321 lines
16 KiB
Plaintext
321 lines
16 KiB
Plaintext
{
|
|
"cells": [
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 1,
|
|
"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": 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 = 10. # [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": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"61.1829727786757\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"print(pressure_conversion(600000,'Pa','mWS'))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 4,
|
|
"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": 5,
|
|
"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": 6,
|
|
"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)\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": 7,
|
|
"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%100 == 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],2))+ ' s / '+str(round(t_vec[-1],2)) + ' s' )\n",
|
|
" fig1.canvas.draw()\n",
|
|
" fig1.tight_layout()\n",
|
|
" fig1.show()\n",
|
|
" plt.pause(0.1) "
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 8,
|
|
"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
|
|
}
|