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fix for numerical runaway of rounding errors

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due to turbine-pipeline interatction
via a convergence method in the turbine
and a "damping" trick on the reservoir velocity
plus: code cleanup with consistent naming of variables
This commit is contained in:
Brantegger Georg
2022-08-03 15:56:56 +02:00
parent 84631ee4cc
commit ba696444bb
13 changed files with 1257 additions and 1198 deletions
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217
Ausgleichsbecken/Ausgleichsbecken_class_file.py
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@@ -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
self.pressure = pressure
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)