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further code cleanup

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Brantegger Georg
2022-07-25 15:59:46 +02:00
parent 0de946f8ac
commit ac8bfdb7c6
9 changed files with 448 additions and 438 deletions
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165
Druckrohrleitung/Druckrohrleitung_class_file.py
View File

@@ -1,51 +1,40 @@
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'$\mathrm{m}/\mathrm{s}^2$'
angle_unit = 'rad'
area_unit = r'$\mathrm{m}^2$'
density_unit = r'$\mathrm{kg}/\mathrm{m}^3$'
flux_unit = r'$\mathrm{m}^3/\mathrm{s}$'
length_unit = 'm'
time_unit = 's'
velocity_unit = r'$\mathrm{m}/\mathrm{s}$' # for flux and pressure propagation
volume_unit = r'$\mathrm{m}^3$'
acceleration_unit = r'$\mathrm{m}/\mathrm{s}^2$'
angle_unit = 'rad'
area_unit = r'$\mathrm{m}^2$'
density_unit = r'$\mathrm{kg}/\mathrm{m}^3$'
flux_unit = r'$\mathrm{m}^3/\mathrm{s}$'
length_unit = 'm'
pressure_unit = 'Pa'
time_unit = 's'
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_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'
# init
def __init__(self,total_length,diameter,number_segments,pipeline_angle,Darcy_friction_factor,rho=1000,g=9.81):
self.length = total_length
self.dia = diameter
self.n_seg = number_segments
self.angle = pipeline_angle
self.f_D = Darcy_friction_factor # = Rohrreibungszahl oder flow coefficient
self.rho = rho
self.g = g
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.density = rho # density of the liquid in the pipeline
self.g = g # gravitational acceleration
self.dx = total_length/number_segments
self.l_vec = np.arange(0,(number_segments+1)*self.dx,self.dx)
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
# initialize for get_info method
self.c = '--'
@@ -53,32 +42,32 @@ class Druckrohrleitung_class:
# setter
def set_pressure_propagation_velocity(self,c):
self.c = c
self.dt = self.dx/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
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,pressure_unit,display_pressure_unit):
if np.size(pressure) == 1:
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
else:
raise Exception('Unable to assign initial pressure. Input has to be of size 1 or' + np.size(self.l_vec))
self.pressure_unit = pressure_unit
self.pressure_unit_print = display_pressure_unit
#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 = np.empty_like(self.p_old)
self.p_old = self.p0.copy()
self.p = self.p0.copy()
def set_initial_flow_velocity(self,velocity):
if np.size(velocity) == 1:
# 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
@@ -86,35 +75,51 @@ class Druckrohrleitung_class:
raise Exception('Unable to assign initial velocity. Input has to be of size 1 or' + np.size(self.l_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 = np.empty_like(self.v_old)
self.v_old = self.v0.copy()
self.v = self.v0.copy()
def set_boundary_conditions_next_timestep(self,v_reservoir,p_reservoir,v_turbine):
rho = self.rho
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
# the boundary velocity at the turbine is specified by the flux through the turbine or an external boundary condition
# the pressure at the turbine will be calculated using the forward characteristic
# the boundary pressure at the reservoir is specified by the level in the reservoir of an external boundary condition
# the velocity at the reservoir will be calculated using the backward characteristic
# constants for a cleaner formula
rho = self.density
c = self.c
f_D = self.f_D
dt = self.dt
D = self.dia
g = self.g
alpha = self.angle
p_old = self.p_old[-2] # @ second to last node (the one before the turbine)
v_old = self.v_old[-2] # @ second to last node (the one before the turbine)
self.v_boundary_res = v_reservoir # at new timestep
p_old_tur = self.p_old[-2] # @ second to last node (the one before the turbine)
v_old_tur = self.v_old[-2] # @ second to last node (the one before the turbine)
p_old_res = self.p_old[1] # @ second node (the one after the reservoir)
v_old_res = self.v_old[1] # @ second node (the one after the reservoir)
# set the boundary conditions derived from reservoir and turbine
self.v_boundary_tur = v_turbine # at new timestep
self.p_boundary_res = p_reservoir
self.p_boundary_tur = p_old-rho*c*(v_turbine-v_old)+rho*c*dt*g*np.sin(alpha)-f_D*rho*c*dt/(2*D)*abs(v_old)*v_old
self.p_boundary_res = p_reservoir # at new timestep
# calculate the missing boundary conditions
self.v_boundary_res = v_old_res+1/(rho*c)*(p_reservoir-p_old_res)+dt*g*np.sin(alpha)-f_D*dt/(2*D)*abs(v_old_res)*v_old_res
self.p_boundary_tur = p_old_tur-rho*c*(v_turbine-v_old_tur)+rho*c*dt*g*np.sin(alpha)-f_D*rho*c*dt/(2*D)*abs(v_old_tur)*v_old_tur
# write boundary conditions to the velocity/pressure vectors of the next timestep
self.v[0] = self.v_boundary_res.copy()
self.v[-1] = self.v_boundary_tur.copy()
self.p[0] = self.p_boundary_res.copy()
self.p[-1] = self.p_boundary_tur.copy()
def set_steady_state(self,ss_flux,ss_level_reservoir,pl_vec,h_vec,pressure_unit,display_pressure_unit):
def set_steady_state(self,ss_flux,ss_level_reservoir,pl_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.dia**2/4*np.pi))
ss_pressure = (self.rho*self.g*(ss_level_reservoir+h_vec)-ss_v0**2*self.rho/2)-(self.f_D*pl_vec/self.dia*self.rho/2*ss_v0**2)
# the static pressure is given by the hydrostatic pressure, corrected for friction losses and dynamic pressure
ss_pressure = (self.density*self.g*(ss_level_reservoir+h_vec)-ss_v0**2*self.density/2)-(self.f_D*pl_vec/self.dia*self.density/2*ss_v0**2)
self.set_initial_flow_velocity(ss_v0)
self.set_initial_pressure(ss_pressure,pressure_unit,display_pressure_unit)
self.set_initial_pressure(ss_pressure)
# getter
def get_info(self):
@@ -142,30 +147,27 @@ class Druckrohrleitung_class:
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_boundary_conditions_next_timestep(self):
print('The pressure at the reservoir for the next timestep is', '\n', \
pressure_conversion(self.p_boundary_res,self.pressure_unit,self.pressure_unit_print), '\n', \
'The velocity at the reservoir for the next timestep is', '\n', \
self.v_boundary_res, self.velocity_unit_print, '\n', \
'The pressure at the turbine for the next timestep is', '\n', \
pressure_conversion(self.p_boundary_tur,self.pressure_unit,self.pressure_unit_print), '\n', \
'The velocity at the turbine for the next timestep is', '\n', \
self.v_boundary_tur, self.velocity_unit_print)
def get_current_pressure_distribution(self):
return self.p
def get_current_velocity_distribution(self):
return self.v
def timestep_characteristic_method(self):
#number of nodes
nn = self.n_seg+1
rho = self.rho
c = self.c
f_D = self.f_D
dt = self.dt
D = self.dia
g = self.g
alpha = self.angle
# 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
nn = self.n_seg+1 # number of nodes
rho = self.density # density of liquid
c = self.c # pressure propagation velocity
f_D = self.f_D # Darcy friction coefficient
dt = self.dt # timestep
D = self.dia # pipeline diametet
g = self.g # graviational acceleration
alpha = self.angle # pipeline angle
# Vectorize this loop?
for i in range(1,nn-1):
self.v[i] = 0.5*(self.v_old[i+1]+self.v_old[i-1])-0.5/(rho*c)*(self.p_old[i+1]-self.p_old[i-1]) \
+dt*g*np.sin(alpha)-f_D*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])
@@ -173,5 +175,8 @@ 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])
# 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
self.p_old = self.p.copy()
self.v_old = self.v.copy()

237
Druckrohrleitung/Druckrohrleitung_test.ipynb
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@@ -1,237 +0,0 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from Druckrohrleitung_class_file import Druckrohrleitung_class\n",
"import matplotlib.pyplot as plt\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"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib qt5\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 = 1 # pipe diameter [m]\n",
"Q0 = 2 # initial flow in whole pipe [m³/s]\n",
"h_res = 20 # water level in upstream reservoir [m]\n",
"n = 10 # number of pipe segments in discretization\n",
"nt = 100 # 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 = 200 # hydraulic head without reservoir [m] \n",
"alpha = np.arcsin(h_pipe/L) # Höhenwinkel der Druckrohrleitung \n",
"\n",
"\n",
"# preparing the discretization and initial conditions\n",
"\n",
"dx = L/n # length of each pipe segment\n",
"dt = dx/c # timestep according to method of characterisitics\n",
"nn = n+1 # number of nodes\n",
"pl_vec = np.arange(0,nn*dx,dx) # pl = pipe-length. position of the nodes on the pipeline\n",
"t_vec = np.arange(0,nt*dt,dt) # time vector\n",
"h_vec = np.arange(0,h_pipe+h_pipe/n,h_pipe/n) # hydraulic head of pipeline at each node\n",
"\n",
"v_init = np.full(nn,Q0/(D**2/4*np.pi))\n",
"p_init = (rho*g*(h_res+h_vec)-v_init**2*rho/2)-(f_D*pl_vec/D*rho/2*v_init**2) # ref Wikipedia: Darcy Weisbach\n",
"\n",
"# storage vectors for old parameters\n",
"v_old = v_init.copy()\n",
"p_old = p_init.copy() \n",
"\n",
"# storage vectors for new parameters\n",
"v_new = np.empty_like(v_old)\n",
"p_new = np.empty_like(p_old)\n",
"\n",
"# storage vector for time evolution of parameters at node 0 (at reservoir)\n",
"p_0 = np.full_like(t_vec,p_init[0])\n",
"v_0 = np.full_like(t_vec,v_init[0])\n",
"\n",
"# storage vector for time evolution of parameters at node N+1 (at valve)\n",
"p_np1 = np.full_like(t_vec,p_init[-1])\n",
"v_np1 = np.full_like(t_vec,v_init[-1])\n",
"\n",
"for it in range(1,nt):\n",
"\n",
" # set boundary conditions\n",
" v_new[-1] = 0 # in front of the instantaneously closing valve, the velocity is 0\n",
" p_new[0] = p_init[0] # hydrostatic pressure from the reservoir\n",
"\n",
" # calculate the new parameters at first and last node\n",
" v_new[0] = v_old[1]+1/(rho*c)*(p_init[0]-p_old[1])+dt*g*np.sin(alpha)-f_D*dt/(2*D)*abs(v_old[1])*v_old[1]\n",
" p_new[-1] = p_old[-2]+rho*c*v_old[-2]-rho*c*f_D*dt/(2*D) *abs(v_old[-2])*v_old[-2]\n",
"\n",
" # calculate parameters at second to second-to-last nodes \n",
" #equation 2-30 plus 2-31 (and refactor for v_i^j+1) in block 2\n",
"\n",
" for i in range(1,nn-1):\n",
" v_new[i] = 0.5*(v_old[i-1]+v_old[i+1])+0.5/(rho*c)*(p_old[i-1]-p_old[i+1]) \\\n",
" +dt*g*np.sin(alpha)-f_D*dt/(4*D)*(abs(v_old[i-1])*v_old[i-1]+abs(v_old[i+1])*v_old[i+1])\n",
"\n",
" p_new[i] = 0.5*rho*c*(v_old[i-1]-v_old[i+1])+0.5*(p_old[i-1]+p_old[i+1]) \\\n",
" -rho*c*f_D*dt/(4*D)*(abs(v_old[i-1])*v_old[i-1]-abs(v_old[i+1])*v_old[i+1])\n",
" \n",
"\n",
" # prepare for next loop\n",
" # use .copy() to avoid that memory address is overwritten and hell breaks loose :D\n",
" #https://www.geeksforgeeks.org/array-copying-in-python/\n",
" p_old = p_new.copy()\n",
" v_old = v_new.copy()\n",
"\n",
" # store parameters of node 1 (at reservoir)\n",
" p_0[it] = p_new[0]\n",
" v_0[it] = v_new[0]\n",
" # store parameters of node N+1 (at reservoir)\n",
" p_np1[it] = p_new[-1]\n",
" v_np1[it] = v_new[-1]"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"pipe = Druckrohrleitung_class(L,D,n,alpha,f_D)\n",
"\n",
"pipe.set_pressure_propagation_velocity(c)\n",
"pipe.set_number_of_timesteps(nt)\n",
"\n",
"pipe.set_initial_pressure(p_init)\n",
"pipe.set_initial_flow_velocity(v_init)\n",
"pipe.set_boundary_conditions_next_timestep(v_0[0],p_0[0],v_np1[0])\n",
"\n",
"# storage vector for time evolution of parameters at node 0 (at reservoir)\n",
"pipe.p_0 = np.full_like(t_vec,p_init[0])\n",
"pipe.v_0 = np.full_like(t_vec,v_init[0])\n",
"\n",
"# storage vector for time evolution of parameters at node N+1 (at valve)\n",
"pipe.p_np1 = np.full_like(t_vec,p_init[-1])\n",
"pipe.v_np1 = np.full_like(t_vec,v_init[-1])\n",
"\n",
"fig2,axs2 = plt.subplots(2,1)\n",
"axs2[0].set_title('Pressure distribution in pipeline')\n",
"axs2[1].set_title('Velocity distribution in pipeline')\n",
"axs2[0].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
"axs2[0].set_ylabel(r'$p$ [mWS]')\n",
"axs2[1].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
"axs2[1].set_ylabel(r'$p$ [mWS]')\n",
"lo_00, = axs2[0].plot(pl_vec,pressure_conversion(pipe.p_old,'Pa','mWS')[0],marker='.')\n",
"lo_01, = axs2[1].plot(pl_vec,pipe.v_old,marker='.')\n",
"axs2[0].set_ylim([-2*np.max(pressure_conversion(p_init,'Pa','mWS')[0]),2*np.max(pressure_conversion(p_init,'Pa','mWS')[0])])\n",
"axs2[1].set_ylim([-2*np.max(v_init),2*np.max(v_init)])\n",
"fig2.tight_layout()\n",
"\n",
"\n",
"for it in range(1,pipe.nt):\n",
" pipe.set_boundary_conditions_next_timestep(v_0[it],p_0[it],v_np1[it])\n",
" pipe.timestep_characteristic_method()\n",
" lo_00.set_ydata(pressure_conversion(pipe.p,'Pa','mWS')[0])\n",
" lo_01.set_ydata(pipe.v)\n",
"\n",
" # store parameters of node 0 (at reservoir)\n",
" pipe.p_0[it] = pipe.p[0]\n",
" pipe.v_0[it] = pipe.v[0]\n",
" # store parameters of node N+1 (at reservoir)\n",
" pipe.p_np1[it] = pipe.p[-1]\n",
" pipe.v_np1[it] = pipe.v[-1]\n",
" \n",
" fig2.suptitle(str(it))\n",
" fig2.canvas.draw()\n",
" fig2.tight_layout()\n",
" plt.pause(0.2)\n"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"fig3,axs3 = plt.subplots(2,2)\n",
"axs3[0,0].plot(t_vec,pressure_conversion(pipe.p_0,'Pa','mWS')[0])\n",
"axs3[0,1].plot(t_vec,pipe.v_0)\n",
"axs3[1,0].plot(t_vec,pressure_conversion(pipe.p_np1,'Pa','mWS')[0])\n",
"axs3[1,1].plot(t_vec,pipe.v_np1)\n",
"axs3[0,0].set_title('Pressure Reservoir')\n",
"axs3[0,1].set_title('Velocity Reservoir')\n",
"axs3[1,0].set_title('Pressure Turbine')\n",
"axs3[1,1].set_title('Velocity Turbine')\n",
"axs3[0,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs3[0,0].set_ylabel(r'$p$ [mWS]')\n",
"axs3[0,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs3[0,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n",
"axs3[1,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs3[1,0].set_ylabel(r'$p$ [mWS]')\n",
"axs3[1,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs3[1,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n",
"fig3.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.29590621205048523\n"
]
}
],
"source": [
"print(np.mean(v_0))"
]
}
],
"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"
},
"orig_nbformat": 4,
"vscode": {
"interpreter": {
"hash": "84fb123bdc47ab647d3782661abcbe80fbb79236dd2f8adf4cef30e8755eb2cd"
}
}
},
"nbformat": 4,
"nbformat_minor": 2
}

202
Druckrohrleitung/Druckrohrleitung_test_steady_state.ipynb Normal file
View File

@@ -0,0 +1,202 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from Druckrohrleitung_class_file import Druckrohrleitung_class\n",
"import matplotlib.pyplot as plt\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"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib qt5\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 = 1 # pipe diameter [m]\n",
"Q0 = 2 # initial flow in whole pipe [m³/s]\n",
"h_res = 20 # water level in upstream reservoir [m]\n",
"n = 10 # number of pipe segments in discretization\n",
"nt = 100 # 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 = 200 # hydraulic head without reservoir [m] \n",
"alpha = np.arcsin(h_pipe/L) # Höhenwinkel der Druckrohrleitung \n",
"\n",
"\n",
"# preparing the discretization and initial conditions\n",
"initial_influx = 2. # m³/s\n",
"initial_level = 10. # 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*dx,dx) # pl = pipe-length. position of the nodes on the pipeline\n",
"t_vec = np.arange(0,nt*dt,dt) # time vector\n",
"h_vec = np.arange(0,h_pipe+h_pipe/n,h_pipe/n) # hydraulic head of pipeline at each node\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"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_influx,initial_level,pl_vec,h_vec)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# initialization for timeloop\n",
"\n",
"# prepare the vectors in which the pressure and velocity distribution in the pipeline from the previous timestep are stored\n",
"v_old = 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 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",
"# 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"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"fig2,axs2 = plt.subplots(2,1)\n",
"axs2[0].set_title('Pressure distribution in pipeline')\n",
"axs2[0].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
"axs2[0].set_ylabel(r'$p$ [mWS]')\n",
"lo_00, = axs2[0].plot(pl_vec,pressure_conversion(p_old,'Pa','mWS'),marker='.')\n",
"axs2[0].set_ylim([0.9*np.min(pressure_conversion(p_old,'Pa','mWS')),1.1*np.max(pressure_conversion(p_old,'Pa','mWS'))])\n",
"\n",
"axs2[1].set_title('Velocity distribution in pipeline')\n",
"axs2[1].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
"axs2[1].set_ylabel(r'$p$ [mWS]')\n",
"lo_01, = axs2[1].plot(pl_vec,v_old,marker='.')\n",
"axs2[1].set_ylim([0.9*np.min(v_old),1.1*np.max(v_boundary_res)])\n",
"\n",
"fig2.tight_layout()\n",
"plt.pause(5)\n",
"\n",
"\n",
"for it in range(1,pipe.nt):\n",
" pipe.set_boundary_conditions_next_timestep(p_boundary_res[0],v_boundary_tur[0])\n",
" pipe.timestep_characteristic_method()\n",
" lo_00.set_ydata(pressure_conversion(pipe.get_current_pressure_distribution(),'Pa','mWS'))\n",
" lo_01.set_ydata(pipe.get_current_velocity_distribution())\n",
"\n",
" v_boundary_res[it] = pipe.get_current_velocity_distribution()[0]\n",
" v_boundary_tur[it] = pipe.get_current_velocity_distribution()[-1]\n",
" p_boundary_res[it] = pipe.get_current_pressure_distribution()[0]\n",
" p_boundary_tur[it] = pipe.get_current_pressure_distribution()[-1]\n",
"\n",
"\n",
" \n",
" fig2.suptitle(str(it))\n",
" fig2.canvas.draw()\n",
" fig2.tight_layout()\n",
" plt.pause(0.2)\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"fig3,axs3 = plt.subplots(2,2)\n",
"axs3[0,0].set_title('Pressure Reservoir')\n",
"axs3[0,0].plot(t_vec,pressure_conversion(p_boundary_res,'Pa','mWS'))\n",
"axs3[0,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs3[0,0].set_ylabel(r'$p$ [mWS]')\n",
"axs3[0,0].set_ylim([0.9*np.min(pressure_conversion(p_boundary_res,'Pa','mWS')),1.1*np.max(pressure_conversion(p_boundary_res,'Pa','mWS'))])\n",
"\n",
"axs3[0,1].set_title('Velocity Reservoir')\n",
"axs3[0,1].plot(t_vec,v_boundary_res)\n",
"axs3[0,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs3[0,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n",
"axs3[0,1].set_ylim([0.9*np.min(v_boundary_res),1.1*np.max(v_boundary_res)])\n",
"\n",
"axs3[1,0].set_title('Pressure Turbine')\n",
"axs3[1,0].plot(t_vec,pressure_conversion(p_boundary_tur,'Pa','mWS'))\n",
"axs3[1,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs3[1,0].set_ylabel(r'$p$ [mWS]')\n",
"axs3[1,0].set_ylim([0.9*np.min(pressure_conversion(p_boundary_tur,'Pa','mWS')),1.1*np.max(pressure_conversion(p_boundary_tur,'Pa','mWS'))])\n",
"\n",
"axs3[1,1].set_title('Velocity Turbine')\n",
"axs3[1,1].plot(t_vec,v_boundary_tur)\n",
"axs3[1,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs3[1,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n",
"axs3[1,1].set_ylim([0.9*np.min(v_boundary_tur),1.1*np.max(v_boundary_tur)])\n",
"\n",
"fig3.tight_layout()\n",
"plt.show()"
]
}
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