probably working combined code :D
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Brantegger Georg
272
combine_pipeline_and_reservoir.ipynb
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272
combine_pipeline_and_reservoir.ipynb
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{
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"cells": [
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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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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"\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\n",
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"from Druckrohrleitung.Druckrohrleitung_class_file import Druckrohrleitung_class\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": 6,
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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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"# physics\n",
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"g = 9.81 # gravitational acceleration [m/s²]\n",
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"rho = 1000. # density of water [kg/m³]\n",
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"\n",
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"# pipeline\n",
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"L = 1000. # length of pipeline [m]\n",
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"D = 1. # pipe diameter [m]\n",
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"#consider replacing Q0 with a vector be be more flexible in initial conditions\n",
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"Q0 = 2 # initial flow in whole pipe [m³/s]\n",
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"A_pipe = D**2/4*np.pi # pipeline area\n",
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"v0 = Q0/A_pipe # initial flow velocity [m/s]\n",
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"h_res = 20. # water level in upstream reservoir [m]\n",
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"n = 10 # number of pipe segments in discretization\n",
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"nt = 10000 # number of time steps after initial conditions\n",
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"f_D = 0.01 # Darcy friction factor\n",
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"c = 400. # propagation velocity of the pressure wave [m/s]\n",
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"h_pipe = 300 # hydraulic head without reservoir [m] \n",
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"alpha = np.arcsin(h_pipe/L) # Höhenwinkel der Druckrohrleitung \n",
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"\n",
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"# derivatives of the pipeline constants\n",
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"p0 = rho*g*h_res-v0**2*rho/2\n",
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"dx = L/n # length of each pipe segment\n",
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"dt = dx/c # timestep according to method of characterisitics\n",
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"nn = n+1 # number of nodes\n",
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"pl_vec = np.arange(0,nn*dx,dx) # pl = pipe-length. position of the nodes on the pipeline\n",
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"t_vec = np.arange(0,nt*dt,dt) # time vector\n",
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"h_vec = np.arange(0,h_pipe+h_pipe/n,h_pipe/n) # hydraulic head of pipeline at each node\n",
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"\n",
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"v_init = np.full(nn,Q0/(D**2/4*np.pi))\n",
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"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",
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"\n",
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"\n",
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"# reservoir\n",
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"initial_level = h_res # m\n",
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"initial_influx = 0. # m³/s\n",
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"initial_outflux = Q0 # m³/s\n",
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"initial_pipeline_pressure = p0 # Pa \n",
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"initial_pressure_unit = 'Pa'\n",
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"conversion_pressure_unit = 'Pa'\n",
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"area_base = 5. # m² really large base are to ensure level never becomes < 0\n",
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"area_outflux = A_pipe # m²\n",
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"critical_level_low = 0. # m\n",
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"critical_level_high = np.inf # m\n",
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"\n",
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"# make sure e-RK4 method of reservoir has a small enough timestep to avoid runaway numerical error\n",
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"nt_eRK4 = 1000 # number of simulation steps of reservoir in between timesteps of pipeline \n",
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"simulation_timestep = dt/nt_eRK4\n",
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"\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": 7,
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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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"(3.6368236494728476, 'mWS')\n"
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]
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}
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],
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"source": [
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"print(pressure_conversion(-np.sum((-v_init**2*rho/2)),'Pa','mWS'))"
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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": 8,
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"metadata": {},
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"outputs": [],
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"source": [
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"# create objects\n",
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"\n",
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"V = Ausgleichsbecken_class(area_base,area_outflux,critical_level_low,critical_level_high,simulation_timestep)\n",
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"V.set_initial_level(initial_level) \n",
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"V.set_influx(initial_influx)\n",
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"V.set_outflux(initial_outflux)\n",
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"V.pressure, V.pressure_unit = pressure_conversion(initial_pipeline_pressure,input_unit = initial_pressure_unit, target_unit = conversion_pressure_unit)\n",
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"\n",
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"pipe = Druckrohrleitung_class(L,D,n,alpha,f_D)\n",
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"pipe.set_pressure_propagation_velocity(c)\n",
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"pipe.set_number_of_timesteps(nt)\n",
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"pipe.set_initial_pressure(p_init)\n",
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"pipe.set_initial_flow_velocity(v_init)"
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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": 9,
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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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"v_old = v_init.copy()\n",
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"p_old = p_init.copy()\n",
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"\n",
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"#vectors to store boundary conditions\n",
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"v_boundary_res = np.empty_like(t_vec)\n",
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"v_boundary_tur = np.empty_like(t_vec)\n",
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"p_boundary_res = np.empty_like(t_vec)\n",
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"p_boundary_tur = np.empty_like(t_vec)\n",
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"level_vec = np.empty_like(t_vec)\n",
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"level_vec_2 = np.full([nt_eRK4],initial_level)\n",
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"\n",
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"v_boundary_res[0] = v_old[0]\n",
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"v_boundary_tur[0] = v_old[-1] # instantaneous closing\n",
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"# v_boundary_tur[1:] = 0\n",
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"v_boundary_tur[0:1000] = np.linspace(v_old[-1],0,1000) # finite closing time - linear case\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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"level_vec[0] = initial_level\n",
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"\n",
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"v_boundary_tur[1:] = 0 # instantaneous closing"
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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": 10,
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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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"# time loop\n",
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"\n",
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"\n",
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"# fig2,axs2 = plt.subplots(3,1)\n",
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"# axs2[0].set_title('Pressure distribution in pipeline')\n",
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"# axs2[1].set_title('Velocity distribution in pipeline')\n",
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"# axs2[0].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
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"# axs2[0].set_ylabel(r'$p$ [mWS]')\n",
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"# axs2[1].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
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"# axs2[1].set_ylabel(r'$p$ [mWS]')\n",
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"# lo_00, = axs2[0].plot(pl_vec,pressure_conversion(pipe.p_old,'Pa','mWS')[0],marker='.')\n",
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"# lo_01, = axs2[1].plot(pl_vec,pipe.v_old,marker='.')\n",
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"# lo_02, = axs2[2].plot(level_vec_2)\n",
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"# axs2[0].autoscale()\n",
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"# axs2[1].autoscale()\n",
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"# axs2[2].autoscale()\n",
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"# fig2.tight_layout()\n",
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"\n",
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"# loop through time steps of the pipeline\n",
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"for it_pipe in range(1,pipe.nt):\n",
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"\n",
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"# for each pipeline timestep, execute nt_eRK4 timesteps of the reservoir code\n",
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" V.pressure = p_old[0]\n",
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" V.outflux = v_old[0]\n",
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" for it_res in range(nt_eRK4):\n",
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" V.e_RK_4()\n",
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" V.level = V.update_level(V.timestep)\n",
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" V.set_volume()\n",
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" level_vec_2[it_res] = V.level\n",
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" if (V.level < critical_level_low) or (V.level > critical_level_high):\n",
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" i_max = it_pipe\n",
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" print('broke')\n",
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" break\n",
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" level_vec[it_pipe] = V.level\n",
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"\n",
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" p_boundary_res[it_pipe] = rho*g*V.level-v_old[1]**2*rho/2\n",
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" 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",
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" +dt*g*np.sin(alpha)\n",
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"\n",
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"\n",
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" pipe.set_boundary_conditions_next_timestep(v_boundary_res[it_pipe],p_boundary_res[it_pipe],v_boundary_tur[it_pipe])\n",
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" p_boundary_tur[it_pipe] = pipe.p_boundary_tur\n",
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"\n",
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" pipe.timestep_characteristic_method()\n",
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"\n",
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"\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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" # lo_00, = axs2[0].plot(pl_vec,pressure_conversion(pipe.p_old,'Pa','mWS')[0],marker='.',c='blue')\n",
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" # lo_01, = axs2[1].plot(pl_vec,pipe.v_old,marker='.',c='blue')\n",
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" # lo_02, = axs2[2].plot(level_vec_2,c='blue')\n",
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" # fig2.suptitle(str(it_pipe))\n",
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" # fig2.canvas.draw()\n",
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" # fig2.canvas.flush_events()\n",
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" # fig2.tight_layout()\n",
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" # plt.pause(0.1) \n",
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"\n",
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" p_old = pipe.p_old\n",
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" v_old = pipe.v_old \n",
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"\n",
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" \n",
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" "
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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": 11,
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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(3,2)\n",
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"axs1[0,0].plot(t_vec,pressure_conversion(p_boundary_res,'Pa','mWS')[0])\n",
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"axs1[0,1].plot(t_vec,v_boundary_res)\n",
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"axs1[1,0].plot(t_vec,pressure_conversion(p_boundary_tur,'Pa','mWS')[0])\n",
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"axs1[1,1].plot(t_vec,v_boundary_tur)\n",
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"axs1[2,0].plot(t_vec,level_vec)\n",
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"axs1[0,0].set_title('Pressure Reservoir')\n",
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"axs1[0,1].set_title('Velocity Reservoir')\n",
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"axs1[1,0].set_title('Pressure Turbine')\n",
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"axs1[1,1].set_title('Velocity Turbine')\n",
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"axs1[0,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
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"axs1[0,0].set_ylabel(r'$p$ [mWS]')\n",
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"axs1[0,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
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"axs1[0,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n",
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"axs1[1,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
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"axs1[1,0].set_ylabel(r'$p$ [mWS]')\n",
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"axs1[1,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
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"axs1[1,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n",
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"fig1.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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"metadata": {
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"kernelspec": {
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"display_name": "Python 3.8.13 ('Georg_DT_Slot3')",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.13"
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},
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"orig_nbformat": 4,
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"vscode": {
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"interpreter": {
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"hash": "84fb123bdc47ab647d3782661abcbe80fbb79236dd2f8adf4cef30e8755eb2cd"
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}
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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