{ "cells": [ { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "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" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "%matplotlib qt5\n", "#define constants pipe\n", "\n", "g = 9.81 # gravitational acceleration [m/s²]\n", "rho = 1000. # density of water [kg/m³]\n", "\n", "L = 1000. # length of pipeline [m]\n", "D = 0.9 # pipe diameter [m]\n", "h_res = 10. # water level in upstream reservoir [m]\n", "n = 50 # number of pipe segments in discretization\n", "nt = 1000 # number of time steps after initial conditions\n", "f_D = 0.01 # Darcy friction factor\n", "c = 400. # propagation velocity of the pressure wave [m/s]\n", "h_pipe = 105. # hydraulic head without reservoir [m] \n", "alpha = np.arcsin(h_pipe/L) # Höhenwinkel der Druckrohrleitung \n", "\n", "\n", "# preparing the discretization and initial conditions\n", "initial_flux = 0.8 # m³/s\n", "initial_level = h_res # m\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", "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", "# define constants reservoir\n", "conversion_pressure_unit = 'mWS'\n", "\n", "area_base = 75. # m²\n", "area_pipe = (D/2)**2*np.pi # m²\n", "critical_level_low = 0. # m\n", "critical_level_high = 100. # m\n", "\n", "# make sure e-RK4 method of reservoir has a small enough timestep to avoid runaway numerical error\n", "nt_eRK4 = 1 # number of simulation steps of reservoir in between timesteps of pipeline \n", "simulation_timestep = dt/nt_eRK4" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "V = Ausgleichsbecken_class(area_base,area_pipe,critical_level_low,critical_level_high,simulation_timestep)\n", "V.set_steady_state(initial_flux,initial_level,conversion_pressure_unit)\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,area_base,pl_vec,h_vec)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.8\n", "0.8\n", "10.0\n", "97309.32104824147\n", "96532.05564888839\n", "96532.05564888839\n", "[0.8 0.8 0.8 ... 0.8 0.8 0.8]\n", "[1.25752054 1.25752054 1.25752054 ... 1.25752054 1.25752054 1.25752054]\n" ] } ], "source": [ "print(V.get_current_influx())\n", "print(V.get_current_outflux())\n", "print(V.get_current_level())\n", "print(rho*g*V.get_current_level()-rho/2*(V.get_current_outflux()/area_pipe)**2)\n", "print(V.get_current_pressure())\n", "print(pipe.get_current_pressure_distribution()[0])\n", "print(pipe.get_current_velocity_distribution()*area_pipe)\n", "print(pipe.get_current_velocity_distribution())" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "# initialization for timeloop\n", "\n", "level_vec = np.zeros_like(t_vec)\n", "level_vec[0] = V.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", "\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" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "fig1,axs1 = plt.subplots(2,1)\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", "lo_00, = axs1[0].plot(pl_vec,pressure_conversion(p_old,'Pa',conversion_pressure_unit),marker='.')\n", "axs1[0].set_ylim([0.9*np.min(pressure_conversion(p_old,'Pa',conversion_pressure_unit)),1.1*np.max(pressure_conversion(p_old,'Pa',conversion_pressure_unit))])\n", "\n", "axs1[1].set_title('Velocity distribution in pipeline')\n", "axs1[1].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", "axs1[1].set_ylabel(r'$v$ [m/s]')\n", "lo_01, = axs1[1].plot(pl_vec,v_old,marker='.')\n", "# axs1[1].set_ylim([0.9*np.min(v_old),1.1*np.max(v_boundary_res)])\n", "\n", "fig1.tight_layout()\n", "plt.pause(1)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "96532.05564888839\n", "96532.05564888839\n", "96532.05564888839\n", "96532.05564888839\n", "96532.05564888839\n", "96532.05564888839\n", "96532.05564888839\n", 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" v_boundary_tur[it_pipe] = initial_flux/area_pipe\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,'Pa', conversion_pressure_unit),marker='.',c='blue')\n", " lo_01, = axs1[1].plot(pl_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", "\n" ] }, { "cell_type": "code", "execution_count": 16, "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,'Pa',conversion_pressure_unit))\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,'Pa',conversion_pressure_unit)),1.1*np.max(pressure_conversion(p_boundary_res,'Pa',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_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", "\n", "axs2[1,0].set_title('Pressure Turbine')\n", "axs2[1,0].plot(t_vec,pressure_conversion(p_boundary_tur,'Pa',conversion_pressure_unit))\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,'Pa',conversion_pressure_unit)),1.1*np.max(pressure_conversion(p_boundary_tur,'Pa',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", "axs2[1,1].set_ylim([0.9*np.min(v_boundary_tur),1.1*np.max(v_boundary_tur)])\n", "\n", "fig2.tight_layout()\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.8.13 ('DT_Slot_3')", 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