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Merge branch 'Dev'

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Brantegger Georg
2022-08-08 07:53:06 +02:00
parent 1aee8debc4 5a790d5ca5
commit 112c9d427a
11 changed files with 1432 additions and 856 deletions
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215
Ausgleichsbecken/Ausgleichsbecken_class_file.py
View File

@@ -15,10 +15,10 @@ def FODE_function(x_out,h,A,A_a,p,rho,g):
# https://www.youtube.com/watch?v=8HO2LwqOhqQ
# adapted for a pressurized pipeline into which the reservoir effuses
# and flow direction
# x_out ... effusion velocity
# x_out ... effusion velocity
# h ... level in the reservoir
# A_a ... Outflux_Area
# A ... Reservoir_Area
# A_a ... Area_outflux
# A ... Area_reservoir_base
# g ... gravitational acceleration
# rho ... density of the liquid in the reservoir
f = x_out*abs(x_out)/h*(A_a/A-1.)+g-p/(rho*h)
@@ -28,168 +28,202 @@ def FODE_function(x_out,h,A,A_a,p,rho,g):
class Ausgleichsbecken_class:
# units
# make sure that units and print units are the same
# units are used to label graphs and print units are used to have a bearable format when using pythons print()
area_unit = r'$\mathrm{m}^2$'
area_outflux_unit = r'$\mathrm{m}^2$'
density_unit = r'$\mathrm{kg}/\mathrm{m}^3$'
flux_unit = r'$\mathrm{m}^3/\mathrm{s}$'
level_unit = 'm'
pressure_unit = 'Pa'
time_unit = 's'
velocity_unit = r'$\mathrm{m}/\mathrm{s}$'
volume_unit = r'$\mathrm{m}^3$'
# units are used to label graphs and disp units are used to have a bearable format when using pythons print()
area_unit = r'$\mathrm{m}^2$'
area_outflux_unit = r'$\mathrm{m}^2$'
density_unit = r'$\mathrm{kg}/\mathrm{m}^3$'
flux_unit = r'$\mathrm{m}^3/\mathrm{s}$'
level_unit = 'm'
pressure_unit = 'Pa'
time_unit = 's'
velocity_unit = r'$\mathrm{m}/\mathrm{s}$'
volume_unit = r'$\mathrm{m}^3$'
area_unit_print = 'm²'
area_outflux_unit_print = 'm²'
density_unit_print = 'kg/m³'
flux_unit_print = 'm³/s'
level_unit_print = 'm'
pressure_unit_print = '--' # will be set by .set_pressure() method
time_unit_print = 's'
velocity_unit_print = 'm/s'
volume_unit_print = 'm³'
area_unit_disp = 'm²'
area_outflux_unit_disp = 'm²'
density_unit_disp = 'kg/m³'
flux_unit_disp = 'm³/s'
level_unit_disp = 'm'
time_unit_disp = 's'
velocity_unit_disp = 'm/s'
volume_unit_disp = 'm³'
g = 9.81 # m/s² gravitational acceleration
# init
def __init__(self,area,outflux_area,level_min = 0,level_max = np.inf ,timestep = 1,rho = 1000):
self.area = area # base area of the rectangular structure
self.area_outflux = outflux_area # area of the outlet towards the pipeline
self.density = rho # density of the liquid in the system
self.level_min = level_min # lowest allowed water level
self.level_max = level_max # highest allowed water level
self.timestep = timestep # timestep of the simulation
def __init__(self,area,area_outflux,timestep,pressure_unit_disp,level_min=0,level_max=np.inf,rho = 1000.):
self.area = area # base area of the cuboid reservoir
self.area_out = area_outflux # area of the outlet towards the pipeline
self.density = rho # density of the liquid in the system
self.level_min = level_min # lowest allowed water level
self.level_max = level_max # highest allowed water level
self.pressure_unit_disp = pressure_unit_disp # pressure unit for displaying
self.timestep = timestep # timestep in the time evolution method
# initialize for get_info
self.influx = "--"
self.level = "--"
self.outflux = "--"
self.volume = "--"
self.influx = "--"
self.outflux = "--"
self.level = "--"
self.pressure = "--"
self.volume = "--"
# setter
def set_initial_level(self,initial_level):
# sets the level in the reservoir and should only be called during initialization
# sets the initial level in the reservoir and should only be called during initialization
if self.level == '--':
self.level = initial_level
self.update_volume(set_flag=True)
else:
raise Exception('Initial level was already set once. Use the .update_level(self,timestep) method to update level based on net flux.')
raise Exception('Initial level was already set once. Use the .update_level(self,timestep,set_flag=True) method to update level based on net flux.')
def set_level(self,level):
self.level = level
def set_initial_pressure(self,initial_pressure):
# sets the initial static pressure present at the outlet of the reservoir and should only be called during initialization
if self.pressure == '--':
self.pressure = initial_pressure
else:
raise Exception('Initial pressure was already set once. Use the .update_pressure(self) method to update pressure based current level.')
def set_influx(self,influx):
# sets influx to the reservoir in m³/s
# positive influx means that liquid flows into the reservoir
self.influx = influx
def set_outflux(self,outflux):
def set_outflux(self,outflux,display_warning=True):
# sets outflux to the reservoir in m³/s
# positive outflux means that liquid flows out of reservoir the reservoir
if display_warning == True:
print('You are setting the outflux from the reservoir manually. \n \
This is not an intended use of this method. \n \
Refer to the timestep_reservoir_evolution() method instead.')
self.outflux = outflux
def set_initial_pressure(self,pressure,display_pressure_unit):
# sets the static pressure present at the outlet of the reservoir
# units are used to convert and display the pressure
self.pressure = pressure
self.pressure_unit_print = display_pressure_unit
def set_level(self,level,display_warning=True):
# sets level in the reservoir in m
if display_warning == True:
print('You are setting the level of the reservoir manually. \n \
This is not an intended use of this method. \n \
Refer to the update_level() method instead.')
self.level = level
def set_pressure(self,pressure):
# sets the static pressure present at the outlet of the reservoir
def set_pressure(self,pressure,display_warning=True):
# sets pressure in the pipeline just below the reservoir in Pa
if display_warning == True:
print('You are setting the pressure below the reservoir manually. \n \
This is not an intended use of this method. \n \
Refer to the update_pressure() method instead.')
self.pressure = pressure
def set_steady_state(self,ss_influx,ss_level,display_pressure_unit):
def set_volume(self,volume,display_warning=True):
if display_warning == True:
print('You are setting the volume in the reservoir manually. \n \
This is not an intended use of this method. \n \
Refer to the .update_volume() or set_initial_level() method instead.')
self.volume = volume
def set_steady_state(self,ss_influx,ss_level):
# set the steady state (ss) condition in which the net flux is zero
# set pressure acting on the outflux area so that the level stays constant
ss_outflux = ss_influx
ss_influx_vel = abs(ss_influx/self.area)
ss_outflux_vel = abs(ss_outflux/self.area_outflux)
ss_outflux_vel = abs(ss_outflux/self.area_out)
ss_pressure = self.density*self.g*ss_level+self.density*ss_outflux_vel*(ss_influx_vel-ss_outflux_vel)
self.set_influx(ss_influx)
self.set_initial_level(ss_level)
self.set_initial_pressure(ss_pressure,display_pressure_unit)
self.set_outflux(ss_outflux)
self.set_initial_pressure(ss_pressure)
self.set_outflux(ss_outflux,display_warning=False)
# getter
def get_info(self, full = False):
new_line = '\n'
p = pressure_conversion(self.pressure,self.pressure_unit,self.pressure_unit_print)
outflux_vel = self.outflux/self.area_outflux
p = pressure_conversion(self.pressure,self.pressure_unit,self.pressure_unit_disp)
outflux_vel = self.outflux/self.area_out
if full == True:
# :<10 pads the self.value to be 10 characters wide
print_str = (f"The cuboid reservoir has the following attributes: {new_line}"
f"----------------------------- {new_line}"
f"Base area = {self.area:<10} {self.area_unit_print} {new_line}"
f"Outflux area = {round(self.area_outflux,3):<10} {self.area_outflux_unit_print} {new_line}"
f"Current level = {self.level:<10} {self.level_unit_print}{new_line}"
f"Critical level low = {self.level_min:<10} {self.level_unit_print} {new_line}"
f"Critical level high = {self.level_max:<10} {self.level_unit_print} {new_line}"
f"Volume in reservoir = {self.volume:<10} {self.volume_unit_print} {new_line}"
f"Current influx = {self.influx:<10} {self.flux_unit_print} {new_line}"
f"Current outflux = {self.outflux:<10} {self.flux_unit_print} {new_line}"
f"Current outflux vel = {round(outflux_vel,3):<10} {self.velocity_unit_print} {new_line}"
f"Current pipe pressure = {round(p,3):<10} {self.pressure_unit_print} {new_line}"
f"Simulation timestep = {self.timestep:<10} {self.time_unit_print} {new_line}"
f"Density of liquid = {self.density:<10} {self.density_unit_print} {new_line}"
f"Base area = {self.area:<10} {self.area_unit_disp} {new_line}"
f"Outflux area = {round(self.area_out,3):<10} {self.area_out_unit_disp} {new_line}"
f"Current level = {self.level:<10} {self.level_unit_disp}{new_line}"
f"Critical level low = {self.level_min:<10} {self.level_unit_disp} {new_line}"
f"Critical level high = {self.level_max:<10} {self.level_unit_disp} {new_line}"
f"Volume in reservoir = {self.volume:<10} {self.volume_unit_disp} {new_line}"
f"Current influx = {self.influx:<10} {self.flux_unit_disp} {new_line}"
f"Current outflux = {self.outflux:<10} {self.flux_unit_disp} {new_line}"
f"Current outflux vel = {round(outflux_vel,3):<10} {self.velocity_unit_disp} {new_line}"
f"Current pipe pressure = {round(p,3):<10} {self.pressure_unit_disp} {new_line}"
f"Simulation timestep = {self.timestep:<10} {self.time_unit_disp} {new_line}"
f"Density of liquid = {self.density:<10} {self.density_unit_disp} {new_line}"
f"----------------------------- {new_line}")
else:
# :<10 pads the self.value to be 10 characters wide
print_str = (f"The current attributes are: {new_line}"
f"----------------------------- {new_line}"
f"Current level = {self.level:<10} {self.level_unit_print}{new_line}"
f"Volume in reservoir = {self.volume:<10} {self.volume_unit_print} {new_line}"
f"Current influx = {self.influx:<10} {self.flux_unit_print} {new_line}"
f"Current outflux = {self.outflux:<10} {self.flux_unit_print} {new_line}"
f"Current outflux vel = {round(outflux_vel,3):<10} {self.velocity_unit_print} {new_line}"
f"Current pipe pressure = {round(p,3):<10} {self.pressure_unit_print} {new_line}"
f"Current level = {self.level:<10} {self.level_unit_disp}{new_line}"
f"Current volume = {self.volume:<10} {self.volume_unit_disp} {new_line}"
f"Current influx = {self.influx:<10} {self.flux_unit_disp} {new_line}"
f"Current outflux = {self.outflux:<10} {self.flux_unit_disp} {new_line}"
f"Current outflux vel = {round(outflux_vel,3):<10} {self.velocity_unit_disp} {new_line}"
f"Current pipe pressure = {round(p,3):<10} {self.pressure_unit_disp} {new_line}"
f"----------------------------- {new_line}")
print(print_str)
def get_current_level(self):
return self.level
def get_current_influx(self):
return self.influx
def get_current_outflux(self):
return self.outflux
def get_current_level(self):
return self.level
def get_current_pressure(self):
return self.pressure
def get_current_volume(self):
return self.volume
# methods
def update_level(self,timestep):
# update methods
def update_level(self,timestep,set_flag=False):
# update level based on net flux and timestep by calculating the volume change in
# the timestep and the converting the new volume to a level by assuming a cuboid reservoir
# cannot set new level directly in this method, because it gets called to calcuate during the Runge Kutta
# to calculate a ficticious level at half the timestep
net_flux = self.influx-self.outflux
delta_level = net_flux*timestep/self.area
new_level = (self.level+delta_level)
return new_level
level_new = (self.level+delta_level)
if set_flag == True:
self.set_level(level_new,display_warning=False)
elif set_flag == False:
return level_new
def update_pressure(self):
def update_pressure(self,set_flag=False):
influx_vel = abs(self.influx/self.area)
outflux_vel = abs(self.outflux/self.area_outflux)
outflux_vel = abs(self.outflux/self.area_out)
p_new = self.density*self.g*self.level+self.density*outflux_vel*(influx_vel-outflux_vel)
return p_new
if set_flag ==True:
self.set_pressure(p_new,display_warning=False)
elif set_flag == False:
return p_new
def update_volume(self,set_flag=False):
volume_new = self.level*self.area
if set_flag == True:
self.set_volume(volume_new,display_warning=False)
elif set_flag == False:
return volume_new
#methods
def timestep_reservoir_evolution(self):
# update outflux and outflux velocity based on current pipeline pressure and waterlevel in reservoir
dt = self.timestep
rho = self.density
g = self.g
A = self.area
A_a = self.area_outflux
A_a = self.area_out
yn = self.outflux/A_a # outflux velocity
h = self.level
h_hs = self.update_level(dt/2)
@@ -203,10 +237,7 @@ class Ausgleichsbecken_class:
ynp1 = yn + dt/6*(FODE_function(Y1,h,A,A_a,p,rho,g)+2*FODE_function(Y2,h_hs,A,A_a,p_hs,rho,g)+ \
2*FODE_function(Y3,h_hs,A,A_a,p_hs,rho,g)+ FODE_function(Y4,h,A,A_a,p,rho,g))
new_outflux = ynp1*A_a
new_level = self.update_level(dt)
new_pressure = self.update_pressure()
self.set_outflux(new_outflux)
self.set_level(new_level)
self.set_pressure(new_pressure)
self.set_outflux(ynp1*A_a,display_warning=False)
self.update_level(dt,set_flag=True)
self.update_volume(set_flag=True)
self.update_pressure(set_flag=True)

187
Ausgleichsbecken/Ausgleichsbecken_test_steady_state.ipynb
View File

@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"execution_count": 29,
"metadata": {},
"outputs": [],
"source": [
@@ -21,126 +21,137 @@
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"L = 1000.\n",
"n = 10000 # number of pipe segments in discretization\n",
"c = 400. \n",
"dx = L/n # length of each pipe segment\n",
"dt = dx/c \n",
"\n",
"# # define constants\n",
"# initial_level = 10.1 # m\n",
"# initial_influx = 0.8 # m³/s\n",
"# conversion_pressure_unit = 'mWS'\n",
"\n",
"# area_base = 75. # m²\n",
"# area_outflux = (0.9/2)**2*np.pi # m²\n",
"# critical_level_low = 0. # m\n",
"# critical_level_high = 10. # m\n",
"# simulation_timestep = dt # s\n",
"\n",
"# # for while loop\n",
"# total_min_level = 0.01 # m\n",
"# total_max_time = 100 # s\n",
"\n",
"# nt = int(total_max_time//simulation_timestep)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"execution_count": 30,
"metadata": {},
"outputs": [],
"source": [
"# define constants\n",
"initial_level = 10.1 # m\n",
"initial_influx = 1. # m³/s\n",
"# initial_outflux = 1. # m³/s\n",
"# initial_pipeline_pressure = 10.\n",
"# initial_pressure_unit = 'mWS'\n",
"conversion_pressure_unit = 'mWS'\n",
"\n",
"area_base = 75. # m²\n",
"area_outflux = 2. # m²\n",
"critical_level_low = 0. # m\n",
"critical_level_high = 10. # m\n",
"simulation_timestep = dt # s\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 while loop\n",
"total_min_level = 0.01 # m\n",
"total_max_time = 100 # s\n",
"\n",
"nt = int(total_max_time//simulation_timestep)"
" # for Turbine\n",
"Tur_Q_nenn = 0.85 # [m³/s] nominal flux of turbine \n",
"Tur_p_nenn = pressure_conversion(10.6,'bar',pUnit_calc) # [Pa] nominal pressure of turbine \n",
"Tur_closingTime = 90. # [s] closing time of turbine\n",
"\n",
"\n",
" # for PI controller\n",
"Con_targetLevel = 8. # [m]\n",
"Con_K_p = 0.1 # [-] proportional constant of PI controller\n",
"Con_T_i = 10. # [s] timespan in which a steady state error is corrected by the intergal term\n",
"Con_deadbandRange = 0.05 # [m] Deadband range around targetLevel for which the controller does NOT intervene\n",
"\n",
"\n",
" # for pipeline\n",
"Pip_length = (535.+478.) # [m] length of pipeline\n",
"Pip_dia = 0.9 # [m] diameter of pipeline\n",
"Pip_area = Pip_dia**2/4*np.pi # [m²] crossectional area of pipeline\n",
"Pip_head = 105. # [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 = 50 # [-] number of pipe segments in discretization\n",
"Pip_f_D = 0.014 # [-] 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",
"\n",
" # for reservoir\n",
"Res_area_base = 5. # [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 = 600. # [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": 4,
"execution_count": 31,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib qt\n",
"# 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_initial_pressure(pressure_conversion(initial_pipeline_pressure,input_unit = initial_pressure_unit, target_unit = 'Pa'),conversion_pressure_unit)\n",
"# V.pressure = converted_pressure\n",
"V.set_steady_state(initial_influx,initial_level,conversion_pressure_unit)\n",
"# Upstream reservoir\n",
"reservoir = Ausgleichsbecken_class(Res_area_base,Res_area_out,Res_dt,Res_level_crit_lo,Res_level_crit_hi,rho)\n",
"reservoir.set_steady_state(flux_init,level_init)\n",
"\n",
"time_vec = np.arange(0,nt+1,1)*simulation_timestep\n",
"outflux_vec = np.zeros_like(time_vec)\n",
"outflux_vec[0] = V.get_current_outflux()\n",
"level_vec = np.zeros_like(time_vec)\n",
"level_vec[0] = V.get_current_level()\n",
"pressure_vec = np.zeros_like(time_vec)\n",
"pressure_vec[0] = V.get_current_pressure()\n",
"\n",
"# pressure_vec = np.full_like(time_vec,converted_pressure)*((np.sin(time_vec)+1)*np.exp(-time_vec/50))\n",
" \n",
"i_max = -1\n",
"reservoir.get_info(full=True)\n",
"\n",
"# initialize vectors\n",
"outflux_vec = np.zeros_like(t_vec)\n",
"outflux_vec[0] = reservoir.get_current_outflux()\n",
"level_vec = np.zeros_like(t_vec)\n",
"level_vec[0] = reservoir.get_current_level()\n",
"volume_vec = np.zeros_like(t_vec)\n",
"volume_vec[0] = reservoir.get_current_volume()\n",
"pressure_vec = np.zeros_like(t_vec)\n",
"pressure_vec[0] = reservoir.get_current_pressure()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# time loop\n",
"for i in range(1,nt+1):\n",
" V.set_pressure(pressure_vec[i-1])\n",
" V.set_outflux(outflux_vec[i-1])\n",
" V.timestep_reservoir_evolution()\n",
" outflux_vec[i] = V.get_current_outflux()\n",
" level_vec[i] = V.get_current_level()\n",
" pressure_vec[i] = V.get_current_pressure()\n",
" if V.level < total_min_level:\n",
" i_max = i\n",
" break\n",
"\n"
" # if i == 500:\n",
" # reservoir.set_influx(0.)\n",
" reservoir.set_pressure(pressure_vec[i-1],display_warning=False)\n",
" reservoir.set_outflux(outflux_vec[i-1],display_warning=False)\n",
" for it_res in range(Res_nt):\n",
" reservoir.timestep_reservoir_evolution() \n",
" \n",
" outflux_vec[i] = reservoir.get_current_outflux()\n",
" level_vec[i] = reservoir.get_current_level()\n",
" pressure_vec[i] = reservoir.get_current_pressure()\n",
"\n",
" reservoir.get_info()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"execution_count": 32,
"metadata": {},
"outputs": [],
"source": [
"\n",
"%matplotlib qt5\n",
"fig1, (ax1, ax2, ax3) = plt.subplots(3, 1)\n",
"fig1.set_figheight(10)\n",
"fig1.suptitle('Ausgleichsbecken')\n",
"\n",
"ax1.plot(time_vec[:i_max],level_vec[:i_max], label='Water level')\n",
"ax1.set_ylabel(r'$h$ ['+V.level_unit+']')\n",
"ax1.set_xlabel(r'$t$ ['+V.time_unit+']')\n",
"ax1.plot(t_vec,level_vec, label='Water level')\n",
"ax1.set_ylabel(r'$h$ ['+reservoir.level_unit+']')\n",
"ax1.set_xlabel(r'$t$ ['+reservoir.time_unit+']')\n",
"ax1.legend()\n",
"\n",
"ax2.plot(time_vec[:i_max],outflux_vec[:i_max], label='Outflux')\n",
"ax2.set_ylabel(r'$Q_{out}$ ['+V.flux_unit+']')\n",
"ax2.set_xlabel(r'$t$ ['+V.time_unit+']')\n",
"ax2.plot(t_vec,outflux_vec, label='Outflux')\n",
"ax2.set_ylabel(r'$Q_{out}$ ['+reservoir.flux_unit+']')\n",
"ax2.set_xlabel(r'$t$ ['+reservoir.time_unit+']')\n",
"ax2.legend()\n",
"\n",
"ax3.plot(time_vec[:i_max],pressure_conversion(pressure_vec[:i_max],'Pa',conversion_pressure_unit), label='Pipeline pressure at reservoir')\n",
"ax3.set_ylabel(r'$p_{pipeline}$ ['+conversion_pressure_unit+']')\n",
"ax3.set_xlabel(r'$t$ ['+V.time_unit+']')\n",
"ax3.plot(t_vec,pressure_conversion(pressure_vec,'Pa',pUnit_conv), label='Pipeline pressure at reservoir')\n",
"ax3.set_ylabel(r'$p_{pipeline}$ ['+pUnit_conv+']')\n",
"ax3.set_xlabel(r'$t$ ['+reservoir.time_unit+']')\n",
"ax3.legend()\n",
"\n",
"\n",

141
Druckrohrleitung/Druckrohrleitung_class_file.py
View File

@@ -1,5 +1,13 @@
import numpy as np
#importing pressure conversion function
import sys
import os
current = os.path.dirname(os.path.realpath(__file__))
parent = os.path.dirname(current)
sys.path.append(parent)
from functions.pressure_conversion import pressure_conversion
class Druckrohrleitung_class:
# units
acceleration_unit = r'$\mathrm{m}/\mathrm{s}^2$'
@@ -13,72 +21,66 @@ class Druckrohrleitung_class:
velocity_unit = r'$\mathrm{m}/\mathrm{s}$' # for flux and pressure propagation
volume_unit = r'$\mathrm{m}^3$'
acceleration_unit_print = 'm/s²'
angle_unit_print = 'rad'
area_unit_print = 'm²'
density_unit_print = 'kg/m³'
flux_unit_print = 'm³/s'
length_unit_print = 'm'
time_unit_print = 's'
velocity_unit_print = 'm/s' # for flux and pressure propagation
volume_unit_print = 'm³'
acceleration_unit_disp = 'm/s²'
angle_unit_disp = 'rad'
area_unit_disp = 'm²'
density_unit_disp = 'kg/m³'
flux_unit_disp = 'm³/s'
length_unit_disp = 'm'
time_unit_disp = 's'
velocity_unit_disp = 'm/s' # for flux and pressure propagation
volume_unit_disp = 'm³'
g = 9.81
# init
def __init__(self,total_length,diameter,number_segments,pipeline_angle,Darcy_friction_factor,rho=1000,g=9.81):
def __init__(self,total_length,diameter,number_segments,pipeline_angle,Darcy_friction_factor,pw_vel,timestep,pressure_unit_disp,rho=1000):
self.length = total_length # total length of the pipeline
self.dia = diameter # diameter of the pipeline
self.n_seg = number_segments # number of segments for the method of characteristics
self.angle = pipeline_angle # angle of the pipeline
self.f_D = Darcy_friction_factor # = Rohrreibungszahl oder flow coefficient
self.c = pw_vel
self.dt = timestep
self.density = rho # density of the liquid in the pipeline
self.g = g # gravitational acceleration
self.A = (diameter/2)**2*np.pi
self.dx = total_length/number_segments # length of each segment
self.l_vec = np.arange(0,(number_segments+1),1)*self.dx # vector giving the distance from each node to the start of the pipeline
self.x_vec = np.arange(0,(number_segments+1),1)*self.dx # vector giving the distance from each node to the start of the pipeline
# initialize for get_info method
self.c = '--'
self.dt = '--'
self.pressure_unit_disp = pressure_unit_disp
# setter
def set_pressure_propagation_velocity(self,c):
self.c = c # propagation velocity of the pressure wave
self.dt = self.dx/c # timestep derived from c, demanded by the method of characteristics
def set_number_of_timesteps(self,number_timesteps):
self.nt = number_timesteps # number of timesteps
if self.c == '--':
raise Exception('Please set the pressure propagation velocity before setting the number of timesteps.')
else:
self.t_vec = np.arange(0,self.nt*self.dt,self.dt)
def set_initial_pressure(self,pressure):
# initialize the pressure distribution in the pipeline
if np.size(pressure) == 1:
self.p0 = np.full_like(self.l_vec,pressure)
elif np.size(pressure) == np.size(self.l_vec):
self.p0 = pressure
p0 = np.full_like(self.x_vec,pressure)
elif np.size(pressure) == np.size(self.x_vec):
p0 = pressure
else:
raise Exception('Unable to assign initial pressure. Input has to be of size 1 or' + np.size(self.l_vec))
raise Exception('Unable to assign initial pressure. Input has to be of size 1 or' + np.size(self.x_vec))
#initialize the vectors in which the old and new pressures are stored for the method of characteristics
self.p_old = self.p0.copy()
self.p = self.p0.copy()
self.p_old = p0.copy()
self.p = p0.copy()
self.p_min = p0.copy()
self.p_max = p0.copy()
def set_initial_flow_velocity(self,velocity):
# initialize the velocity distribution in the pipeline
if np.size(velocity) == 1:
self.v0 = np.full_like(self.l_vec,velocity)
elif np.size(velocity) == np.size(self.l_vec):
self.v0 = velocity
v0 = np.full_like(self.x_vec,velocity)
elif np.size(velocity) == np.size(self.x_vec):
v0 = velocity
else:
raise Exception('Unable to assign initial velocity. Input has to be of size 1 or' + np.size(self.l_vec))
raise Exception('Unable to assign initial velocity. Input has to be of size 1 or' + np.size(self.x_vec))
#initialize the vectors in which the old and new velocities are stored for the method of characteristics
self.v_old = self.v0.copy()
self.v = self.v0.copy()
self.v_old = v0.copy()
self.v = v0.copy()
self.v_min = v0.copy()
self.v_max = v0.copy()
def set_boundary_conditions_next_timestep(self,p_reservoir,v_turbine):
# derived from the method of characteristics, one can set the boundary conditions for the pressures and flow velocities at the reservoir and the turbine
@@ -112,16 +114,16 @@ class Druckrohrleitung_class:
self.p[0] = p_boundary_res
self.p[-1] = p_boundary_tur
def set_steady_state(self,ss_flux,ss_level_reservoir,area_reservoir,pl_vec,h_vec):
def set_steady_state(self,ss_flux,ss_level_reservoir,area_reservoir,x_vec,h_vec):
# set the pressure and velocity distributions, that allow a constant flow of water from the (steady-state) reservoir to the (steady-state) turbine
# the flow velocity is given by the constant flow through the pipe
ss_v0 = np.full(self.n_seg+1,ss_flux/self.A)
ss_v0 = np.full_like(self.x_vec,ss_flux/self.A)
# the static pressure is given by static state pressure of the reservoir, corrected for the hydraulic head of the pipe and friction losses
ss_v_in_res = abs(ss_flux/area_reservoir)
ss_v_out_res = abs(ss_flux/self.A)
ss_pressure_res = self.density*self.g*(ss_level_reservoir)+self.density*ss_v_out_res*(ss_v_in_res-ss_v_out_res)
ss_pressure = ss_pressure_res+(self.density*self.g*h_vec)-(self.f_D*pl_vec/self.dia*self.density/2*ss_v0**2)
ss_pressure = ss_pressure_res+(self.density*self.g*h_vec)-(self.f_D*x_vec/self.dia*self.density/2*ss_v0**2)
self.set_initial_flow_velocity(ss_v0)
self.set_initial_pressure(ss_pressure)
@@ -135,30 +137,61 @@ class Druckrohrleitung_class:
# :<10 pads the self.value to be 10 characters wide
print_str = (f"The pipeline has the following attributes: {new_line}"
f"----------------------------- {new_line}"
f"Length = {self.length:<10} {self.length_unit_print} {new_line}"
f"Diameter = {self.dia:<10} {self.length_unit_print} {new_line}"
f"Length = {self.length:<10} {self.length_unit_disp} {new_line}"
f"Diameter = {self.dia:<10} {self.length_unit_disp} {new_line}"
f"Number of segments = {self.n_seg:<10} {new_line}"
f"Number of nodes = {self.n_seg+1:<10} {new_line}"
f"Length per segments = {self.dx:<10} {self.length_unit_print} {new_line}"
f"Pipeline angle = {round(self.angle,3):<10} {self.angle_unit_print} {new_line}"
f"Length per segments = {self.dx:<10} {self.length_unit_disp} {new_line}"
f"Pipeline angle = {round(self.angle,3):<10} {self.angle_unit_disp} {new_line}"
f"Pipeline angle = {angle_deg}° {new_line}"
f"Darcy friction factor = {self.f_D:<10} {new_line}"
f"Density of liquid = {self.density:<10} {self.density_unit_print} {new_line}"
f"Pressure wave vel. = {self.c:<10} {self.velocity_unit_print} {new_line}"
f"Simulation timestep = {self.dt:<10} {self.time_unit_print} {new_line}"
f"Density of liquid = {self.density:<10} {self.density_unit_disp} {new_line}"
f"Pressure wave vel. = {self.c:<10} {self.velocity_unit_disp} {new_line}"
f"Simulation timestep = {self.dt:<10} {self.time_unit_disp} {new_line}"
f"Number of timesteps = {self.nt:<10} {new_line}"
f"Total simulation time = {self.nt*self.dt:<10} {self.time_unit_print} {new_line}"
f"Total simulation time = {self.nt*self.dt:<10} {self.time_unit_disp} {new_line}"
f"----------------------------- {new_line}"
f"Velocity and pressure distribution are vectors and are accessible by the .v and .p attribute of the pipeline object")
print(print_str)
def get_current_pressure_distribution(self):
return self.p
def get_current_pressure_distribution(self,disp=False):
if disp == True:
return pressure_conversion(self.p,self.pressure_unit,self.pressure_unit_disp)
elif disp == False:
return self.p
def get_current_velocity_distribution(self):
return self.v
def get_current_flux_distribution(self):
return self.v*self.A
def get_lowest_pressure_per_node(self,disp=False):
if disp == True:
return pressure_conversion(self.p_min,self.pressure_unit,self.pressure_unit_disp)
elif disp == False:
return self.p_min
def get_highest_pressure_per_node(self,disp=False):
if disp == True:
return pressure_conversion(self.p_max,self.pressure_unit,self.pressure_unit_disp)
elif disp == False:
return self.p_max
def get_lowest_velocity_per_node(self):
return self.v_min
def get_highest_velocity_per_node(self):
return self.v_max
def get_lowest_flux_per_node(self):
return self.v_min*self.A
def get_highest_flux_per_node(self):
return self.v_max*self.A
def timestep_characteristic_method(self):
# use the method of characteristics to calculate the pressure and velocities at all nodes except the boundary ones
# they are set with the .set_boundary_conditions_next_timestep() method beforehand
@@ -180,6 +213,12 @@ class Druckrohrleitung_class:
self.p[i] = 0.5*(self.p_old[i+1]+self.p_old[i-1]) - 0.5*rho*c*(self.v_old[i+1]-self.v_old[i-1]) \
+f_D*rho*c*dt/(4*D)*(abs(self.v_old[i+1])*self.v_old[i+1]-abs(self.v_old[i-1])*self.v_old[i-1])
# update overall min and max values for pressure and velocity per node
self.p_min = np.minimum(self.p_min,self.p)
self.p_max = np.maximum(self.p_max,self.p)
self.v_min = np.minimum(self.v_min,self.v)
self.v_max = np.maximum(self.v_max,self.v)
# prepare for next call
# use .copy() to write data to another memory location and avoid the usual python reference pointer
# else one can overwrite data by accidient and change two variables at once without noticing

180
Druckrohrleitung/Druckrohrleitung_test_steady_state.ipynb
View File

@@ -26,45 +26,60 @@
"metadata": {},
"outputs": [],
"source": [
"%matplotlib qt5\n",
"#define constants pipe\n",
"# define constants\n",
"\n",
"g = 9.81 # gravitational acceleration [m/s²]\n",
"rho = 1000. # density of water [kg/m³]\n",
"\n",
"L = 1000. # length of pipeline [m]\n",
"D = 0.9 # pipe diameter [m]\n",
"h_res = 10. # water level in upstream reservoir [m]\n",
"n = 50 # number of pipe segments in discretization\n",
"nt = 9000 # 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 = 105. # hydraulic head without reservoir [m] \n",
"alpha = np.arcsin(h_pipe/L) # Höhenwinkel der Druckrohrleitung \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",
"\n",
"# preparing the discretization and initial conditions\n",
"initial_flux = 0.8 # m³/s\n",
"initial_level = h_res # m\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,1)*dx # pl = pipe-length. position of the nodes on the pipeline\n",
"t_vec = np.arange(0,nt,1)*dt # time vector\n",
"h_vec = np.arange(0,nn,1)*h_pipe/n # hydraulic head of pipeline at each node\n",
" # for Turbine\n",
"Tur_Q_nenn = 0.85 # [m³/s] nominal flux of turbine \n",
"Tur_p_nenn = pressure_conversion(10.6,'bar',pUnit_calc) # [Pa] nominal pressure of turbine \n",
"Tur_closingTime = 90. # [s] closing time of turbine\n",
"\n",
"\n",
"# define constants reservoir\n",
"conversion_pressure_unit = 'mWS'\n",
" # for PI controller\n",
"Con_targetLevel = 8. # [m]\n",
"Con_K_p = 0.1 # [-] proportional constant of PI controller\n",
"Con_T_i = 10. # [s] timespan in which a steady state error is corrected by the intergal term\n",
"Con_deadbandRange = 0.05 # [m] Deadband range around targetLevel for which the controller does NOT intervene\n",
"\n",
"area_base = 75. # m²\n",
"area_pipe = (D/2)**2*np.pi # m²\n",
"critical_level_low = 0. # m\n",
"critical_level_high = 100. # m\n",
"\n",
"# make sure e-RK4 method of reservoir has a small enough timestep to avoid runaway numerical error\n",
"nt_eRK4 = 100 # number of simulation steps of reservoir in between timesteps of pipeline \n",
"simulation_timestep = dt/nt_eRK4"
" # for pipeline\n",
"Pip_length = (535.+478.) # [m] length of pipeline\n",
"Pip_dia = 0.9 # [m] diameter of pipeline\n",
"Pip_area = Pip_dia**2/4*np.pi # [m²] crossectional area of pipeline\n",
"Pip_head = 105. # [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 = 50 # [-] number of pipe segments in discretization\n",
"Pip_f_D = 0.014 # [-] 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",
"\n",
" # for reservoir\n",
"Res_area_base = 74. # [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 = 600. # [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"
]
},
{
@@ -73,51 +88,37 @@
"metadata": {},
"outputs": [],
"source": [
"V = Ausgleichsbecken_class(area_base,area_pipe,critical_level_low,critical_level_high,simulation_timestep)\n",
"V.set_steady_state(initial_flux,initial_level,conversion_pressure_unit)\n",
"# create objects\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_steady_state(initial_flux,initial_level,area_base,pl_vec,h_vec)"
"# Upstream reservoir\n",
"reservoir = Ausgleichsbecken_class(Res_area_base,Res_area_out,Res_dt,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_n_seg,Pip_angle,Pip_f_D,Pip_pw_vel,Pip_dt,pUnit_conv,rho)\n",
"pipe.set_steady_state(flux_init,level_init,Res_area_base,Pip_x_vec,Pip_h_vec)\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"reservoir.get_info(full=True)\n",
"pipe.get_info(full=True)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The current attributes are: \n",
"----------------------------- \n",
"Current level = 10.0 m\n",
"Volume in reservoir = -- m³ \n",
"Current influx = 0.8 m³/s \n",
"Current outflux = 0.8 m³/s \n",
"Current outflux vel = 1.258 m/s \n",
"Current pipe pressure = 9.844 mWS \n",
"----------------------------- \n",
"\n"
]
}
],
"source": [
"V.get_info()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"# initialization for timeloop\n",
"\n",
"level_vec = np.zeros_like(t_vec)\n",
"level_vec[0] = V.get_current_level()\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",
@@ -141,21 +142,23 @@
},
{
"cell_type": "code",
"execution_count": 6,
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib qt5\n",
"fig1,axs1 = plt.subplots(2,1)\n",
"axs1[0].set_title('Pressure distribution in pipeline')\n",
"axs1[0].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
"axs1[0].set_ylabel(r'$p$ [mWS]')\n",
"lo_00, = axs1[0].plot(pl_vec,pressure_conversion(p_old,'Pa',conversion_pressure_unit),marker='.')\n",
"axs1[0].set_ylim([0.9*np.min(pressure_conversion(p_old,'Pa',conversion_pressure_unit)),1.1*np.max(pressure_conversion(p_old,'Pa',conversion_pressure_unit))])\n",
"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",
"lo_00, = axs1[0].plot(Pip_x_vec,pressure_conversion(p_old,'Pa',pUnit_conv),marker='.')\n",
"\n",
"axs1[1].set_title('Velocity distribution in pipeline')\n",
"axs1[1].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
"axs1[1].set_ylabel(r'$v$ [m/s]')\n",
"lo_01, = axs1[1].plot(pl_vec,v_old,marker='.')\n",
"lo_01, = axs1[1].plot(Pip_x_vec,v_old,marker='.')\n",
"axs1[1].autoscale()\n",
"# axs1[1].set_ylim([0.9*np.min(v_old),1.1*np.max(v_boundary_res)])\n",
"\n",
"fig1.tight_layout()\n",
@@ -164,7 +167,7 @@
},
{
"cell_type": "code",
"execution_count": 7,
"execution_count": 6,
"metadata": {},
"outputs": [
{
@@ -201,21 +204,20 @@
}
],
"source": [
"\n",
"for it_pipe in range(1,nt):\n",
"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",
" V.set_pressure(p_old[0])\n",
" V.set_outflux(v_old[0]*area_pipe)\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(nt_eRK4):\n",
" V.timestep_reservoir_evolution() \n",
" level_vec[it_pipe] = V.get_current_level() \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] = V.get_current_pressure()\n",
" v_boundary_tur[it_pipe] = initial_flux/area_pipe\n",
" p_boundary_res[it_pipe] = reservoir.get_current_pressure()\n",
" v_boundary_tur[it_pipe] = flux_init/Pip_area\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",
@@ -235,28 +237,30 @@
" 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(p_old,'Pa', conversion_pressure_unit),marker='.',c='blue')\n",
" lo_01, = axs1[1].plot(pl_vec,v_old,marker='.',c='blue')\n",
" lo_00, = axs1[0].plot(Pip_x_vec,pressure_conversion(p_old,'Pa', pUnit_conv),marker='.',c='blue')\n",
" lo_01, = axs1[1].plot(Pip_x_vec,v_old,marker='.',c='blue')\n",
" \n",
" fig1.suptitle(str(round(t_vec[it_pipe],2)) + '/' + str(round(t_vec[-1],2)))\n",
" fig1.canvas.draw()\n",
" fig1.tight_layout()\n",
" plt.pause(0.000001)\n",
"\n"
"\n",
"reservoir.get_info(full=True)\n",
"pipe.get_info(full=True)"
]
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 12,
"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,'Pa',conversion_pressure_unit))\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,'Pa',conversion_pressure_unit)),1.1*np.max(pressure_conversion(p_boundary_res,'Pa',conversion_pressure_unit))])\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[0,1].set_title('Velocity Reservoir')\n",
"axs2[0,1].plot(t_vec,v_boundary_res)\n",
@@ -265,16 +269,16 @@
"axs2[0,1].set_ylim([0.9*np.min(v_boundary_res),1.1*np.max(v_boundary_res)])\n",
"\n",
"axs2[1,0].set_title('Pressure Turbine')\n",
"axs2[1,0].plot(t_vec,pressure_conversion(p_boundary_tur,'Pa',conversion_pressure_unit))\n",
"axs2[1,0].plot(t_vec,pressure_conversion(p_boundary_tur,pUnit_calc,pUnit_conv))\n",
"axs2[1,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs2[1,0].set_ylabel(r'$p$ [mWS]')\n",
"axs2[1,0].set_ylim([0.9*np.min(pressure_conversion(p_boundary_tur,'Pa',conversion_pressure_unit)),1.1*np.max(pressure_conversion(p_boundary_tur,'Pa',conversion_pressure_unit))])\n",
"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",
"\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([0.9*np.min(v_boundary_tur),1.1*np.max(v_boundary_tur)])\n",
"axs2[1,1].set_ylim([0.95*np.min(v_boundary_tur),1.05*np.max(v_boundary_tur)])\n",
"\n",
"fig2.tight_layout()\n",
"plt.show()"

290
Regler/Pegelregler_test.ipynb
View File

@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
"execution_count": 20,
"execution_count": 27,
"metadata": {},
"outputs": [],
"source": [
@@ -23,85 +23,108 @@
},
{
"cell_type": "code",
"execution_count": 21,
"execution_count": 28,
"metadata": {},
"outputs": [],
"source": [
"#define constants\n",
"# define constants\n",
"\n",
"#Turbine\n",
"Q_nenn = 0.85 # m³/s\n",
"p_nenn = pressure_conversion(10.6,'bar','Pa')\n",
"closing_time = 480. #s\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",
"# physics\n",
"g = 9.81 # gravitational acceleration [m/s²]\n",
"rho = 1000. # density of water [kg/m³]\n",
"\n",
"# define controller constants\n",
"target_level = 8. # m\n",
"Kp = 0.01\n",
"Ti = 200.\n",
"deadband_range = 0.05 # m\n",
" # for Turbine\n",
"Tur_Q_nenn = 0.85 # [m³/s] nominal flux of turbine \n",
"Tur_p_nenn = pressure_conversion(10.6,'bar',pUnit_calc) # [Pa] nominal pressure of turbine \n",
"Tur_closingTime = 90. # [s] closing time of turbine\n",
"\n",
"# reservoir\n",
"initial_level = target_level\n",
"initial_influx = Q_nenn/2 # initial influx of volume to the reservoir [m³/s]\n",
"initial_pressure_unit = 'Pa' # DO NOT CHANGE! for pressure conversion in print statements and plot labels \n",
"conversion_pressure_unit = 'bar' # for pressure conversion in print statements and plot labels\n",
"area_base = 74. # total base are of the cuboid reservoir [m²] \n",
"area_outflux = 1. # outflux 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",
"p0 = rho*g*initial_level-0.5*rho*(initial_influx/area_outflux)**2\n",
" # for PI controller\n",
"Con_targetLevel = 8. # [m]\n",
"Con_K_p = 0.1 # [-] proportional constant of PI controller\n",
"Con_T_i = 10. # [s] timespan in which a steady state error is corrected by the intergal term\n",
"Con_deadbandRange = 0.05 # [m] Deadband range around targetLevel for which the controller does NOT intervene\n",
"\n",
"# offset the pressure in front of the turbine to get realisitc fluxes\n",
"h_fict = 100\n",
"offset_pressure = rho*g*h_fict\n",
"\n",
"t_max = 1e4 #s\n",
"dt = 1e-2 # simulation timestep\n",
"nt = int(t_max//dt) # number of simulation steps of reservoir in between timesteps of pipeline \n",
" # for pipeline\n",
"Pip_length = (535.+478.) # [m] length of pipeline\n",
"Pip_dia = 0.9 # [m] diameter of pipeline\n",
"Pip_area = Pip_dia**2/4*np.pi # [m²] crossectional area of pipeline\n",
"Pip_head = 105. # [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 = 50 # [-] number of pipe segments in discretization\n",
"Pip_f_D = 0.014 # [-] 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",
"t_vec = np.arange(0,nt+1,1)*dt\n",
"\n"
"\n",
" # for reservoir\n",
"Res_area_base = 10. # [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 = 600. # [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": 22,
"execution_count": 29,
"metadata": {},
"outputs": [],
"source": [
"# create objects\n",
"offset_pressure = pressure_conversion(Pip_head,'mws',pUnit_calc)\n",
"\n",
"V = Ausgleichsbecken_class(area_base,area_outflux,critical_level_low,critical_level_high,dt)\n",
"V.set_steady_state(initial_influx,initial_level,conversion_pressure_unit)\n",
"# Upstream reservoir\n",
"reservoir = Ausgleichsbecken_class(Res_area_base,Res_area_out,Res_dt,Res_level_crit_lo,Res_level_crit_hi,rho)\n",
"reservoir.set_steady_state(flux_init,level_init)\n",
"\n",
"T1 = Francis_Turbine(Q_nenn,p_nenn,closing_time,dt)\n",
"T1.set_steady_state(initial_influx,p0+offset_pressure)\n",
"# downstream turbine\n",
"turbine = Francis_Turbine(Tur_Q_nenn,Tur_p_nenn,Tur_closingTime,Pip_dt,pUnit_conv)\n",
"turbine.set_steady_state(flux_init,reservoir.get_current_pressure()+offset_pressure)\n",
"\n",
"Pegelregler = PI_controller_class(target_level,deadband_range,Kp,Ti,dt)"
"\n",
"# level controll\n",
"level_control = PI_controller_class(Con_targetLevel,Con_deadbandRange,Con_K_p,Con_T_i,Pip_dt)\n",
"level_control.set_control_variable(turbine.get_current_LA(),display_warning=False)\n"
]
},
{
"cell_type": "code",
"execution_count": 23,
"execution_count": 30,
"metadata": {},
"outputs": [],
"source": [
"level_vec = np.full(nt+1,V.level)\n",
"LA_ist_vec = np.full(nt+1,T1.LA)\n",
"LA_soll_vec = np.full(nt+1,T1.LA)\n",
"Q_vec = np.full(nt+1,initial_influx)\n",
"\n",
"Pegelregler.control_variable = T1.get_current_LA()"
"level_vec = np.zeros_like(t_vec)\n",
"level_vec[0] = level_init\n",
"LA_ist_vec = np.zeros_like(t_vec)\n",
"LA_ist_vec[0] = turbine.get_current_LA()\n",
"LA_soll_vec = np.zeros_like(t_vec)\n",
"LA_soll_vec[0] = turbine.get_current_LA()\n",
"Q_vec = np.zeros_like(t_vec)\n",
"Q_vec[0] = turbine.get_current_Q()"
]
},
{
"cell_type": "code",
"execution_count": 24,
"execution_count": 31,
"metadata": {},
"outputs": [
{
@@ -109,105 +132,20 @@
"output_type": "stream",
"text": [
"0.0\n",
"100.0\n",
"200.0\n",
"300.0\n",
"400.0\n",
"500.0\n",
"600.0\n",
"700.0\n",
"800.0\n",
"900.0\n",
"1000.0\n",
"1100.0\n",
"1200.0\n",
"1300.0\n",
"1400.0\n",
"1500.0\n",
"1600.0\n",
"1700.0\n",
"1800.0\n",
"1900.0\n",
"2000.0\n",
"2100.0\n",
"2200.0\n",
"2300.0\n",
"2400.0\n",
"2500.0\n",
"2600.0\n",
"2700.0\n",
"2800.0\n",
"2900.0\n",
"3000.0\n",
"3100.0\n",
"3200.0\n",
"3300.0\n",
"3400.0\n",
"3500.0\n",
"3600.0\n",
"3700.0\n",
"3800.0\n",
"3900.0\n",
"4000.0\n",
"4100.0\n",
"4200.0\n",
"4300.0\n",
"4400.0\n",
"4500.0\n",
"4600.0\n",
"4700.0\n",
"4800.0\n",
"4900.0\n",
"5000.0\n",
"5100.0\n",
"5200.0\n",
"5300.0\n",
"5400.0\n",
"5500.0\n",
"5600.0\n",
"5700.0\n",
"5800.0\n",
"5900.0\n",
"6000.0\n",
"6100.0\n",
"6200.0\n",
"6300.0\n",
"6400.0\n",
"6500.0\n",
"6600.0\n",
"6700.0\n",
"6800.0\n",
"6900.0\n",
"7000.0\n",
"7100.0\n",
"7200.0\n",
"7300.0\n",
"7400.0\n",
"7500.0\n",
"7600.0\n",
"7700.0\n",
"7800.0\n",
"7900.0\n",
"8000.0\n",
"8100.0\n",
"8200.0\n",
"8300.0\n",
"8400.0\n",
"8500.0\n",
"8600.0\n",
"8700.0\n",
"8800.0\n",
"8900.0\n",
"9000.0\n",
"9100.0\n",
"9200.0\n",
"9300.0\n",
"9400.0\n",
"9500.0\n",
"9600.0\n",
"9700.0\n",
"9800.0\n",
"9900.0\n"
"40.52\n",
"81.04\n",
"121.56\n",
"162.08\n",
"202.6\n",
"243.12\n",
"283.64\n",
"324.16\n",
"364.68\n",
"405.2\n",
"445.72\n",
"486.24\n",
"526.76\n",
"567.28\n"
]
}
],
@@ -216,39 +154,34 @@
"\n",
"for i in range(nt+1):\n",
"\n",
" if np.mod(i,1e4) == 0:\n",
" if np.mod(i,1e3) == 0:\n",
" print(t_vec[i])\n",
"\n",
" if i == 0.2*(nt+1):\n",
" V.set_influx(0.)\n",
" elif i == 0.5*(nt+1):\n",
" V.set_influx(0.5*Q_nenn)\n",
" elif i == 0.8*(nt+1):\n",
" V.set_influx(Q_nenn)\n",
" if i > 0.1*(nt+1):\n",
" reservoir.set_influx(0.)\n",
"\n",
"\n",
" p = V.get_current_pressure()\n",
" Pegelregler.update_control_variable(V.level)\n",
" LA_soll = Pegelregler.get_current_control_variable()\n",
" T1.update_LA(LA_soll)\n",
" T1.set_pressure(p+offset_pressure)\n",
" p = reservoir.get_current_pressure()\n",
" level_control.update_control_variable(reservoir.level)\n",
" LA_soll = level_control.get_current_control_variable()\n",
" turbine.update_LA(LA_soll)\n",
" turbine.set_pressure(p+offset_pressure)\n",
" LA_soll_vec[i] = LA_soll\n",
" LA_ist_vec[i] = T1.get_current_LA()\n",
" Q_vec[i] = T1.get_current_Q()\n",
" LA_ist_vec[i] = turbine.get_current_LA()\n",
" Q_vec[i] = turbine.get_current_Q()\n",
"\n",
" \n",
" V.set_outflux(Q_vec[i])\n",
" reservoir.set_outflux(Q_vec[i],display_warning=False)\n",
"\n",
" V.timestep_reservoir_evolution() \n",
" \n",
" level_vec[i] = V.get_current_level()\n",
" for it_res in range(Res_nt):\n",
" reservoir.timestep_reservoir_evolution() \n",
" level_vec[i] = reservoir.get_current_level()\n",
" \n",
" "
]
},
{
"cell_type": "code",
"execution_count": 25,
"execution_count": 32,
"metadata": {},
"outputs": [],
"source": [
@@ -261,12 +194,12 @@
"axs1[0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs1[0].set_ylabel(r'$h$ [$\\mathrm{m}$]')\n",
"axs1[0].plot(t_vec,level_vec)\n",
"axs1[0].set_ylim([0*initial_level,1.5*initial_level])\n",
"axs1[0].set_ylim([0*level_init,1.5*level_init])\n",
"axs1[1].set_title('Flux')\n",
"axs1[1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs1[1].set_ylabel(r'$Q$ [$\\mathrm{m} / \\mathrm{s}^3$]')\n",
"axs1[1].plot(t_vec,Q_vec)\n",
"axs1[1].set_ylim([0,2*initial_influx])\n",
"axs1[1].set_ylim([0,2*flux_init])\n",
"axs1[2].set_title('LA')\n",
"axs1[2].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs1[2].set_ylabel(r'$LA$ [%]')\n",
@@ -276,27 +209,6 @@
"fig1.tight_layout()\n",
"fig1.show()\n"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x151d938bc40>]"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"fig2 = plt.figure()\n",
"plt.plot(t_vec,Pegelregler.get_error_history())"
]
}
],
"metadata": {

6
Regler/Regler_class_file.py
View File

@@ -84,17 +84,17 @@ class PI_controller_class:
# use a list to be able to append more easily - will get converted to np.array when needed
self.error_history = [0]
self.control_variable = -99
self.cv_lower_limit = lower_limit # limits for the controll variable
self.cv_upper_limit = upper_limit # limits for the controll variable
# setter
def set_setpoint(self,setpoint):
self.SP = setpoint
def set_control_variable(self,control_variable, display_warning=True):
if display_warning == True and self.control_variable != -99:
if display_warning == True:
print('WARNING! You are setting the control variable of the PI controller manually \
and are not using the .update_controll_variable() method')
self.control_variable = control_variable

131
Turbinen/Turbinen_class_file.py
View File

@@ -1,8 +1,10 @@
from time import time
import numpy as np
#importing pressure conversion function
import sys
import os
from pyparsing import alphanums
current = os.path.dirname(os.path.realpath(__file__))
parent = os.path.dirname(current)
sys.path.append(parent)
@@ -11,7 +13,7 @@ from functions.pressure_conversion import pressure_conversion
class Francis_Turbine:
# units
# make sure that units and print units are the same
# units are used to label graphs and print units are used to have a bearable format when using pythons print()
# units are used to label graphs and disp units are used to have a bearable format when using pythons print()
density_unit = r'$\mathrm{kg}/\mathrm{m}^3$'
flux_unit = r'$\mathrm{m}^3/\mathrm{s}$'
LA_unit = '%'
@@ -20,30 +22,28 @@ class Francis_Turbine:
velocity_unit = r'$\mathrm{m}/\mathrm{s}$'
volume_unit = r'$\mathrm{m}^3$'
density_unit_print = 'kg/m³'
flux_unit_print = 'm³/s'
LA_unit_print = '%'
pressure_unit_print = 'mWS'
time_unit_print = 's'
velocity_unit_print = 'm/s'
volume_unit_print = 'm³'
density_unit_disp = 'kg/m³'
flux_unit_disp = 'm³/s'
LA_unit_disp = '%'
time_unit_disp = 's'
velocity_unit_disp = 'm/s'
volume_unit_disp = 'm³'
g = 9.81 # m/s² gravitational acceleration
# init
def __init__(self, Q_nenn,p_nenn,t_closing=-1.,timestep=-1.):
def __init__(self, Q_nenn,p_nenn,t_closing,timestep,pressure_unit_disp):
self.Q_n = Q_nenn # nominal flux
self.p_n = p_nenn # nominal pressure
self.LA_n = 1. # 100% # nominal Leitapparatöffnung
h = pressure_conversion(p_nenn,'Pa','MWs') # nominal pressure in terms of hydraulic head
self.A = Q_nenn/(np.sqrt(2*self.g*h)*0.98) # Ersatzfläche
self.dt = timestep # simulation timestep
self.t_c = t_closing # closing time
self.t_c = t_closing # closing time
self.d_LA_max_dt = 1/t_closing # maximal change of LA per second
self.pressure_unit_disp = pressure_unit_disp
# initialize for get_info() - parameters will be converted to display -1 if not overwritten
self.p = pressure_conversion(-1,self.pressure_unit_print,self.pressure_unit)
self.p = pressure_conversion(-1,self.pressure_unit_disp,self.pressure_unit)
self.Q = -1.
self.LA = -0.01
@@ -54,19 +54,22 @@ class Francis_Turbine:
self.LA = LA
# warn user, that the .set_LA() method should not be used ot set LA manually
if display_warning == True:
print('Consider using the .update_LA() method instead of setting LA manually')
def set_timestep(self,timestep,display_warning=True):
# set Leitapparatöffnung
self.dt = time
# warn user, that the .set_LA() method should not be used ot set LA manually
if display_warning == True:
print('WARNING: You are changing the timestep of the turbine simulation. This has implications on the simulated closing speed!')
print('You are setting the guide vane opening of the turbine manually. \n \
This is not an intended use of this method. \n \
Refer to the .update_LA() method instead.')
def set_pressure(self,pressure):
# set pressure in front of the turbine
self.p = pressure
def set_steady_state(self,ss_flux,ss_pressure):
# calculate and set steady state LA, that allows the flow of ss_flux at ss_pressure through the
# turbine at the steady state LA
ss_LA = self.LA_n*ss_flux/self.Q_n*np.sqrt(self.p_n/ss_pressure)
if ss_LA < 0 or ss_LA > 1:
raise Exception('LA out of range [0;1]')
self.set_LA(ss_LA,display_warning=False)
#getter
def get_current_Q(self):
# return the flux through the turbine, based on the current pressure in front
@@ -80,10 +83,13 @@ class Francis_Turbine:
def get_current_LA(self):
return self.LA
def get_current_pressure(self):
return pressure_conversion(self.p,self.pressure_unit,self.pressure_unit_disp)
def get_info(self, full = False):
new_line = '\n'
p = pressure_conversion(self.p,self.pressure_unit,self.pressure_unit_print)
p_n = pressure_conversion(self.p_n,self.pressure_unit,self.pressure_unit_print)
p = pressure_conversion(self.p,self.pressure_unit,self.pressure_unit_disp)
p_n = pressure_conversion(self.p_n,self.pressure_unit,self.pressure_unit_disp)
if full == True:
@@ -91,33 +97,34 @@ class Francis_Turbine:
print_str = (f"Turbine has the following attributes: {new_line}"
f"----------------------------- {new_line}"
f"Type = Francis {new_line}"
f"Nominal flux = {self.Q_n:<10} {self.flux_unit_print} {new_line}"
f"Nominal pressure = {round(p_n,3):<10} {self.pressure_unit_print}{new_line}"
f"Nominal LA = {self.LA_n*100:<10} {self.LA_unit_print} {new_line}"
f"Closing time = {self.t_c:<10} {self.time_unit_print} {new_line}"
f"Current flux = {self.Q:<10} {self.flux_unit_print} {new_line}"
f"Current pipe pressure = {round(p,3):<10} {self.pressure_unit_print} {new_line}"
f"Current LA = {self.LA*100:<10} {self.LA_unit_print} {new_line}"
f"Simulation timestep = {self.dt:<10} {self.time_unit_print} {new_line}"
f"Nominal flux = {self.Q_n:<10} {self.flux_unit_disp} {new_line}"
f"Nominal pressure = {round(p_n,3):<10} {self.pressure_unit_disp}{new_line}"
f"Nominal LA = {self.LA_n*100:<10} {self.LA_unit_disp} {new_line}"
f"Closing time = {self.t_c:<10} {self.time_unit_disp} {new_line}"
f"Current flux = {self.Q:<10} {self.flux_unit_disp} {new_line}"
f"Current pipe pressure = {round(p,3):<10} {self.pressure_unit_disp} {new_line}"
f"Current LA = {self.LA*100:<10} {self.LA_unit_disp} {new_line}"
f"Simulation timestep = {self.dt:<10} {self.time_unit_disp} {new_line}"
f"----------------------------- {new_line}")
else:
# :<10 pads the self.value to be 10 characters wide
print_str = (f"The current attributes are: {new_line}"
f"----------------------------- {new_line}"
f"Current flux = {self.Q:<10} {self.flux_unit_print} {new_line}"
f"Current pipe pressure = {round(p,3):<10} {self.pressure_unit_print} {new_line}"
f"Current LA = {self.LA*100:<10} {self.LA_unit_print} {new_line}"
f"Current flux = {self.Q:<10} {self.flux_unit_disp} {new_line}"
f"Current pipe pressure = {round(p,3):<10} {self.pressure_unit_disp} {new_line}"
f"Current LA = {self.LA*100:<10} {self.LA_unit_disp} {new_line}"
f"----------------------------- {new_line}")
print(print_str)
# methods
# update methods
def update_LA(self,LA_soll):
# update the Leitappartöffnung and consider the restrictions of the closing time of the turbine
LA_diff = self.LA-LA_soll # calculate the difference to the target LA
LA_diff_max = self.d_LA_max_dt*self.dt # calculate the maximum change in LA based on the given timestep
LA_diff = self.LA-LA_soll # calculate the difference to the target LA
LA_diff_max = self.d_LA_max_dt*self.dt # calculate the maximum possible change in LA based on the given timestep
LA_diff = np.sign(LA_diff)*np.min(np.abs([LA_diff,LA_diff_max])) # calulate the correct change in LA
# make sure that the LA is not out of the range [0;1]
LA_new = self.LA-LA_diff
if LA_new < 0.:
LA_new = 0.
@@ -125,10 +132,42 @@ class Francis_Turbine:
LA_new = 1.
self.set_LA(LA_new,display_warning=False)
def set_steady_state(self,ss_flux,ss_pressure):
# calculate and set steady state LA, that allows the flow of ss_flux at ss_pressure through the
# turbine at the steady state LA
ss_LA = self.LA_n*ss_flux/self.Q_n*np.sqrt(self.p_n/ss_pressure)
if ss_LA < 0 or ss_LA > 1:
raise Exception('LA out of range [0;1]')
self.set_LA(ss_LA,display_warning=False)
# methods
def converge(self,convergence_parameters):
# small numerical disturbances (~1e-12 m/s) in the velocity can get amplified at the turbine node, because the new velocity of the turbine and the
# new pressure from the forward characteristic are not compatible.
eps = 1e-12 # convergence criterion: iteration change < eps
iteration_change = 1. # change in Q from one iteration to the next
i = 0 # safety variable. break loop if it exceeds 1e6 iterations
g = self.g # gravitational acceleration
p = convergence_parameters[0] # pressure at second to last node (see method of characterisctics - boundary condidtions)
v = convergence_parameters[1] # velocity at second to last node (see method of characterisctics - boundary condidtions)
D = convergence_parameters[2] # diameter of the pipeline
area_pipe = convergence_parameters[3] # area of the pipeline
alpha = convergence_parameters[4] # elevation angle of the pipeline
f_D = convergence_parameters[5] # Darcy friction coefficient
c = convergence_parameters[6] # pressure wave propagtation velocity
rho = convergence_parameters[7] # density of the liquid
dt = convergence_parameters[8] # timestep of the characteristic method
p_old = self.get_current_pressure()
Q_old = self.get_current_Q()
v_old = Q_old/area_pipe
while iteration_change > eps:
self.set_pressure(p_old)
Q_new = self.get_current_Q()
v_new = Q_new/area_pipe
p_new = p-rho*c*(v_old-v)+rho*c*dt*g*np.sin(alpha)-f_D*rho*c*dt/(2*D)*abs(v)*v
iteration_change = abs(Q_old-Q_new)
Q_old = Q_new.copy()
p_old = p_new.copy()
v_old = v_new.copy()
i = i+1
if i == 1e6:
print('did not converge')
break
# print(i)
self.Q = Q_new

370
Turbinen/Turbinen_test_steady_state.ipynb Normal file
View File

@@ -0,0 +1,370 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from Turbinen_class_file import Francis_Turbine\n",
"\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\n",
"from Druckrohrleitung.Druckrohrleitung_class_file import Druckrohrleitung_class\n",
"from Regler.Regler_class_file import PI_controller_class"
]
},
{
"cell_type": "code",
"execution_count": 9,
"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",
"\n",
" # for Turbine\n",
"Tur_Q_nenn = 0.85 # [m³/s] nominal flux of turbine \n",
"Tur_p_nenn = pressure_conversion(10.6,'bar',pUnit_calc) # [Pa] nominal pressure of turbine \n",
"Tur_closingTime = 90. # [s] closing time of turbine\n",
"\n",
"\n",
" # for PI controller\n",
"Con_targetLevel = 8. # [m]\n",
"Con_K_p = 0.1 # [-] proportional constant of PI controller\n",
"Con_T_i = 10. # [s] timespan in which a steady state error is corrected by the intergal term\n",
"Con_deadbandRange = 0.05 # [m] Deadband range around targetLevel for which the controller does NOT intervene\n",
"\n",
"\n",
" # for pipeline\n",
"Pip_length = (535.+478.) # [m] length of pipeline\n",
"Pip_dia = 0.9 # [m] diameter of pipeline\n",
"Pip_area = Pip_dia**2/4*np.pi # [m²] crossectional area of pipeline\n",
"Pip_head = 105. # [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 = 50 # [-] number of pipe segments in discretization\n",
"Pip_f_D = 0.014 # [-] 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",
"\n",
" # for reservoir\n",
"Res_area_base = 74. # [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 = 600. # [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": 10,
"metadata": {},
"outputs": [],
"source": [
"# create objects\n",
"\n",
"# Upstream reservoir\n",
"reservoir = Ausgleichsbecken_class(Res_area_base,Res_area_out,Res_dt,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_n_seg,Pip_angle,Pip_f_D,Pip_pw_vel,Pip_dt,pUnit_conv,rho)\n",
"pipe.set_steady_state(flux_init,level_init,Res_area_base,Pip_x_vec,Pip_h_vec)\n",
"\n",
"# downstream turbine\n",
"turbine = Francis_Turbine(Tur_Q_nenn,Tur_p_nenn,Tur_closingTime,Pip_dt,pUnit_conv)\n",
"turbine.set_steady_state(flux_init,pipe.get_current_pressure_distribution()[-1])\n",
"\n",
"# influx setting turbine\n",
"turbine_in = Francis_Turbine(Tur_Q_nenn,Tur_p_nenn,Tur_closingTime/2,Pip_dt,pUnit_conv)\n",
"turbine_in.set_steady_state(flux_init,Tur_p_nenn)\n",
"\n",
"# level controll\n",
"level_control = PI_controller_class(Con_targetLevel,Con_deadbandRange,Con_K_p,Con_T_i,Pip_dt)\n",
"level_control.set_control_variable(turbine.get_current_LA(),display_warning=False)\n"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"# initialization for Timeloop\n",
"\n",
"v_old = pipe.get_current_velocity_distribution()\n",
"v_min = pipe.get_current_velocity_distribution()\n",
"v_max = pipe.get_current_velocity_distribution()\n",
"Q_old = pipe.get_current_flux_distribution()\n",
"Q_min = pipe.get_current_flux_distribution()\n",
"Q_max = pipe.get_current_flux_distribution()\n",
"p_old = pipe.get_current_pressure_distribution()\n",
"p_min = pipe.get_current_pressure_distribution()\n",
"p_max = pipe.get_current_pressure_distribution()\n",
"\n",
"Q_in_vec = np.zeros_like(t_vec)\n",
"Q_in_vec[0] = flux_init\n",
"\n",
"v_boundary_res = np.zeros_like(t_vec)\n",
"v_boundary_tur = np.zeros_like(t_vec)\n",
"Q_boundary_res = np.zeros_like(t_vec)\n",
"Q_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",
"level_vec = np.full_like(t_vec,level_init) # level at the end of each pipeline timestep\n",
"volume_vec = np.full_like(t_vec,reservoir.get_current_volume()) # volume at the end of each pipeline timestep\n",
"\n",
"v_boundary_res[0] = v_old[0]\n",
"v_boundary_tur[0] = v_old[-1] \n",
"Q_boundary_res[0] = Q_old[0]\n",
"Q_boundary_tur[0] = Q_old[-1]\n",
"p_boundary_res[0] = p_old[0]\n",
"p_boundary_tur[0] = p_old[-1]\n",
"\n",
"LA_soll_vec = np.full_like(t_vec,turbine.get_current_LA())\n",
"LA_ist_vec = np.full_like(t_vec,turbine.get_current_LA())\n",
"\n",
"LA_soll_vec2 = np.full_like(t_vec,turbine_in.get_current_LA())\n"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib qt5\n",
"# Con_T_ime 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",
"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[1].set_title('Flux distribution in pipeline')\n",
"axs1[1].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
"axs1[1].set_ylabel(r'$Q$ [$\\mathrm{m}^3 / \\mathrm{s}$]')\n",
"lo_p, = axs1[0].plot(Pip_x_vec,pressure_conversion(p_old,pUnit_calc, pUnit_conv),marker='.')\n",
"lo_q, = axs1[1].plot(Pip_x_vec,Q_old,marker='.')\n",
"lo_pmin, = axs1[0].plot(Pip_x_vec,pipe.get_lowest_pressure_per_node(disp=True),c='red')\n",
"lo_pmax, = axs1[0].plot(Pip_x_vec,pipe.get_highest_pressure_per_node(disp=True),c='red')\n",
"lo_qmin, = axs1[1].plot(Pip_x_vec,pipe.get_lowest_flux_per_node(),c='red')\n",
"lo_qmax, = axs1[1].plot(Pip_x_vec,pipe.get_highest_flux_per_node(),c='red')\n",
"\n",
"axs1[0].autoscale()\n",
"axs1[1].autoscale()\n",
"\n",
"fig1.tight_layout()\n",
"fig1.show()\n",
"plt.pause(1)\n"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"convergence_parameters = [p_old[-2],v_old[-2],Pip_dia,Pip_area,Pip_angle,Pip_f_D,Pip_pw_vel,rho,Pip_dt]\n",
"\n",
"# loop through Con_T_ime steps of the pipeline\n",
"for it_pipe in range(1,nt+1):\n",
"\n",
" turbine_in.update_LA(LA_soll_vec2[it_pipe])\n",
" turbine_in.set_pressure(Tur_p_nenn)\n",
" Q_in_vec[it_pipe] = turbine_in.get_current_Q()\n",
" reservoir.set_influx(Q_in_vec[it_pipe])\n",
"\n",
"# for each pipeline timestep, execute nt_eRK4 timesteps of the reservoir code\n",
" # set initial condition for the reservoir Con_T_ime evolution calculted with e-RK4\n",
" reservoir.set_pressure(p_old[0],display_warning=False)\n",
" reservoir.set_outflux(Q_old[0],display_warning=False)\n",
" # calculate the Con_T_ime 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",
" volume_vec[it_pipe] = reservoir.get_current_volume() \n",
"\n",
" # get the control variable\n",
" level_control.update_control_variable(level_vec[it_pipe])\n",
" LA_soll_vec[it_pipe] = level_control.get_current_control_variable()\n",
" \n",
" # change the Leitapparatöffnung based on the target value\n",
" turbine.update_LA(LA_soll_vec[it_pipe])\n",
" LA_ist_vec[it_pipe] = turbine.get_current_LA()\n",
"\n",
" # set boundary condition for the next timestep of the characterisCon_T_ic method\n",
" turbine.set_pressure(p_old[-1])\n",
" convergence_parameters[0] = p_old[-2]\n",
" convergence_parameters[1] = v_old[-2]\n",
" turbine.converge(convergence_parameters)\n",
" p_boundary_res[it_pipe] = reservoir.get_current_pressure()\n",
" v_boundary_tur[it_pipe] = 1/Pip_area*turbine.get_current_Q()\n",
" Q_boundary_tur[it_pipe] = turbine.get_current_Q()\n",
"\n",
" # the the boundary condition 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",
" pipe.v[0] = (0.8*pipe.v[0]+0.2*reservoir.get_current_outflux()/Res_area_out)\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",
" Q_boundary_res[it_pipe] = pipe.get_current_flux_distribution()[0]\n",
"\n",
" # perform the next timestep via the characterisCon_T_ic method\n",
" pipe.timestep_characteristic_method()\n",
"\n",
" # prepare for next loop\n",
" p_old = pipe.get_current_pressure_distribution()\n",
" v_old = pipe.get_current_velocity_distribution()\n",
" Q_old = pipe.get_current_flux_distribution()\n",
"\n",
"\n",
" # plot some stuff\n",
" # remove line-objects to autoscale axes (there is definetly a better way, but this works ¯\\_(ツ)_/¯ )\n",
" lo_p.remove()\n",
" lo_pmin.remove()\n",
" lo_pmax.remove()\n",
" lo_q.remove()\n",
" lo_qmin.remove()\n",
" lo_qmax.remove()\n",
" # plot new pressure and velocity distribution in the pipeline\n",
" lo_p, = axs1[0].plot(Pip_x_vec,pipe.get_current_pressure_distribution(disp=True),marker='.',c='blue')\n",
" lo_pmin, = axs1[0].plot(Pip_x_vec,pipe.get_lowest_pressure_per_node(disp=True),c='red')\n",
" lo_pmax, = axs1[0].plot(Pip_x_vec,pipe.get_highest_pressure_per_node(disp=True),c='red')\n",
" lo_q, = axs1[1].plot(Pip_x_vec,pipe.get_current_flux_distribution(),marker='.',c='blue')\n",
" lo_qmin, = axs1[1].plot(Pip_x_vec,pipe.get_lowest_flux_per_node(),c='red')\n",
" lo_qmax, = axs1[1].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(0.001) "
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"# plot Con_T_ime evolution of boundary pressure and velocity as well as the reservoir level\n",
"\n",
"fig2,axs2 = plt.subplots(1,1)\n",
"axs2.set_title('Level and Volume reservoir')\n",
"axs2.plot(t_vec,level_vec,label='level')\n",
"axs2.set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs2.set_ylabel(r'$h$ [m]')\n",
"x_twin_00 = axs2.twinx()\n",
"x_twin_00.set_ylabel(r'$V$ [$\\mathrm{m}^3$]')\n",
"x_twin_00.plot(t_vec,volume_vec)\n",
"axs2.legend()\n",
"\n",
"fig2,axs2 = plt.subplots(1,1)\n",
"axs2.set_title('LA')\n",
"axs2.plot(t_vec,100*LA_soll_vec,label='Target')\n",
"axs2.plot(t_vec,100*LA_ist_vec,label='Actual')\n",
"axs2.set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs2.set_ylabel(r'$LA$ [%]')\n",
"axs2.legend()\n",
"\n",
"fig2,axs2 = plt.subplots(1,1)\n",
"axs2.set_title('Pressure reservoir and turbine')\n",
"axs2.plot(t_vec,pressure_conversion(p_boundary_res,pUnit_calc, pUnit_conv),label='Reservoir')\n",
"axs2.plot(t_vec,pressure_conversion(p_boundary_tur,pUnit_calc, pUnit_conv),label='Turbine')\n",
"axs2.set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs2.set_ylabel(r'$p$ ['+pUnit_conv+']')\n",
"axs2.legend()\n",
"\n",
"fig2,axs2 = plt.subplots(1,1)\n",
"axs2.set_title('Fluxes')\n",
"axs2.plot(t_vec,Q_boundary_res,label='Outflux')\n",
"axs2.plot(t_vec,Q_in_vec,label='Influx')\n",
"axs2.plot(t_vec,Q_boundary_tur,label='Flux Turbine')\n",
"axs2.set_ylim(-2*Tur_Q_nenn,+2*Tur_Q_nenn)\n",
"axs2.set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs2.set_ylabel(r'$Q$ [$\\mathrm{m}^3/\\mathrm{s}$]')\n",
"axs2.legend()\n",
"\n",
"fig2,axs2 = plt.subplots(1,1)\n",
"axs2.set_title('Min and Max Pressure')\n",
"axs2.plot(Pip_x_vec,pipe.get_lowest_pressure_per_node(disp=True),c='red')\n",
"axs2.plot(Pip_x_vec,pipe.get_highest_pressure_per_node(disp=True),c='red')\n",
"axs2.set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
"axs2.set_ylabel(r'$p$ ['+pUnit_conv+']')\n",
"\n",
"fig2,axs2 = plt.subplots(1,1)\n",
"axs2.set_title('Min and Max Fluxes')\n",
"axs2.plot(Pip_x_vec,pipe.get_lowest_flux_per_node(),c='red')\n",
"axs2.plot(Pip_x_vec,pipe.get_highest_flux_per_node(),c='red')\n",
"axs2.set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
"axs2.set_ylabel(r'$Q$ [$\\mathrm{m}^3/\\mathrm{s}$]')\n",
"\n",
"# axs2[0,1].legend()\n",
"# axs2[1,0].legend()\n",
"# axs2[1,1].legend()\n",
"# # axs2[2,0].legend()\n",
"# # axs2[2,1].legend()\n",
"\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"
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"orig_nbformat": 4,
"vscode": {
"interpreter": {
"hash": "84fb123bdc47ab647d3782661abcbe80fbb79236dd2f8adf4cef30e8755eb2cd"
}
}
},
"nbformat": 4,
"nbformat_minor": 2
}

168
Turbinen/old/convergence_turbine.py Normal file
View File

@@ -0,0 +1,168 @@
import numpy as np
#importing pressure conversion function
import sys
import os
current = os.path.dirname(os.path.realpath(__file__))
parent = os.path.dirname(current)
sys.path.append(parent)
from functions.pressure_conversion import pressure_conversion
class Francis_Turbine_test:
# units
# make sure that units and print units are the same
# units are used to label graphs and print units are used to have a bearable format when using pythons print()
density_unit = r'$\mathrm{kg}/\mathrm{m}^3$'
flux_unit = r'$\mathrm{m}^3/\mathrm{s}$'
LA_unit = '%'
pressure_unit = 'Pa'
time_unit = 's'
velocity_unit = r'$\mathrm{m}/\mathrm{s}$'
volume_unit = r'$\mathrm{m}^3$'
density_unit_print = 'kg/m³'
flux_unit_print = 'm³/s'
LA_unit_print = '%'
pressure_unit_print = 'mWS'
time_unit_print = 's'
velocity_unit_print = 'm/s'
volume_unit_print = 'm³'
g = 9.81 # m/s² gravitational acceleration
# init
def __init__(self, Q_nenn,p_nenn,t_closing=-1.,timestep=-1.):
self.Q_n = Q_nenn # nominal flux
self.p_n = p_nenn # nominal pressure
self.LA_n = 1. # 100% # nominal Leitapparatöffnung
h = pressure_conversion(p_nenn,'Pa','MWs') # nominal pressure in terms of hydraulic head
self.A = Q_nenn/(np.sqrt(2*self.g*h)*0.98) # Ersatzfläche
self.dt = timestep # simulation timestep
self.t_c = t_closing # closing time
self.d_LA_max_dt = 1/t_closing # maximal change of LA per second
# initialize for get_info() - parameters will be converted to display -1 if not overwritten
self.p = pressure_conversion(-1,self.pressure_unit_print,self.pressure_unit)
self.Q = -1.
self.LA = -0.01
# setter
def set_LA(self,LA,display_warning=True):
# set Leitapparatöffnung
self.LA = LA
# warn user, that the .set_LA() method should not be used ot set LA manually
if display_warning == True:
print('Consider using the .update_LA() method instead of setting LA manually')
def set_timestep(self,timestep,display_warning=True):
# set Leitapparatöffnung
self.dt = timestep
# warn user, that the .set_LA() method should not be used ot set LA manually
if display_warning == True:
print('WARNING: You are changing the timestep of the turbine simulation. This has implications on the simulated closing speed!')
def set_pressure(self,pressure):
# set pressure in front of the turbine
self.p = pressure
#getter
def get_current_Q(self):
# return the flux through the turbine, based on the current pressure in front
# of the turbine and the Leitapparatöffnung
if self.p < 0:
self.Q = 0
else:
self.Q = self.Q_n*(self.LA/self.LA_n)*np.sqrt(self.p/self.p_n)
return self.Q
def get_current_pressure(self):
return self.p
def get_current_LA(self):
return self.LA
def get_info(self, full = False):
new_line = '\n'
p = pressure_conversion(self.p,self.pressure_unit,self.pressure_unit_print)
p_n = pressure_conversion(self.p_n,self.pressure_unit,self.pressure_unit_print)
if full == True:
# :<10 pads the self.value to be 10 characters wide
print_str = (f"Turbine has the following attributes: {new_line}"
f"----------------------------- {new_line}"
f"Type = Francis {new_line}"
f"Nominal flux = {self.Q_n:<10} {self.flux_unit_print} {new_line}"
f"Nominal pressure = {round(p_n,3):<10} {self.pressure_unit_print}{new_line}"
f"Nominal LA = {self.LA_n*100:<10} {self.LA_unit_print} {new_line}"
f"Closing time = {self.t_c:<10} {self.time_unit_print} {new_line}"
f"Current flux = {self.Q:<10} {self.flux_unit_print} {new_line}"
f"Current pipe pressure = {round(p,3):<10} {self.pressure_unit_print} {new_line}"
f"Current LA = {self.LA*100:<10} {self.LA_unit_print} {new_line}"
f"Simulation timestep = {self.dt:<10} {self.time_unit_print} {new_line}"
f"----------------------------- {new_line}")
else:
# :<10 pads the self.value to be 10 characters wide
print_str = (f"The current attributes are: {new_line}"
f"----------------------------- {new_line}"
f"Current flux = {self.Q:<10} {self.flux_unit_print} {new_line}"
f"Current pipe pressure = {round(p,3):<10} {self.pressure_unit_print} {new_line}"
f"Current LA = {self.LA*100:<10} {self.LA_unit_print} {new_line}"
f"----------------------------- {new_line}")
print(print_str)
# methods
def update_LA(self,LA_soll):
# update the Leitappartöffnung and consider the restrictions of the closing time of the turbine
LA_diff = self.LA-LA_soll # calculate the difference to the target LA
LA_diff_max = self.d_LA_max_dt*self.dt # calculate the maximum change in LA based on the given timestep
LA_diff = np.sign(LA_diff)*np.min(np.abs([LA_diff,LA_diff_max])) # calulate the correct change in LA
LA_new = self.LA-LA_diff
if LA_new < 0.:
LA_new = 0.
elif LA_new > 1.:
LA_new = 1.
self.set_LA(LA_new,display_warning=False)
def set_steady_state(self,ss_flux,ss_pressure):
# calculate and set steady state LA, that allows the flow of ss_flux at ss_pressure through the
# turbine at the steady state LA
ss_LA = self.LA_n*ss_flux/self.Q_n*np.sqrt(self.p_n/ss_pressure)
if ss_LA < 0 or ss_LA > 1:
raise Exception('LA out of range [0;1]')
self.set_LA(ss_LA,display_warning=False)
def converge(self,area_pipe,pressure_s2l_node,velocity_s2l_node,alpha,f_D,dt):
eps = 1e-9
error = 1.
i = 0
p = pressure_s2l_node
v = velocity_s2l_node
rho = 1000
g = self.g
c = 400
D = area_pipe
p_old = self.get_current_pressure()
Q_old = self.get_current_Q()
v_old = Q_old/area_pipe
while error > eps:
self.set_pressure(p_old)
Q_new = self.get_current_Q()
v_new = Q_new/area_pipe
p_new = p-rho*c*(v_old-v)+rho*c*dt*g*np.sin(alpha)-f_D*rho*c*dt/(2*D)*abs(v)*v
error = abs(Q_old-Q_new)
Q_old = Q_new.copy()
p_old = p_new.copy()
v_old = v_new.copy()
i = i+1
if i == 1e6:
print('did not converge')
break
self.Q = Q_new

248
Untertweng.ipynb → Turbinen/old/turbine_convergence_test.ipynb
View File

@@ -8,11 +8,18 @@
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from convergence_turbine import Francis_Turbine_test\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\n",
"from Druckrohrleitung.Druckrohrleitung_class_file import Druckrohrleitung_class\n",
"from Turbinen.Turbinen_class_file import Francis_Turbine"
"from Regler.Regler_class_file import PI_controller_class"
]
},
{
@@ -21,55 +28,59 @@
"metadata": {},
"outputs": [],
"source": [
"#define constants\n",
"%matplotlib qt5\n",
"\n",
"#Turbine\n",
"Q_nenn = 0.85 # m³/s\n",
"p_nenn = pressure_conversion(10.6,'bar','Pa')\n",
"closing_time = 5 #s\n",
"closing_time = 90. #s\n",
"\n",
"# physics\n",
"g = 9.81 # gravitational acceleration [m/s²]\n",
"rho = 1000. # density of water [kg/m³]\n",
"#define constants pipe\n",
"\n",
"# pipeline\n",
"L = 535.+478. # length of pipeline [m]\n",
"D = 0.9 # pipe diameter [m]\n",
"A_pipe = D**2/4*np.pi # pipeline area\n",
"h_pipe = 105 # hydraulic head without reservoir [m] \n",
"alpha = np.arcsin(h_pipe/L) # Höhenwinkel der Druckrohrleitung \n",
"n = 50 # number of pipe segments in discretization # initial flow velocity [m/s]\n",
"f_D = 0.014 # 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 = 9000 # number of time steps after initial conditions\n",
"g = 9.81 # gravitational acceleration [m/s²]\n",
"rho = 1000. # density of water [kg/m³]\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",
"initial_level = 8. # water level in upstream reservoir [m]\n",
"pl_vec = np.arange(0,nn,1)*dx # pl = pipe-length. position of the nodes on the pipeline\n",
"t_vec = np.arange(0,nt+1)*dt # time vector\n",
"h_vec = np.arange(0,nn,1)*h_pipe/n # hydraulic head of pipeline at each node \n",
"# define controller constants\n",
"target_level = 8. # m\n",
"Kp = 0.1\n",
"Ti = 1000.\n",
"deadband_range = 0.05 # m\n",
"\n",
"L = 535.+478. # length of pipeline [m]\n",
"D = 0.9 # pipe diameter [m]\n",
"h_res = target_level # water level in upstream reservoir [m]\n",
"n = 50 # number of pipe segments in discretization\n",
"nt = 10000 # number of time steps after initial conditions\n",
"f_D = 0.014 # Darcy friction factor\n",
"c = 400. # propagation velocity of the pressure wave [m/s]\n",
"h_pipe = 105. # hydraulic head without reservoir [m] \n",
"alpha = np.arcsin(h_pipe/L) # Höhenwinkel der Druckrohrleitung \n",
"\n",
"# define constants reservoir\n",
"conversion_pressure_unit = 'mWS'\n",
"\n",
"# preparing the discretization and initial conditions\n",
"initial_flux = Q_nenn/1.1 # m³/s\n",
"initial_level = h_res # m\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,1)*dx # pl = pipe-length. position of the nodes on the pipeline\n",
"t_vec = np.arange(0,nt,1)*dt # time vector\n",
"h_vec = np.arange(0,nn,1)*h_pipe/n # hydraulic head of pipeline at each node\n",
"\n",
"\n",
"# define constants reservoir\n",
"conversion_pressure_unit = 'mWS'\n",
"\n",
"# reservoir\n",
"# replace influx by vector\n",
"initial_flux = Q_nenn/1.1 # initial influx of volume to the reservoir [m³/s]\n",
"initial_pressure_unit = 'Pa' # DO NOT CHANGE! for pressure conversion in print statements and plot labels \n",
"conversion_pressure_unit = 'bar' # for pressure conversion in print statements and plot labels\n",
"area_base = 74. # 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",
"area_base = 75. # m²\n",
"area_pipe = (D/2)**2*np.pi # m²\n",
"critical_level_low = 0. # m\n",
"critical_level_high = 100. # m\n",
"\n",
"# make sure e-RK4 method of reservoir has a small enough timestep to avoid runaway numerical error\n",
"nt_eRK4 = 100 # number of simulation steps of reservoir in between timesteps of pipeline \n",
"simulation_timestep = dt/nt_eRK4\n",
"\n",
"\n"
"nt_eRK4 = 100 # number of simulation steps of reservoir in between timesteps of pipeline \n",
"simulation_timestep = dt/nt_eRK4"
]
},
{
@@ -78,21 +89,24 @@
"metadata": {},
"outputs": [],
"source": [
"# create objects\n",
"\n",
"V = Ausgleichsbecken_class(area_base,area_outflux,critical_level_low,critical_level_high,simulation_timestep)\n",
"V = Ausgleichsbecken_class(area_base,area_pipe,critical_level_low,critical_level_high,simulation_timestep)\n",
"V.set_steady_state(initial_flux,initial_level,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_steady_state(initial_flux,initial_level,area_base,pl_vec,h_vec)\n",
"\n",
"initial_pressure_turbine = pipe.get_current_pressure_distribution()[-1]\n",
"\n",
"T1 = Francis_Turbine(Q_nenn,p_nenn,closing_time,timestep=dt)\n",
"T1.set_steady_state(initial_flux,initial_pressure_turbine)\n"
"initial_pressure_turbine = pipe.get_current_pressure_distribution()[-1]\n",
"T1 = Francis_Turbine_test(Q_nenn,p_nenn,closing_time,timestep=dt)\n",
"T1.set_steady_state(initial_flux,initial_pressure_turbine)\n",
"\n",
"T_in = Francis_Turbine_test(Q_nenn,p_nenn,closing_time/2,timestep=dt)\n",
"T_in.set_steady_state(initial_flux,p_nenn)\n",
"\n",
"Pegelregler = PI_controller_class(target_level,deadband_range,Kp,Ti,dt)\n",
"Pegelregler.control_variable = T1.get_current_LA()"
]
},
{
@@ -103,33 +117,36 @@
"source": [
"# initialization for timeloop\n",
"\n",
"level_vec = np.zeros_like(t_vec)\n",
"level_vec[0] = V.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",
"\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 follow from boundary conditions\n",
" # reservoir level and flow through turbine\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",
"# prepare the vectors that store the temporal evolution of the level in the reservoir\n",
"level_vec = np.full(nt+1,initial_level) # level at the end of each pipeline timestep\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",
"LA_soll_vec = np.full_like(t_vec,T1.LA)\n",
"# LA_soll_vec[500:]= 0\n",
"LA_ist_vec = np.full_like(t_vec,T1.LA)\n",
"LA_soll_vec = np.full_like(t_vec,T1.get_current_LA())\n",
"LA_ist_vec = np.full_like(t_vec,T1.get_current_LA())\n",
"\n",
"\n"
"LA_soll_vec2 = np.full_like(t_vec,T_in.get_current_LA())\n",
"LA_soll_vec2[500:1000] = 0.\n",
"LA_soll_vec2[1000:1500] = 1. \n",
"LA_soll_vec2[1500:2000] = 0.\n",
"LA_soll_vec2[2000:2500] = 0.5 "
]
},
{
@@ -138,26 +155,22 @@
"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",
"fig1.suptitle(str(0) +' s / '+str(round(t_vec[-1],2)) + ' s' )\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[0].set_ylabel(r'$p$ [mWS]')\n",
"lo_00, = axs1[0].plot(pl_vec,pressure_conversion(p_old,'Pa',conversion_pressure_unit),marker='.')\n",
"\n",
"axs1[1].set_title('Velocity distribution in pipeline')\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(p_old,initial_pressure_unit, conversion_pressure_unit),marker='.')\n",
"axs1[1].set_ylabel(r'$v$ [m/s]')\n",
"lo_01, = axs1[1].plot(pl_vec,v_old,marker='.')\n",
"\n",
"axs1[0].autoscale()\n",
"axs1[1].autoscale()\n",
"\n",
"fig1.tight_layout()\n",
"fig1.show()\n",
"plt.pause(1)\n"
"plt.pause(1)"
]
},
{
@@ -166,33 +179,39 @@
"metadata": {},
"outputs": [],
"source": [
"# loop through time steps of the pipeline\n",
"for it_pipe in range(1,pipe.nt+1):\n",
"\n",
" # if it_pipe == 250:\n",
" # V.set_influx(0.)\n",
"\n",
"for it_pipe in range(1,nt):\n",
"# for each pipeline timestep, execute nt_eRK4 timesteps of the reservoir code\n",
" \n",
" T_in.update_LA(LA_soll_vec2[it_pipe])\n",
" T_in.set_pressure(p_nenn)\n",
" V.set_influx(T_in.get_current_Q())\n",
"\n",
" # set initial conditions for the reservoir time evolution calculted with e-RK4\n",
" V.set_pressure(p_old[0])\n",
" V.set_outflux(v_old[0]*area_outflux)\n",
" V.set_outflux(v_old[0]*area_pipe)\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.timestep_reservoir_evolution() \n",
" level_vec[it_pipe] = V.get_current_level() \n",
" level_vec[it_pipe] = V.get_current_level() \n",
"\n",
" # get the control variable\n",
" Pegelregler.update_control_variable(level_vec[it_pipe])\n",
" LA_soll_vec[it_pipe] = Pegelregler.get_current_control_variable()\n",
" \n",
" # change the Leitapparatöffnung based on the target value\n",
" T1.update_LA(LA_soll_vec[it_pipe])\n",
" T1.set_pressure(p_old[-1])\n",
"\n",
" LA_ist_vec[it_pipe] = T1.get_current_LA()\n",
"\n",
" # set boundary conditions for the next timestep of the characteristic method\n",
" T1.set_pressure(p_old[-1])\n",
" T1.converge(area_pipe,p_old[-2],v_old[-2],alpha,f_D,dt)\n",
" p_boundary_res[it_pipe] = V.get_current_pressure()\n",
" v_boundary_tur[it_pipe] = 1/A_pipe*T1.get_current_Q()\n",
" v_boundary_tur[it_pipe] = T1.get_current_Q()/area_pipe\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",
" pipe.v[0] = (0.8*pipe.v[0]+0.2*V.get_current_outflux()/area_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",
@@ -209,34 +228,13 @@
" 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(p_old,initial_pressure_unit, conversion_pressure_unit),marker='.',c='blue')\n",
" lo_00, = axs1[0].plot(pl_vec,pressure_conversion(p_old,'Pa', conversion_pressure_unit),marker='.',c='blue')\n",
" lo_01, = axs1[1].plot(pl_vec,v_old,marker='.',c='blue')\n",
" # lo_02, = axs1[2].plot(level_vec_2,c='blue')\n",
" fig1.suptitle(str(round(t_vec[it_pipe],2))+ ' s / '+str(round(t_vec[-1],2)) + ' s' )\n",
" \n",
" fig1.suptitle(str(round(t_vec[it_pipe],2)) + '/' + str(round(t_vec[-1],2)))\n",
" fig1.canvas.draw()\n",
" fig1.tight_layout()\n",
" fig1.show()\n",
" plt.pause(0.001) \n",
"\n",
" \n",
" "
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.7727272727272726\n"
]
}
],
"source": [
"print(V.get_current_influx())"
" plt.pause(0.000001)"
]
},
{
@@ -249,7 +247,7 @@
"\n",
"fig2,axs2 = plt.subplots(3,2)\n",
"axs2[0,0].set_title('Pressure reservoir')\n",
"axs2[0,0].plot(t_vec,pressure_conversion(p_boundary_res,initial_pressure_unit, conversion_pressure_unit))\n",
"axs2[0,0].plot(t_vec,pressure_conversion(p_boundary_res,'Pa', conversion_pressure_unit))\n",
"axs2[0,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs2[0,0].set_ylabel(r'$p$ ['+conversion_pressure_unit+']')\n",
"\n",
@@ -260,7 +258,7 @@
"axs2[0,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n",
"\n",
"axs2[1,0].set_title('Pressure turbine')\n",
"axs2[1,0].plot(t_vec,pressure_conversion(p_boundary_tur,initial_pressure_unit, conversion_pressure_unit))\n",
"axs2[1,0].plot(t_vec,pressure_conversion(p_boundary_tur,'Pa', conversion_pressure_unit))\n",
"axs2[1,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs2[1,0].set_ylabel(r'$p$ ['+conversion_pressure_unit+']')\n",
"\n",
@@ -282,52 +280,6 @@
"fig2.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The cuboid reservoir has the following attributes: \n",
"----------------------------- \n",
"Base area = 74.0 m² \n",
"Outflux area = 0.636 m² \n",
"Current level = 8.020201323491174 m\n",
"Critical level low = 0.0 m \n",
"Critical level high = inf m \n",
"Volume in reservoir = -- m³ \n",
"Current influx = 0.7727272727272726 m³/s \n",
"Current outflux = -3.529572535198196 m³/s \n",
"Current outflux vel = -5.548 m/s \n",
"Current pipe pressure = 0.479 bar \n",
"Simulation timestep = 0.0005065 s \n",
"Density of liquid = 1000 kg/m³ \n",
"----------------------------- \n",
"\n",
"9.47597527926513\n",
"10.931749235039087\n",
"12.387523190813043\n",
"13.843297146587\n",
"15.299071102360957\n",
"16.75484505813491\n",
"18.210619013908868\n",
"19.666392969682825\n",
"21.12216692545678\n",
"22.577940881230738\n"
]
}
],
"source": [
"V.get_info(full=True)\n",
"V.set_outflux(-10.)\n",
"for i in range(10):\n",
" V.level = V.update_level(10.)\n",
" print(V.get_current_level())"
]
}
],
"metadata": {

348
Untertweng_mit_Pegelregler.ipynb
View File

@@ -22,63 +22,60 @@
"metadata": {},
"outputs": [],
"source": [
"#define constants\n",
"# define constants\n",
"\n",
"#Turbine\n",
"Q_nenn = 0.85 # m³/s\n",
"p_nenn = pressure_conversion(10.6,'bar','Pa')\n",
"closing_time = 30. #s\n",
"\n",
"# physics\n",
"g = 9.81 # gravitational acceleration [m/s²]\n",
"rho = 1000. # density of water [kg/m³]\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",
"\n",
"# define controller constants\n",
"target_level = 8. # m\n",
"Kp = 0.1\n",
"Ti = 7.\n",
"deadband_range = 0.05 # m\n",
" # for Turbine\n",
"Tur_Q_nenn = 0.85 # [m³/s] nominal flux of turbine \n",
"Tur_p_nenn = pressure_conversion(10.6,'bar',pUnit_calc) # [Pa] nominal pressure of turbine \n",
"Tur_closingTime = 90. # [s] closing time of turbine\n",
"\n",
"\n",
"# pipeline\n",
"L = 535.+478. # length of pipeline [m]\n",
"D = 0.9 # pipe diameter [m]\n",
"A_pipe = D**2/4*np.pi # pipeline area\n",
"h_pipe = 105 # hydraulic head without reservoir [m] \n",
"alpha = np.arcsin(h_pipe/L) # Höhenwinkel der Druckrohrleitung \n",
"n = 50 # number of pipe segments in discretization\n",
"f_D = 0.014 # 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 = 12000 # 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",
"initial_level = target_level # water level in upstream reservoir [m]\n",
"pl_vec = np.arange(0,nn,1)*dx # pl = pipe-length. position of the nodes on the pipeline\n",
"t_vec = np.arange(0,nt+1)*dt # time vector\n",
"h_vec = np.arange(0,nn,1)*h_pipe/n # hydraulic head of pipeline at each node \n",
" # for PI controller\n",
"Con_targetLevel = 8. # [m]\n",
"Con_K_p = 0.1 # [-] proportional constant of PI controller\n",
"Con_T_i = 1000. # [s] timespan in which a steady state error is corrected by the intergal term\n",
"Con_deadbandRange = 0.05 # [m] Deadband range around targetLevel for which the controller does NOT intervene\n",
"\n",
"\n",
" # for pipeline\n",
"Pip_length = (535.+478.) # [m] length of pipeline\n",
"Pip_dia = 0.9 # [m] diameter of pipeline\n",
"Pip_area = Pip_dia**2/4*np.pi # [m²] crossectional area of pipeline\n",
"Pip_head = 105. # [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 = 50 # [-] number of pipe segments in discretization\n",
"Pip_f_D = 0.014 # [-] 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",
"# reservoir\n",
"# replace influx by vector\n",
"initial_flux = Q_nenn/1.1 # initial influx of volume to the reservoir [m³/s]\n",
"initial_pressure_unit = 'Pa' # DO NOT CHANGE! for pressure conversion in print statements and plot labels \n",
"conversion_pressure_unit = 'bar' # for pressure conversion in print statements and plot labels\n",
"area_base = 74. # 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 = 100 # number of simulation steps of reservoir in between timesteps of pipeline \n",
"simulation_timestep = dt/nt_eRK4\n",
" # for reservoir\n",
"Res_area_base = 74. # [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",
"\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 = 600. # [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"
]
},
{
@@ -89,87 +86,101 @@
"source": [
"# create objects\n",
"\n",
"V = Ausgleichsbecken_class(area_base,area_outflux,critical_level_low,critical_level_high,simulation_timestep)\n",
"V.set_steady_state(initial_flux,initial_level,conversion_pressure_unit)\n",
"# Upstream reservoir\n",
"reservoir = Ausgleichsbecken_class(Res_area_base,Res_area_out,Res_dt,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_n_seg,Pip_angle,Pip_f_D,Pip_pw_vel,Pip_dt,pUnit_conv,rho)\n",
"pipe.set_steady_state(flux_init,level_init,Res_area_base,Pip_x_vec,Pip_h_vec)\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_steady_state(initial_flux,initial_level,area_base,pl_vec,h_vec)\n",
"# downstream turbine\n",
"turbine = Francis_Turbine(Tur_Q_nenn,Tur_p_nenn,Tur_closingTime,Pip_dt,pUnit_conv)\n",
"turbine.set_steady_state(flux_init,pipe.get_current_pressure_distribution()[-1])\n",
"\n",
"initial_pressure_turbine = pipe.get_current_pressure_distribution()[-1]\n",
"# influx setting turbine\n",
"turbine_in = Francis_Turbine(Tur_Q_nenn,Tur_p_nenn,Tur_closingTime,Pip_dt,pUnit_conv)\n",
"turbine_in.set_steady_state(flux_init,Tur_p_nenn)\n",
"\n",
"T1 = Francis_Turbine(Q_nenn,p_nenn,closing_time,timestep=dt)\n",
"T1.set_steady_state(initial_flux,initial_pressure_turbine)\n",
"\n",
"T_in = Francis_Turbine(Q_nenn,p_nenn,closing_time/2,timestep=dt)\n",
"T_in.set_steady_state(initial_flux,p_nenn)\n",
"\n",
"Pegelregler = PI_controller_class(target_level,deadband_range,Kp,Ti,dt)\n",
"Pegelregler.control_variable = T1.get_current_LA()\n"
"# level controll\n",
"level_control = PI_controller_class(Con_targetLevel,Con_deadbandRange,Con_K_p,Con_T_i,Pip_dt)\n",
"level_control.set_control_variable(turbine.get_current_LA(),display_warning=False)\n"
]
},
{
"cell_type": "code",
"execution_count": 11,
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"# initialization for timeloop\n",
"# 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 = pipe.get_current_velocity_distribution()\n",
"v_min = pipe.get_current_velocity_distribution()\n",
"v_max = pipe.get_current_velocity_distribution()\n",
"Q_old = pipe.get_current_flux_distribution()\n",
"Q_min = pipe.get_current_flux_distribution()\n",
"Q_max = pipe.get_current_flux_distribution()\n",
"p_old = pipe.get_current_pressure_distribution()\n",
"p_min = pipe.get_current_pressure_distribution()\n",
"p_max = pipe.get_current_pressure_distribution()\n",
"\n",
"Q_in_vec = np.zeros_like(t_vec)\n",
"Q_in_vec[0] = flux_init\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 follow from boundary conditions\n",
" # reservoir level and flow through turbine\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",
"Q_boundary_res = np.zeros_like(t_vec)\n",
"Q_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",
"# prepare the vectors that store the temporal evolution of the level in the reservoir\n",
"level_vec = np.full(nt+1,initial_level) # level at the end of each pipeline timestep\n",
"level_vec = np.full_like(t_vec,level_init) # level at the end of each pipeline timestep\n",
"volume_vec = np.full_like(t_vec,reservoir.get_current_volume()) # volume at the end of each pipeline timestep\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",
"Q_boundary_res[0] = Q_old[0]\n",
"Q_boundary_tur[0] = Q_old[-1]\n",
"p_boundary_res[0] = p_old[0]\n",
"p_boundary_tur[0] = p_old[-1]\n",
"\n",
"LA_soll_vec = np.full_like(t_vec,T1.get_current_LA())\n",
"LA_ist_vec = np.full_like(t_vec,T1.get_current_LA())\n",
"LA_soll_vec = np.full_like(t_vec,turbine.get_current_LA())\n",
"LA_ist_vec = np.full_like(t_vec,turbine.get_current_LA())\n",
"\n",
"LA_soll_vec2 = np.full_like(t_vec,T_in.get_current_LA())\n",
"LA_soll_vec2[500:1000] = 0.\n",
"LA_soll_vec2[1000:1500] = 1. \n",
"LA_soll_vec2[1500:2000] = 0.\n",
"LA_soll_vec2[2000:2500] = 0.5 \n"
"LA_soll_vec2 = np.full_like(t_vec,turbine_in.get_current_LA())\n",
"LA_soll_vec2[500:] = 0\n",
"# LA_soll_vec2[500:1000] = 0.\n",
"# LA_soll_vec2[1000:1500] = 1. \n",
"# LA_soll_vec2[1500:2000] = 0.\n",
"# LA_soll_vec2[2000:2500] = 0.5 \n"
]
},
{
"cell_type": "code",
"execution_count": 12,
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib qt5\n",
"# time loop\n",
"# Con_T_ime 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",
"fig1.suptitle(str(0) +' s / '+str(round(t_vec[-1],2)) + ' s' )\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[0].set_ylabel(r'$p$ ['+pUnit_conv+']')\n",
"axs1[1].set_title('Flux distribution in pipeline')\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(p_old,initial_pressure_unit, conversion_pressure_unit),marker='.')\n",
"lo_01, = axs1[1].plot(pl_vec,v_old,marker='.')\n",
"axs1[1].set_ylabel(r'$Q$ [$\\mathrm{m}^3 / \\mathrm{s}$]')\n",
"lo_p, = axs1[0].plot(Pip_x_vec,pressure_conversion(p_old,pUnit_calc, pUnit_conv),marker='.')\n",
"lo_q, = axs1[1].plot(Pip_x_vec,Q_old,marker='.')\n",
"lo_pmin, = axs1[0].plot(Pip_x_vec,pipe.get_lowest_pressure_per_node(disp=True),c='red')\n",
"lo_pmax, = axs1[0].plot(Pip_x_vec,pipe.get_highest_pressure_per_node(disp=True),c='red')\n",
"lo_qmin, = axs1[1].plot(Pip_x_vec,pipe.get_lowest_flux_per_node(),c='red')\n",
"lo_qmax, = axs1[1].plot(Pip_x_vec,pipe.get_highest_flux_per_node(),c='red')\n",
"\n",
"axs1[0].autoscale()\n",
"axs1[1].autoscale()\n",
"\n",
@@ -180,111 +191,150 @@
},
{
"cell_type": "code",
"execution_count": 13,
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"# loop through time steps of the pipeline\n",
"for it_pipe in range(1,pipe.nt+1):\n",
"convergence_parameters = [p_old[-2],v_old[-2],Pip_dia,Pip_area,Pip_angle,Pip_f_D,Pip_pw_vel,rho,Pip_dt]\n",
"\n",
" T_in.update_LA(LA_soll_vec2[it_pipe])\n",
" T_in.set_pressure(p_nenn)\n",
" V.set_influx(T_in.get_current_Q())\n",
"# loop through Con_T_ime steps of the pipeline\n",
"for it_pipe in range(1,nt+1):\n",
"\n",
" turbine_in.update_LA(LA_soll_vec2[it_pipe])\n",
" turbine_in.set_pressure(Tur_p_nenn)\n",
" Q_in_vec[it_pipe] = turbine_in.get_current_Q()\n",
" reservoir.set_influx(Q_in_vec[it_pipe])\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.set_pressure(p_old[0])\n",
" V.set_outflux(v_old[0]*area_outflux)\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.timestep_reservoir_evolution() \n",
" level_vec[it_pipe] = V.get_current_level() \n",
" # set initial condition for the reservoir Con_T_ime evolution calculted with e-RK4\n",
" reservoir.set_pressure(p_old[0],display_warning=False)\n",
" reservoir.set_outflux(Q_old[0],display_warning=False)\n",
" # calculate the Con_T_ime 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",
" volume_vec[it_pipe] = reservoir.get_current_volume() \n",
"\n",
" # get the control variable\n",
" Pegelregler.update_control_variable(level_vec[it_pipe])\n",
" LA_soll_vec[it_pipe] = Pegelregler.get_current_control_variable()\n",
" level_control.update_control_variable(level_vec[it_pipe])\n",
" LA_soll_vec[it_pipe] = level_control.get_current_control_variable()\n",
" \n",
" # change the Leitapparatöffnung based on the target value\n",
" T1.update_LA(LA_soll_vec[it_pipe])\n",
" LA_ist_vec[it_pipe] = T1.get_current_LA()\n",
" turbine.update_LA(LA_soll_vec[it_pipe])\n",
" LA_ist_vec[it_pipe] = turbine.get_current_LA()\n",
"\n",
" T1.set_pressure(p_old[-1])\n",
" # set boundary conditions for the next timestep of the characteristic method\n",
" p_boundary_res[it_pipe] = V.get_current_pressure()\n",
" v_boundary_tur[it_pipe] = 1/A_pipe*T1.get_current_Q()\n",
" # set boundary condition for the next timestep of the characterisCon_T_ic method\n",
" turbine.set_pressure(p_old[-1])\n",
" convergence_parameters[0] = p_old[-2]\n",
" convergence_parameters[1] = v_old[-2]\n",
" turbine.converge(convergence_parameters)\n",
" p_boundary_res[it_pipe] = reservoir.get_current_pressure()\n",
" v_boundary_tur[it_pipe] = 1/Pip_area*turbine.get_current_Q()\n",
" Q_boundary_tur[it_pipe] = turbine.get_current_Q()\n",
"\n",
" # the the boundary conditions in the pipe.object and thereby calculate boundary pressure at turbine\n",
" # the the boundary condition 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",
" pipe.v[0] = (0.8*pipe.v[0]+0.2*reservoir.get_current_outflux()/Res_area_out)\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",
" Q_boundary_res[it_pipe] = pipe.get_current_flux_distribution()[0]\n",
"\n",
"\n",
" # perform the next timestep via the characteristic method\n",
" # perform the next timestep via the characterisCon_T_ic method\n",
" pipe.timestep_characteristic_method()\n",
"\n",
" # prepare for next loop\n",
" p_old = pipe.get_current_pressure_distribution()\n",
" v_old = pipe.get_current_velocity_distribution()\n",
" Q_old = pipe.get_current_flux_distribution()\n",
"\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",
" lo_p.remove()\n",
" lo_pmin.remove()\n",
" lo_pmax.remove()\n",
" lo_q.remove()\n",
" lo_qmin.remove()\n",
" lo_qmax.remove()\n",
" # plot new pressure and velocity distribution in the pipeline\n",
" lo_00, = axs1[0].plot(pl_vec,pressure_conversion(p_old,initial_pressure_unit, conversion_pressure_unit),marker='.',c='blue')\n",
" lo_01, = axs1[1].plot(pl_vec,v_old,marker='.',c='blue')\n",
" # lo_02, = axs1[2].plot(level_vec_2,c='blue')\n",
" lo_p, = axs1[0].plot(Pip_x_vec,pipe.get_current_pressure_distribution(disp=True),marker='.',c='blue')\n",
" lo_pmin, = axs1[0].plot(Pip_x_vec,pipe.get_lowest_pressure_per_node(disp=True),c='red')\n",
" lo_pmax, = axs1[0].plot(Pip_x_vec,pipe.get_highest_pressure_per_node(disp=True),c='red')\n",
" lo_q, = axs1[1].plot(Pip_x_vec,pipe.get_current_flux_distribution(),marker='.',c='blue')\n",
" lo_qmin, = axs1[1].plot(Pip_x_vec,pipe.get_lowest_flux_per_node(),c='red')\n",
" lo_qmax, = axs1[1].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(0.001) \n",
"\n",
" \n",
" "
" plt.pause(0.001) "
]
},
{
"cell_type": "code",
"execution_count": 14,
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"# plot time evolution of boundary pressure and velocity as well as the reservoir level\n",
"# plot Con_T_ime evolution of boundary pressure and velocity as well as the reservoir level\n",
"\n",
"fig2,axs2 = plt.subplots(3,2)\n",
"axs2[0,0].set_title('Pressure reservoir')\n",
"axs2[0,0].plot(t_vec,pressure_conversion(p_boundary_res,initial_pressure_unit, conversion_pressure_unit))\n",
"axs2[0,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs2[0,0].set_ylabel(r'$p$ ['+conversion_pressure_unit+']')\n",
"fig2,axs2 = plt.subplots(1,1)\n",
"axs2.set_title('Level and Volume reservoir')\n",
"axs2.plot(t_vec,level_vec,label='level')\n",
"axs2.set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs2.set_ylabel(r'$h$ [m]')\n",
"x_twin_00 = axs2.twinx()\n",
"x_twin_00.set_ylabel(r'$V$ [$\\mathrm{m}^3$]')\n",
"x_twin_00.plot(t_vec,volume_vec)\n",
"axs2.legend()\n",
"\n",
"axs2[0,1].set_title('Velocity reservoir')\n",
"axs2[0,1].plot(t_vec,v_boundary_res)\n",
"axs2[0,1].set_ylim(-2*Q_nenn,+2*Q_nenn)\n",
"axs2[0,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs2[0,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n",
"fig2,axs2 = plt.subplots(1,1)\n",
"axs2.set_title('LA')\n",
"axs2.plot(t_vec,100*LA_soll_vec,label='Target')\n",
"axs2.plot(t_vec,100*LA_ist_vec,label='Actual')\n",
"axs2.set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs2.set_ylabel(r'$LA$ [%]')\n",
"axs2.legend()\n",
"\n",
"axs2[1,0].set_title('Pressure turbine')\n",
"axs2[1,0].plot(t_vec,pressure_conversion(p_boundary_tur,initial_pressure_unit, conversion_pressure_unit))\n",
"axs2[1,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs2[1,0].set_ylabel(r'$p$ ['+conversion_pressure_unit+']')\n",
"fig2,axs2 = plt.subplots(1,1)\n",
"axs2.set_title('Pressure reservoir and turbine')\n",
"axs2.plot(t_vec,pressure_conversion(p_boundary_res,pUnit_calc, pUnit_conv),label='Reservoir')\n",
"axs2.plot(t_vec,pressure_conversion(p_boundary_tur,pUnit_calc, pUnit_conv),label='Turbine')\n",
"axs2.set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs2.set_ylabel(r'$p$ ['+pUnit_conv+']')\n",
"axs2.legend()\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",
"fig2,axs2 = plt.subplots(1,1)\n",
"axs2.set_title('Fluxes')\n",
"axs2.plot(t_vec,Q_boundary_res,label='Outflux')\n",
"axs2.plot(t_vec,Q_in_vec,label='Influx')\n",
"axs2.plot(t_vec,Q_boundary_tur,label='Flux Turbine')\n",
"axs2.set_ylim(-2*Tur_Q_nenn,+2*Tur_Q_nenn)\n",
"axs2.set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs2.set_ylabel(r'$Q$ [$\\mathrm{m}^3/\\mathrm{s}$]')\n",
"axs2.legend()\n",
"\n",
"fig2,axs2 = plt.subplots(1,1)\n",
"axs2.set_title('Min and Max Pressure')\n",
"axs2.plot(Pip_x_vec,pipe.get_lowest_pressure_per_node(disp=True),c='red')\n",
"axs2.plot(Pip_x_vec,pipe.get_highest_pressure_per_node(disp=True),c='red')\n",
"axs2.set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
"axs2.set_ylabel(r'$p$ ['+pUnit_conv+']')\n",
"\n",
"fig2,axs2 = plt.subplots(1,1)\n",
"axs2.set_title('Min and Max Fluxes')\n",
"axs2.plot(Pip_x_vec,pipe.get_lowest_flux_per_node(),c='red')\n",
"axs2.plot(Pip_x_vec,pipe.get_highest_flux_per_node(),c='red')\n",
"axs2.set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
"axs2.set_ylabel(r'$Q$ [$\\mathrm{m}^3/\\mathrm{s}$]')\n",
"\n",
"# axs2[0,1].legend()\n",
"# axs2[1,0].legend()\n",
"# axs2[1,1].legend()\n",
"# # axs2[2,0].legend()\n",
"# # axs2[2,1].legend()\n",
"\n",
"axs2[2,0].set_title('Level reservoir')\n",
"axs2[2,0].plot(t_vec,level_vec)\n",
"axs2[2,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs2[2,0].set_ylabel(r'$h$ [m]')\n",
"\n",
"axs2[2,1].set_title('LA')\n",
"axs2[2,1].plot(t_vec,100*LA_soll_vec)\n",
"axs2[2,1].plot(t_vec,100*LA_ist_vec)\n",
"axs2[2,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs2[2,1].set_ylabel(r'$LA$ [%]')\n",
"fig2.tight_layout()\n",
"plt.show()"
]