Georg_Brantegger/Python-DT_Slot_3
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4510aeaaf8d4e9cea083f49957f4a487acdd93e2
Python-DT_Slot_3/Druckrohrleitung/Druckstoß.ipynb
Brantegger Georg 4510aeaaf8 ETH vorläufiges Druckstoßskript eingearbeitet
2022-06-21 15:35:37 +02:00

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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"#imports\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"#define constants\n",
"\n",
"g = 9.81 # gravitational acceleration [m/s²]\n",
"\n",
"L = 100 # length of pipeline [m]\n",
"rho = 1000 # density of water [kg/m³]\n",
"D = 1 # pipe diameter \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 = 150 # number of time steps\n",
"f_coeff = 0.01 # lambda = 0.01 Friction loss coefficient [m]\n",
"c = 400 # propagation velocity of the pressure wave\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# 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_coeff*pl_vec/D*rho/2*v0**2) # ref Wikipedia: Rohrreibungszahls\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 nn (at reservoir)\n",
"p_nn = np.zeros_like(t_vec)\n",
"v_nn = np.zeros_like(t_vec)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# time loop\n",
"\n",
"for it in range(nt):\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_coeff*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_coeff*dt/(2*D) *abs(v_old[-2])*v_old[-2]\n",
"\n",
" # calculate parameters at second to second-to-last nodes\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_coeff*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_coeff*dt/(4*D)*(abs(v_old[i-1])*v_old[i-1]-abs(v_old[i+1])*v_old[i+1])\n",
"\n",
" # store parameters of node nn (at reservoir)\n",
" p_nn[it] = p_old[0]\n",
" v_nn[it] = v_old[0]\n",
"\n",
" # prepare for next loop\n",
" p_old = p_new\n",
" v_old = v_new\n",
"\n",
"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x1752545d940>]"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "78fffc8456214ec192f3fd8de7cba537",
"version_major": 2,
"version_minor": 0
},
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",
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" Figure\n",
" </div>\n",
" <img 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' width=640.0/>\n",
" </div>\n",
" "
],
"text/plain": [
"Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%matplotlib widget\n",
"\n",
"plt.plot(t_vec,v_nn,'.-')"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x17525e36be0>]"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "34175cae75db4ff8a456381820a2deca",
"version_major": 2,
"version_minor": 0
},
"image/png": 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",
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" <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
" Figure\n",
" </div>\n",
" <img 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' width=640.0/>\n",
" </div>\n",
" "
],
"text/plain": [
"Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%matplotlib widget\n",
"\n",
"plt.plot(t_vec,p_nn,'.-')"
]
}
],
"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
}
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