219 lines
7.6 KiB
Plaintext
219 lines
7.6 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"from Druckrohrleitung_class_file import Druckrohrleitung_class\n",
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"import matplotlib.pyplot as plt\n",
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"from pressure_conversion import pressure_conversion"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"%matplotlib qt5\n",
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"#define constants\n",
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"\n",
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"g = 9.81 # gravitational acceleration [m/s²]\n",
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"\n",
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"L = 1000 # length of pipeline [m]\n",
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"rho = 1000 # density of water [kg/m³]\n",
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"D = 1 # pipe diameter [m]\n",
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"Q0 = 2 # initial flow in whole pipe [m³/s]\n",
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"h = 20 # water level in upstream reservoir [m]\n",
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"n = 10 # number of pipe segments in discretization\n",
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"nt = 500 # number of time steps after initial conditions\n",
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"f_D = 0.01 # Darcy friction factor\n",
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"c = 400 # propagation velocity of the pressure wave [m/s]\n",
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"\n",
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"\n",
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"# preparing the discretization and initial conditions\n",
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"\n",
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"dx = L/n # length of each pipe segment\n",
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"dt = dx/c # timestep according to method of characterisitics\n",
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"nn = n+1 # number of nodes\n",
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"pl_vec = np.arange(0,nn*dx,dx) # pl = pipe-length. position of the nodes on the pipeline\n",
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"t_vec = np.arange(0,nt*dt,dt) # time vector\n",
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"\n",
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"v0 = Q0/(D**2/4*np.pi)\n",
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"p0 = (rho*g*h-v0**2*rho/2)\n",
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"\n",
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"# storage vectors for old parameters\n",
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"v_old = np.full(nn,v0)\n",
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"p_old = p0-(f_D*pl_vec/D*rho/2*v0**2) # ref Wikipedia: Darcy Weisbach\n",
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"\n",
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"# storage vectors for new parameters\n",
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"v_new = np.zeros_like(v_old)\n",
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"p_new = np.zeros_like(p_old)\n",
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"\n",
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"# storage vector for time evolution of parameters at node 1 (at reservoir)\n",
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"p_1 = np.full_like(t_vec,p0)\n",
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"v_1 = np.full_like(t_vec,v0)\n",
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"\n",
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"# storage vector for time evolution of parameters at node N+1 (at valve)\n",
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"p_np1 = np.full_like(t_vec,p0)\n",
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"v_np1 = np.full_like(t_vec,v0)\n",
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"\n",
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"for it in range(1,nt):\n",
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"\n",
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" # set boundary conditions\n",
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" v_new[-1] = 0 # in front of the instantaneously closing valve, the velocity is 0\n",
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" p_new[0] = p0 # hydrostatic pressure from the reservoir\n",
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"\n",
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" # calculate the new parameters at first and last node\n",
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" 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",
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" 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",
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"\n",
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" # calculate parameters at second to second-to-last nodes \n",
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" #equation 2-30 plus 2-31 (and refactor for v_i^j+1) in block 2\n",
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"\n",
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" for i in range(1,nn-1):\n",
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" 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",
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" -f_D*dt/(4*D)*(abs(v_old[i-1])*v_old[i-1]+abs(v_old[i+1])*v_old[i+1])\n",
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"\n",
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" 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",
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" -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",
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" \n",
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"\n",
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" # prepare for next loop\n",
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" # use .copy() to avoid that memory address is overwritten and hell breaks loose :D\n",
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" #https://www.geeksforgeeks.org/array-copying-in-python/\n",
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" p_old = p_new.copy()\n",
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" v_old = v_new.copy()\n",
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"\n",
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" # store parameters of node 1 (at reservoir)\n",
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" p_1[it] = p_new[0]\n",
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" v_1[it] = v_new[0]\n",
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" # store parameters of node N+1 (at reservoir)\n",
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" p_np1[it] = p_new[-1]\n",
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" v_np1[it] = v_new[-1]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"fig1,axs1 = plt.subplots(2,2)\n",
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"axs1[0,0].plot(t_vec,p_1)\n",
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"axs1[0,1].plot(t_vec,v_1)\n",
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"axs1[1,0].plot(t_vec,p_np1)\n",
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"axs1[1,1].plot(t_vec,v_np1)\n",
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"axs1[0,0].set_title('Pressure Reservoir')\n",
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"axs1[0,1].set_title('Velocity Reservoir')\n",
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"axs1[1,0].set_title('Pressure Turbine')\n",
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"axs1[1,1].set_title('Velocity Turbine')\n",
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"fig1.tight_layout()\n",
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"plt.show()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"pipe = Druckrohrleitung_class(L,D,n,0,f_D)\n",
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"\n",
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"pipe.set_pressure_propagation_velocity(c)\n",
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"pipe.set_number_of_timesteps(nt)\n",
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"\n",
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"pipe.set_initial_pressure(p0)\n",
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"pipe.set_initial_flow_velocity(v0)\n",
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"pipe.set_boundary_conditions_next_timestep(v_1[0],p_1[0],v_np1[0])\n",
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"\n",
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"# storage vector for time evolution of parameters at node 1 (at reservoir)\n",
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"pipe.p_1 = np.full_like(t_vec,p0)\n",
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"pipe.v_1 = np.full_like(t_vec,v0)\n",
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"\n",
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"# storage vector for time evolution of parameters at node N+1 (at valve)\n",
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"pipe.p_np1 = np.full_like(t_vec,p0)\n",
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"pipe.v_np1 = np.full_like(t_vec,v0)\n",
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"\n",
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"fig2,axs2 = plt.subplots(2,1)\n",
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"axs2[0].set_title('Pressure distribution in pipeline')\n",
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"axs2[1].set_title('Velocity distribution in pipeline')\n",
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"\n",
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"lo_00, = axs2[0].plot(pl_vec,pipe.p_old,marker='.')\n",
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"lo_01, = axs2[1].plot(pl_vec,pipe.v_old,marker='.')\n",
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"axs2[0].set_ylim([-20*p0,20*p0])\n",
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"axs2[1].set_ylim([-2*v0,2*v0])\n",
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"fig2.tight_layout()\n",
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"\n",
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"\n",
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"for it in range(1,pipe.nt):\n",
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" pipe.set_boundary_conditions_next_timestep(v_1[it],p_1[it],v_np1[it])\n",
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" pipe.timestep_characteristic_method()\n",
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" lo_00.set_ydata(pipe.p_new)\n",
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" lo_01.set_ydata(pipe.v_new)\n",
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"\n",
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" # store parameters of node 1 (at reservoir)\n",
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" pipe.p_1[it] = pipe.p_new[0]\n",
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" pipe.v_1[it] = pipe.v_new[0]\n",
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" # store parameters of node N+1 (at reservoir)\n",
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" pipe.p_np1[it] = pipe.p_new[-1]\n",
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" pipe.v_np1[it] = pipe.v_new[-1]\n",
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" \n",
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" fig2.suptitle(str(it))\n",
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" fig2.canvas.draw()\n",
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" fig2.tight_layout()\n",
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" plt.pause(0.001)\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"fig3,axs3 = plt.subplots(2,2)\n",
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"axs3[0,0].plot(t_vec,pipe.p_1)\n",
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"axs3[0,1].plot(t_vec,pipe.v_1)\n",
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"axs3[1,0].plot(t_vec,pipe.p_np1)\n",
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"axs3[1,1].plot(t_vec,pipe.v_np1)\n",
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"axs3[0,0].set_title('Pressure Reservoir')\n",
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"axs3[0,1].set_title('Velocity Reservoir')\n",
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"axs3[1,0].set_title('Pressure Turbine')\n",
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"axs3[1,1].set_title('Velocity Turbine')\n",
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"fig3.tight_layout()\n",
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"plt.show()"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3.8.13 ('Georg_DT_Slot3')",
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"language": "python",
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"codemirror_mode": {
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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