From b9634e378bd4a2c6ff791048389b108a06a3e12d Mon Sep 17 00:00:00 2001 From: Brantegger Georg Date: Thu, 8 Sep 2022 09:15:27 +0200 Subject: [PATCH] added file to simulate KW Hammer and added visualization for pressure surge presentation --- .../Druckrohrleitung_test_steady_state.ipynb | 8 +- .../Druckstoß Visualisierung.ipynb | 296 + KW Hammer.ipynb | 477 + Untertweng.ipynb | 12856 +--------------- 4 files changed, 788 insertions(+), 12849 deletions(-) create mode 100644 Druckrohrleitung/Druckstoß Visualisierung.ipynb create mode 100644 KW Hammer.ipynb diff --git a/Druckrohrleitung/Druckrohrleitung_test_steady_state.ipynb b/Druckrohrleitung/Druckrohrleitung_test_steady_state.ipynb index 86d90d3..dd4c313 100644 --- a/Druckrohrleitung/Druckrohrleitung_test_steady_state.ipynb +++ b/Druckrohrleitung/Druckrohrleitung_test_steady_state.ipynb @@ -124,7 +124,11 @@ "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" + "p_boundary_tur[0] = p_old[-1]\n", + "\n", + "v_boundary_tur[:np.argmin(np.abs(t_vec-100))] = v_old[-1] \n", + "v_boundary_tur[np.argmin(np.abs(t_vec-100)):] = 0\n", + "\n" ] }, { @@ -171,7 +175,7 @@ " \n", " # set boundary conditions for the next timestep of the characteristic method\n", " p_boundary_res[it_pipe] = reservoir.get_current_pressure()\n", - " v_boundary_tur[it_pipe] = flux_init/Pip_area\n", + " # v_boundary_tur[it_pipe] = flux_init/Pip_area\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", diff --git a/Druckrohrleitung/Druckstoß Visualisierung.ipynb b/Druckrohrleitung/Druckstoß Visualisierung.ipynb new file mode 100644 index 0000000..379c76e --- /dev/null +++ b/Druckrohrleitung/Druckstoß Visualisierung.ipynb @@ -0,0 +1,296 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 35, + "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\n", + "from Ausgleichsbecken.Ausgleichsbecken_class_file import Ausgleichsbecken_class" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [], + "source": [ + "# define constants\n", + "\n", + " # for physics\n", + "g = 9.81 # [m/s²] gravitational acceleration \n", + "rho = 1000. # [kg/m³] density of water \n", + "pUnit_calc = 'Pa' # [text] DO NOT CHANGE! for pressure conversion in print statements and plot labels \n", + "pUnit_conv = 'mWS' # [text] for pressure conversion in print statements and plot labels\n", + "\n", + " # for Turbine\n", + "Tur_Q_nenn = 1 # [m³/s] nominal flux of turbine \n", + "Tur_p_nenn = pressure_conversion(10.,'bar',pUnit_calc) # [Pa] nominal pressure of turbine \n", + "Tur_closingTime = 10. # [s] closing time of turbine\n", + "\n", + " # for PI controller\n", + "Con_targetLevel = 10. # [m]\n", + "\n", + " # for pipeline\n", + "Pip_length = 100 # [m] length of pipeline\n", + "Pip_dia = 1. # [m] diameter of pipeline\n", + "Pip_area = Pip_dia**2/4*np.pi # [m²] crossectional area of pipeline\n", + "Pip_head = 100. # [m] hydraulic head of pipeline without reservoir\n", + "Pip_angle = np.arcsin(Pip_head/Pip_length) # [rad] elevation angle of pipeline \n", + "Pip_n_seg = 1000 # [-] number of pipe segments in discretization\n", + "Pip_f_D = 0.6 # [-] Darcy friction factor\n", + "Pip_pw_vel = 500. # [m/s] propagation velocity of the pressure wave (pw) in the given pipeline\n", + " # derivatives of the pipeline constants\n", + "Pip_dx = Pip_length/Pip_n_seg # [m] length of each pipe segment\n", + "Pip_dt = Pip_dx/Pip_pw_vel # [s] timestep according to method of characteristics\n", + "Pip_nn = Pip_n_seg+1 # [1] number of nodes\n", + "Pip_x_vec = np.arange(0,Pip_nn,1)*Pip_dx # [m] vector holding the distance of each node from the upstream reservoir along the pipeline\n", + "Pip_h_vec = np.arange(0,Pip_nn,1)*Pip_head/Pip_n_seg # [m] vector holding the vertival distance of each node from the upstream reservoir\n", + "\n", + " # for reservoir\n", + "Res_area_base = 100. # [m²] total base are of the cuboid reservoir \n", + "Res_area_out = Pip_area # [m²] outflux area of the reservoir, given by pipeline area\n", + "Res_level_crit_lo = 0. # [m] for yet-to-be-implemented warnings\n", + "Res_level_crit_hi = np.inf # [m] for yet-to-be-implemented warnings\n", + "Res_dt_approx = 1e-3 # [s] approx. timestep of reservoir time evolution to ensure numerical stability (see Res_nt why approx.)\n", + "Res_nt = max(1,int(Pip_dt//Res_dt_approx)) # [1] number of timesteps of the reservoir time evolution within one timestep of the pipeline\n", + "Res_dt = Pip_dt/Res_nt # [s] harmonised timestep of reservoir time evolution\n", + "\n", + " # for general simulation\n", + "flux_init = Tur_Q_nenn/1.1 # [m³/s] initial flux through whole system for steady state initialization \n", + "level_init = Con_targetLevel # [m] initial water level in upstream reservoir for steady state initialization\n", + "simTime_target = 10. # [s] target for total simulation time (will vary slightly to fit with Pip_dt)\n", + "nt = int(simTime_target//Pip_dt) # [1] Number of timesteps of the whole system\n", + "t_vec = np.arange(0,nt+1,1)*Pip_dt # [s] time vector. At each step of t_vec the system parameters are stored\n" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [], + "source": [ + "# create objects\n", + "\n", + "# Upstream reservoir\n", + "reservoir = Ausgleichsbecken_class(Res_area_base,Res_area_out,Res_dt,pUnit_conv,Res_level_crit_lo,Res_level_crit_hi,rho)\n", + "reservoir.set_steady_state(flux_init,level_init)\n", + "\n", + "# pipeline\n", + "pipe = Druckrohrleitung_class(Pip_length,Pip_dia,Pip_head,Pip_n_seg,Pip_f_D,Pip_pw_vel,Pip_dt,pUnit_conv,rho)\n", + "pipe.set_steady_state(flux_init,reservoir.get_current_pressure())\n" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [], + "source": [ + "# initialization for timeloop\n", + "\n", + "level_vec = np.zeros_like(t_vec)\n", + "level_vec[0] = reservoir.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", + "\n", + "v_boundary_tur[:np.argmin(np.abs(t_vec-1))] = v_old[-1] \n", + "t1 = 0.1\n", + "t2 = 2.5\n", + "ind_t1 = np.argmin(np.abs(t_vec-t1))\n", + "ind_t2 = np.argmin(np.abs(t_vec-t2))\n", + "ind_t_vec = np.linspace(t_vec[ind_t1]-(t2-t1)/2,t_vec[ind_t2]-(t2-t1)/2,ind_t2-ind_t1)\n", + "v_trans = v_old[-1]/(np.exp(ind_t_vec/(5e-2))+1)\n", + "v_boundary_tur[ind_t1:ind_t2] = v_trans\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%matplotlib qt5\n", + "fig = plt.figure()\n", + "plt.plot(v_trans)\n", + "fig = plt.figure()\n", + "plt.plot(t_vec,v_boundary_tur)" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [], + "source": [ + "%matplotlib qt5\n", + "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", + "axs1[0].autoscale()\n", + "lo_00, = axs1[0].plot(Pip_x_vec,pressure_conversion(p_old,'Pa',pUnit_conv),marker='.')\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(Pip_x_vec,v_old,marker='.')\n", + "# axs1[1].autoscale()\n", + "axs1[1].set_ylim([-1.5,1.5])\n", + "\n", + "fig1.tight_layout()\n", + "plt.pause(1)" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": {}, + "outputs": [], + "source": [ + "for it_pipe in range(1,nt+1):\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", + " reservoir.set_pressure(p_old[0],display_warning=False)\n", + " reservoir.set_outflux(v_old[0]*Pip_area,display_warning=False)\n", + " # calculate the time evolution of the reservoir level within each pipeline timestep to avoid runaway numerical error\n", + " for it_res in range(Res_nt):\n", + " reservoir.timestep_reservoir_evolution() \n", + " level_vec[it_pipe] = reservoir.get_current_level() \n", + "\n", + " \n", + " # set boundary conditions for the next timestep of the characteristic method\n", + " p_boundary_res[it_pipe] = reservoir.get_current_pressure()\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", + " 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_vectorized()\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", + " if it_pipe%100 == 0:\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(Pip_x_vec,pressure_conversion(p_old,'Pa', pUnit_conv),marker='.',c='blue')\n", + " lo_01, = axs1[1].plot(Pip_x_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": 42, + "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,pUnit_calc,pUnit_conv))\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,pUnit_calc,pUnit_conv)),1.1*np.max(pressure_conversion(p_boundary_res,pUnit_calc,pUnit_conv))])\n", + "\n", + "axs2[1,1].set_title('Velocity Reservoir')\n", + "axs2[1,1].plot(t_vec,v_boundary_res)\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([-1.1*np.max(v_boundary_res),1.1*np.max(v_boundary_res)])\n", + "\n", + "axs2[0,1].set_title('Pressure Turbine')\n", + "axs2[0,1].plot(t_vec,pressure_conversion(p_boundary_tur,pUnit_calc,pUnit_conv))\n", + "axs2[0,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs2[0,1].set_ylabel(r'$p$ [mWS]')\n", + "axs2[0,1].set_ylim([0.9*np.min(pressure_conversion(p_boundary_tur,pUnit_calc,pUnit_conv)),1.1*np.max(pressure_conversion(p_boundary_tur,pUnit_calc,pUnit_conv))])\n", + "\n", + "axs2[1,0].set_title('Velocity Turbine')\n", + "axs2[1,0].plot(t_vec,v_boundary_tur)\n", + "axs2[1,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs2[1,0].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n", + "axs2[1,0].set_ylim([-0.1,1.05*np.max(v_boundary_tur)])\n", + "\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 +} diff --git a/KW Hammer.ipynb b/KW Hammer.ipynb new file mode 100644 index 0000000..c50fd49 --- /dev/null +++ b/KW Hammer.ipynb @@ -0,0 +1,477 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\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\n", + "from Turbinen.Turbinen_class_file import Francis_Turbine\n", + "from Regler.Regler_class_file import PI_controller_class\n", + "from Kraftwerk.Kraftwerk_class_file import Kraftwerk_class" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [], + "source": [ + "# define constants\n", + "\n", + " # for physics\n", + "g = 9.81 # [m/s²] gravitational acceleration \n", + "rho = 1000. # [kg/m³] density of water \n", + "pUnit_calc = 'Pa' # [string] DO NOT CHANGE! for pressure conversion in print statements and plot labels \n", + "pUnit_conv = 'mWS' # [string] for pressure conversion in print statements and plot labels\n", + "\n", + " # for KW OL \n", + "OL_T1_Q_nenn = 0.85 # [m³/s] nominal flux of turbine \n", + "OL_T1_p_nenn = pressure_conversion(10.6,'bar',pUnit_calc) # [Pa] nominal pressure of turbine \n", + "OL_T1_closingTime = 90. # [s] closing time of turbine\n", + "\n", + "OL_T2_Q_nenn = 0.85/2 # [m³/s] nominal flux of turbine \n", + "OL_T2_p_nenn = pressure_conversion(10.6,'bar',pUnit_calc) # [Pa] nominal pressure of turbine \n", + "OL_T2_closingTime = 90. # [s] closing time of turbine\n", + "\n", + " # for KW UL\n", + "UL_T1_Q_nenn = 0.85 # [m³/s] nominal flux of turbine \n", + "UL_T1_p_nenn = pressure_conversion(10.6,'bar',pUnit_calc) # [Pa] nominal pressure of turbine \n", + "UL_T1_closingTime = 90. # [s] closing time of turbine\n", + "\n", + "UL_T2_Q_nenn = 0.85/2 # [m³/s] nominal flux of turbine \n", + "UL_T2_p_nenn = pressure_conversion(10.6,'bar',pUnit_calc) # [Pa] nominal pressure of turbine \n", + "UL_T2_closingTime = 90. # [s] closing time of turbine\n", + "\n", + " # for PI controller\n", + "Con_targetLevel = 8. # [m]\n", + "\n", + " # for pipeline\n", + "Pip_length = (535.+478.) # [m] length of pipeline\n", + "Pip_dia = 0.9 # [m] diameter of pipeline\n", + "Pip_area = Pip_dia**2/4*np.pi # [m²] crossectional area of pipeline\n", + "Pip_head = 105. # [m] hydraulic head of pipeline without reservoir\n", + "Pip_angle = np.arcsin(Pip_head/Pip_length) # [rad] elevation angle of pipeline \n", + "Pip_n_seg = 50 # [-] number of pipe segments in discretization\n", + "Pip_f_D = 0.014 # [-] Darcy friction factor\n", + "Pip_pw_vel = 500. # [m/s] propagation velocity of the pressure wave (pw) in the given pipeline\n", + " # derivatives of the pipeline constants\n", + "Pip_dx = Pip_length/Pip_n_seg # [m] length of each pipe segment\n", + "Pip_dt = Pip_dx/Pip_pw_vel # [s] timestep according to method of characteristics\n", + "Pip_nn = Pip_n_seg+1 # [1] number of nodes\n", + "Pip_x_vec = np.arange(0,Pip_nn,1)*Pip_dx # [m] vector holding the distance of each node from the upstream reservoir along the pipeline\n", + "Pip_h_vec = np.arange(0,Pip_nn,1)*Pip_head/Pip_n_seg # [m] vector holding the vertival distance of each node from the upstream reservoir\n", + "\n", + " # for reservoir\n", + "Res_area_base = 74. # [m²] total base are of the cuboid reservoir \n", + "Res_area_out = Pip_area # [m²] outflux area of the reservoir, given by pipeline area\n", + "Res_level_crit_lo = 0. # [m] for yet-to-be-implemented warnings\n", + "Res_level_crit_hi = np.inf # [m] for yet-to-be-implemented warnings\n", + "Res_dt_approx = 1e-3 # [s] approx. timestep of reservoir time evolution to ensure numerical stability (see Res_nt why approx.)\n", + "Res_nt = max(1,int(Pip_dt//Res_dt_approx)) # [1] number of timesteps of the reservoir time evolution within one timestep of the pipeline\n", + "Res_dt = Pip_dt/Res_nt # [s] harmonised timestep of reservoir time evolution\n", + "\n", + " # for general simulation\n", + "flux_init = (OL_T1_Q_nenn+OL_T2_Q_nenn)/1.1 # [m³/s] initial flux through whole system for steady state initialization \n", + "level_init = Con_targetLevel # [m] initial water level in upstream reservoir for steady state initialization\n", + "simTime_target = 500. # [s] target for total simulation time (will vary slightly to fit with Pip_dt)\n", + "nt = int(simTime_target//Pip_dt) # [1] Number of timesteps of the whole system\n", + "t_vec = np.arange(0,nt+1,1)*Pip_dt # [s] time vector. At each step of t_vec the system parameters are stored\n" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [ + "# create objects\n", + "\n", + "# Upstream reservoir\n", + "reservoir = Ausgleichsbecken_class(Res_area_base,Res_area_out,Res_dt,pUnit_conv,Res_level_crit_lo,Res_level_crit_hi,rho)\n", + "reservoir.set_steady_state(flux_init,level_init)\n", + "\n", + "# pipeline\n", + "pipe = Druckrohrleitung_class(Pip_length,Pip_dia,Pip_head,Pip_n_seg,Pip_f_D,Pip_pw_vel,Pip_dt,pUnit_conv,rho)\n", + "pipe.set_steady_state(flux_init,reservoir.get_current_pressure())\n", + "\n", + "# influx setting turbines\n", + "OL_T1 = Francis_Turbine(OL_T1_Q_nenn,OL_T1_p_nenn,OL_T1_closingTime,Pip_dt,pUnit_conv)\n", + "OL_T2 = Francis_Turbine(OL_T2_Q_nenn,OL_T2_p_nenn,OL_T2_closingTime,Pip_dt,pUnit_conv)\n", + "\n", + "KW_OL = Kraftwerk_class()\n", + "KW_OL.add_turbine(OL_T1)\n", + "KW_OL.add_turbine(OL_T2)\n", + "\n", + "KW_OL.set_steady_state(flux_init,OL_T1_p_nenn)\n", + "\n", + "# downstream turbines\n", + "UL_T1 = Francis_Turbine(UL_T1_Q_nenn,UL_T1_p_nenn,UL_T1_closingTime,Pip_dt,pUnit_conv)\n", + "UL_T2 = Francis_Turbine(UL_T2_Q_nenn,UL_T2_p_nenn,UL_T2_closingTime,Pip_dt,pUnit_conv)\n", + "\n", + "KW_UL = Kraftwerk_class()\n", + "KW_UL.add_turbine(UL_T1)\n", + "KW_UL.add_turbine(UL_T2)\n", + "\n", + "KW_UL.set_steady_state(flux_init,pipe.get_current_pressure_distribution()[-1])\n" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [], + "source": [ + "# initialization for Timeloop\n", + "\n", + "# pipeline\n", + "v_old = pipe.get_current_velocity_distribution() # storing the velocity from the last timestep\n", + "v_min = pipe.get_lowest_velocity_per_node() # storing minimal flux velocity at each node\n", + "v_max = pipe.get_highest_velocity_per_node() # storing maximal flux velocity at each node\n", + "Q_old = pipe.get_current_flux_distribution() # storing the flux from the last timestep\n", + "Q_min = pipe.get_lowest_flux_per_node() # storing minimal flux at each node\n", + "Q_max = pipe.get_highest_flux_per_node() # storing maximal flux at each node\n", + "p_old = pipe.get_current_pressure_distribution() # storing the pressure from the last timestep\n", + "p_min = pipe.get_lowest_pressure_per_node() # storing minimal pressure at each node\n", + "p_max = pipe.get_highest_pressure_per_node() # storing maximal pressure at each node\n", + "p_0 = pipe.get_initial_pressure_distribution() # storing initial pressure at each node\n", + "\n", + "v_boundary_res = np.zeros_like(t_vec) # storing the boundary velocity at the reservoir\n", + "v_boundary_tur = np.zeros_like(t_vec) # storing the boundary velocity at the turbine\n", + "Q_boundary_res = np.zeros_like(t_vec) # storing the boundary flux at the reservoir\n", + "Q_boundary_tur = np.zeros_like(t_vec) # storing the boundary flux at the turbine\n", + "p_boundary_res = np.zeros_like(t_vec) # storing the boundary pressure at the reservoir\n", + "p_boundary_tur = np.zeros_like(t_vec) # storing the boundary pressure at the turbine\n", + "\n", + "v_boundary_res[0] = v_old[0] # storing the initial value for the boundary velocity at the reservoir\n", + "v_boundary_tur[0] = v_old[-1] # storing the initial value for the boundary velocity at the turbine\n", + "Q_boundary_res[0] = Q_old[0] # storing the initial value for the boundary flux at the reservoir\n", + "Q_boundary_tur[0] = Q_old[-1] # storing the initial value for the boundary flux at the turbine\n", + "p_boundary_res[0] = p_old[0] # storing the initial value for the boundary pressure at the reservoir\n", + "p_boundary_tur[0] = p_old[-1] # storing the initial value for the boundary pressure at the turbine\n", + "\n", + "# reservoir\n", + "Q_in_vec = np.zeros_like(t_vec) # storing the influx to the reservoir\n", + "Q_in_vec[0] = flux_init # storing the initial influx to the reservoir\n", + "# Outflux from reservoir is stored in Q_boundary_res\n", + "level_vec = np.zeros_like(t_vec) # storing the level in the reservoir at the end of each pipeline timestep\n", + "level_vec[0] = level_init # storing the initial level in the reservoir\n", + "volume_vec = np.zeros_like(t_vec) # storing the volume in the reservoir at the end of each pipeline timestep\n", + "volume_vec[0] = reservoir.get_current_volume() # storing the initial volume in the reservoir\n", + "\n", + "# OL KW\n", + " # manual input to modulate influx\n", + "OL_T1_LA_soll_vec = np.full_like(t_vec,OL_T1.get_current_LA())\n", + "OL_T1_LA_soll_vec[np.argmin(np.abs(t_vec-100)):] = 0.\n", + "\n", + "OL_T2_LA_soll_vec = np.full_like(t_vec,OL_T2.get_current_LA()) # storing the target value for the guide van opening\n", + "OL_T2_LA_soll_vec[np.argmin(np.abs(t_vec-100)):] = 0.\n", + "\n", + "OL_T1_LA_ist_vec = np.zeros_like(t_vec) # storing the actual value of the guide vane opening\n", + "OL_T1_LA_ist_vec[0] = OL_T1.get_current_LA() # storing the initial value of the guide vane opening\n", + "\n", + "OL_T2_LA_ist_vec = np.zeros_like(t_vec) # storing the actual value of the guide vane opening\n", + "OL_T2_LA_ist_vec[0] = OL_T2.get_current_LA() # storing the initial value of the guide vane opening\n", + "\n", + "# UL KW\n", + "UL_T1_LA_soll_vec = np.full_like(t_vec,UL_T1.get_current_LA()) # storing the target value of the guide vane opening\n", + "UL_T1_LA_soll_vec[np.argmin(np.abs(t_vec-100)):] = 0.\n", + "\n", + "UL_T2_LA_soll_vec = np.full_like(t_vec,UL_T2.get_current_LA()) # storing the target value of the guide vane opening\n", + "UL_T2_LA_soll_vec[np.argmin(np.abs(t_vec-100)):] = 0.\n", + "\n", + "UL_T1_LA_ist_vec = np.zeros_like(t_vec) # storing the actual value of the guide vane opening\n", + "UL_T1_LA_ist_vec[0] = UL_T1.get_current_LA() # storing the initial value of the guide vane opening\n", + "\n", + "UL_T2_LA_ist_vec = np.zeros_like(t_vec) # storing the actual value of the guide vane opening\n", + "UL_T2_LA_ist_vec[0] = UL_T2.get_current_LA() # storing the initial value of the guide vane opening\n" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "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(3,1)\n", + "fig1.suptitle(str(0) +' s / '+str(round(t_vec[-1],2)) + ' s' )\n", + "axs1[0].set_title('Pressure distribution in pipeline')\n", + "axs1[0].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", + "axs1[0].set_ylabel(r'$p$ ['+pUnit_conv+']')\n", + "# axs1[0].set_ylim([-2,2])\n", + "axs1[1].set_title('Pressure distribution in pipeline \\n Difference to t=0')\n", + "axs1[1].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", + "axs1[1].set_ylabel(r'$p$ ['+pUnit_conv+']')\n", + "axs1[1].set_ylim([-2,6])\n", + "axs1[2].set_title('Flux distribution in pipeline')\n", + "axs1[2].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", + "axs1[2].set_ylabel(r'$Q$ [$\\mathrm{m}^3 / \\mathrm{s}$]')\n", + "axs1[2].set_ylim([-1,2])\n", + "lo_0, = axs1[0].plot(Pip_x_vec,pressure_conversion(p_old,pUnit_calc, pUnit_conv),marker='.')\n", + "lo_0min, = axs1[0].plot(Pip_x_vec,pressure_conversion(pipe.get_lowest_pressure_per_node(),pUnit_calc,pUnit_conv),c='red')\n", + "lo_0max, = axs1[0].plot(Pip_x_vec,pressure_conversion(pipe.get_highest_pressure_per_node(),pUnit_calc,pUnit_conv),c='red')\n", + "lo_1, = axs1[1].plot(Pip_x_vec,pressure_conversion(p_old-p_0,pUnit_calc, pUnit_conv),marker='.')\n", + "lo_2, = axs1[1].plot(Pip_x_vec,Q_old,marker='.')\n", + "lo_1min, = axs1[1].plot(Pip_x_vec,pressure_conversion(pipe.get_lowest_pressure_per_node()-p_0,pUnit_calc,pUnit_conv),c='red')\n", + "lo_1max, = axs1[1].plot(Pip_x_vec,pressure_conversion(pipe.get_highest_pressure_per_node()-p_0,pUnit_calc,pUnit_conv),c='red')\n", + "lo_2min, = axs1[2].plot(Pip_x_vec,pipe.get_lowest_flux_per_node(),c='red')\n", + "lo_2max, = axs1[2].plot(Pip_x_vec,pipe.get_highest_flux_per_node(),c='red')\n", + "\n", + "# axs1[0].autoscale()\n", + "# axs1[1].autoscale()\n", + "\n", + "fig1.tight_layout()\n", + "fig1.show()\n", + "plt.pause(1)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [], + "source": [ + "# needed for turbine convergence\n", + "convergence_parameters = [p_old[-2],v_old[-2],Pip_dia,Pip_area,Pip_angle,Pip_f_D,Pip_pw_vel,rho,Pip_dt]\n", + "\n", + "# loop through time steps of the pipeline\n", + "for it_pipe in range(1,nt+1):\n", + "\n", + " KW_OL.update_LAs([OL_T1_LA_soll_vec[it_pipe],OL_T2_LA_soll_vec[it_pipe]])\n", + " KW_OL.set_pressure(OL_T1_p_nenn)\n", + " Q_in_vec[it_pipe] = KW_OL.get_current_Q()\n", + " reservoir.set_influx(Q_in_vec[it_pipe])\n", + "\n", + "# for each pipeline timestep, execute Res_nt timesteps of the reservoir code\n", + " # set initial condition for the reservoir time evolution calculted with the timestep_reservoir_evolution() method\n", + " reservoir.set_pressure(p_old[0],display_warning=False)\n", + " reservoir.set_outflux(Q_old[0],display_warning=False)\n", + " # calculate the time evolution of the reservoir level within each pipeline timestep to avoid runaway numerical error\n", + " for it_res in range(Res_nt):\n", + " reservoir.timestep_reservoir_evolution() \n", + " level_vec[it_pipe] = reservoir.get_current_level() \n", + " volume_vec[it_pipe] = reservoir.get_current_volume() \n", + " \n", + " # change the guide vane opening based on the target value and closing time limitation\n", + " KW_UL.update_LAs([UL_T1_LA_soll_vec[it_pipe],UL_T2_LA_soll_vec[it_pipe]])\n", + " OL_T1_LA_ist_vec[it_pipe], OL_T2_LA_ist_vec[it_pipe] = KW_OL.get_current_LAs()\n", + " UL_T1_LA_ist_vec[it_pipe], UL_T2_LA_ist_vec[it_pipe] = KW_UL.get_current_LAs()\n", + "\n", + " # set boundary condition for the next timestep of the characteristic method\n", + " convergence_parameters[0] = p_old[-2]\n", + " convergence_parameters[1] = v_old[-2]\n", + " KW_UL.set_pressure(p_old[-1])\n", + " KW_UL.converge(convergence_parameters)\n", + " p_boundary_res[it_pipe] = reservoir.get_current_pressure()\n", + " v_boundary_tur[it_pipe] = 1/Pip_area*KW_UL.get_current_Q()\n", + " Q_boundary_tur[it_pipe] = KW_UL.get_current_Q()\n", + "\n", + " # the the boundary condition 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] = (0.8*pipe.v[0]+0.2*reservoir.get_current_outflux()/Res_area_out) # unnecessary\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", + " Q_boundary_res[it_pipe] = pipe.get_current_flux_distribution()[0]\n", + "\n", + " # perform the next timestep via the characteristic method\n", + " pipe.timestep_characteristic_method_vectorized()\n", + "\n", + " # prepare for next loop\n", + " p_old = pipe.get_current_pressure_distribution()\n", + " v_old = pipe.get_current_velocity_distribution()\n", + " Q_old = pipe.get_current_flux_distribution()\n", + "\n", + " # plot some stuff\n", + " # remove line-objects to autoscale axes (there is definetly a better way, but this works ¯\\_(ツ)_/¯ )\n", + " if it_pipe%25 == 0:\n", + " lo_0.remove()\n", + " lo_0min.remove()\n", + " lo_0max.remove()\n", + " lo_1.remove()\n", + " lo_1min.remove()\n", + " lo_1max.remove()\n", + " lo_2.remove()\n", + " lo_2min.remove()\n", + " lo_2max.remove()\n", + " # plot new pressure and velocity distribution in the pipeline\n", + " lo_0, = axs1[0].plot(Pip_x_vec,pressure_conversion(pipe.get_current_pressure_distribution(),pUnit_calc,pUnit_conv),marker='.',c='blue')\n", + " lo_0min, = axs1[0].plot(Pip_x_vec,pressure_conversion(pipe.get_lowest_pressure_per_node(),pUnit_calc,pUnit_conv),c='red')\n", + " lo_0max, = axs1[0].plot(Pip_x_vec,pressure_conversion(pipe.get_highest_pressure_per_node(),pUnit_calc,pUnit_conv),c='red') \n", + " lo_1, = axs1[1].plot(Pip_x_vec,pressure_conversion(pipe.get_current_pressure_distribution()-p_0,pUnit_calc,pUnit_conv),marker='.',c='blue')\n", + " lo_1min, = axs1[1].plot(Pip_x_vec,pressure_conversion(pipe.get_lowest_pressure_per_node()-p_0,pUnit_calc,pUnit_conv),c='red')\n", + " lo_1max, = axs1[1].plot(Pip_x_vec,pressure_conversion(pipe.get_highest_pressure_per_node()-p_0,pUnit_calc,pUnit_conv),c='red')\n", + " lo_2, = axs1[2].plot(Pip_x_vec,pipe.get_current_flux_distribution(),marker='.',c='blue')\n", + " lo_2min, = axs1[2].plot(Pip_x_vec,pipe.get_lowest_flux_per_node(),c='red')\n", + " lo_2max, = axs1[2].plot(Pip_x_vec,pipe.get_highest_flux_per_node(),c='red')\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(0.000001) " + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [], + "source": [ + "fig2,axs2 = plt.subplots(1,1)\n", + "axs2.set_title('Level and Volume reservoir')\n", + "axs2.plot(t_vec,level_vec,label='level')\n", + "axs2.set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs2.set_ylabel(r'$h$ [m]')\n", + "x_twin_00 = axs2.twinx()\n", + "x_twin_00.set_ylabel(r'$V$ [$\\mathrm{m}^3$]')\n", + "x_twin_00.plot(t_vec,volume_vec)\n", + "axs2.legend()\n", + "\n", + "fig2,axs2 = plt.subplots(1,1)\n", + "axs2.set_title('LA')\n", + "axs2.plot(t_vec,100*OL_T1_LA_soll_vec,label='OL_T1 Target',c='b')\n", + "axs2.scatter(t_vec[::200],100*OL_T1_LA_ist_vec[::200],label='OL_T1 Actual',c='b',marker='+')\n", + "axs2.plot(t_vec,100*OL_T2_LA_soll_vec,label='OL_T2 Target',c='g')\n", + "axs2.scatter(t_vec[::200],100*OL_T2_LA_ist_vec[::200],label='OL_T2 Actual',c='g',marker='+')\n", + "axs2.plot(t_vec,100*UL_T1_LA_soll_vec,label='UL_T1 Target',c='r')\n", + "axs2.scatter(t_vec[::200],100*UL_T1_LA_ist_vec[::200],label='UL_T1 Actual',c='r',marker='+')\n", + "axs2.plot(t_vec,100*UL_T2_LA_soll_vec,label='UL_T2 Target',c='k')\n", + "axs2.scatter(t_vec[::200],100*UL_T2_LA_ist_vec[::200],label='UL_T2 Actual',c='k',marker='+')\n", + "axs2.set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs2.set_ylabel(r'$LA$ [%]')\n", + "axs2.legend()\n", + "\n", + "fig2,axs2 = plt.subplots(1,1)\n", + "axs2.set_title('Pressure change vs t=0 at reservoir and turbine')\n", + "axs2.plot(t_vec,pressure_conversion(p_boundary_res-p_boundary_res[0],pUnit_calc, pUnit_conv),label='Reservoir')\n", + "axs2.plot(t_vec,pressure_conversion(p_boundary_tur-p_boundary_tur[0],pUnit_calc, pUnit_conv),label='Turbine')\n", + "axs2.set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs2.set_ylabel(r'$p$ ['+pUnit_conv+']')\n", + "axs2.legend()\n", + "\n", + "fig2,axs2 = plt.subplots(1,1)\n", + "axs2.set_title('Fluxes')\n", + "axs2.plot(t_vec,Q_in_vec,label='Influx')\n", + "axs2.plot(t_vec,Q_boundary_res,label='Outflux')\n", + "axs2.scatter(t_vec[::200],Q_boundary_tur[::200],label='Flux Turbine',c='g',marker='+')\n", + "axs2.set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs2.set_ylabel(r'$Q$ [$\\mathrm{m}^3/\\mathrm{s}$]')\n", + "axs2.legend()\n", + "\n", + "fig2,axs2 = plt.subplots(1,1)\n", + "axs2.set_title('Min and Max Pressure')\n", + "axs2.plot(Pip_x_vec,pipe.get_lowest_pressure_per_node(disp_flag=True),c='red')\n", + "axs2.plot(Pip_x_vec,pipe.get_highest_pressure_per_node(disp_flag=True),c='red')\n", + "axs2.set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", + "axs2.set_ylabel(r'$p$ ['+pUnit_conv+']')\n", + "\n", + "# fig2,axs2 = plt.subplots(1,1)\n", + "# axs2.set_title('Min and Max Fluxes')\n", + "# axs2.plot(Pip_x_vec,pipe.get_lowest_flux_per_node(),c='red')\n", + "# axs2.plot(Pip_x_vec,pipe.get_highest_flux_per_node(),c='red')\n", + "# axs2.set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", + "# axs2.set_ylabel(r'$Q$ [$\\mathrm{m}^3/\\mathrm{s}$]')\n", + "\n", + "\n", + "fig2.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "fig3,axs3 = plt.subplots(2,2)\n", + "axs3[0,0].set_title('Level and Volume reservoir')\n", + "axs3[0,0].plot(t_vec,level_vec,label='level')\n", + "axs3[0,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs3[0,0].set_ylabel(r'$h$ [m]')\n", + "x_twin_00 = axs3[0,0].twinx()\n", + "x_twin_00.set_ylabel(r'$V$ [$\\mathrm{m}^3$]')\n", + "x_twin_00.plot(t_vec,volume_vec)\n", + "axs3[0,0].legend()\n", + "\n", + "axs3[0,1].set_title('LA')\n", + "axs3[0,1].plot(t_vec,100*OL_T1_LA_soll_vec,label='OL_T1 Target',c='b')\n", + "axs3[0,1].scatter(t_vec[::200],100*OL_T1_LA_ist_vec[::200],label='OL_T1 Actual',c='b',marker='+')\n", + "axs3[0,1].plot(t_vec,100*OL_T2_LA_soll_vec,label='OL_T2 Target',c='g')\n", + "axs3[0,1].scatter(t_vec[::200],100*OL_T2_LA_ist_vec[::200],label='OL_T2 Actual',c='g',marker='+')\n", + "axs3[0,1].plot(t_vec,100*UL_T1_LA_soll_vec,label='UL_T1 Target',c='r')\n", + "axs3[0,1].scatter(t_vec[::200],100*UL_T1_LA_ist_vec[::200],label='UL_T1 Actual',c='r',marker='+')\n", + "axs3[0,1].plot(t_vec,100*UL_T2_LA_soll_vec,label='UL_T2 Target',c='k')\n", + "axs3[0,1].scatter(t_vec[::200],100*UL_T2_LA_ist_vec[::200],label='UL_T2 Actual',c='k',marker='+')\n", + "axs3[0,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs3[0,1].set_ylabel(r'$LA$ [%]')\n", + "axs3[0,1].legend()\n", + "\n", + "axs3[1,0].set_title('Fluxes')\n", + "axs3[1,0].plot(t_vec,Q_in_vec,label='Influx')\n", + "axs3[1,0].plot(t_vec,Q_boundary_res,label='Outflux')\n", + "axs3[1,0].scatter(t_vec[::200],Q_boundary_tur[::200],label='Flux Turbine',c='g',marker='+')\n", + "axs3[1,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs3[1,0].set_ylabel(r'$Q$ [$\\mathrm{m}^3/\\mathrm{s}$]')\n", + "axs3[1,0].legend()\n", + "\n", + "axs3[1,1].set_title('Pressure change vs t=0 at reservoir and turbine')\n", + "axs3[1,1].plot(t_vec,pressure_conversion(p_boundary_res-p_boundary_res[0],pUnit_calc, pUnit_conv),label='Reservoir')\n", + "axs3[1,1].plot(t_vec,pressure_conversion(p_boundary_tur-p_boundary_tur[0],pUnit_calc, pUnit_conv),label='Turbine')\n", + "axs3[1,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs3[1,1].set_ylabel(r'$p$ ['+pUnit_conv+']')\n", + "axs3[1,1].legend()\n", + "\n", + "fig3.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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 +} diff --git a/Untertweng.ipynb b/Untertweng.ipynb index a66726b..7ab1373 100644 --- a/Untertweng.ipynb +++ b/Untertweng.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 9, "metadata": {}, "outputs": [], "source": [ @@ -24,7 +24,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 10, "metadata": {}, "outputs": [], "source": [ @@ -95,7 +95,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 11, "metadata": {}, "outputs": [], "source": [ @@ -136,7 +136,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 12, "metadata": {}, "outputs": [], "source": [ @@ -209,7 +209,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ @@ -244,12847 +244,9 @@ }, { "cell_type": "code", - 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978694.6891772 998772.5946572 1018850.5001372\n", - " 1038928.4056172 1059006.31109719 1079084.21657719]\n", - "[ 75188.94257732 95266.84805731 115344.75353731 135422.65901731\n", - " 155500.56449731 175578.4699773 195656.3754573 215734.2809373\n", - " 235812.1864173 255890.09189729 275967.99737729 296045.90285729\n", - " 316123.80833729 336201.71381728 356279.61929728 376357.52477728\n", - " 396435.43025728 416513.33573727 436591.24121727 456669.14669727\n", - " 476747.05217727 496824.95765726 516902.86313726 536980.76861726\n", - " 557058.67409726 577136.57957725 597214.48505725 617292.39053725\n", - " 637370.29601725 657448.20149724 677526.10697724 697604.01245724\n", - " 717681.91793724 737759.82341723 757837.72889723 777915.63437723\n", - " 797993.53985723 818071.44533722 838149.35081722 858227.25629722\n", - " 878305.16177722 898383.06725721 918460.97273721 938538.87821721\n", - " 958616.78369721 978694.6891772 998772.5946572 1018850.5001372\n", - " 1038928.4056172 1059006.31109719 1079084.21657719]\n" - ] - } - ], + "outputs": [], "source": [ "# needed for turbine convergence\n", "convergence_parameters = [p_old[-2],v_old[-2],Pip_dia,Pip_area,Pip_angle,Pip_f_D,Pip_pw_vel,rho,Pip_dt]\n", @@ -13165,7 +327,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 15, "metadata": {}, "outputs": [], "source": [ @@ -13231,7 +393,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 16, "metadata": {}, "outputs": [], "source": [