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Brantegger Georg
2022-07-06 12:24:14 +02:00
parent eb267866cf
commit c854fe7da8
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.vscode/settings.json vendored
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{
}

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Main_Programm.ipynb
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"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",

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Main_Programm_demo.ipynb Normal file
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{
"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()"
]
}
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__pycache__/Druckrohrleitung.cpython-38.pyc
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