{ "cells": [ { "cell_type": "code", "execution_count": 5, "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" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "#define constants\n", "\n", "# physics\n", "g = 9.81 # gravitational acceleration [m/s²]\n", "rho = 1000. # density of water [kg/m³]\n", "\n", "# pipeline\n", "L = 1000. # length of pipeline [m]\n", "D = 1. # pipe diameter [m]\n", "#consider replacing Q0 with a vector be be more flexible in initial conditions\n", "Q0 = 2 # initial flow in whole pipe [m³/s]\n", "A_pipe = D**2/4*np.pi # pipeline area\n", "v0 = Q0/A_pipe # initial flow velocity [m/s]\n", "h_res = 20. # water level in upstream reservoir [m]\n", "n = 10 # number of pipe segments in discretization\n", "nt = 10000 # 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 = 300 # hydraulic head without reservoir [m] \n", "alpha = np.arcsin(h_pipe/L) # Höhenwinkel der Druckrohrleitung \n", "\n", "# derivatives of the pipeline constants\n", "p0 = rho*g*h_res-v0**2*rho/2\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*dx,dx) # pl = pipe-length. position of the nodes on the pipeline\n", "t_vec = np.arange(0,nt*dt,dt) # time vector\n", "h_vec = np.arange(0,h_pipe+h_pipe/n,h_pipe/n) # hydraulic head of pipeline at each node\n", "\n", "v_init = np.full(nn,Q0/(D**2/4*np.pi))\n", "p_init = (rho*g*(h_res+h_vec)-v_init**2*rho/2)-(f_D*pl_vec/D*rho/2*v_init**2) # ref Wikipedia: Darcy Weisbach\n", "\n", "\n", "# reservoir\n", "initial_level = h_res # m\n", "initial_influx = 0. # m³/s\n", "initial_outflux = Q0 # m³/s\n", "initial_pipeline_pressure = p0 # Pa \n", "initial_pressure_unit = 'Pa'\n", "conversion_pressure_unit = 'Pa'\n", "area_base = 5. # m² really large base are to ensure level never becomes < 0\n", "area_outflux = A_pipe # m²\n", "critical_level_low = 0. # m\n", "critical_level_high = np.inf # 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" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(3.6368236494728476, 'mWS')\n" ] } ], "source": [ "print(pressure_conversion(-np.sum((-v_init**2*rho/2)),'Pa','mWS'))" ] }, { "cell_type": "code", "execution_count": 8, "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_initial_level(initial_level) \n", "V.set_influx(initial_influx)\n", "V.set_outflux(initial_outflux)\n", "V.pressure, V.pressure_unit = pressure_conversion(initial_pipeline_pressure,input_unit = initial_pressure_unit, target_unit = 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_initial_pressure(p_init)\n", "pipe.set_initial_flow_velocity(v_init)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "# initialization for timeloop\n", "\n", "v_old = v_init.copy()\n", "p_old = p_init.copy()\n", "\n", "#vectors to store boundary conditions\n", "v_boundary_res = np.empty_like(t_vec)\n", "v_boundary_tur = np.empty_like(t_vec)\n", "p_boundary_res = np.empty_like(t_vec)\n", "p_boundary_tur = np.empty_like(t_vec)\n", "level_vec = np.empty_like(t_vec)\n", "level_vec_2 = np.full([nt_eRK4],initial_level)\n", "\n", "v_boundary_res[0] = v_old[0]\n", "v_boundary_tur[0] = v_old[-1] # instantaneous closing\n", "# v_boundary_tur[1:] = 0\n", "v_boundary_tur[0:1000] = np.linspace(v_old[-1],0,1000) # finite closing time - linear case\n", "p_boundary_res[0] = p_old[0]\n", "p_boundary_tur[0] = p_old[-1]\n", "level_vec[0] = initial_level\n", "\n", "v_boundary_tur[1:] = 0 # instantaneous closing" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "%matplotlib qt5\n", "# time loop\n", "\n", "\n", "# fig2,axs2 = plt.subplots(3,1)\n", "# axs2[0].set_title('Pressure distribution in pipeline')\n", "# axs2[1].set_title('Velocity distribution in pipeline')\n", "# axs2[0].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", "# axs2[0].set_ylabel(r'$p$ [mWS]')\n", "# axs2[1].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", "# axs2[1].set_ylabel(r'$p$ [mWS]')\n", "# lo_00, = axs2[0].plot(pl_vec,pressure_conversion(pipe.p_old,'Pa','mWS')[0],marker='.')\n", "# lo_01, = axs2[1].plot(pl_vec,pipe.v_old,marker='.')\n", "# lo_02, = axs2[2].plot(level_vec_2)\n", "# axs2[0].autoscale()\n", "# axs2[1].autoscale()\n", "# axs2[2].autoscale()\n", "# fig2.tight_layout()\n", "\n", "# loop through time steps of the pipeline\n", "for it_pipe in range(1,pipe.nt):\n", "\n", "# for each pipeline timestep, execute nt_eRK4 timesteps of the reservoir code\n", " V.pressure = p_old[0]\n", " V.outflux = v_old[0]\n", " for it_res in range(nt_eRK4):\n", " V.e_RK_4()\n", " V.level = V.update_level(V.timestep)\n", " V.set_volume()\n", " level_vec_2[it_res] = V.level\n", " if (V.level < critical_level_low) or (V.level > critical_level_high):\n", " i_max = it_pipe\n", " print('broke')\n", " break\n", " level_vec[it_pipe] = V.level\n", "\n", " p_boundary_res[it_pipe] = rho*g*V.level-v_old[1]**2*rho/2\n", " v_boundary_res[it_pipe] = v_old[1]+1/(rho*c)*(p_boundary_res[it_pipe]-p_old[1])-f_D*dt/(2*D)*abs(v_old[1])*v_old[1] \\\n", " +dt*g*np.sin(alpha)\n", "\n", "\n", " pipe.set_boundary_conditions_next_timestep(v_boundary_res[it_pipe],p_boundary_res[it_pipe],v_boundary_tur[it_pipe])\n", " p_boundary_tur[it_pipe] = pipe.p_boundary_tur\n", "\n", " pipe.timestep_characteristic_method()\n", "\n", "\n", " # lo_00.remove()\n", " # lo_01.remove()\n", " # lo_02.remove()\n", " # lo_00, = axs2[0].plot(pl_vec,pressure_conversion(pipe.p_old,'Pa','mWS')[0],marker='.',c='blue')\n", " # lo_01, = axs2[1].plot(pl_vec,pipe.v_old,marker='.',c='blue')\n", " # lo_02, = axs2[2].plot(level_vec_2,c='blue')\n", " # fig2.suptitle(str(it_pipe))\n", " # fig2.canvas.draw()\n", " # fig2.canvas.flush_events()\n", " # fig2.tight_layout()\n", " # plt.pause(0.1) \n", "\n", " p_old = pipe.p_old\n", " v_old = pipe.v_old \n", "\n", " \n", " " ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "%matplotlib qt5\n", "fig1,axs1 = plt.subplots(3,2)\n", "axs1[0,0].plot(t_vec,pressure_conversion(p_boundary_res,'Pa','mWS')[0])\n", "axs1[0,1].plot(t_vec,v_boundary_res)\n", "axs1[1,0].plot(t_vec,pressure_conversion(p_boundary_tur,'Pa','mWS')[0])\n", "axs1[1,1].plot(t_vec,v_boundary_tur)\n", "axs1[2,0].plot(t_vec,level_vec)\n", "axs1[0,0].set_title('Pressure Reservoir')\n", "axs1[0,1].set_title('Velocity Reservoir')\n", "axs1[1,0].set_title('Pressure Turbine')\n", "axs1[1,1].set_title('Velocity Turbine')\n", "axs1[0,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", "axs1[0,0].set_ylabel(r'$p$ [mWS]')\n", "axs1[0,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", "axs1[0,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n", "axs1[1,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", "axs1[1,0].set_ylabel(r'$p$ [mWS]')\n", "axs1[1,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", "axs1[1,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n", "fig1.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 }