{ "cells": [ { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from functions.pressure_conversion import pressure_conversion\n", "from Ausgleichsbecken.Ausgleichsbecken_class_file import Ausgleichsbecken_class\n", "from Druckrohrleitung.Druckrohrleitung_class_file import Druckrohrleitung_class\n", "from Turbinen.Turbinen_class_file import Francis_Turbine\n", "from Regler.Regler_class_file import PI_controller_class" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "#define constants\n", "\n", "#Turbine\n", "Q_nenn = 0.85 # m³/s\n", "p_nenn = pressure_conversion(10.6,'bar','Pa')\n", "closing_time = 70 #s\n", "\n", "# physics\n", "g = 9.81 # gravitational acceleration [m/s²]\n", "rho = 1000. # density of water [kg/m³]\n", "\n", "\n", "# define controller constants\n", "target_level = 8. # m\n", "Kp = 0.1\n", "Ti = 10.\n", "deadband_range = 0.05 # m\n", "\n", "\n", "# pipeline\n", "L = 535.+478. # length of pipeline [m]\n", "D = 0.9 # pipe diameter [m]\n", "A_pipe = D**2/4*np.pi # pipeline area\n", "h_pipe = 105 # hydraulic head without reservoir [m] \n", "alpha = np.arcsin(h_pipe/L) # Höhenwinkel der Druckrohrleitung \n", "n = 50 # number of pipe segments in discretization\n", "f_D = 0.014 # Darcy friction factor\n", "c = 500. # propagation velocity of the pressure wave [m/s]\n", "# consider prescribing a total simulation time and deducting the number of timesteps from that\n", "nt = 1000 # number of time steps after initial conditions\n", "\n", "# derivatives of the pipeline constants\n", "dx = L/n # length of each pipe segment\n", "dt = dx/c # timestep according to method of characterisitics\n", "nn = n+1 # number of nodes\n", "initial_level = target_level # water level in upstream reservoir [m]\n", "pl_vec = np.arange(0,nn,1)*dx # pl = pipe-length. position of the nodes on the pipeline\n", "t_vec = np.arange(0,nt+1)*dt # time vector\n", "h_vec = np.arange(0,nn,1)*h_pipe/n # hydraulic head of pipeline at each node \n", "\n", "\n", "\n", "# reservoir\n", "# replace influx by vector\n", "initial_flux = Q_nenn/1.1 # initial influx of volume to the reservoir [m³/s]\n", "initial_pressure_unit = 'Pa' # DO NOT CHANGE! for pressure conversion in print statements and plot labels \n", "conversion_pressure_unit = 'bar' # for pressure conversion in print statements and plot labels\n", "area_base = 74. # total base are of the cuboid reservoir [m²] \n", "area_outflux = A_pipe # outlfux area of the reservoir, given by pipeline area [m²]\n", "critical_level_low = 0. # for yet-to-be-implemented warnings[m]\n", "critical_level_high = np.inf # for yet-to-be-implemented warnings[m]\n", "\n", "# make sure e-RK4 method of reservoir has a small enough timestep to avoid runaway numerical error\n", "nt_eRK4 = 1000 # number of simulation steps of reservoir in between timesteps of pipeline \n", "simulation_timestep = dt/nt_eRK4\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "# create objects\n", "\n", "V = Ausgleichsbecken_class(area_base,area_outflux,critical_level_low,critical_level_high,simulation_timestep)\n", "V.set_steady_state(initial_flux,initial_level,conversion_pressure_unit)\n", "\n", "\n", "pipe = Druckrohrleitung_class(L,D,n,alpha,f_D)\n", "pipe.set_pressure_propagation_velocity(c)\n", "pipe.set_number_of_timesteps(nt)\n", "pipe.set_steady_state(initial_flux,initial_level,pl_vec,h_vec)\n", "\n", "initial_pressure_turbine = pipe.get_current_pressure_distribution()[-1]\n", "\n", "T1 = Francis_Turbine(Q_nenn,p_nenn,closing_time,timestep = dt)\n", "T1.set_steady_state(initial_flux,initial_pressure_turbine)\n", "\n", "Pegelregler = PI_controller_class(target_level,deadband_range,Kp,Ti,dt)\n", "Pegelregler.control_variable = T1.get_current_LA()\n" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "# initialization for timeloop\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", "p_old = pipe.get_current_pressure_distribution()\n", "\n", "# prepare the vectors in which the temporal evolution of the boundary conditions are stored\n", " # keep in mind, that the velocity at the turbine and the pressure at the reservoir follow from boundary conditions\n", " # reservoir level and flow through turbine\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", "p_boundary_res = np.zeros_like(t_vec)\n", "p_boundary_tur = np.zeros_like(t_vec)\n", "\n", "# prepare the vectors that store the temporal evolution of the level in the reservoir\n", "level_vec = np.full(nt+1,initial_level) # level at the end of each pipeline timestep\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", "p_boundary_tur[0] = p_old[-1]\n", "\n", "LA_soll_vec = np.full_like(t_vec,T1.LA)\n", "LA_ist_vec = np.full_like(t_vec,T1.LA)\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "%matplotlib qt5\n", "# time loop\n", "\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(2,1)\n", "fig1.suptitle(str(0) +' s / '+str(round(t_vec[-1],2)) + ' s' )\n", "axs1[0].set_title('Pressure distribution in pipeline')\n", "axs1[1].set_title('Velocity distribution in pipeline')\n", "axs1[0].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", "axs1[0].set_ylabel(r'$p$ ['+conversion_pressure_unit+']')\n", "axs1[1].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", "axs1[1].set_ylabel(r'$v$ [$\\mathrm{m} / \\mathrm{s}$]')\n", "lo_00, = axs1[0].plot(pl_vec,pressure_conversion(p_old,initial_pressure_unit, conversion_pressure_unit),marker='.')\n", "lo_01, = axs1[1].plot(pl_vec,v_old,marker='.')\n", "axs1[0].autoscale()\n", "axs1[1].autoscale()\n", "\n", "fig1.tight_layout()\n", "fig1.show()\n", "plt.pause(1)\n" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.2146505196687856\n" ] } ], "source": [ "print(initial_flux/area_outflux)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "# loop through time steps of the pipeline\n", "for it_pipe in range(1,pipe.nt+1):\n", "\n", "\n", " if it_pipe > 0.015*(nt+1):\n", " if V.get_current_influx() > 0:\n", " V.set_influx(np.max([V.get_current_influx()-initial_flux*5*1e-3,0.]))\n", "# for each pipeline timestep, execute nt_eRK4 timesteps of the reservoir code\n", " # set initial conditions for the reservoir time evolution calculted with e-RK4\n", " V.set_pressure = p_old[0]\n", " V.set_outflux = v_old[0]\n", " # calculate the time evolution of the reservoir level within each pipeline timestep to avoid runaway numerical error\n", " for it_res in range(nt_eRK4):\n", " V.timestep_reservoir_evolution() \n", " level_vec[it_pipe] = V.get_current_level() \n", "\n", " # get the control variable\n", " Pegelregler.update_control_variable(level_vec[it_pipe])\n", " LA_soll_vec[it_pipe] = Pegelregler.get_current_control_variable()\n", " \n", " # change the Leitapparatöffnung based on the target value\n", " T1.update_LA(LA_soll_vec[it_pipe])\n", " T1.set_pressure(p_old[-1])\n", "\n", " LA_ist_vec[it_pipe] = T1.LA\n", "\n", " # set boundary conditions for the next timestep of the characteristic method\n", " p_boundary_res[it_pipe] = V.get_current_pressure()\n", " v_boundary_tur[it_pipe] = 1/A_pipe*T1.get_current_Q()\n", "\n", " # the the boundary conditions in the pipe.object and thereby calculate boundary pressure at turbine\n", " 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", "\n", " # perform the next timestep via the characteristic method\n", " pipe.timestep_characteristic_method()\n", "\n", " # prepare for next loop\n", " p_old = pipe.get_current_pressure_distribution()\n", " v_old = pipe.get_current_velocity_distribution()\n", "\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(pl_vec,pressure_conversion(p_old,initial_pressure_unit, conversion_pressure_unit),marker='.',c='blue')\n", " lo_01, = axs1[1].plot(pl_vec,v_old,marker='.',c='blue')\n", " # lo_02, = axs1[2].plot(level_vec_2,c='blue')\n", " fig1.suptitle(str(round(t_vec[it_pipe],2))+ ' s / '+str(round(t_vec[-1],2)) + ' s' )\n", " fig1.canvas.draw()\n", " fig1.tight_layout()\n", " fig1.show()\n", " plt.pause(0.001) \n", "\n", " \n", " " ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "# plot time evolution of boundary pressure and velocity as well as the reservoir level\n", "\n", "fig2,axs2 = plt.subplots(3,2)\n", "axs2[0,0].set_title('Pressure reservoir')\n", "axs2[0,0].plot(t_vec,pressure_conversion(p_boundary_res,initial_pressure_unit, conversion_pressure_unit))\n", "axs2[0,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", "axs2[0,0].set_ylabel(r'$p$ ['+conversion_pressure_unit+']')\n", "\n", "axs2[0,1].set_title('Velocity reservoir')\n", "axs2[0,1].plot(t_vec,v_boundary_res)\n", "axs2[0,1].set_ylim(-2*Q_nenn,+2*Q_nenn)\n", "axs2[0,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", "axs2[0,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n", "\n", "axs2[1,0].set_title('Pressure turbine')\n", "axs2[1,0].plot(t_vec,pressure_conversion(p_boundary_tur,initial_pressure_unit, conversion_pressure_unit))\n", "axs2[1,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", "axs2[1,0].set_ylabel(r'$p$ ['+conversion_pressure_unit+']')\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", "\n", "axs2[2,0].set_title('Level reservoir')\n", "axs2[2,0].plot(t_vec,level_vec)\n", "axs2[2,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", "axs2[2,0].set_ylabel(r'$h$ [m]')\n", "\n", "axs2[2,1].set_title('LA')\n", "axs2[2,1].plot(t_vec,100*LA_soll_vec)\n", "axs2[2,1].plot(t_vec,100*LA_ist_vec)\n", "axs2[2,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", "axs2[2,1].set_ylabel(r'$LA$ [%]')\n", "fig2.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.0\n" ] } ], "source": [ "print(np.sum(v_boundary_res[2500:])*area_outflux)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.8.13 ('Georg_DT_Slot3')", "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": "3.8.13" }, "orig_nbformat": 4, "vscode": { "interpreter": { "hash": "84fb123bdc47ab647d3782661abcbe80fbb79236dd2f8adf4cef30e8755eb2cd" } } }, "nbformat": 4, "nbformat_minor": 2 }