{ "cells": [ { "cell_type": "code", "execution_count": 66, "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": 67, "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 = 1200. # [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": 68, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The pipeline has the following attributes: \n", "----------------------------- \n", "Length = 1013.0 m \n", "Diameter = 0.9 m \n", "Hydraulic head = 105.0 m \n", "Number of segments = 50 \n", "Number of nodes = 51 \n", "Length per segments = 20.26 m \n", "Pipeline angle = 0.104 rad \n", "Pipeline angle = 5.95° \n", "Darcy friction factor = 0.014 \n", "Density of liquid = 1000.0 kg/m³ \n", "Pressure wave vel. = 500.0 m/s \n", "Simulation timestep = 0.04052 s \n", "----------------------------- \n", "Velocity and pressure distribution are vectors and are accessible via the \n", " get_current_velocity_distribution() and get_current_pressure_distribution() methods of the pipeline object. \n", " See also get_lowest_XXX_per_node() and get_highest_XXX_per_node() methods.\n" ] } ], "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", "pipe.get_info()\n", "\n", "p_0 = pipe.get_initial_pressure_distribution()" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [], "source": [ "# initialization for timeloop\n", "\n", "level_vec = np.zeros_like(t_vec)\n", "level_vec[0] = reservoir.get_current_level()\n", "volume_vec = np.zeros_like(t_vec) \n", "volume_vec[0] = reservoir.get_current_volume()\n", "\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", "Q_old = pipe.get_current_flux_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.full_like(t_vec,v_old[-1])\n", "p_boundary_res = np.zeros_like(t_vec)\n", "p_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", "\n", "# set the boundary conditions for the first timestep\n", "v_boundary_res[0] = v_old[0]\n", "p_boundary_res[0] = p_old[0]\n", "Q_boundary_res[0] = Q_old[0]\n", "p_boundary_tur[0] = p_old[-1]\n", "Q_boundary_tur[0] = Q_old[-1]\n" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [], "source": [ "%matplotlib qt5\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)\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,Pip_head*1.1])\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[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", "# create line objects (lo) whoes values can be updated in time loop to animate the evolution\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,Q_old,marker='.')\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", "\n", "# axs1[0].autoscale()\n", "# axs1[1].autoscale()\n", "\n", "fig1.tight_layout()\n", "fig1.show()" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The cuboid reservoir has the following attributes: \n", "----------------------------- \n", "Base area = 74.0 m² \n", "Outflux area = 0.636 m² \n", "Current level = 8.0 m\n", "Critical level low = 0.0 m \n", "Critical level high = inf m \n", "Volume in reservoir = 592.0 m³ \n", "Current influx = 0.773 m³/s \n", "Current outflux = 0.773 m³/s \n", "Current outflux vel = 1.215 m/s \n", "Current pipe pressure = 7.854 mWS \n", "Simulation timestep = 0.001013 s \n", "Density of liquid = 1000.0 kg/m³ \n", "----------------------------- \n", "\n", "The pipeline has the following attributes: \n", "----------------------------- \n", "Length = 1013.0 m \n", "Diameter = 0.9 m \n", "Hydraulic head = 105.0 m \n", "Number of segments = 50 \n", "Number of nodes = 51 \n", "Length per segments = 20.26 m \n", "Pipeline angle = 0.104 rad \n", "Pipeline angle = 5.95° \n", "Darcy friction factor = 0.014 \n", "Density of liquid = 1000.0 kg/m³ \n", "Pressure wave vel. = 500.0 m/s \n", "Simulation timestep = 0.04052 s \n", "----------------------------- \n", "Velocity and pressure distribution are vectors and are accessible via the \n", " get_current_velocity_distribution() and get_current_pressure_distribution() methods of the pipeline object. \n", " See also get_lowest_XXX_per_node() and get_highest_XXX_per_node() methods.\n" ] } ], "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", " volume_vec[it_pipe] = reservoir.get_current_volume() \n", " \n", " # set boundary conditions for the next timestep of the characteristic method\n", " p_boundary_res[it_pipe] = reservoir.get_current_pressure()\n", " # v_boundary_tur[it_pipe] = flux_init/Pip_area\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", " Q_boundary_res[it_pipe] = pipe.get_current_flux_distribution()[0]\n", " Q_boundary_tur[it_pipe] = pipe.get_current_flux_distribution()[-1]\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", " # remove line-objects to autoscale axes (there is definetly a better way, but this works ¯\\_(ツ)_/¯ )\n", " if it_pipe%50 == 0: # only plot every 50th iteration for performance reasons (plotting takes the most amount of time)\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],2))+ ' s / '+str(round(t_vec[-1],2)) + ' s' )\n", " fig1.canvas.draw() # force figure output\n", " fig1.tight_layout()\n", " fig1.show()\n", " plt.pause(0.1) \n", "\n", "reservoir.get_info(full=True)\n", "pipe.get_info()" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [], "source": [ "level_plot_min = 0\n", "level_plot_max = 15\n", "\n", "fig3,axs3 = plt.subplots(2,2,figsize=(16,9))\n", "fig3.suptitle('Fläche = '+str(Res_area_base)+'\\n'+'Kp = '+str(Con_K_p)+' Ti = '+str(Con_T_i))\n", "axs3[0,0].set_title('Level and Volume reservoir')\n", "axs3[0,0].plot(t_vec,level_vec,label='level')\n", "axs3[0,0].plot(t_vec,np.full_like(t_vec,Res_level_crit_lo),label='level_limit',c='r')\n", "axs3[0,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", "axs3[0,0].set_ylabel(r'$h$ [m]')\n", "axs3[0,0].set_ylim(level_plot_min,level_plot_max)\n", "x_twin_00 = axs3[0,0].twinx()\n", "x_twin_00.set_ylabel(r'$V$ [$\\mathrm{m}^3$]')\n", "x_twin_00.plot(t_vec,volume_vec)\n", "x_twin_00.set_ylim(volume_plot_min,volume_plot_max)\n", "axs3[0,0].legend()\n", "\n", "# axs3[0,1].set_title('LA')\n", "# axs3[0,1].plot(t_vec,100*OL_T1_LA_soll_vec,label='OL_T1 Target',c='b')\n", "# axs3[0,1].scatter(t_vec[::200],100*OL_T1_LA_ist_vec[::200],label='OL_T1 Actual',c='b',marker='+')\n", "# axs3[0,1].plot(t_vec,100*OL_T2_LA_soll_vec,label='OL_T2 Target',c='g')\n", "# axs3[0,1].scatter(t_vec[::200],100*OL_T2_LA_ist_vec[::200],label='OL_T2 Actual',c='g',marker='+')\n", "# axs3[0,1].plot(t_vec,100*UL_T1_LA_soll_vec,label='UL_T1 Target',c='r')\n", "# axs3[0,1].scatter(t_vec[::200],100*UL_T1_LA_ist_vec[::200],label='UL_T1 Actual',c='r',marker='+')\n", "# axs3[0,1].plot(t_vec,100*UL_T2_LA_soll_vec,label='UL_T2 Target',c='k')\n", "# axs3[0,1].scatter(t_vec[::200],100*UL_T2_LA_ist_vec[::200],label='UL_T2 Actual',c='k',marker='+')\n", "# axs3[0,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", "# axs3[0,1].set_ylabel(r'$LA$ [%]')\n", "# axs3[0,1].legend()\n", "\n", "axs3[1,0].set_title('Fluxes')\n", "axs3[1,0].plot(t_vec,np.full_like(t_vec,flux_init),label='Influx')\n", "axs3[1,0].plot(t_vec,Q_boundary_res,label='Outflux')\n", "axs3[1,0].scatter(t_vec[::200],Q_boundary_tur[::200],label='Flux Turbine',c='g',marker='+')\n", "axs3[1,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", "axs3[1,0].set_ylabel(r'$Q$ [$\\mathrm{m}^3/\\mathrm{s}$]')\n", "axs3[1,0].legend()\n", "\n", "axs3[1,1].set_title('Pressure change vs t=0 at reservoir and turbine')\n", "axs3[1,1].plot(t_vec,pressure_conversion(p_boundary_res-p_boundary_res[0],pUnit_calc, pUnit_conv),label='Reservoir')\n", "axs3[1,1].plot(t_vec,pressure_conversion(p_boundary_tur-p_boundary_tur[0],pUnit_calc, pUnit_conv),label='Turbine')\n", "axs3[1,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", "axs3[1,1].set_ylabel(r'$p$ ['+pUnit_conv+']')\n", "axs3[1,1].legend()\n", "\n", "fig3.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 }