343 lines
14 KiB
Plaintext
343 lines
14 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"\n",
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"from functions.pressure_conversion import pressure_conversion\n",
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"from Ausgleichsbecken.Ausgleichsbecken_class_file import Ausgleichsbecken_class\n",
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"from Druckrohrleitung.Druckrohrleitung_class_file import Druckrohrleitung_class\n",
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"from Turbinen.Turbinen_class_file import Francis_Turbine\n",
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"from Regler.Regler_class_file import PI_controller_class"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"#define constants\n",
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"\n",
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"#Turbine\n",
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"Q_nenn = 0.85 # m³/s\n",
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"p_nenn = pressure_conversion(10.6,'bar','Pa')\n",
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"closing_time = 30. #s\n",
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"\n",
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"# physics\n",
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"g = 9.81 # gravitational acceleration [m/s²]\n",
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"rho = 1000. # density of water [kg/m³]\n",
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"\n",
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"\n",
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"# define controller constants\n",
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"target_level = 8. # m\n",
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"Kp = 0.1\n",
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"Ti = 7.\n",
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"deadband_range = 0.05 # m\n",
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"\n",
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"\n",
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"# pipeline\n",
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"L = (535.+478.) # length of pipeline [m]\n",
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"D = 0.9 # pipe diameter [m]\n",
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"A_pipe = D**2/4*np.pi # pipeline area\n",
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"h_pipe = 105 # hydraulic head without reservoir [m] \n",
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"alpha = np.arcsin(h_pipe/L) # Höhenwinkel der Druckrohrleitung \n",
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"n = 50 # number of pipe segments in discretization\n",
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"f_D = 0.014 # Darcy friction factor\n",
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"c = 500. # propagation velocity of the pressure wave [m/s]\n",
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"# consider prescribing a total simulation time and deducting the number of timesteps from that\n",
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"nt = 9000 # number of time steps after initial conditions\n",
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"\n",
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"# derivatives of the pipeline constants\n",
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"dx = L/n # length of each pipe segment\n",
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"dt = dx/c # timestep according to method of characterisitics\n",
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"nn = n+1 # number of nodes\n",
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"initial_level = target_level # water level in upstream reservoir [m]\n",
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"pl_vec = np.arange(0,nn,1)*dx # pl = pipe-length. position of the nodes on the pipeline\n",
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"t_vec = np.arange(0,nt+1)*dt # time vector\n",
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"h_vec = np.arange(0,nn,1)*h_pipe/n # hydraulic head of pipeline at each node \n",
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"\n",
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"\n",
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"\n",
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"# reservoir\n",
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"# replace influx by vector\n",
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"initial_flux = Q_nenn/1.1 # initial influx of volume to the reservoir [m³/s]\n",
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"initial_pressure_unit = 'Pa' # DO NOT CHANGE! for pressure conversion in print statements and plot labels \n",
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"conversion_pressure_unit = 'bar' # for pressure conversion in print statements and plot labels\n",
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"area_base = 74. # total base are of the cuboid reservoir [m²] \n",
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"area_outflux = A_pipe # outlfux area of the reservoir, given by pipeline area [m²]\n",
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"critical_level_low = 0. # for yet-to-be-implemented warnings[m]\n",
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"critical_level_high = np.inf # for yet-to-be-implemented warnings[m]\n",
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"\n",
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"# make sure e-RK4 method of reservoir has a small enough timestep to avoid runaway numerical error\n",
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"nt_eRK4 = 100 # number of simulation steps of reservoir in between timesteps of pipeline \n",
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"simulation_timestep = dt/nt_eRK4\n",
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"\n",
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"\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"# create objects\n",
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"\n",
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"V = Ausgleichsbecken_class(area_base,area_outflux,critical_level_low,critical_level_high,simulation_timestep)\n",
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"V.set_steady_state(initial_flux,initial_level,conversion_pressure_unit)\n",
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"\n",
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"\n",
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"pipe = Druckrohrleitung_class(L,D,n,alpha,f_D)\n",
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"pipe.set_pressure_propagation_velocity(c)\n",
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"pipe.set_number_of_timesteps(nt)\n",
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"pipe.set_steady_state(initial_flux,initial_level,area_base,pl_vec,h_vec)\n",
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"\n",
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"initial_pressure_turbine = pipe.get_current_pressure_distribution()[-1]\n",
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"\n",
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"T1 = Francis_Turbine(Q_nenn,p_nenn,closing_time,timestep=dt)\n",
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"T1.set_steady_state(initial_flux,initial_pressure_turbine)\n",
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"\n",
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"T_in = Francis_Turbine(Q_nenn,p_nenn,closing_time/2,timestep=dt)\n",
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"T_in.set_steady_state(initial_flux,p_nenn)\n",
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"\n",
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"Pegelregler = PI_controller_class(target_level,deadband_range,Kp,Ti,dt)\n",
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"Pegelregler.control_variable = T1.get_current_LA()\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [],
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"source": [
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"# initialization for timeloop\n",
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"\n",
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"# prepare the vectors in which the pressure and velocity distribution in the pipeline from the previous timestep are stored\n",
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"v_old = pipe.get_current_velocity_distribution()\n",
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"p_old = pipe.get_current_pressure_distribution()\n",
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"\n",
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"# prepare the vectors in which the temporal evolution of the boundary conditions are stored\n",
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" # keep in mind, that the velocity at the turbine and the pressure at the reservoir follow from boundary conditions\n",
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" # reservoir level and flow through turbine\n",
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" # the pressure at the turbine and the velocity at the reservoir are calculated from the method of characteristics\n",
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"v_boundary_res = np.zeros_like(t_vec)\n",
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"v_boundary_tur = np.zeros_like(t_vec)\n",
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"p_boundary_res = np.zeros_like(t_vec)\n",
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"p_boundary_tur = np.zeros_like(t_vec)\n",
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"\n",
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"# prepare the vectors that store the temporal evolution of the level in the reservoir\n",
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"level_vec = np.full(nt+1,initial_level) # level at the end of each pipeline timestep\n",
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"\n",
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"# set the boundary conditions for the first timestep\n",
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"v_boundary_res[0] = v_old[0]\n",
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"v_boundary_tur[0] = v_old[-1] \n",
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"p_boundary_res[0] = p_old[0]\n",
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"p_boundary_tur[0] = p_old[-1]\n",
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"\n",
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"LA_soll_vec = np.full_like(t_vec,T1.get_current_LA())\n",
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"LA_ist_vec = np.full_like(t_vec,T1.get_current_LA())\n",
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"\n",
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"LA_soll_vec2 = np.full_like(t_vec,T_in.get_current_LA())\n",
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"LA_soll_vec2[500:1000] = 0.\n",
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"LA_soll_vec2[1000:1500] = 1. \n",
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"LA_soll_vec2[1500:2000] = 0.\n",
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"LA_soll_vec2[2000:2500] = 0.5 \n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [],
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"source": [
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"%matplotlib qt5\n",
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"# time loop\n",
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"\n",
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"# create a figure and subplots to display the velocity and pressure distribution across the pipeline in each pipeline step\n",
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"fig1,axs1 = plt.subplots(2,1)\n",
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"fig1.suptitle(str(0) +' s / '+str(round(t_vec[-1],2)) + ' s' )\n",
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"axs1[0].set_title('Pressure distribution in pipeline')\n",
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"axs1[1].set_title('Velocity distribution in pipeline')\n",
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"axs1[0].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
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"axs1[0].set_ylabel(r'$p$ ['+conversion_pressure_unit+']')\n",
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"axs1[1].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
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"axs1[1].set_ylabel(r'$v$ [$\\mathrm{m} / \\mathrm{s}$]')\n",
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"lo_00, = axs1[0].plot(pl_vec,pressure_conversion(p_old,initial_pressure_unit, conversion_pressure_unit),marker='.')\n",
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"lo_01, = axs1[1].plot(pl_vec,v_old,marker='.')\n",
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"axs1[0].autoscale()\n",
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"axs1[1].autoscale()\n",
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"\n",
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"fig1.tight_layout()\n",
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"fig1.show()\n",
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"plt.pause(1)\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [],
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"source": [
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"error_vec = np.zeros_like(t_vec)\n",
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"# loop through time steps of the pipeline\n",
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"for it_pipe in range(1,pipe.nt+1):\n",
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"\n",
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" T_in.update_LA(LA_soll_vec2[it_pipe])\n",
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" T_in.set_pressure(p_nenn)\n",
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" V.set_influx(T_in.get_current_Q())\n",
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"\n",
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"# for each pipeline timestep, execute nt_eRK4 timesteps of the reservoir code\n",
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" # set initial conditions for the reservoir time evolution calculted with e-RK4\n",
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" V.set_pressure(p_old[0])\n",
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" V.set_outflux(v_old[0]*area_outflux)\n",
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" # calculate the time evolution of the reservoir level within each pipeline timestep to avoid runaway numerical error\n",
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" for it_res in range(nt_eRK4):\n",
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" V.timestep_reservoir_evolution() \n",
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" level_vec[it_pipe] = V.get_current_level() \n",
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"\n",
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" # get the control variable\n",
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" Pegelregler.update_control_variable(level_vec[it_pipe])\n",
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" LA_soll_vec[it_pipe] = Pegelregler.get_current_control_variable()\n",
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" \n",
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" # change the Leitapparatöffnung based on the target value\n",
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" T1.update_LA(LA_soll_vec[it_pipe])\n",
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" LA_ist_vec[it_pipe] = T1.get_current_LA()\n",
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"\n",
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" T1.set_pressure(p_old[-1])\n",
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" # set boundary conditions for the next timestep of the characteristic method\n",
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" p_boundary_res[it_pipe] = V.get_current_pressure()\n",
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" v_boundary_tur[it_pipe] = 1/A_pipe*T1.get_current_Q()\n",
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"\n",
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" # the the boundary conditions in the pipe.object and thereby calculate boundary pressure at turbine\n",
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" pipe.set_boundary_conditions_next_timestep(p_boundary_res[it_pipe],v_boundary_tur[it_pipe])\n",
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" p_boundary_tur[it_pipe] = pipe.get_current_pressure_distribution()[-1]\n",
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" v_boundary_res[it_pipe] = pipe.get_current_velocity_distribution()[0]\n",
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"\n",
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" error_vec[it_pipe] = abs(v_boundary_res[it_pipe]-V.get_current_outflux()/A_pipe)\n",
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"\n",
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" # perform the next timestep via the characteristic method\n",
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" pipe.timestep_characteristic_method()\n",
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"\n",
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" # prepare for next loop\n",
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" p_old = pipe.get_current_pressure_distribution()\n",
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" v_old = pipe.get_current_velocity_distribution()\n",
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"\n",
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" # plot some stuff\n",
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" # remove line-objects to autoscale axes (there is definetly a better way, but this works ¯\\_(ツ)_/¯ )\n",
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" lo_00.remove()\n",
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" lo_01.remove()\n",
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" # lo_02.remove()\n",
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" # plot new pressure and velocity distribution in the pipeline\n",
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" lo_00, = axs1[0].plot(pl_vec,pressure_conversion(p_old,initial_pressure_unit, conversion_pressure_unit),marker='.',c='blue')\n",
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" lo_01, = axs1[1].plot(pl_vec,v_old,marker='.',c='blue')\n",
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" # lo_02, = axs1[2].plot(level_vec_2,c='blue')\n",
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" fig1.suptitle(str(round(t_vec[it_pipe],2))+ ' s / '+str(round(t_vec[-1],2)) + ' s' )\n",
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" fig1.canvas.draw()\n",
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" fig1.tight_layout()\n",
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" fig1.show()\n",
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" plt.pause(0.001) \n",
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"\n",
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" \n",
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" "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [],
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"source": [
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"# plot time evolution of boundary pressure and velocity as well as the reservoir level\n",
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"\n",
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"fig2,axs2 = plt.subplots(3,2)\n",
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"axs2[0,0].set_title('Pressure reservoir')\n",
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"axs2[0,0].plot(t_vec,pressure_conversion(p_boundary_res,initial_pressure_unit, conversion_pressure_unit))\n",
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"axs2[0,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
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"axs2[0,0].set_ylabel(r'$p$ ['+conversion_pressure_unit+']')\n",
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"\n",
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"axs2[0,1].set_title('Velocity reservoir')\n",
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"axs2[0,1].plot(t_vec,v_boundary_res)\n",
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"axs2[0,1].set_ylim(-2*Q_nenn,+2*Q_nenn)\n",
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"axs2[0,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
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"axs2[0,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n",
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"\n",
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"axs2[1,0].set_title('Pressure turbine')\n",
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"axs2[1,0].plot(t_vec,pressure_conversion(p_boundary_tur,initial_pressure_unit, conversion_pressure_unit))\n",
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"axs2[1,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
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"axs2[1,0].set_ylabel(r'$p$ ['+conversion_pressure_unit+']')\n",
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"\n",
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"axs2[1,1].set_title('Velocity turbine')\n",
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"axs2[1,1].plot(t_vec,v_boundary_tur)\n",
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"axs2[1,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
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"axs2[1,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n",
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"\n",
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"axs2[2,0].set_title('Level reservoir')\n",
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"axs2[2,0].plot(t_vec,level_vec)\n",
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"axs2[2,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
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"axs2[2,0].set_ylabel(r'$h$ [m]')\n",
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"\n",
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"axs2[2,1].set_title('LA')\n",
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"axs2[2,1].plot(t_vec,100*LA_soll_vec)\n",
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"axs2[2,1].plot(t_vec,100*LA_ist_vec)\n",
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"axs2[2,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
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"axs2[2,1].set_ylabel(r'$LA$ [%]')\n",
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"fig2.tight_layout()\n",
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"plt.show()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[<matplotlib.lines.Line2D at 0x1ac81d70af0>]"
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]
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},
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"execution_count": 10,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"plt.semilogy(t_vec,error_vec)"
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]
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}
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],
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"kernelspec": {
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