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first try at fixing convergence issues at turbine

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This commit is contained in:
Brantegger Georg
2022-08-02 07:47:10 +02:00
parent ed710a7371
commit 84631ee4cc
5 changed files with 501 additions and 24 deletions
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20
Ausgleichsbecken/Ausgleichsbecken_test_steady_state.ipynb
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@@ -71,14 +71,14 @@
"\n",
"# for while loop\n",
"total_min_level = 0.01 # m\n",
"total_max_time = 100 # s\n",
"total_max_time = 1000 # s\n",
"\n",
"nt = int(total_max_time//simulation_timestep)"
]
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@@ -158,7 +158,7 @@
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@@ -170,7 +170,7 @@
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22
Druckrohrleitung/Druckrohrleitung_test_steady_state.ipynb
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@@ -36,7 +36,7 @@
"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 = 1000 # number of time steps after initial conditions\n",
"nt = 5000 # 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",
@@ -69,7 +69,7 @@
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169
Turbinen/convergence_turbine.py Normal file
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from time import time
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 = 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!')
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

286
Turbinen/turbine_convergence_test.ipynb Normal file
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"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"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"%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",
"\n",
"#define constants pipe\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 = 10000 # 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",
"\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",
"\n",
"\n",
"# define constants reservoir\n",
"conversion_pressure_unit = 'mWS'\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 = 1 # number of simulation steps of reservoir in between timesteps of pipeline \n",
"simulation_timestep = dt/nt_eRK4"
]
},
{
"cell_type": "code",
"execution_count": 3,
"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",
"\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",
"\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)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"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 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": [
"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",
"\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",
"# axs1[1].set_ylim([0.9*np.min(v_old),1.1*np.max(v_boundary_res)])\n",
"\n",
"fig1.tight_layout()\n",
"plt.pause(1)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"\n",
"for it_pipe in range(1,nt):\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",
" # 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",
"\n",
" \n",
" # set boundary conditions for the next timestep of the characteristic method\n",
" p_boundary_res[it_pipe] = V.get_current_pressure()\n",
" T1.set_pressure(p_old[-1])\n",
" T1.converge(area_pipe,p_old[-2],v_old[-2],alpha,f_D,dt)\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] = (pipe.v[0]+V.get_current_outflux()/area_pipe)/2\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",
" # perform the next timestep via the characteristic 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",
"\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",
" # 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",
" \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)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"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].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",
"\n",
"axs2[0,1].set_title('Velocity Reservoir')\n",
"axs2[0,1].plot(t_vec,v_boundary_res)\n",
"axs2[0,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
"axs2[0,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n",
"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].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",
"\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",
"\n",
"fig2.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x1783803c0d0>]"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plt.plot(level_vec)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3.8.13 ('Georg_DT_Slot3')",
"language": "python",
"name": "python3"
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26
Untertweng_mit_Pegelregler.ipynb
View File

@@ -42,7 +42,7 @@
"\n",
"\n",
"# pipeline\n",
"L = 535.+478. # length of pipeline [m]\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",
@@ -51,7 +51,7 @@
"f_D = 0.014 # Darcy friction factor\n",
"c = 500. # 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 = 4500 # number of time steps after initial conditions\n",
"nt = 9000 # number of time steps after initial conditions\n",
"\n",
"# derivatives of the pipeline constants\n",
"dx = L/n # length of each pipe segment\n",
@@ -184,6 +184,7 @@
"metadata": {},
"outputs": [],
"source": [
"error_vec = np.zeros_like(t_vec)\n",
"# loop through time steps of the pipeline\n",
"for it_pipe in range(1,pipe.nt+1):\n",
"\n",
@@ -218,6 +219,7 @@
" 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",
" error_vec[it_pipe] = abs(v_boundary_res[it_pipe]-V.get_current_outflux()/A_pipe)\n",
"\n",
" # perform the next timestep via the characteristic method\n",
" pipe.timestep_characteristic_method()\n",
@@ -288,6 +290,26 @@
"fig2.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x1ac81d70af0>]"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plt.semilogy(t_vec,error_vec)"
]
}
],
"metadata": {