348 lines
17 KiB
Plaintext
348 lines
17 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"from Druckrohrleitung_class_file import Druckrohrleitung_class\n",
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"import matplotlib.pyplot as plt\n",
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"\n",
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"#importing pressure conversion function\n",
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"import sys\n",
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"import os\n",
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"current = os.path.dirname(os.path.realpath('Main_Programm.ipynb'))\n",
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"parent = os.path.dirname(current)\n",
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"sys.path.append(parent)\n",
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"from functions.pressure_conversion import pressure_conversion\n",
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"from Ausgleichsbecken.Ausgleichsbecken_class_file import Ausgleichsbecken_class"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"# define constants\n",
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"\n",
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" # for physics\n",
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"g = 9.81 # [m/s²] gravitational acceleration \n",
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"rho = 1000. # [kg/m³] density of water \n",
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"pUnit_calc = 'Pa' # [text] DO NOT CHANGE! for pressure conversion in print statements and plot labels \n",
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"pUnit_conv = 'mWS' # [text] for pressure conversion in print statements and plot labels\n",
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"\n",
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" # for Turbine\n",
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"Tur_Q_nenn = 0.85 # [m³/s] nominal flux of turbine \n",
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"Tur_p_nenn = pressure_conversion(10.6,'bar',pUnit_calc) # [Pa] nominal pressure of turbine \n",
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"Tur_closingTime = 90. # [s] closing time of turbine\n",
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"\n",
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" # for PI controller\n",
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"Con_targetLevel = 8. # [m]\n",
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"Con_K_p = 0.1 # [-] proportional constant of PI controller\n",
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"Con_T_i = 10. # [s] timespan in which a steady state error is corrected by the intergal term\n",
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"Con_deadbandRange = 0.05 # [m] Deadband range around targetLevel for which the controller does NOT intervene\n",
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"\n",
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" # for pipeline\n",
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"Pip_length = (535.+478.) # [m] length of pipeline\n",
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"Pip_dia = 0.9 # [m] diameter of pipeline\n",
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"Pip_area = Pip_dia**2/4*np.pi # [m²] crossectional area of pipeline\n",
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"Pip_head = 105. # [m] hydraulic head of pipeline without reservoir\n",
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"Pip_angle = np.arcsin(Pip_head/Pip_length) # [rad] elevation angle of pipeline \n",
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"Pip_n_seg = 50 # [-] number of pipe segments in discretization\n",
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"Pip_f_D = 0.014 # [-] Darcy friction factor\n",
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"Pip_pw_vel = 500. # [m/s] propagation velocity of the pressure wave (pw) in the given pipeline\n",
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" # derivatives of the pipeline constants\n",
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"Pip_dx = Pip_length/Pip_n_seg # [m] length of each pipe segment\n",
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"Pip_dt = Pip_dx/Pip_pw_vel # [s] timestep according to method of characteristics\n",
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"Pip_nn = Pip_n_seg+1 # [1] number of nodes\n",
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"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",
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"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",
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"\n",
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" # for reservoir\n",
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"Res_area_base = 74. # [m²] total base are of the cuboid reservoir \n",
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"Res_area_out = Pip_area # [m²] outflux area of the reservoir, given by pipeline area\n",
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"Res_level_crit_lo = 0. # [m] for yet-to-be-implemented warnings\n",
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"Res_level_crit_hi = np.inf # [m] for yet-to-be-implemented warnings\n",
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"Res_dt_approx = 1e-3 # [s] approx. timestep of reservoir time evolution to ensure numerical stability (see Res_nt why approx.)\n",
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"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",
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"Res_dt = Pip_dt/Res_nt # [s] harmonised timestep of reservoir time evolution\n",
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"\n",
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" # for general simulation\n",
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"flux_init = Tur_Q_nenn/1.1 # [m³/s] initial flux through whole system for steady state initialization \n",
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"level_init = Con_targetLevel # [m] initial water level in upstream reservoir for steady state initialization\n",
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"simTime_target = 600. # [s] target for total simulation time (will vary slightly to fit with Pip_dt)\n",
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"nt = int(simTime_target//Pip_dt) # [1] Number of timesteps of the whole system\n",
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"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"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"The pipeline has the following attributes: \n",
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"----------------------------- \n",
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"Length = 1013.0 m \n",
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"Diameter = 0.9 m \n",
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"Hydraulic head = 105.0 m \n",
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"Number of segments = 50 \n",
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"Number of nodes = 51 \n",
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"Length per segments = 20.26 m \n",
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"Pipeline angle = 0.104 rad \n",
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"Pipeline angle = 5.95° \n",
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"Darcy friction factor = 0.014 \n",
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"Density of liquid = 1000.0 kg/m³ \n",
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"Pressure wave vel. = 500.0 m/s \n",
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"Simulation timestep = 0.04052 s \n",
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"----------------------------- \n",
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"Velocity and pressure distribution are vectors and are accessible by the .v and .p attribute of the pipeline object\n",
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"The pipeline has the following attributes: \n",
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"----------------------------- \n",
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"Length = 1013.0 m \n",
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"Diameter = 0.9 m \n",
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"Hydraulic head = 105.0 m \n",
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"Number of segments = 50 \n",
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"Number of nodes = 51 \n",
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"Length per segments = 20.26 m \n",
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"Pipeline angle = 0.104 rad \n",
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"Pipeline angle = 5.95° \n",
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"Darcy friction factor = 0.014 \n",
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"Density of liquid = 1000.0 kg/m³ \n",
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"Pressure wave vel. = 500.0 m/s \n",
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"Simulation timestep = 0.04052 s \n",
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"----------------------------- \n",
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"Velocity and pressure distribution are vectors and are accessible by the .v and .p attribute of the pipeline object\n"
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]
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}
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],
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"source": [
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"# create objects\n",
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"\n",
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"# Upstream reservoir\n",
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"reservoir = Ausgleichsbecken_class(Res_area_base,Res_area_out,Res_dt,pUnit_conv,Res_level_crit_lo,Res_level_crit_hi,rho)\n",
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"reservoir.set_steady_state(flux_init,level_init)\n",
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"\n",
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"# pipeline\n",
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"pipe = Druckrohrleitung_class(Pip_length,Pip_dia,Pip_head,Pip_n_seg,Pip_f_D,Pip_pw_vel,Pip_dt,pUnit_conv,rho)\n",
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"pipe.set_steady_state(flux_init,reservoir.get_current_pressure())\n",
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"pipe.get_info()\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [],
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"source": [
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"# initialization for timeloop\n",
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"\n",
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"level_vec = np.zeros_like(t_vec)\n",
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"level_vec[0] = reservoir.get_current_level()\n",
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"\n",
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"# prepare the vectors in which the pressure and velocity distribution in the pipeline from the previous timestep are stored\n",
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"v_old = pipe.get_current_velocity_distribution()\n",
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"p_old = pipe.get_current_pressure_distribution()\n",
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"\n",
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"# prepare the vectors in which the temporal evolution of the boundary conditions are stored\n",
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" # keep in mind, that the velocity at the turbine and the pressure at the reservoir are set manually and\n",
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" # through the time evolution of the reservoir respectively \n",
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" # the pressure at the turbine and the velocity at the reservoir are calculated from the method of characteristics\n",
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"v_boundary_res = np.zeros_like(t_vec)\n",
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"v_boundary_tur = np.zeros_like(t_vec)\n",
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"p_boundary_res = np.zeros_like(t_vec)\n",
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"p_boundary_tur = np.zeros_like(t_vec)\n",
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"\n",
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"# set the boundary conditions for the first timestep\n",
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"v_boundary_res[0] = v_old[0]\n",
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"v_boundary_tur[0] = v_old[-1] \n",
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"p_boundary_res[0] = p_old[0]\n",
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"p_boundary_tur[0] = p_old[-1]\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [],
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"source": [
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"%matplotlib qt5\n",
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"fig1,axs1 = plt.subplots(2,1)\n",
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"axs1[0].set_title('Pressure distribution in pipeline')\n",
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"axs1[0].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
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"axs1[0].set_ylabel(r'$p$ [mWS]')\n",
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"axs1[0].set_ylim([0.9*np.min(pressure_conversion(p_old,'Pa',pUnit_conv)),1.1*np.max(pressure_conversion(p_old,'Pa',pUnit_conv))])\n",
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"lo_00, = axs1[0].plot(Pip_x_vec,pressure_conversion(p_old,'Pa',pUnit_conv),marker='.')\n",
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"\n",
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"axs1[1].set_title('Velocity distribution in pipeline')\n",
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"axs1[1].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
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"axs1[1].set_ylabel(r'$v$ [m/s]')\n",
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"lo_01, = axs1[1].plot(Pip_x_vec,v_old,marker='.')\n",
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"axs1[1].autoscale()\n",
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"# axs1[1].set_ylim([0.9*np.min(v_old),1.1*np.max(v_boundary_res)])\n",
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"\n",
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"fig1.tight_layout()\n",
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"plt.pause(1)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"The cuboid reservoir has the following attributes: \n",
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"----------------------------- \n",
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"Base area = 74.0 m² \n",
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"Outflux area = 0.636 m² \n",
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"Current level = 8.0 m\n",
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"Critical level low = 0.0 m \n",
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"Critical level high = inf m \n",
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"Volume in reservoir = 592.0 m³ \n",
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"Current influx = 0.773 m³/s \n",
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"Current outflux = 0.773 m³/s \n",
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"Current outflux vel = 1.215 m/s \n",
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"Current pipe pressure = 7.854 mWS \n",
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"Simulation timestep = 0.001013 s \n",
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"Density of liquid = 1000.0 kg/m³ \n",
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"----------------------------- \n",
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"\n",
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"The pipeline has the following attributes: \n",
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"----------------------------- \n",
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"Length = 1013.0 m \n",
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"Diameter = 0.9 m \n",
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"Hydraulic head = 105.0 m \n",
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"Number of segments = 50 \n",
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"Number of nodes = 51 \n",
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"Length per segments = 20.26 m \n",
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"Pipeline angle = 0.104 rad \n",
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"Pipeline angle = 5.95° \n",
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"Darcy friction factor = 0.014 \n",
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"Density of liquid = 1000.0 kg/m³ \n",
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"Pressure wave vel. = 500.0 m/s \n",
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"Simulation timestep = 0.04052 s \n",
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"----------------------------- \n",
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"Velocity and pressure distribution are vectors and are accessible by the .v and .p attribute of the pipeline object\n"
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]
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}
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],
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"source": [
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"for it_pipe in range(1,nt+1):\n",
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"# for each pipeline timestep, execute nt_eRK4 timesteps of the reservoir code\n",
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" # set initial conditions for the reservoir time evolution calculted with e-RK4\n",
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" reservoir.set_pressure(p_old[0],display_warning=False)\n",
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" reservoir.set_outflux(v_old[0]*Pip_area,display_warning=False)\n",
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" # calculate the time evolution of the reservoir level within each pipeline timestep to avoid runaway numerical error\n",
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" for it_res in range(Res_nt):\n",
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" reservoir.timestep_reservoir_evolution() \n",
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" level_vec[it_pipe] = reservoir.get_current_level() \n",
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"\n",
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" \n",
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" # set boundary conditions for the next timestep of the characteristic method\n",
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" p_boundary_res[it_pipe] = reservoir.get_current_pressure()\n",
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" v_boundary_tur[it_pipe] = flux_init/Pip_area\n",
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"\n",
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" # the the boundary conditions in the pipe.object and thereby calculate boundary pressure at turbine\n",
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" pipe.set_boundary_conditions_next_timestep(p_boundary_res[it_pipe],v_boundary_tur[it_pipe])\n",
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" p_boundary_tur[it_pipe] = pipe.get_current_pressure_distribution()[-1]\n",
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" v_boundary_res[it_pipe] = pipe.get_current_velocity_distribution()[0]\n",
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"\n",
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" # perform the next timestep via the characteristic method\n",
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" pipe.timestep_characteristic_method()\n",
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"\n",
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" # prepare for next loop\n",
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" p_old = pipe.get_current_pressure_distribution()\n",
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" v_old = pipe.get_current_velocity_distribution()\n",
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"\n",
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" # plot some stuff\n",
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" # remove line-objects to autoscale axes (there is definetly a better way, but this works ¯\\_(ツ)_/¯ )\n",
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" lo_00.remove()\n",
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" lo_01.remove()\n",
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" # lo_02.remove()\n",
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" # plot new pressure and velocity distribution in the pipeline\n",
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" lo_00, = axs1[0].plot(Pip_x_vec,pressure_conversion(p_old,'Pa', pUnit_conv),marker='.',c='blue')\n",
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" lo_01, = axs1[1].plot(Pip_x_vec,v_old,marker='.',c='blue')\n",
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" \n",
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" fig1.suptitle(str(round(t_vec[it_pipe],2)) + '/' + str(round(t_vec[-1],2)))\n",
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" fig1.canvas.draw()\n",
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" fig1.tight_layout()\n",
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" plt.pause(0.000001)\n",
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"\n",
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"reservoir.get_info(full=True)\n",
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"pipe.get_info()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [],
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"source": [
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"fig2,axs2 = plt.subplots(2,2)\n",
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"axs2[0,0].set_title('Pressure Reservoir')\n",
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"axs2[0,0].plot(t_vec,pressure_conversion(p_boundary_res,pUnit_calc,pUnit_conv))\n",
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"axs2[0,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
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"axs2[0,0].set_ylabel(r'$p$ [mWS]')\n",
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"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",
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"\n",
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"axs2[0,1].set_title('Velocity Reservoir')\n",
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"axs2[0,1].plot(t_vec,v_boundary_res)\n",
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"axs2[0,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
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"axs2[0,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n",
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"axs2[0,1].set_ylim([0.9*np.min(v_boundary_res),1.1*np.max(v_boundary_res)])\n",
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"\n",
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"axs2[1,0].set_title('Pressure Turbine')\n",
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"axs2[1,0].plot(t_vec,pressure_conversion(p_boundary_tur,pUnit_calc,pUnit_conv))\n",
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"axs2[1,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
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"axs2[1,0].set_ylabel(r'$p$ [mWS]')\n",
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"axs2[1,0].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",
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"\n",
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"axs2[1,1].set_title('Velocity Turbine')\n",
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"axs2[1,1].plot(t_vec,v_boundary_tur)\n",
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"axs2[1,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
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"axs2[1,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n",
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"axs2[1,1].set_ylim([0.95*np.min(v_boundary_tur),1.05*np.max(v_boundary_tur)])\n",
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"\n",
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"fig2.tight_layout()\n",
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"plt.show()"
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]
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}
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],
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