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adapted Druckrohrleitungscode to include pipeline

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incline - not sure if code reproduces physical behavior because initial
pressure seems to disipate way too quickly
This commit is contained in:
Brantegger Georg
2022-07-05 09:30:27 +02:00
parent 28d38e8bb4
commit 7506da8b2e
4 changed files with 253 additions and 102 deletions
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171
Druckrohrleitung/Druckrohrleitung_ETH_class_file.py Normal file
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@@ -0,0 +1,171 @@
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 = '°'
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 = '°'
area_unit_print = 'm²'
density_unit_print = 'kg/m³'
flux_unit_print = 'm³/s'
length_unit_print = 'm'
pressure_unit_print = 'Pa'
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.density = 1000
self.g = g
self.dx = total_length/number_segments
self.l_vec = np.arange(0,(number_segments+1)*self.dx,self.dx)
# initialize for get_info method
self.c = '--'
self.dt = '--'
# setter
def set_pressure_propagation_velocity(self,c):
self.c = c
self.dt = self.dx/c
def set_number_of_timesteps(self,number_timesteps):
self.nt = number_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,input_unit = 'Pa'):
p,_ = pressure_conversion(pressure,input_unit,target_unit=self.pressure_unit)
if np.size(p) == 1:
self.p0 = np.full_like(self.l_vec,p)
elif np.size(p) == np.size(self.l_vec):
self.p0 = p
else:
raise Exception('Unable to assign initial pressure. Input has to be of size 1 or' + np.size(self.l_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 = np.empty_like(self.p_old)
def set_initial_flow_velocity(self,velocity):
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
else:
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)
def set_boundary_conditions_next_timestep(self,v_reservoir,p_reservoir,v_turbine,input_unit_pressure = 'Pa'):
rho = self.density
c = self.c
f_D = self.f_D
dt = self.dt
D = self.dia
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
self.v_boundary_tur = v_turbine
self.p_boundary_res,_ = pressure_conversion(p_reservoir,input_unit_pressure,target_unit=self.pressure_unit)
self.p_boundary_tur = p_old+rho*c*v_old-rho*c*f_D*dt/(2*D)*abs(v_old)*v_old
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()
# getter
def get_info(self):
new_line = '\n'
# :<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"Number of segemnts = {self.n_seg:<10} {new_line}"
f"Number of nodes = {self.n_seg+1:<10} {new_line}"
f"Length per segment = {self.dx:<10} {self.length_unit_print} {new_line}"
f"Pipeline angle = {self.angle:<10} {self.angle_unit_print} {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 timesteps = {self.dt:<10} {self.time_unit_print } {new_line}"
f"Number of timesteps = {self.nt:<10} {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_boundary_conditions_next_timestep(self,target_unit_pressure ='bar'):
print('The pressure at the reservoir for the next timestep is', '\n', \
pressure_conversion(self.p_boundary_res,self.pressure_unit_print,target_unit_pressure), '\n', \
'The velocity at the reservoir for the next timestep is', '\n', \
self.v_boundary_res, self.velocity_unit, '\n', \
'The pressure at the turbine for the next timestep is', '\n', \
pressure_conversion(self.p_boundary_tur,self.pressure_unit_print,target_unit_pressure), '\n', \
'The velocity at the turbine for the next timestep is', '\n', \
self.v_boundary_tur, self.velocity_unit)
def timestep_characteristic_method(self):
#number of nodes
nn = self.n_seg+1
rho = self.density
c = self.c
f_D = self.f_D
dt = self.dt
D = self.dia
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]) \
-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])
self.p[i] = 0.5*rho*c*(self.v_old[i-1]-self.v_old[i+1])+0.5*(self.p_old[i-1]+self.p_old[i+1]) \
-rho*c*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])
self.p_old = self.p.copy()
self.v_old = self.v.copy()

22
Druckrohrleitung/Druckrohrleitung_class_file.py
View File

@@ -12,7 +12,7 @@ from functions.pressure_conversion import pressure_conversion
class Druckrohrleitung_class:
# units
acceleration_unit = r'$\mathrm{m}/\mathrm{s}^2$'
angle_unit = '°'
angle_unit = 'rad'
area_unit = r'$\mathrm{m}^2$'
density_unit = r'$\mathrm{kg}/\mathrm{m}^3$'
flux_unit = r'$\mathrm{m}^3/\mathrm{s}$'
@@ -23,7 +23,7 @@ class Druckrohrleitung_class:
volume_unit = r'$\mathrm{m}^3$'
acceleration_unit_print = 'm/s²'
angle_unit_print = '°'
angle_unit_print = 'rad'
area_unit_print = 'm²'
density_unit_print = 'kg/m³'
flux_unit_print = 'm³/s'
@@ -94,12 +94,14 @@ class Druckrohrleitung_class:
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
self.v_boundary_tur = v_turbine
self.v_boundary_res = v_reservoir # at new timestep
self.v_boundary_tur = v_turbine # at new timestep
self.p_boundary_res,_ = pressure_conversion(p_reservoir,input_unit_pressure,target_unit=self.pressure_unit)
self.p_boundary_tur = p_old+rho*c*v_old-rho*c*f_D*dt/(2*D)*abs(v_old)*v_old
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.v[0] = self.v_boundary_res.copy()
self.v[-1] = self.v_boundary_tur.copy()
self.p[0] = self.p_boundary_res.copy()
@@ -148,13 +150,15 @@ class Druckrohrleitung_class:
f_D = self.f_D
dt = self.dt
D = self.dia
g = self.g
alpha = self.angle
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]) \
-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])
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])
self.p[i] = 0.5*rho*c*(self.v_old[i-1]-self.v_old[i+1])+0.5*(self.p_old[i-1]+self.p_old[i+1]) \
-rho*c*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])
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])
self.p_old = self.p.copy()
self.v_old = self.v.copy()

114
Druckrohrleitung/Main_Programm.ipynb
View File

@@ -2,11 +2,12 @@
"cells": [
{
"cell_type": "code",
"execution_count": 5,
"execution_count": 52,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from numpy import sin, arcsin\n",
"from Druckrohrleitung_class_file import Druckrohrleitung_class\n",
"import matplotlib.pyplot as plt\n",
"\n",
@@ -21,7 +22,7 @@
},
{
"cell_type": "code",
"execution_count": 6,
"execution_count": 53,
"metadata": {},
"outputs": [],
"source": [
@@ -29,16 +30,18 @@
"#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",
"rho = 1000 # density of water [kg/m³]\n",
"D = 1 # pipe diameter [m]\n",
"Q0 = 2 # initial flow in whole pipe [m³/s]\n",
"h = 20 # water level in upstream reservoir [m]\n",
"h_res = 20 # water level in upstream reservoir [m]\n",
"n = 10 # number of pipe segments in discretization\n",
"nt = 500 # number of time steps after initial conditions\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 = 1e-5 # hydraulic head without reservoir [m] \n",
"alpha = arcsin(h_pipe/L) # Höhenwinkel der Druckrohrleitung \n",
"\n",
"\n",
"# preparing the discretization and initial conditions\n",
@@ -48,34 +51,35 @@
"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",
"v0 = Q0/(D**2/4*np.pi)\n",
"p0 = (rho*g*h-v0**2*rho/2)\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 = np.full(nn,v0)\n",
"p_old = p0-(f_D*pl_vec/D*rho/2*v0**2) # ref Wikipedia: Darcy Weisbach\n",
"v_old = v_init.copy()\n",
"p_old = p_init.copy() \n",
"\n",
"# storage vectors for new parameters\n",
"v_new = np.zeros_like(v_old)\n",
"p_new = np.zeros_like(p_old)\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 1 (at reservoir)\n",
"p_1 = np.full_like(t_vec,p0)\n",
"v_1 = np.full_like(t_vec,v0)\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,p0)\n",
"v_np1 = np.full_like(t_vec,v0)\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] = p0 # hydrostatic pressure from the reservoir\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)*(p0-p_old[1])-f_D*dt/(2*D)*abs(v_old[1])*v_old[1]\n",
" v_new[0] = v_old[1]+1/(rho*c)*(p_init[0]-p_old[1])+dt*g*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",
@@ -83,7 +87,7 @@
"\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",
" -f_D*dt/(4*D)*(abs(v_old[i-1])*v_old[i-1]+abs(v_old[i+1])*v_old[i+1])\n",
" +dt*g*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",
@@ -96,8 +100,8 @@
" v_old = v_new.copy()\n",
"\n",
" # store parameters of node 1 (at reservoir)\n",
" p_1[it] = p_new[0]\n",
" v_1[it] = v_new[0]\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]"
@@ -105,35 +109,7 @@
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"fig1,axs1 = plt.subplots(2,2)\n",
"axs1[0,0].plot(t_vec,p_1)\n",
"axs1[0,1].plot(t_vec,v_1)\n",
"axs1[1,0].plot(t_vec,p_np1)\n",
"axs1[1,1].plot(t_vec,v_np1)\n",
"axs1[0,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs1[0,0].set_ylabel(r'$p$ [Pa]')\n",
"axs1[0,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs1[0,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n",
"axs1[1,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs1[1,0].set_ylabel(r'$p$ [Pa]')\n",
"axs1[1,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs1[1,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n",
"\n",
"axs1[0,0].set_title('Pressure Reservoir')\n",
"axs1[0,1].set_title('Velocity Reservoir')\n",
"axs1[1,0].set_title('Pressure Turbine')\n",
"axs1[1,1].set_title('Velocity Turbine')\n",
"fig1.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 8,
"execution_count": 54,
"metadata": {},
"outputs": [],
"source": [
@@ -142,17 +118,17 @@
"pipe.set_pressure_propagation_velocity(c)\n",
"pipe.set_number_of_timesteps(nt)\n",
"\n",
"pipe.set_initial_pressure(p0)\n",
"pipe.set_initial_flow_velocity(v0)\n",
"pipe.set_boundary_conditions_next_timestep(v_1[0],p_1[0],v_np1[0])\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 1 (at reservoir)\n",
"pipe.p_1 = np.full_like(t_vec,p0)\n",
"pipe.v_1 = np.full_like(t_vec,v0)\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,p0)\n",
"pipe.v_np1 = np.full_like(t_vec,v0)\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",
@@ -161,22 +137,22 @@
"axs2[0].set_ylabel(r'$p$ [Pa]')\n",
"axs2[1].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
"axs2[1].set_ylabel(r'$p$ [Pa]')\n",
"lo_00, = axs2[0].plot(pl_vec,pipe.p_old,marker='.')\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([-20*p0,20*p0])\n",
"axs2[1].set_ylim([-2*v0,2*v0])\n",
"axs2[0].set_ylim([-5*np.max(pressure_conversion(pipe.p_old,'Pa','mWs')[0]),5*np.max(pressure_conversion(pipe.p_old,'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_1[it],p_1[it],v_np1[it])\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(pipe.p)\n",
" lo_01.set_ydata(pipe.v)\n",
"\n",
" # store parameters of node 1 (at reservoir)\n",
" pipe.p_1[it] = pipe.p[0]\n",
" pipe.v_1[it] = pipe.v[0]\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",
@@ -184,18 +160,18 @@
" fig2.suptitle(str(it))\n",
" fig2.canvas.draw()\n",
" fig2.tight_layout()\n",
" plt.pause(0.001)\n"
" plt.pause(0.2)\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"execution_count": 55,
"metadata": {},
"outputs": [],
"source": [
"fig3,axs3 = plt.subplots(2,2)\n",
"axs3[0,0].plot(t_vec,pipe.p_1)\n",
"axs3[0,1].plot(t_vec,pipe.v_1)\n",
"axs3[0,0].plot(t_vec,pipe.p_0)\n",
"axs3[0,1].plot(t_vec,pipe.v_0)\n",
"axs3[1,0].plot(t_vec,pipe.p_np1)\n",
"axs3[1,1].plot(t_vec,pipe.v_np1)\n",
"axs3[0,0].set_title('Pressure Reservoir')\n",

0
Messing Around/messy_nb.ipynb Normal file
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