{ "cells": [ { "cell_type": "code", "execution_count": 1, "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", "\n", "#importing pressure conversion function\n", "current = os.path.dirname(os.path.realpath('Main_Programm.ipynb'))\n", "parent = os.path.dirname(current)\n", "sys.path.append(parent)\n", "from Ausgleichsbecken.Ausgleichsbecken_class_file import Ausgleichsbecken_class\n", "from functions.pressure_conversion import pressure_conversion" ] }, { "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 = 1 # [m³/s] nominal flux of turbine \n", "Tur_p_nenn = pressure_conversion(10.,'bar',pUnit_calc) # [Pa] nominal pressure of turbine \n", "Tur_closingTime = 10. # [s] closing time of turbine\n", "\n", " # for PI controller\n", "Con_targetLevel = 10. # [m]\n", "\n", " # for pipeline\n", "Pip_length = 100 # [m] length of pipeline\n", "Pip_dia = 1. # [m] diameter of pipeline\n", "Pip_area = Pip_dia**2/4*np.pi # [m²] crossectional area of pipeline\n", "Pip_head = 100. # [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 = 1000 # [-] number of pipe segments in discretization\n", "Pip_f_D = 0.6 # [-] 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 = 100. # [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 = 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" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# create objects\n", "\n", "# Upstream reservoir\n", "reservoir = Ausgleichsbecken_class(Res_area_base,Res_area_out,Res_dt,pUnit_conv,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" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# initialization for timeloop\n", "reservoir.set_influx = 0.\n", "\n", "level_vec = np.zeros_like(t_vec)\n", "level_vec[0] = reservoir.get_current_level()\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", "p_0 = pipe.get_initial_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 are set manually and\n", " # 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", "p_boundary_res = np.zeros_like(t_vec)\n", "p_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", "p_boundary_tur[0] = p_old[-1]\n", "\n", "v_boundary_tur[:np.argmin(np.abs(t_vec-1))] = v_old[-1] \n", "t1 = 0.1\n", "t2 = 2.5\n", "ind_t1 = np.argmin(np.abs(t_vec-t1))\n", "ind_t2 = np.argmin(np.abs(t_vec-t2))\n", "ind_t_vec = np.linspace(t_vec[ind_t1]-(t2-t1)/2,t_vec[ind_t2]-(t2-t1)/2,ind_t2-ind_t1)\n", "v_trans = v_old[-1]/(np.exp(ind_t_vec/(5e-2))+1)\n", "v_boundary_tur[ind_t1:ind_t2] = v_trans\n", "\n", "# v_boundary_tur[:np.argmin(np.abs(t_vec-1))] = v_old[-1] \n", "# v_boundary_tur[np.argmin(np.abs(t_vec-1)):] = 0" ] }, { "cell_type": "code", "execution_count": 5, "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(3,1, figsize=(16,9))\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[0].set_ylim([-2,200])\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'$p$ ['+pUnit_conv+']')\n", "axs1[1].set_ylim([-76,76])\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", "axs1[2].set_ylim([-1.5,1.5])\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,v_old,marker='.')\n", "lo_2min, = axs1[2].plot(Pip_x_vec,pipe.get_lowest_velocity_per_node(),c='red')\n", "lo_2max, = axs1[2].plot(Pip_x_vec,pipe.get_highest_velocity_per_node(),c='red')\n", "\n", "fig1.tight_layout()\n", "fig1.show()\n", "plt.pause(1)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "for it_pipe in range(1,nt+1):\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", " reservoir.set_pressure(p_old[0],display_warning=False)\n", " reservoir.set_outflux(v_old[0]*Pip_area,display_warning=False)\n", " # 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", " \n", " # set boundary conditions for the next timestep of the characteristic method\n", " p_boundary_res[it_pipe] = reservoir.get_current_pressure()\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_vectorized()\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", " 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", " 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]-1,2))+ ' s / '+str(round(t_vec[-1]-1,2)) + ' s' )\n", " fig1.canvas.draw()\n", " fig1.tight_layout()\n", " fig1.show()\n", " # if int(it_pipe/100) < 10:\n", " # figname = 'GIF Plots\\ GIF00'+str(int(it_pipe/100))+'.png'\n", " # elif int(it_pipe/100) < 100:\n", " # figname = 'GIF Plots\\ GIF0'+str(int(it_pipe/100))+'.png'\n", " # else:\n", " # figname = 'GIF Plots\\ GIF'+str(int(it_pipe/100))+'.png'\n", " # print(figname)\n", " # fig1.savefig(fname=figname)\n", " plt.pause(0.000001) " ] }, { "cell_type": "code", "execution_count": 7, "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", "\n", "axs2[1,0].set_title('Velocity Reservoir')\n", "axs2[1,0].plot(t_vec,v_boundary_res)\n", "axs2[1,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", "axs2[1,0].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n", "axs2[1,0].set_ylim([-1.1*np.max(v_boundary_res),1.1*np.max(v_boundary_res)])\n", "\n", "axs2[0,1].set_title('Pressure Turbine')\n", "axs2[0,1].plot(t_vec,pressure_conversion(p_boundary_tur,pUnit_calc,pUnit_conv))\n", "axs2[0,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", "axs2[0,1].set_ylabel(r'$p$ [mWS]')\n", "axs2[0,1].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", "\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([-0.1,1.05*np.max(v_boundary_tur)])\n", "\n", "fig2.tight_layout()\n", "plt.show()" ] } ], "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 }