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added Druckrohrleitungs class, based on ETH Code

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Brantegger Georg
2022-06-29 13:51:53 +02:00
parent 57cb951f5b
commit 8cfd14838c
7 changed files with 401 additions and 16 deletions
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162
Druckrohrleitung/Druckrohrleitung_class_file.py Normal file
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@@ -0,0 +1,162 @@
from pressure_conversion import pressure_conversion
import numpy as np
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'$\mathrm{m}^3$'
# 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)
# workaround for try-except construct in set_number_of_timesteps
self.c = 0
# 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 == 0:
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_new = 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_new = 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_new[0] = self.v_boundary_res.copy()
self.v_new[-1] = self.v_boundary_tur.copy()
self.p_new[0] = self.p_boundary_res.copy()
self.p_new[-1] = self.p_boundary_tur.copy()
# getter
def get_pipeline_geometry(self):
print('The total length of the pipeline is', '\n', \
self.length, self.length_unit, '\n', \
'The diameter of the pipeline is', '\n', \
self.dia, self.length_unit, '\n', \
'The pipeline is divided into', self.n_seg , 'segments of length', '\n', \
round(self.dx,1), self.length_unit, '\n', \
'The pipeline has an inclination angle of', '\n', \
self.angle, self.angle_unit)
def get_other_pipeline_info(self):
print('The Darcy-friction factor of the pipeline is', '\n', \
self.f_D, '\n', \
'The pipeline is filled with a liquid with density', '\n', \
self.density, self.density_unit, '\n', \
'The gravitational acceleration is set to', '\n', \
self.g, self.acceleration_unit)
def get_pressure_propagation_velocity(self):
print('The pressure propagation velocity in the pipeline is', '\n', \
self.c, self.velocity_unit)
def get_number_of_timesteps(self):
print(self.nt, 'timesteps are performed in the simulation')
def get_initial_pressure(self,target_unit='bar'):
print('The inital pressure distribution in is', '\n', \
pressure_conversion(self.p0,self.pressure_unit,target_unit))
def get_initial_flow_velocity(self):
print('The inital velocity distribution is', '\n', \
self.v0, self.velocity_unit)
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,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,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_new[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_new[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_new.copy()
self.v_old = self.v_new.copy()

0
Druckrohrleitung/Druckrohrleitung.py → Druckrohrleitung/Druckrohrleitung_functions.py
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20
Druckrohrleitung/Druckstoß_ETH.ipynb
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@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
"execution_count": 22,
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
@@ -14,7 +14,7 @@
},
{
"cell_type": "code",
"execution_count": 23,
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
@@ -28,14 +28,14 @@
"Q0 = 2 # initial flow in whole pipe [m³/s]\n",
"h = 20 # water level in upstream reservoir [m]\n",
"n = 10 # number of pipe segments in discretization\n",
"nt = 1500 # number of time steps after initial conditions\n",
"nt = 500 # 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]"
]
},
{
"cell_type": "code",
"execution_count": 24,
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
@@ -70,7 +70,7 @@
},
{
"cell_type": "code",
"execution_count": 25,
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
@@ -90,7 +90,7 @@
},
{
"cell_type": "code",
"execution_count": 26,
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
@@ -139,7 +139,7 @@
},
{
"cell_type": "code",
"execution_count": 27,
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
@@ -159,7 +159,7 @@
],
"metadata": {
"kernelspec": {
"display_name": "Python 3.9.7 ('base')",
"display_name": "Python 3.8.13 ('Georg_DT_Slot3')",
"language": "python",
"name": "python3"
},
@@ -173,12 +173,12 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.7"
"version": "3.8.13"
},
"orig_nbformat": 4,
"vscode": {
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}
}
},

218
Druckrohrleitung/Main_Programm.ipynb Normal file
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@@ -0,0 +1,218 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from Druckrohrleitung_class_file import Druckrohrleitung_class\n",
"import matplotlib.pyplot as plt\n",
"from pressure_conversion import pressure_conversion"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib qt5\n",
"#define constants\n",
"\n",
"g = 9.81 # gravitational acceleration [m/s²]\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",
"n = 10 # number of pipe segments in discretization\n",
"nt = 500 # 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",
"\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",
"\n",
"v0 = Q0/(D**2/4*np.pi)\n",
"p0 = (rho*g*h-v0**2*rho/2)\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",
"\n",
"# storage vectors for new parameters\n",
"v_new = np.zeros_like(v_old)\n",
"p_new = np.zeros_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",
"\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",
"\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",
"\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",
" 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",
" -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_1[it] = p_new[0]\n",
" v_1[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": null,
"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_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": null,
"metadata": {},
"outputs": [],
"source": [
"pipe = Druckrohrleitung_class(L,D,n,0,f_D)\n",
"\n",
"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",
"\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",
"\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",
"\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",
"\n",
"lo_00, = axs2[0].plot(pl_vec,pipe.p_old,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",
"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.timestep_characteristic_method()\n",
" lo_00.set_ydata(pipe.p_new)\n",
" lo_01.set_ydata(pipe.v_new)\n",
"\n",
" # store parameters of node 1 (at reservoir)\n",
" pipe.p_1[it] = pipe.p_new[0]\n",
" pipe.v_1[it] = pipe.v_new[0]\n",
" # store parameters of node N+1 (at reservoir)\n",
" pipe.p_np1[it] = pipe.p_new[-1]\n",
" pipe.v_np1[it] = pipe.v_new[-1]\n",
" \n",
" fig2.suptitle(str(it))\n",
" fig2.canvas.draw()\n",
" fig2.tight_layout()\n",
" plt.pause(0.001)\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"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[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",
"axs3[0,1].set_title('Velocity Reservoir')\n",
"axs3[1,0].set_title('Pressure Turbine')\n",
"axs3[1,1].set_title('Velocity Turbine')\n",
"fig3.tight_layout()\n",
"plt.show()"
]
}
],
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