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code cleanup and commentary

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Brantegger Georg
2022-07-06 10:29:22 +02:00
parent b03bb43c63
commit c81c0ab142
6 changed files with 188 additions and 156 deletions
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combine_pipeline_and_reservoir.ipynb
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@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
"execution_count": 5,
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
@@ -16,7 +16,7 @@
},
{
"cell_type": "code",
"execution_count": 6,
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
@@ -24,47 +24,48 @@
"\n",
"# physics\n",
"g = 9.81 # gravitational acceleration [m/s²]\n",
"rho = 1000. # density of water [kg/m³]\n",
"rho = 1000. # density of water [kg/m³]\n",
"\n",
"# pipeline\n",
"L = 1000. # length of pipeline [m]\n",
"D = 1. # pipe diameter [m]\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",
"A_pipe = D**2/4*np.pi # pipeline area\n",
"v0 = Q0/A_pipe # initial flow velocity [m/s]\n",
"h_res = 20. # water level in upstream reservoir [m]\n",
"n = 10 # number of pipe segments in discretization\n",
"nt = 10000 # number of time steps after initial conditions\n",
"f_D = 0.01 # Darcy friction factor\n",
"c = 400. # propagation velocity of the pressure wave [m/s]\n",
"h_pipe = 300 # hydraulic head without reservoir [m] \n",
"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",
"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",
"nt = 500 # number of time steps after initial conditions\n",
"\n",
"# derivatives of the pipeline constants\n",
"p0 = rho*g*h_res-v0**2*rho/2\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",
"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,h_pipe+h_pipe/n,h_pipe/n) # hydraulic head of pipeline at each node\n",
"\n",
"v_init = np.full(nn,Q0/(D**2/4*np.pi))\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",
"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 # m\n",
"initial_influx = 0. # m³/s\n",
"initial_outflux = Q0 # m³/s\n",
"initial_pipeline_pressure = p0 # Pa \n",
"initial_pressure_unit = 'Pa'\n",
"conversion_pressure_unit = 'Pa'\n",
"area_base = 5. # m² really large base are to ensure level never becomes < 0\n",
"area_outflux = A_pipe # m²\n",
"critical_level_low = 0. # m\n",
"critical_level_high = np.inf # m\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' # for pressure conversion in print statements and plot labels\n",
"conversion_pressure_unit = 'Pa' # for pressure conversion in print statements and plot labels\n",
"area_base = 20. # total base are of the cuboid reservoir [m²] \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",
@@ -73,27 +74,64 @@
]
},
{
"cell_type": "code",
"execution_count": 7,
"cell_type": "markdown",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(3.6368236494728476, 'mWS')\n"
]
}
],
"source": [
"print(pressure_conversion(-np.sum((-v_init**2*rho/2)),'Pa','mWS'))"
"#### Ideas for checks after constant definitions: \n",
"\n",
"- Check that the initial pressure is not negative:\n",
" - may happen, if there is too little hydraulic head to create the initial flow conditions with the given friction\n",
"<br>\n",
"<br>\n",
"- stupidity checks?\n",
" - area > area_outflux ?\n",
" - propable ranges for parameters?\n",
" - angle and height/length fit together?\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The cuboid reservoir has the following attributes: \n",
"----------------------------- \n",
"Base area = 20.0 m² \n",
"Outflux area = 0.785 m² \n",
"Current level = 20.0 m\n",
"Critical level low = 0.0 m \n",
"Critical level high = inf m \n",
"Volume in reservoir = 400.0 m³ \n",
"Current influx = 0.0 m³/s \n",
"Current outflux = 2.0 m³/s \n",
"Simulation timestep = 0.00025 s \n",
"----------------------------- \n",
"\n",
"The pipeline has the following attributes: \n",
"----------------------------- \n",
"Length = 1000.0 m \n",
"Diameter = 1.0 m \n",
"Number of segments = 10 \n",
"Number of nodes = 11 \n",
"Length per segments = 100.0 m \n",
"Pipeline angle = 0.201 rad \n",
"Pipeline angle = 11.537° \n",
"Darcy friction factor = 0.1 \n",
"Density of liquid = 1000 kg/m³ \n",
"Pressure wave vel. = 400.0 m/s \n",
"Simulation timestep = 0.25 s \n",
"Number of timesteps = 500 \n",
"Total simulation time = 125.0 s \n",
"----------------------------- \n",
"Velocity and pressure distribution are vectors and are accessible by the .v and .p attribute of the pipeline object\n"
]
}
],
"source": [
"# create objects\n",
"\n",
@@ -103,11 +141,16 @@
"V.set_outflux(initial_outflux)\n",
"V.pressure, V.pressure_unit = pressure_conversion(initial_pipeline_pressure,input_unit = initial_pressure_unit, target_unit = conversion_pressure_unit)\n",
"\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)\n",
"pipe.set_initial_flow_velocity(v_init)"
"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()"
]
},
{
@@ -118,26 +161,33 @@
"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",
"#vectors to store boundary conditions\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",
"level_vec = np.empty_like(t_vec)\n",
"level_vec_2 = np.full([nt_eRK4],initial_level)\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",
"v_boundary_tur[0] = v_old[-1] # instantaneous closing\n",
"# v_boundary_tur[1:] = 0\n",
"v_boundary_tur[0:1000] = np.linspace(v_old[-1],0,1000) # finite closing time - linear case\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\n",
"p_boundary_res[0] = p_old[0]\n",
"p_boundary_tur[0] = p_old[-1]\n",
"level_vec[0] = initial_level\n",
"\n",
"v_boundary_tur[1:] = 0 # instantaneous closing"
"\n"
]
},
{
@@ -149,62 +199,73 @@
"%matplotlib qt5\n",
"# time loop\n",
"\n",
"\n",
"# fig2,axs2 = plt.subplots(3,1)\n",
"# axs2[0].set_title('Pressure distribution in pipeline')\n",
"# axs2[1].set_title('Velocity distribution in pipeline')\n",
"# axs2[0].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
"# axs2[0].set_ylabel(r'$p$ [mWS]')\n",
"# axs2[1].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
"# axs2[1].set_ylabel(r'$p$ [mWS]')\n",
"# lo_00, = axs2[0].plot(pl_vec,pressure_conversion(pipe.p_old,'Pa','mWS')[0],marker='.')\n",
"# lo_01, = axs2[1].plot(pl_vec,pipe.v_old,marker='.')\n",
"# lo_02, = axs2[2].plot(level_vec_2)\n",
"# axs2[0].autoscale()\n",
"# axs2[1].autoscale()\n",
"# axs2[2].autoscale()\n",
"# fig2.tight_layout()\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'$p$ [mWS]')\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,'Pa','mWS')[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()\n",
" V.level = V.update_level(V.timestep)\n",
" V.set_volume()\n",
" level_vec_2[it_res] = V.level\n",
" if (V.level < critical_level_low) or (V.level > critical_level_high):\n",
" i_max = it_pipe\n",
" print('broke')\n",
" break\n",
" level_vec[it_pipe] = V.level\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",
"\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",
"\n",
" # lo_00.remove()\n",
" # lo_01.remove()\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",
" # lo_00, = axs2[0].plot(pl_vec,pressure_conversion(pipe.p_old,'Pa','mWS')[0],marker='.',c='blue')\n",
" # lo_01, = axs2[1].plot(pl_vec,pipe.v_old,marker='.',c='blue')\n",
" # lo_02, = axs2[2].plot(level_vec_2,c='blue')\n",
" # fig2.suptitle(str(it_pipe))\n",
" # fig2.canvas.draw()\n",
" # fig2.canvas.flush_events()\n",
" # fig2.tight_layout()\n",
" # plt.pause(0.1) \n",
" # plot new pressure and velocity distribution in the pipeline\n",
" lo_00, = axs1[0].plot(pl_vec,pressure_conversion(pipe.p_old,'Pa','mWS')[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",
@@ -218,26 +279,31 @@
"metadata": {},
"outputs": [],
"source": [
"%matplotlib qt5\n",
"fig1,axs1 = plt.subplots(3,2)\n",
"axs1[0,0].plot(t_vec,pressure_conversion(p_boundary_res,'Pa','mWS')[0])\n",
"axs1[0,1].plot(t_vec,v_boundary_res)\n",
"axs1[1,0].plot(t_vec,pressure_conversion(p_boundary_tur,'Pa','mWS')[0])\n",
"axs1[1,1].plot(t_vec,v_boundary_tur)\n",
"axs1[2,0].plot(t_vec,level_vec)\n",
"axs1[0,0].set_title('Pressure Reservoir')\n",
"axs1[0,1].set_title('Velocity Reservoir')\n",
"axs1[1,0].set_title('Pressure Turbine')\n",
"axs1[1,1].set_title('Velocity Turbine')\n",
"axs1[0,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs1[0,0].set_ylabel(r'$p$ [mWS]')\n",
"axs1[0,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs1[0,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n",
"axs1[1,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs1[1,0].set_ylabel(r'$p$ [mWS]')\n",
"axs1[1,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs1[1,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n",
"fig1.tight_layout()\n",
"# 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,'Pa','mWS')[0])\n",
"axs2[0,1].plot(t_vec,v_boundary_res)\n",
"axs2[1,0].plot(t_vec,pressure_conversion(p_boundary_tur,'Pa','mWS')[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'$p$ [mWS]')\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'$p$ [mWS]')\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()"
]
}