_conversion(p_old,'Pa',pUnit_conv)),1.1*np.max(pressure_conversion(p_old,'Pa',pUnit_conv))])\n", - "lo_00, = axs1[0].plot(Pip_x_vec,pressure_conversion(p_old,'Pa',pUnit_conv),marker='.')\n", - "\n", - "axs1[1].set_title('Velocity distribution in pipeline')\n", + "axs1[0].set_ylabel(r'$p$ ['+pUnit_conv+']')\n", + "axs1[0].set_ylim([-2,Pip_head*1.1])\n", + "axs1[1].set_title('Pressure distribution in pipeline \\n Difference to t=0')\n", "axs1[1].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", - "axs1[1].set_ylabel(r'$v$ [m/s]')\n", - "lo_01, = axs1[1].plot(Pip_x_vec,v_old,marker='.')\n", - "axs1[1].autoscale()\n", - "# axs1[1].set_ylim([0.9*np.min(v_old),1.1*np.max(v_boundary_res)])\n", + "axs1[1].set_ylabel(r'$p$ ['+pUnit_conv+']')\n", + "axs1[2].set_title('Flux distribution in pipeline')\n", + "axs1[2].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", + "axs1[2].set_ylabel(r'$Q$ [$\\mathrm{m}^3 / \\mathrm{s}$]')\n", + "# create line objects (lo) whoes values can be updated in time loop to animate the evolution\n", + "lo_0, = axs1[0].plot(Pip_x_vec,pressure_conversion(p_old,pUnit_calc, pUnit_conv),marker='.')\n", + "lo_0min, = axs1[0].plot(Pip_x_vec,pressure_conversion(pipe.get_lowest_pressure_per_node(),pUnit_calc,pUnit_conv),c='red')\n", + "lo_0max, = axs1[0].plot(Pip_x_vec,pressure_conversion(pipe.get_highest_pressure_per_node(),pUnit_calc,pUnit_conv),c='red')\n", + "lo_1, = axs1[1].plot(Pip_x_vec,pressure_conversion(p_old-p_0,pUnit_calc, pUnit_conv),marker='.')\n", + "lo_1min, = axs1[1].plot(Pip_x_vec,pressure_conversion(pipe.get_lowest_pressure_per_node()-p_0,pUnit_calc,pUnit_conv),c='red')\n", + "lo_1max, = axs1[1].plot(Pip_x_vec,pressure_conversion(pipe.get_highest_pressure_per_node()-p_0,pUnit_calc,pUnit_conv),c='red')\n", + "lo_2, = axs1[1].plot(Pip_x_vec,Q_old,marker='.')\n", + "lo_2min, = axs1[2].plot(Pip_x_vec,pipe.get_lowest_flux_per_node(),c='red')\n", + "lo_2max, = axs1[2].plot(Pip_x_vec,pipe.get_highest_flux_per_node(),c='red')\n", + "\n", + "# axs1[0].autoscale()\n", + "# axs1[1].autoscale()\n", "\n", "fig1.tight_layout()\n", - "plt.pause(1)" + "fig1.show()" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 71, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The cuboid reservoir has the following attributes: \n", + "----------------------------- \n", + "Base area = 74.0 m² \n", + "Outflux area = 0.636 m² \n", + "Current level = 8.0 m\n", + "Critical level low = 0.0 m \n", + "Critical level high = inf m \n", + "Volume in reservoir = 592.0 m³ \n", + "Current influx = 0.773 m³/s \n", + "Current outflux = 0.773 m³/s \n", + "Current outflux vel = 1.215 m/s \n", + "Current pipe pressure = 7.854 mWS \n", + "Simulation timestep = 0.001013 s \n", + "Density of liquid = 1000.0 kg/m³ \n", + "----------------------------- \n", + "\n", + "The pipeline has the following attributes: \n", + "----------------------------- \n", + "Length = 1013.0 m \n", + "Diameter = 0.9 m \n", + "Hydraulic head = 105.0 m \n", + "Number of segments = 50 \n", + "Number of nodes = 51 \n", + "Length per segments = 20.26 m \n", + "Pipeline angle = 0.104 rad \n", + "Pipeline angle = 5.95° \n", + "Darcy friction factor = 0.014 \n", + "Density of liquid = 1000.0 kg/m³ \n", + "Pressure wave vel. = 500.0 m/s \n", + "Simulation timestep = 0.04052 s \n", + "----------------------------- \n", + "Velocity and pressure distribution are vectors and are accessible via the \n", + " get_current_velocity_distribution() and get_current_pressure_distribution() methods of the pipeline object. \n", + " See also get_lowest_XXX_per_node() and get_highest_XXX_per_node() methods.\n" + ] + } + ], "source": [ "for it_pipe in range(1,nt+1):\n", "# for each pipeline timestep, execute nt_eRK4 timesteps of the reservoir code\n", @@ -170,8 +254,8 @@ " # calculate the time evolution of the reservoir level within each pipeline timestep to avoid runaway numerical error\n", " for it_res in range(Res_nt):\n", " reservoir.timestep_reservoir_evolution() \n", - " level_vec[it_pipe] = reservoir.get_current_level() \n", - "\n", + " level_vec[it_pipe] = reservoir.get_current_level()\n", + " volume_vec[it_pipe] = reservoir.get_current_volume() \n", " \n", " # set boundary conditions for the next timestep of the characteristic method\n", " p_boundary_res[it_pipe] = reservoir.get_current_pressure()\n", @@ -181,6 +265,8 @@ " pipe.set_boundary_conditions_next_timestep(p_boundary_res[it_pipe],v_boundary_tur[it_pipe])\n", " p_boundary_tur[it_pipe] = pipe.get_current_pressure_distribution()[-1]\n", " v_boundary_res[it_pipe] = pipe.get_current_velocity_distribution()[0]\n", + " Q_boundary_res[it_pipe] = pipe.get_current_flux_distribution()[0]\n", + " Q_boundary_tur[it_pipe] = pipe.get_current_flux_distribution()[-1]\n", "\n", " # perform the next timestep via the characteristic method\n", " pipe.timestep_characteristic_method_vectorized()\n", @@ -191,17 +277,31 @@ "\n", " # plot some stuff\n", " # remove line-objects to autoscale axes (there is definetly a better way, but this works ¯\\_(ツ)_/¯ )\n", - " lo_00.remove()\n", - " lo_01.remove()\n", - " # lo_02.remove()\n", - " # plot new pressure and velocity distribution in the pipeline\n", - " lo_00, = axs1[0].plot(Pip_x_vec,pressure_conversion(p_old,'Pa', pUnit_conv),marker='.',c='blue')\n", - " lo_01, = axs1[1].plot(Pip_x_vec,v_old,marker='.',c='blue')\n", - " \n", - " fig1.suptitle(str(round(t_vec[it_pipe],2)) + '/' + str(round(t_vec[-1],2)))\n", - " fig1.canvas.draw()\n", - " fig1.tight_layout()\n", - " plt.pause(0.000001)\n", + " if it_pipe%50 == 0: # only plot every 50th iteration for performance reasons (plotting takes the most amount of time)\n", + " lo_0.remove()\n", + " lo_0min.remove()\n", + " lo_0max.remove()\n", + " lo_1.remove()\n", + " lo_1min.remove()\n", + " lo_1max.remove()\n", + " lo_2.remove()\n", + " lo_2min.remove()\n", + " lo_2max.remove()\n", + " # plot new pressure and velocity distribution in the pipeline\n", + " lo_0, = axs1[0].plot(Pip_x_vec,pressure_conversion(pipe.get_current_pressure_distribution(),pUnit_calc,pUnit_conv),marker='.',c='blue')\n", + " lo_0min, = axs1[0].plot(Pip_x_vec,pressure_conversion(pipe.get_lowest_pressure_per_node(),pUnit_calc,pUnit_conv),c='red')\n", + " lo_0max, = axs1[0].plot(Pip_x_vec,pressure_conversion(pipe.get_highest_pressure_per_node(),pUnit_calc,pUnit_conv),c='red') \n", + " lo_1, = axs1[1].plot(Pip_x_vec,pressure_conversion(pipe.get_current_pressure_distribution()-p_0,pUnit_calc,pUnit_conv),marker='.',c='blue')\n", + " lo_1min, = axs1[1].plot(Pip_x_vec,pressure_conversion(pipe.get_lowest_pressure_per_node()-p_0,pUnit_calc,pUnit_conv),c='red')\n", + " lo_1max, = axs1[1].plot(Pip_x_vec,pressure_conversion(pipe.get_highest_pressure_per_node()-p_0,pUnit_calc,pUnit_conv),c='red')\n", + " lo_2, = axs1[2].plot(Pip_x_vec,pipe.get_current_flux_distribution(),marker='.',c='blue')\n", + " lo_2min, = axs1[2].plot(Pip_x_vec,pipe.get_lowest_flux_per_node(),c='red')\n", + " lo_2max, = axs1[2].plot(Pip_x_vec,pipe.get_highest_flux_per_node(),c='red')\n", + " fig1.suptitle(str(round(t_vec[it_pipe],2))+ ' s / '+str(round(t_vec[-1],2)) + ' s' )\n", + " fig1.canvas.draw() # force figure output\n", + " fig1.tight_layout()\n", + " fig1.show()\n", + " plt.pause(0.1) \n", "\n", "reservoir.get_info(full=True)\n", "pipe.get_info()" @@ -209,36 +309,56 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 73, "metadata": {}, "outputs": [], "source": [ - "fig2,axs2 = plt.subplots(2,2)\n", - "axs2[0,0].set_title('Pressure Reservoir')\n", - "axs2[0,0].plot(t_vec,pressure_conversion(p_boundary_res,pUnit_calc,pUnit_conv))\n", - "axs2[0,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", - "axs2[0,0].set_ylabel(r'$p$ [mWS]')\n", - "axs2[0,0].set_ylim([0.9*np.min(pressure_conversion(p_boundary_res,pUnit_calc,pUnit_conv)),1.1*np.max(pressure_conversion(p_boundary_res,pUnit_calc,pUnit_conv))])\n", + "level_plot_min = 0\n", + "level_plot_max = 15\n", "\n", - "axs2[0,1].set_title('Velocity Reservoir')\n", - "axs2[0,1].plot(t_vec,v_boundary_res)\n", - "axs2[0,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", - "axs2[0,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n", - "axs2[0,1].set_ylim([0.9*np.min(v_boundary_res),1.1*np.max(v_boundary_res)])\n", + "fig3,axs3 = plt.subplots(2,2,figsize=(16,9))\n", + "fig3.suptitle('Fläche = '+str(Res_area_base)+'\\n'+'Kp = '+str(Con_K_p)+' Ti = '+str(Con_T_i))\n", + "axs3[0,0].set_title('Level and Volume reservoir')\n", + "axs3[0,0].plot(t_vec,level_vec,label='level')\n", + "axs3[0,0].plot(t_vec,np.full_like(t_vec,Res_level_crit_lo),label='level_limit',c='r')\n", + "axs3[0,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs3[0,0].set_ylabel(r'$h$ [m]')\n", + "axs3[0,0].set_ylim(level_plot_min,level_plot_max)\n", + "x_twin_00 = axs3[0,0].twinx()\n", + "x_twin_00.set_ylabel(r'$V$ [$\\mathrm{m}^3$]')\n", + "x_twin_00.plot(t_vec,volume_vec)\n", + "x_twin_00.set_ylim(volume_plot_min,volume_plot_max)\n", + "axs3[0,0].legend()\n", "\n", - "axs2[1,0].set_title('Pressure Turbine')\n", - "axs2[1,0].plot(t_vec,pressure_conversion(p_boundary_tur,pUnit_calc,pUnit_conv))\n", - "axs2[1,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", - "axs2[1,0].set_ylabel(r'$p$ [mWS]')\n", - "axs2[1,0].set_ylim([0.9*np.min(pressure_conversion(p_boundary_tur,pUnit_calc,pUnit_conv)),1.1*np.max(pressure_conversion(p_boundary_tur,pUnit_calc,pUnit_conv))])\n", + "# axs3[0,1].set_title('LA')\n", + "# axs3[0,1].plot(t_vec,100*OL_T1_LA_soll_vec,label='OL_T1 Target',c='b')\n", + "# axs3[0,1].scatter(t_vec[::200],100*OL_T1_LA_ist_vec[::200],label='OL_T1 Actual',c='b',marker='+')\n", + "# axs3[0,1].plot(t_vec,100*OL_T2_LA_soll_vec,label='OL_T2 Target',c='g')\n", + "# axs3[0,1].scatter(t_vec[::200],100*OL_T2_LA_ist_vec[::200],label='OL_T2 Actual',c='g',marker='+')\n", + "# axs3[0,1].plot(t_vec,100*UL_T1_LA_soll_vec,label='UL_T1 Target',c='r')\n", + "# axs3[0,1].scatter(t_vec[::200],100*UL_T1_LA_ist_vec[::200],label='UL_T1 Actual',c='r',marker='+')\n", + "# axs3[0,1].plot(t_vec,100*UL_T2_LA_soll_vec,label='UL_T2 Target',c='k')\n", + "# axs3[0,1].scatter(t_vec[::200],100*UL_T2_LA_ist_vec[::200],label='UL_T2 Actual',c='k',marker='+')\n", + "# axs3[0,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "# axs3[0,1].set_ylabel(r'$LA$ [%]')\n", + "# axs3[0,1].legend()\n", "\n", - "axs2[1,1].set_title('Velocity Turbine')\n", - "axs2[1,1].plot(t_vec,v_boundary_tur)\n", - "axs2[1,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", - "axs2[1,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n", - "axs2[1,1].set_ylim([0.95*np.min(v_boundary_tur),1.05*np.max(v_boundary_tur)])\n", + "axs3[1,0].set_title('Fluxes')\n", + "axs3[1,0].plot(t_vec,np.full_like(t_vec,flux_init),label='Influx')\n", + "axs3[1,0].plot(t_vec,Q_boundary_res,label='Outflux')\n", + "axs3[1,0].scatter(t_vec[::200],Q_boundary_tur[::200],label='Flux Turbine',c='g',marker='+')\n", + "axs3[1,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs3[1,0].set_ylabel(r'$Q$ [$\\mathrm{m}^3/\\mathrm{s}$]')\n", + "axs3[1,0].legend()\n", "\n", - "fig2.tight_layout()\n", + "axs3[1,1].set_title('Pressure change vs t=0 at reservoir and turbine')\n", + "axs3[1,1].plot(t_vec,pressure_conversion(p_boundary_res-p_boundary_res[0],pUnit_calc, pUnit_conv),label='Reservoir')\n", + "axs3[1,1].plot(t_vec,pressure_conversion(p_boundary_tur-p_boundary_tur[0],pUnit_calc, pUnit_conv),label='Turbine')\n", + "axs3[1,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs3[1,1].set_ylabel(r'$p$ ['+pUnit_conv+']')\n", + "axs3[1,1].legend()\n", + "\n", + "fig3.tight_layout()\n", "plt.show()" ] } diff --git a/Druckrohrleitung/Druckstoß Visualisierung.ipynb b/Druckrohrleitung/Druckstoß Visualisierung.ipynb index 880f491..9fb90c9 100644 --- a/Druckrohrleitung/Druckstoß Visualisierung.ipynb +++ b/Druckrohrleitung/Druckstoß Visualisierung.ipynb @@ -6,18 +6,19 @@ "metadata": {}, "outputs": [], "source": [ + "import os\n", + "import sys\n", + "\n", + "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from Druckrohrleitung_class_file import Druckrohrleitung_class\n", - "import matplotlib.pyplot as plt\n", "\n", "#importing pressure conversion function\n", - "import sys\n", - "import os\n", "current = os.path.dirname(os.path.realpath('Main_Programm.ipynb'))\n", "parent = os.path.dirname(current)\n", "sys.path.append(parent)\n", - "from functions.pressure_conversion import pressure_conversion\n", - "from Ausgleichsbecken.Ausgleichsbecken_class_file import Ausgleichsbecken_class" + "from Ausgleichsbecken.Ausgleichsbecken_class_file import Ausgleichsbecken_class\n", + "from functions.pressure_conversion import pressure_conversion" ] }, { @@ -70,7 +71,7 @@ " # for general simulation\n", "flux_init = Tur_Q_nenn/1.1 # [m³/s] initial flux through whole system for steady state initialization \n", "level_init = Con_targetLevel # [m] initial water level in upstream reservoir for steady state initialization\n", - "simTime_target = 3. # [s] target for total simulation time (will vary slightly to fit with Pip_dt)\n", + "simTime_target = 62. # [s] target for total simulation time (will vary slightly to fit with Pip_dt)\n", "nt = int(simTime_target//Pip_dt) # [1] Number of timesteps of the whole system\n", "t_vec = np.arange(0,nt+1,1)*Pip_dt # [s] time vector. At each step of t_vec the system parameters are stored\n" ] @@ -79,23 +80,6 @@ "cell_type": "code", "execution_count": 3, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "61.1829727786757\n" - ] - } - ], - "source": [ - "print(pressure_conversion(600000,'Pa','mWS'))" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, "outputs": [], "source": [ "# create objects\n", @@ -111,7 +95,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -156,7 +140,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ @@ -195,7 +179,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ @@ -226,7 +210,7 @@ " v_old = pipe.get_current_velocity_distribution()\n", "\n", " # plot some stuff\n", - " if it_pipe%100 == 0:\n", + " if it_pipe%200 == 0:\n", " # remove line-objects to autoscale axes (there is definetly a better way, but this works ¯\\_(ツ)_/¯ )\n", " lo_0.remove()\n", " lo_0min.remove()\n", @@ -264,7 +248,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 7, "metadata": {}, "outputs": [], "source": [