{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from Turbinen_class_file import Francis_Turbine\n", "\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\n", "from Druckrohrleitung.Druckrohrleitung_class_file import Druckrohrleitung_class\n", "from Regler.Regler_class_file import PI_controller_class" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# define constants\n", "\n", " # for physics\n", "g = 9.81 # [m/s²] gravitational acceleration \n", "rho = 1000. # [kg/m³] density of water \n", "pUnit_calc = 'Pa' # [text] DO NOT CHANGE! for pressure conversion in print statements and plot labels \n", "pUnit_conv = 'mWS' # [text] for pressure conversion in print statements and plot labels\n", "\n", " # for Turbine\n", "Tur_Q_nenn = 0.85 # [m³/s] nominal flux of turbine \n", "Tur_p_nenn = pressure_conversion(10.6,'bar',pUnit_calc) # [Pa] nominal pressure of turbine \n", "Tur_closingTime = 90. # [s] closing time of turbine\n", "\n", " # for PI controller\n", "Con_targetLevel = 8. # [m]\n", "Con_K_p = 0.1 # [-] proportional constant of PI controller\n", "Con_T_i = 10. # [s] timespan in which a steady state error is corrected by the intergal term\n", "Con_deadbandRange = 0.05 # [m] Deadband range around targetLevel for which the controller does NOT intervene\n", "\n", " # for pipeline\n", "Pip_length = (535.+478.) # [m] length of pipeline\n", "Pip_dia = 0.9 # [m] diameter of pipeline\n", "Pip_area = Pip_dia**2/4*np.pi # [m²] crossectional area of pipeline\n", "Pip_head = 105. # [m] hydraulic head of pipeline without reservoir\n", "Pip_angle = np.arcsin(Pip_head/Pip_length) # [rad] elevation angle of pipeline \n", "Pip_n_seg = 50 # [-] number of pipe segments in discretization\n", "Pip_f_D = 0.014 # [-] Darcy friction factor\n", "Pip_pw_vel = 500. # [m/s] propagation velocity of the pressure wave (pw) in the given pipeline\n", " # derivatives of the pipeline constants\n", "Pip_dx = Pip_length/Pip_n_seg # [m] length of each pipe segment\n", "Pip_dt = Pip_dx/Pip_pw_vel # [s] timestep according to method of characteristics\n", "Pip_nn = Pip_n_seg+1 # [1] number of nodes\n", "Pip_x_vec = np.arange(0,Pip_nn,1)*Pip_dx # [m] vector holding the distance of each node from the upstream reservoir along the pipeline\n", "Pip_h_vec = np.arange(0,Pip_nn,1)*Pip_head/Pip_n_seg # [m] vector holding the vertival distance of each node from the upstream reservoir\n", "\n", " # for reservoir\n", "Res_area_base = 74. # [m²] total base are of the cuboid reservoir \n", "Res_area_out = Pip_area # [m²] outflux area of the reservoir, given by pipeline area\n", "Res_level_crit_lo = 0. # [m] for yet-to-be-implemented warnings\n", "Res_level_crit_hi = np.inf # [m] for yet-to-be-implemented warnings\n", "Res_dt_approx = 1e-3 # [s] approx. timestep of reservoir time evolution to ensure numerical stability (see Res_nt why approx.)\n", "Res_nt = max(1,int(Pip_dt//Res_dt_approx)) # [1] number of timesteps of the reservoir time evolution within one timestep of the pipeline\n", "Res_dt = Pip_dt/Res_nt # [s] harmonised timestep of reservoir time evolution\n", "\n", " # 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 = 600. # [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" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# create objects\n", "\n", "# Upstream reservoir\n", "reservoir = Ausgleichsbecken_class(Res_area_base,Res_area_out,Res_dt,Res_level_crit_lo,Res_level_crit_hi,rho)\n", "reservoir.set_steady_state(flux_init,level_init)\n", "\n", "# 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", "\n", "# downstream turbine\n", "turbine = Francis_Turbine(Tur_Q_nenn,Tur_p_nenn,Tur_closingTime,Pip_dt,pUnit_conv)\n", "turbine.set_steady_state_by_flux(flux_init,pipe.get_current_pressure_distribution()[-1])\n", "\n", "# influx setting turbine\n", "turbine_in = Francis_Turbine(Tur_Q_nenn,Tur_p_nenn,Tur_closingTime/2,Pip_dt,pUnit_conv)\n", "turbine_in.set_steady_state_by_flux(flux_init,Tur_p_nenn)\n", "\n", "# level controll\n", "level_control = PI_controller_class(Con_targetLevel,Con_deadbandRange,Con_K_p,Con_T_i,Pip_dt)\n", "level_control.set_control_variable(turbine.get_current_LA(),display_warning=False)\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# initialization for Timeloop\n", "\n", "v_old = pipe.get_current_velocity_distribution()\n", "v_min = pipe.get_current_velocity_distribution()\n", "v_max = pipe.get_current_velocity_distribution()\n", "Q_old = pipe.get_current_flux_distribution()\n", "Q_min = pipe.get_current_flux_distribution()\n", "Q_max = pipe.get_current_flux_distribution()\n", "p_old = pipe.get_current_pressure_distribution()\n", "p_min = pipe.get_current_pressure_distribution()\n", "p_max = pipe.get_current_pressure_distribution()\n", "\n", "Q_in_vec = np.zeros_like(t_vec)\n", "Q_in_vec[0] = flux_init\n", "\n", "v_boundary_res = np.zeros_like(t_vec)\n", "v_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", "p_boundary_res = np.zeros_like(t_vec)\n", "p_boundary_tur = np.zeros_like(t_vec)\n", "\n", "level_vec = np.full_like(t_vec,level_init) # level at the end of each pipeline timestep\n", "volume_vec = np.full_like(t_vec,reservoir.get_current_volume()) # volume at the end of each pipeline timestep\n", "\n", "v_boundary_res[0] = v_old[0]\n", "v_boundary_tur[0] = v_old[-1] \n", "Q_boundary_res[0] = Q_old[0]\n", "Q_boundary_tur[0] = Q_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,turbine.get_current_LA())\n", "LA_ist_vec = np.full_like(t_vec,turbine.get_current_LA())\n", "\n", "LA_soll_vec2 = np.full_like(t_vec,turbine_in.get_current_LA())\n", "# LA_soll_vec2[100:] = 0\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "%matplotlib qt5\n", "# Con_T_ime 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[0].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", "axs1[0].set_ylabel(r'$p$ ['+pUnit_conv+']')\n", "axs1[1].set_title('Flux distribution in pipeline')\n", "axs1[1].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", "axs1[1].set_ylabel(r'$Q$ [$\\mathrm{m}^3 / \\mathrm{s}$]')\n", "lo_p, = axs1[0].plot(Pip_x_vec,pressure_conversion(p_old,pUnit_calc, pUnit_conv),marker='.')\n", "lo_q, = axs1[1].plot(Pip_x_vec,Q_old,marker='.')\n", "lo_pmin, = axs1[0].plot(Pip_x_vec,pipe.get_lowest_pressure_per_node(disp_flag=True),c='red')\n", "lo_pmax, = axs1[0].plot(Pip_x_vec,pipe.get_highest_pressure_per_node(disp_flag=True),c='red')\n", "lo_qmin, = axs1[1].plot(Pip_x_vec,pipe.get_lowest_flux_per_node(),c='red')\n", "lo_qmax, = axs1[1].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", "fig1.show()\n", "plt.pause(1)\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "convergence_parameters = [p_old[-2],v_old[-2],Pip_dia,Pip_area,Pip_angle,Pip_f_D,Pip_pw_vel,rho,Pip_dt,p_old[-1]]\n", "\n", "# loop through Con_T_ime steps of the pipeline\n", "for it_pipe in range(1,nt+1):\n", "\n", " turbine_in.update_LA(LA_soll_vec2[it_pipe])\n", " turbine_in.set_pressure(Tur_p_nenn)\n", " Q_in_vec[it_pipe] = turbine_in.get_current_Q()\n", " reservoir.set_influx(Q_in_vec[it_pipe])\n", "\n", "# for each pipeline timestep, execute nt_eRK4 timesteps of the reservoir code\n", " # set initial condition for the reservoir Con_T_ime evolution calculted with e-RK4\n", " reservoir.set_pressure(p_old[0],display_warning=False)\n", " reservoir.set_outflux(Q_old[0],display_warning=False)\n", " # calculate the Con_T_ime 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", " volume_vec[it_pipe] = reservoir.get_current_volume() \n", "\n", " # get the control variable\n", " level_control.update_control_variable(level_vec[it_pipe])\n", " LA_soll_vec[it_pipe] = level_control.get_current_control_variable()\n", " \n", " # change the Leitapparatöffnung based on the target value\n", " turbine.update_LA(LA_soll_vec[it_pipe])\n", " LA_ist_vec[it_pipe] = turbine.get_current_LA()\n", "\n", " # set boundary condition for the next timestep of the characterisCon_T_ic method\n", " turbine.set_pressure(p_old[-1])\n", " convergence_parameters[0] = p_old[-2]\n", " convergence_parameters[1] = v_old[-2]\n", " convergence_parameters[9] = p_old[-1]\n", " turbine.converge(convergence_parameters)\n", " p_boundary_res[it_pipe] = reservoir.get_current_pressure()\n", " v_boundary_tur[it_pipe] = 1/Pip_area*turbine.get_current_Q()\n", " Q_boundary_tur[it_pipe] = turbine.get_current_Q()\n", "\n", " # the the boundary condition 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", " Q_boundary_res[it_pipe] = pipe.get_current_flux_distribution()[0]\n", "\n", " # perform the next timestep via the characterisCon_T_ic 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", " Q_old = pipe.get_current_flux_distribution()\n", "\n", " # plot some stuff\n", " if it_pipe%50 == 0:\n", " # remove line-objects to autoscale axes (there is definetly a better way, but this works ¯\\_(ツ)_/¯ )\n", " lo_p.remove()\n", " lo_pmin.remove()\n", " lo_pmax.remove()\n", " lo_q.remove()\n", " lo_qmin.remove()\n", " lo_qmax.remove()\n", " # plot new pressure and velocity distribution in the pipeline\n", " lo_p, = axs1[0].plot(Pip_x_vec,pipe.get_current_pressure_distribution(disp_flag=True),marker='.',c='blue')\n", " lo_pmin, = axs1[0].plot(Pip_x_vec,pipe.get_lowest_pressure_per_node(disp_flag=True),c='red')\n", " lo_pmax, = axs1[0].plot(Pip_x_vec,pipe.get_highest_pressure_per_node(disp_flag=True),c='red')\n", " lo_q, = axs1[1].plot(Pip_x_vec,pipe.get_current_flux_distribution(),marker='.',c='blue')\n", " lo_qmin, = axs1[1].plot(Pip_x_vec,pipe.get_lowest_flux_per_node(),c='red')\n", " lo_qmax, = axs1[1].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()\n", " fig1.tight_layout()\n", " fig1.show()\n", " plt.pause(0.001) " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "# plot Con_T_ime evolution of boundary pressure and velocity as well as the reservoir level\n", "\n", "fig2,axs2 = plt.subplots(1,1)\n", "axs2.set_title('Level and Volume reservoir')\n", "axs2.plot(t_vec,level_vec,label='level')\n", "axs2.set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", "axs2.set_ylabel(r'$h$ [m]')\n", "x_twin_00 = axs2.twinx()\n", "x_twin_00.set_ylabel(r'$V$ [$\\mathrm{m}^3$]')\n", "x_twin_00.plot(t_vec,volume_vec)\n", "axs2.legend()\n", "\n", "fig2,axs2 = plt.subplots(1,1)\n", "axs2.set_title('LA')\n", "axs2.plot(t_vec,100*LA_soll_vec,label='Target')\n", "axs2.plot(t_vec,100*LA_ist_vec,label='Actual')\n", "axs2.set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", "axs2.set_ylabel(r'$LA$ [%]')\n", "axs2.legend()\n", "\n", "fig2,axs2 = plt.subplots(1,1)\n", "axs2.set_title('Pressure reservoir and turbine')\n", "axs2.plot(t_vec,pressure_conversion(p_boundary_res,pUnit_calc, pUnit_conv),label='Reservoir')\n", "axs2.plot(t_vec,pressure_conversion(p_boundary_tur,pUnit_calc, pUnit_conv),label='Turbine')\n", "axs2.set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", "axs2.set_ylabel(r'$p$ ['+pUnit_conv+']')\n", "axs2.legend()\n", "\n", "fig2,axs2 = plt.subplots(1,1)\n", "axs2.set_title('Fluxes')\n", "axs2.plot(t_vec,Q_boundary_res,label='Outflux')\n", "axs2.plot(t_vec,Q_in_vec,label='Influx')\n", "axs2.plot(t_vec,Q_boundary_tur,label='Flux Turbine')\n", "axs2.set_ylim(-2*Tur_Q_nenn,+2*Tur_Q_nenn)\n", "axs2.set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", "axs2.set_ylabel(r'$Q$ [$\\mathrm{m}^3/\\mathrm{s}$]')\n", "axs2.legend()\n", "\n", "fig2,axs2 = plt.subplots(1,1)\n", "axs2.set_title('Min and Max Pressure')\n", "axs2.plot(Pip_x_vec,pipe.get_lowest_pressure_per_node(disp_flag=True),c='red')\n", "axs2.plot(Pip_x_vec,pipe.get_highest_pressure_per_node(disp_flag=True),c='red')\n", "axs2.set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", "axs2.set_ylabel(r'$p$ ['+pUnit_conv+']')\n", "\n", "fig2,axs2 = plt.subplots(1,1)\n", "axs2.set_title('Min and Max Fluxes')\n", "axs2.plot(Pip_x_vec,pipe.get_lowest_flux_per_node(),c='red')\n", "axs2.plot(Pip_x_vec,pipe.get_highest_flux_per_node(),c='red')\n", "axs2.set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", "axs2.set_ylabel(r'$Q$ [$\\mathrm{m}^3/\\mathrm{s}$]')\n", "\n", "fig2.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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 }