diff --git a/.vscode/settings.json b/.vscode/settings.json deleted file mode 100644 index 7a73a41..0000000 --- a/.vscode/settings.json +++ /dev/null @@ -1,2 +0,0 @@ -{ -} \ No newline at end of file diff --git a/Main_Programm.ipynb b/Main_Programm.ipynb index 5fd7abf..9e54cdf 100644 --- a/Main_Programm.ipynb +++ b/Main_Programm.ipynb @@ -33,12 +33,12 @@ "h_pipe = 200 # hydraulic head without reservoir [m] \n", "alpha = np.arcsin(h_pipe/L) # Höhenwinkel der Druckrohrleitung \n", "n = 10 # number of pipe segments in discretization\n", - "#consider replacing Q0 with a vector be be more flexible in initial conditions\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", "v0 = Q0/A_pipe # initial flow velocity [m/s]\n", "f_D = 0.1 # Darcy friction factor\n", "c = 400. # propagation velocity of the pressure wave [m/s]\n", - "#consider prescribing a total simulation time and deducting the number of timesteps from that\n", + "# consider prescribing a total simulation time and deducting the number of timesteps from that\n", "nt = 100 # number of time steps after initial conditions\n", "\n", "# derivatives of the pipeline constants\n", diff --git a/Main_Programm_demo.ipynb b/Main_Programm_demo.ipynb new file mode 100644 index 0000000..ecf05fe --- /dev/null +++ b/Main_Programm_demo.ipynb @@ -0,0 +1,305 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 8, + "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" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# for demoing I\n", + "# pipeline\n", + "L = 1000. # length of pipeline [m]\n", + "D = 1. # pipe diameter [m]\n", + "h_pipe = 200 # hydraulic head without reservoir [m] \n", + "Q0 = 2. # initial flow in whole pipe [m³/s]\n", + "f_D = 0.1 # Darcy friction factor\n", + "c = 400. # propagation velocity of the pressure wave [m/s]\n", + "\n", + "\n", + "# reservoir\n", + "area_base = 20. # total base are of the cuboid reservoir [m²] \n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "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", + "\n", + "A_pipe = D**2/4*np.pi # pipeline area\n", + "alpha = np.arcsin(h_pipe/L) # Höhenwinkel der Druckrohrleitung \n", + "n = 10 # number of pipe segments in discretization\n", + "# consider replacing Q0 with a vector be be more flexible in initial conditions\n", + "v0 = Q0/A_pipe # initial flow velocity [m/s]\n", + "# consider prescribing a total simulation time and deducting the number of timesteps from that\n", + "nt = 100 # number of time steps after initial conditions\n", + "\n", + "# derivatives of the pipeline constants\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", + "h_res = 20. # water level in upstream reservoir [m]\n", + "p0 = rho*g*h_res-v0**2*rho/2\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,n+1)*h_pipe/n # hydraulic head of pipeline at each node np.arange(0,0) does not yield the intended result\n", + "v_init = np.full(nn,Q0/(D**2/4*np.pi)) # initial velocity distribution in pipeline\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 # water level in upstream reservoir [m]\n", + "# replace influx by vector\n", + "initial_influx = 0. # initial influx of volume to the reservoir [m³/s]\n", + "initial_outflux = Q0 # initial outflux of volume from the reservoir to the pipeline [m³/s]\n", + "initial_pipeline_pressure = p0 # Initial condition for the static pipeline pressure at the reservoir (= hydrostatic pressure - dynamic pressure) \n", + "initial_pressure_unit = 'Pa' # DO NOT CHANGE! for pressure conversion in print statements and plot labels \n", + "conversion_pressure_unit = 'mWS' # for pressure conversion in print statements and plot labels\n", + "area_outflux = A_pipe # outlfux area of the reservoir, given by pipeline area [m²]\n", + "critical_level_low = 0. # for yet-to-be-implemented warnings[m]\n", + "critical_level_high = np.inf # for yet-to-be-implemented warnings[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": 10, + "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.set_pressure(initial_pipeline_pressure,initial_pressure_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,initial_pressure_unit,conversion_pressure_unit)\n", + "pipe.set_initial_flow_velocity(v_init)\n", + "\n", + "# display the attributes of the created reservoir and pipeline object\n", + "# V.get_info(full=True)\n", + "# pipe.get_info()" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "# initialization for timeloop\n", + "\n", + "# prepare the vectors in which the pressure and velocity distribution in the pipeline from the previous timestep are stored\n", + "v_old = v_init.copy()\n", + "p_old = p_init.copy()\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.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", + "\n", + "# prepare the vectors that store the temporal evolution of the level in the reservoir\n", + "level_vec = np.full_like(t_vec,initial_level) # level at the end of each pipeline timestep\n", + "level_vec_2 = np.empty([nt_eRK4]) # level throughout each reservoir timestep-used for plotting and overwritten afterwards\n", + "\n", + "# set the boudary conditions for the first timestep\n", + "v_boundary_res[0] = v_old[0]\n", + "p_boundary_res[0] = p_old[0]\n", + "p_boundary_tur[0] = p_old[-1]\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# for demoing II\n", + "v_boundary_tur[0] = v_old[-1] \n", + "v_boundary_tur[1:] = 0 # instantaneous closing\n", + "# v_boundary_tur[0:20] = np.linspace(v_old[-1],0,20) # overwrite for finite closing time - linear case\n", + "const = int(np.min([100,round(nt/1.1)]))\n", + "v_boundary_tur[0:const] = v_old[1]*np.cos(t_vec[0:const]*2*np.pi/5)**2" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "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(2,1)\n", + "axs1[0].set_title('Pressure distribution in pipeline')\n", + "axs1[1].set_title('Velocity distribution in pipeline')\n", + "axs1[0].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", + "axs1[0].set_ylabel(r'$p$ ['+conversion_pressure_unit+']')\n", + "axs1[1].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", + "axs1[1].set_ylabel(r'$v$ [$\\mathrm{m} / \\mathrm{s}$]')\n", + "lo_00, = axs1[0].plot(pl_vec,pressure_conversion(pipe.p_old,initial_pressure_unit, conversion_pressure_unit)[0],marker='.')\n", + "lo_01, = axs1[1].plot(pl_vec,pipe.v_old,marker='.')\n", + "axs1[0].autoscale()\n", + "axs1[1].autoscale()\n", + "# displaying the reservoir level within each pipeline timestep\n", + "# axs1[2].set_title('Level reservoir')\n", + "# axs1[2].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "# axs1[2].set_ylabel(r'$h$ [m]')\n", + "# lo_02, = axs1[2].plot(level_vec_2)\n", + "# axs1[2].autoscale()\n", + "fig1.tight_layout()\n", + "plt.show()\n", + "plt.pause(1)\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", + " # set initial conditions for the reservoir time evolution calculted with e-RK4\n", + " V.pressure = p_old[0]\n", + " V.outflux = v_old[0]\n", + " # calculate the time evolution of the reservoir level within each pipeline timestep to avoid runaway numerical error\n", + " for it_res in range(nt_eRK4):\n", + " V.e_RK_4() # call e-RK4 to update outflux\n", + " V.level = V.update_level(V.timestep) # \n", + " V.set_volume() # update volume in reservoir\n", + " level_vec_2[it_res] = V.level # save for plotting\n", + " if (V.level < critical_level_low) or (V.level > critical_level_high): # make sure to never exceed critical levels\n", + " i_max = it_pipe # for plotting only calculated values\n", + " break \n", + " level_vec[it_pipe] = V.level \n", + "\n", + " # set boundary conditions for the next timestep of the characteristic method\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", + " # the the boundary conditions in the pipe.object and thereby calculate boundary pressure at turbine\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", + " # perform the next timestep via the characteristic method\n", + " pipe.timestep_characteristic_method()\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(pipe.p_old,initial_pressure_unit, conversion_pressure_unit)[0],marker='.',c='blue')\n", + " lo_01, = axs1[1].plot(pl_vec,pipe.v_old,marker='.',c='blue')\n", + " # lo_02, = axs1[2].plot(level_vec_2,c='blue')\n", + " fig1.suptitle(str(it_pipe))\n", + " fig1.canvas.draw()\n", + " fig1.tight_layout()\n", + " plt.pause(0.00001) \n", + "\n", + " # prepare for next loop\n", + " p_old = pipe.p_old\n", + " v_old = pipe.v_old \n", + "\n", + " \n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "# plot time evolution of boundary pressure and velocity as well as the reservoir level\n", + "\n", + "fig2,axs2 = plt.subplots(3,2)\n", + "axs2[0,0].plot(t_vec,pressure_conversion(p_boundary_res,initial_pressure_unit, conversion_pressure_unit)[0])\n", + "axs2[0,1].plot(t_vec,v_boundary_res)\n", + "axs2[1,0].plot(t_vec,pressure_conversion(p_boundary_tur,initial_pressure_unit, conversion_pressure_unit)[0])\n", + "axs2[1,1].plot(t_vec,v_boundary_tur)\n", + "axs2[2,0].plot(t_vec,level_vec)\n", + "axs2[0,0].set_title('Pressure reservoir')\n", + "axs2[0,1].set_title('Velocity reservoir')\n", + "axs2[1,0].set_title('Pressure turbine')\n", + "axs2[1,1].set_title('Velocity turbine')\n", + "axs2[2,0].set_title('Level reservoir')\n", + "axs2[0,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs2[0,0].set_ylabel(r'$p$ ['+conversion_pressure_unit+']')\n", + "axs2[0,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs2[0,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n", + "axs2[1,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs2[1,0].set_ylabel(r'$p$ ['+conversion_pressure_unit+']')\n", + "axs2[1,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs2[1,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n", + "axs2[2,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs2[2,0].set_ylabel(r'$h$ [m]')\n", + "axs2[2,1].axis('off')\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 +} diff --git a/__pycache__/Druckrohrleitung.cpython-38.pyc b/__pycache__/Druckrohrleitung.cpython-38.pyc deleted file mode 100644 index 82b5992..0000000 Binary files a/__pycache__/Druckrohrleitung.cpython-38.pyc and /dev/null differ