{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from Druckrohrleitung_class_file import Druckrohrleitung_class\n",
    "import matplotlib.pyplot as plt\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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib qt5\n",
    "#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",
    "D       = 1                 # pipe diameter [m]\n",
    "Q0      = 2                 # initial flow in whole pipe [m³/s]\n",
    "h_res   = 20                # water level in upstream reservoir [m]\n",
    "n       = 10                # number of pipe segments in discretization\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  = 200              # 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",
    "\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",
    "h_vec   = np.arange(0,h_pipe+h_pipe/n,h_pipe/n) # hydraulic head of pipeline at each node\n",
    "\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 = v_init.copy()\n",
    "p_old = p_init.copy()   \n",
    "\n",
    "# storage vectors for new parameters\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 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,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]    = 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)*(p_init[0]-p_old[1])+dt*g*np.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",
    "    #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",
    "            +dt*g*np.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",
    "    \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_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]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "pipe = Druckrohrleitung_class(L,D,n,alpha,f_D)\n",
    "\n",
    "pipe.set_pressure_propagation_velocity(c)\n",
    "pipe.set_number_of_timesteps(nt)\n",
    "\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 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,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",
    "axs2[1].set_title('Velocity distribution in pipeline')\n",
    "axs2[0].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
    "axs2[0].set_ylabel(r'$p$ [mWS]')\n",
    "axs2[1].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
    "axs2[1].set_ylabel(r'$p$ [mWS]')\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([-2*np.max(pressure_conversion(p_init,'Pa','mWS')[0]),2*np.max(pressure_conversion(p_init,'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_0[it],p_0[it],v_np1[it])\n",
    "    pipe.timestep_characteristic_method()\n",
    "    lo_00.set_ydata(pressure_conversion(pipe.p,'Pa','mWS')[0])\n",
    "    lo_01.set_ydata(pipe.v)\n",
    "\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",
    "    \n",
    "    fig2.suptitle(str(it))\n",
    "    fig2.canvas.draw()\n",
    "    fig2.tight_layout()\n",
    "    plt.pause(0.2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig3,axs3 = plt.subplots(2,2)\n",
    "axs3[0,0].plot(t_vec,pressure_conversion(pipe.p_0,'Pa','mWS')[0])\n",
    "axs3[0,1].plot(t_vec,pipe.v_0)\n",
    "axs3[1,0].plot(t_vec,pressure_conversion(pipe.p_np1,'Pa','mWS')[0])\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",
    "axs3[0,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
    "axs3[0,0].set_ylabel(r'$p$ [mWS]')\n",
    "axs3[0,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
    "axs3[0,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n",
    "axs3[1,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
    "axs3[1,0].set_ylabel(r'$p$ [mWS]')\n",
    "axs3[1,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
    "axs3[1,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n",
    "fig3.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.29590621205048523\n"
     ]
    }
   ],
   "source": [
    "print(np.mean(v_0))"
   ]
  }
 ],
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