{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\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\n",
    "from Turbinen.Turbinen_class_file import Francis_Turbine"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "#define constants\n",
    "\n",
    "#Turbine\n",
    "Q_nenn = 0.85\n",
    "p_nenn,_ = pressure_conversion(10.6,'bar','Pa')\n",
    "\n",
    "# physics\n",
    "g               = 9.81                          # gravitational acceleration [m/s²]\n",
    "rho             = 1000.                         # density of water [kg/m³]\n",
    "\n",
    "# pipeline\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",
    "alpha           = np.arcsin(h_pipe/L)           # Höhenwinkel der Druckrohrleitung \n",
    "n               = 50                           # number of pipe segments in discretization\n",
    "# consider replacing Q0 with a vector be be more flexible in initial conditions\n",
    "Q0              = Q_nenn                            # initial flow in whole pipe [m³/s]\n",
    "v0              = Q0/A_pipe                     # initial flow velocity [m/s]\n",
    "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              = 2000                           # number of time steps after initial conditions\n",
    "\n",
    "# derivatives of the pipeline constants\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",
    "initial_level   = 8.                           # water level in upstream reservoir [m]\n",
    "p0              = rho*g*initial_level-v0**2*rho/2\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+1)*dt          # time vector\n",
    "h_vec           = np.arange(0,n+1)*h_pipe/n     # hydraulic head of pipeline at each node \n",
    "v_init          = np.full(nn,Q0/(D**2/4*np.pi)) # initial velocity distribution in pipeline\n",
    "p_init          = (rho*g*(initial_level+h_vec)-v_init**2*rho/2)-(f_D*pl_vec/D*rho/2*v_init**2) # ref Wikipedia: Darcy Weisbach\n",
    "\n",
    "\n",
    "# reservoir\n",
    "# replace influx by vector\n",
    "initial_influx              = 0.        # initial influx  of volume to the reservoir [m³/s]\n",
    "initial_outflux             = Q0        # initial outflux of volume from the reservoir to the pipeline [m³/s]\n",
    "initial_pipeline_pressure   = p0        # Initial condition for the static pipeline pressure at the reservoir (= hydrostatic pressure - dynamic pressure) \n",
    "initial_pressure_unit       = 'Pa'      # DO NOT CHANGE! for pressure conversion in print statements and plot labels \n",
    "conversion_pressure_unit    = 'bar'      # for pressure conversion in print statements and plot labels\n",
    "area_base                   = 74.       # total base are of the cuboid reservoir [m²]   \n",
    "area_outflux                = A_pipe    # outlfux area of the reservoir, given by pipeline area [m²]\n",
    "critical_level_low          = 0.        # for yet-to-be-implemented warnings[m]\n",
    "critical_level_high         = np.inf    # for yet-to-be-implemented warnings[m]\n",
    "\n",
    "# make sure e-RK4 method of reservoir has a small enough timestep to avoid runaway numerical error\n",
    "nt_eRK4                     = 1000      # number of simulation steps of reservoir in between timesteps of pipeline              \n",
    "simulation_timestep         = dt/nt_eRK4\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Ideas for checks after constant definitions: \n",
    "\n",
    "- Check that the initial pressure is not negative:\n",
    "    - may happen, if there is too little hydraulic head to create the initial flow conditions with the given friction\n",
    "<br>\n",
    "<br>\n",
    "- plausbility checks?\n",
    "    - area > area_outflux ?\n",
    "    - propable ranges for parameters?\n",
    "    - angle and height/length fit together?\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create objects\n",
    "\n",
    "V = Ausgleichsbecken_class(area_base,area_outflux,critical_level_low,critical_level_high,simulation_timestep)\n",
    "V.set_initial_level(initial_level) \n",
    "V.set_influx(initial_influx)\n",
    "V.set_outflux(initial_outflux)\n",
    "V.set_pressure(initial_pipeline_pressure,initial_pressure_unit,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_initial_pressure(p_init,initial_pressure_unit,conversion_pressure_unit)\n",
    "pipe.set_initial_flow_velocity(v_init)\n",
    "\n",
    "\n",
    "T1 = Francis_Turbine(Q_nenn,p_nenn)\n",
    "T1.set_LA(1.)\n",
    "T1.set_closing_time(30)\n",
    "\n",
    "# display the attributes of the created reservoir and pipeline object\n",
    "# V.get_info(full=True)\n",
    "# pipe.get_info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "# initialization for timeloop\n",
    "\n",
    "# prepare the vectors in which the pressure and velocity distribution in the pipeline from the previous timestep are stored\n",
    "v_old = v_init.copy()\n",
    "p_old = p_init.copy()\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.empty_like(t_vec)\n",
    "v_boundary_tur  = np.empty_like(t_vec)\n",
    "p_boundary_res  = np.empty_like(t_vec)\n",
    "p_boundary_tur  = np.empty_like(t_vec)\n",
    "\n",
    "# prepare the vectors that store the temporal evolution of the level in the reservoir\n",
    "level_vec       = np.full(nt+1,initial_level)  # level at the end of each pipeline timestep\n",
    "level_vec_2     = np.empty([nt_eRK4])   # level throughout each reservoir timestep-used for plotting and overwritten afterwards\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",
    "\n",
    "LA_soll_vec = np.zeros_like(t_vec)\n",
    "LA_soll_vec[0] = 1\n",
    "LA_soll_vec[1000:] = 1\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib qt5\n",
    "# time loop\n",
    "\n",
    "# create a figure and subplots to display the velocity and pressure distribution across the pipeline in each pipeline step\n",
    "fig1,axs1 = plt.subplots(2,1)\n",
    "fig1.suptitle(str(0) +' s / '+str(round(t_vec[-1],2)) + ' s' )\n",
    "axs1[0].set_title('Pressure distribution in pipeline')\n",
    "axs1[1].set_title('Velocity distribution in pipeline')\n",
    "axs1[0].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
    "axs1[0].set_ylabel(r'$p$ ['+conversion_pressure_unit+']')\n",
    "axs1[1].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
    "axs1[1].set_ylabel(r'$v$ [$\\mathrm{m} / \\mathrm{s}$]')\n",
    "lo_00, = axs1[0].plot(pl_vec,pressure_conversion(pipe.p_old,initial_pressure_unit, conversion_pressure_unit)[0],marker='.')\n",
    "lo_01, = axs1[1].plot(pl_vec,pipe.v_old,marker='.')\n",
    "axs1[0].autoscale()\n",
    "axs1[1].autoscale()\n",
    "# displaying the reservoir level within each pipeline timestep\n",
    "# axs1[2].set_title('Level reservoir')\n",
    "# axs1[2].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
    "# axs1[2].set_ylabel(r'$h$ [m]')\n",
    "# lo_02, = axs1[2].plot(level_vec_2)\n",
    "# axs1[2].autoscale()\n",
    "fig1.tight_layout()\n",
    "fig1.show()\n",
    "plt.pause(1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "# loop through time steps of the pipeline\n",
    "for it_pipe in range(1,pipe.nt+1):\n",
    "\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.pressure      = p_old[0]\n",
    "    V.outflux_vel   = v_old[0]\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.e_RK_4()                                                              # call e-RK4 to update outflux\n",
    "        V.level = V.update_level(V.timestep)                                    # \n",
    "        V.set_volume()                                                          # update volume in reservoir\n",
    "        level_vec_2[it_res] = V.level                                           # save for plotting\n",
    "        if (V.level < critical_level_low) or (V.level > critical_level_high):   # make sure to never exceed critical levels\n",
    "            i_max = it_pipe                                                     # for plotting only calculated values\n",
    "            break                                                               \n",
    "    level_vec[it_pipe] = V.level                                                  \n",
    "\n",
    "    # set boundary conditions for the next timestep of the characteristic method\n",
    "    p_boundary_res[it_pipe] = rho*g*V.level-V.outflux_vel**2*rho/2\n",
    "    v_boundary_res[it_pipe] = v_old[1]+1/(rho*c)*(p_boundary_res[it_pipe]-p_old[1])-f_D*dt/(2*D)*abs(v_old[1])*v_old[1] \\\n",
    "        +dt*g*np.sin(alpha)\n",
    "\n",
    "    T1.change_LA(LA_soll_vec[it_pipe],dt)\n",
    "    v_boundary_tur[it_pipe] = 1/A_pipe*T1.get_Q(p_old[-1])\n",
    "\n",
    "    # the the boundary conditions in the pipe.object and thereby calculate boundary pressure at turbine\n",
    "    pipe.set_boundary_conditions_next_timestep(v_boundary_res[it_pipe],p_boundary_res[it_pipe],v_boundary_tur[it_pipe])\n",
    "    p_boundary_tur[it_pipe] = pipe.p_boundary_tur\n",
    "\n",
    "    # perform the next timestep via the characteristic method\n",
    "    pipe.timestep_characteristic_method()\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(pipe.p_old,initial_pressure_unit, conversion_pressure_unit)[0],marker='.',c='blue')\n",
    "    lo_01, = axs1[1].plot(pl_vec,pipe.v_old,marker='.',c='blue')\n",
    "    # lo_02, = axs1[2].plot(level_vec_2,c='blue')\n",
    "    fig1.suptitle(str(round(t_vec[it_pipe],2))+ ' s / '+str(round(t_vec[-1],2)) + ' s' )\n",
    "    fig1.canvas.draw()\n",
    "    fig1.tight_layout()\n",
    "    fig1.show()\n",
    "    plt.pause(0.00001)    \n",
    "\n",
    "    # prepare for next loop\n",
    "    p_old = pipe.p_old\n",
    "    v_old = pipe.v_old  \n",
    "\n",
    "        \n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "# plot time evolution of boundary pressure and velocity as well as the reservoir level\n",
    "\n",
    "fig2,axs2 = plt.subplots(3,2)\n",
    "axs2[0,0].plot(t_vec,pressure_conversion(p_boundary_res,initial_pressure_unit, conversion_pressure_unit)[0])\n",
    "axs2[0,1].plot(t_vec,v_boundary_res)\n",
    "axs2[1,0].plot(t_vec,pressure_conversion(p_boundary_tur,initial_pressure_unit, conversion_pressure_unit)[0])\n",
    "axs2[1,1].plot(t_vec,v_boundary_tur)\n",
    "axs2[2,0].plot(t_vec,level_vec)\n",
    "axs2[0,0].set_title('Pressure reservoir')\n",
    "axs2[0,1].set_title('Velocity reservoir')\n",
    "axs2[1,0].set_title('Pressure turbine')\n",
    "axs2[1,1].set_title('Velocity turbine')\n",
    "axs2[2,0].set_title('Level reservoir')\n",
    "axs2[0,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
    "axs2[0,0].set_ylabel(r'$p$ ['+conversion_pressure_unit+']')\n",
    "axs2[0,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
    "axs2[0,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n",
    "axs2[1,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
    "axs2[1,0].set_ylabel(r'$p$ ['+conversion_pressure_unit+']')\n",
    "axs2[1,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
    "axs2[1,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n",
    "axs2[2,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
    "axs2[2,0].set_ylabel(r'$h$ [m]')\n",
    "axs2[2,1].axis('off')\n",
    "fig2.tight_layout()\n",
    "plt.show()"
   ]
  }
 ],
 "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
}
