fix for numerical runaway of rounding errors
due to turbine-pipeline interatction via a convergence method in the turbine and a "damping" trick on the reservoir velocity plus: code cleanup with consistent naming of variables
This commit is contained in:
Brantegger Georg
@@ -18,67 +18,64 @@
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"execution_count": 9,
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"metadata": {},
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"outputs": [],
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"source": [
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"#define constants\n",
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"# define constants\n",
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"\n",
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"#Turbine\n",
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"Q_nenn = 0.85 # m³/s\n",
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"p_nenn = pressure_conversion(10.6,'bar','Pa')\n",
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"closing_time = 30. #s\n",
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"\n",
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"# physics\n",
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"g = 9.81 # gravitational acceleration [m/s²]\n",
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"rho = 1000. # density of water [kg/m³]\n",
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" # for physics\n",
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"g = 9.81 # [m/s²] gravitational acceleration \n",
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"rho = 1000. # [kg/m³] density of water \n",
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"pUnit_calc = 'Pa' # [text] DO NOT CHANGE! for pressure conversion in print statements and plot labels \n",
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"pUnit_conv = 'mWS' # [text] for pressure conversion in print statements and plot labels\n",
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"\n",
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"\n",
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"# define controller constants\n",
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"target_level = 8. # m\n",
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"Kp = 0.1\n",
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"Ti = 7.\n",
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"deadband_range = 0.05 # m\n",
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" # for Turbine\n",
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"Tur_Q_nenn = 0.85 # [m³/s] nominal flux of turbine \n",
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"Tur_p_nenn = pressure_conversion(10.6,'bar',pUnit_calc) # [Pa] nominal pressure of turbine \n",
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"Tur_closingTime = 90. # [s] closing time of turbine\n",
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"\n",
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"\n",
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"# pipeline\n",
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"L = (535.+478.) # length of pipeline [m]\n",
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"D = 0.9 # pipe diameter [m]\n",
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"A_pipe = D**2/4*np.pi # pipeline area\n",
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"h_pipe = 105 # hydraulic head without reservoir [m] \n",
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"alpha = np.arcsin(h_pipe/L) # Höhenwinkel der Druckrohrleitung \n",
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"n = 50 # number of pipe segments in discretization\n",
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"f_D = 0.014 # Darcy friction factor\n",
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"c = 500. # propagation velocity of the pressure wave [m/s]\n",
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"# consider prescribing a total simulation time and deducting the number of timesteps from that\n",
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"nt = 9000 # number of time steps after initial conditions\n",
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"\n",
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"# derivatives of the pipeline constants\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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"initial_level = target_level # water level in upstream reservoir [m]\n",
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"pl_vec = np.arange(0,nn,1)*dx # pl = pipe-length. position of the nodes on the pipeline\n",
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"t_vec = np.arange(0,nt+1)*dt # time vector\n",
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"h_vec = np.arange(0,nn,1)*h_pipe/n # hydraulic head of pipeline at each node \n",
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" # for PI controller\n",
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"Con_targetLevel = 8. # [m]\n",
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"Con_K_p = 0.1 # [-] proportional constant of PI controller\n",
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"Con_T_i = 10. # [s] timespan in which a steady state error is corrected by the intergal term\n",
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"Con_deadbandRange = 0.05 # [m] Deadband range around targetLevel for which the controller does NOT intervene\n",
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"\n",
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"\n",
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" # for pipeline\n",
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"Pip_length = (535.+478.) # [m] length of pipeline\n",
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"Pip_dia = 0.9 # [m] diameter of pipeline\n",
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"Pip_area = Pip_dia**2/4*np.pi # [m²] crossectional area of pipeline\n",
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"Pip_head = 105. # [m] hydraulic head of pipeline without reservoir\n",
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"Pip_angle = np.arcsin(Pip_head/Pip_length) # [rad] elevation angle of pipeline \n",
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"Pip_n_seg = 50 # [-] number of pipe segments in discretization\n",
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"Pip_f_D = 0.014 # [-] Darcy friction factor\n",
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"Pip_pw_vel = 500. # [m/s] propagation velocity of the pressure wave (pw) in the given pipeline\n",
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" # derivatives of the pipeline constants\n",
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"Pip_dx = Pip_length/Pip_n_seg # [m] length of each pipe segment\n",
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"Pip_dt = Pip_dx/Pip_pw_vel # [s] timestep according to method of characteristics\n",
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"Pip_nn = Pip_n_seg+1 # [1] number of nodes\n",
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"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",
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"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",
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"\n",
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"# reservoir\n",
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"# replace influx by vector\n",
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"initial_flux = Q_nenn/1.1 # initial influx of volume to the reservoir [m³/s]\n",
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"initial_pressure_unit = 'Pa' # DO NOT CHANGE! for pressure conversion in print statements and plot labels \n",
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"conversion_pressure_unit = 'bar' # for pressure conversion in print statements and plot labels\n",
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"area_base = 74. # total base are of the cuboid reservoir [m²] \n",
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"area_outflux = A_pipe # outlfux area of the reservoir, given by pipeline area [m²]\n",
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"critical_level_low = 0. # for yet-to-be-implemented warnings[m]\n",
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"critical_level_high = np.inf # for yet-to-be-implemented warnings[m]\n",
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"\n",
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"# make sure e-RK4 method of reservoir has a small enough timestep to avoid runaway numerical error\n",
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"nt_eRK4 = 100 # number of simulation steps of reservoir in between timesteps of pipeline \n",
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"simulation_timestep = dt/nt_eRK4\n",
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" # for reservoir\n",
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"Res_area_base = 74. # [m²] total base are of the cuboid reservoir \n",
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"Res_area_out = Pip_area # [m²] outflux area of the reservoir, given by pipeline area\n",
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"Res_level_crit_lo = 0. # [m] for yet-to-be-implemented warnings\n",
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"Res_level_crit_hi = np.inf # [m] for yet-to-be-implemented warnings\n",
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"Res_dt_approx = 1e-3 # [s] approx. timestep of reservoir time evolution to ensure numerical stability (see Res_nt why approx.)\n",
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"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",
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"Res_dt = Pip_dt/Res_nt # [s] harmonised timestep of reservoir time evolution\n",
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"\n",
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"\n"
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" # for general simulation\n",
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"flux_init = Tur_Q_nenn/1.1 # [m³/s] initial flux through whole system for steady state initialization \n",
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"level_init = Con_targetLevel # [m] initial water level in upstream reservoir for steady state initialization\n",
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"simTime_target = 600. # [s] target for total simulation time (will vary slightly to fit with Pip_dt)\n",
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"nt = int(simTime_target//Pip_dt) # [1] Number of timesteps of the whole system\n",
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"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"
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]
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},
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{
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@@ -89,65 +86,25 @@
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"source": [
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"# create objects\n",
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"\n",
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"V = Ausgleichsbecken_class(area_base,area_outflux,critical_level_low,critical_level_high,simulation_timestep)\n",
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"V.set_steady_state(initial_flux,initial_level,conversion_pressure_unit)\n",
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"# Upstream reservoir\n",
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"reservoir = Ausgleichsbecken_class(Res_area_base,Res_area_out,Res_dt,Res_level_crit_lo,Res_level_crit_hi,rho)\n",
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"reservoir.set_steady_state(flux_init,level_init)\n",
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"\n",
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"# pipeline\n",
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"pipe = Druckrohrleitung_class(Pip_length,Pip_dia,Pip_n_seg,Pip_angle,Pip_f_D,Pip_pw_vel,Pip_dt,pUnit_conv,rho)\n",
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"pipe.set_steady_state(flux_init,level_init,Res_area_base,Pip_x_vec,Pip_h_vec)\n",
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"\n",
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"pipe = Druckrohrleitung_class(L,D,n,alpha,f_D)\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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"pipe.set_steady_state(initial_flux,initial_level,area_base,pl_vec,h_vec)\n",
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"# downstream turbine\n",
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"turbine = Francis_Turbine(Tur_Q_nenn,Tur_p_nenn,Tur_closingTime,Pip_dt,pUnit_conv)\n",
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"turbine.set_steady_state(flux_init,pipe.get_current_pressure_distribution()[-1])\n",
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"\n",
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"initial_pressure_turbine = pipe.get_current_pressure_distribution()[-1]\n",
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"# influx setting turbine\n",
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"turbine_in = Francis_Turbine(Tur_Q_nenn,Tur_p_nenn,Tur_closingTime/2,Pip_dt,pUnit_conv)\n",
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"turbine_in.set_steady_state(flux_init,Tur_p_nenn)\n",
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"\n",
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"T1 = Francis_Turbine(Q_nenn,p_nenn,closing_time,timestep=dt)\n",
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"T1.set_steady_state(initial_flux,initial_pressure_turbine)\n",
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"\n",
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"T_in = Francis_Turbine(Q_nenn,p_nenn,closing_time/2,timestep=dt)\n",
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"T_in.set_steady_state(initial_flux,p_nenn)\n",
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"\n",
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"Pegelregler = PI_controller_class(target_level,deadband_range,Kp,Ti,dt)\n",
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"Pegelregler.control_variable = T1.get_current_LA()\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": 4,
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"metadata": {},
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"outputs": [],
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"source": [
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"# initialization for timeloop\n",
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"\n",
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"# prepare the vectors in which the pressure and velocity distribution in the pipeline from the previous timestep are stored\n",
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"v_old = pipe.get_current_velocity_distribution()\n",
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"p_old = pipe.get_current_pressure_distribution()\n",
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"\n",
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"# prepare the vectors in which the temporal evolution of the boundary conditions are stored\n",
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" # keep in mind, that the velocity at the turbine and the pressure at the reservoir follow from boundary conditions\n",
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" # reservoir level and flow through turbine\n",
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" # the pressure at the turbine and the velocity at the reservoir are calculated from the method of characteristics\n",
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"v_boundary_res = np.zeros_like(t_vec)\n",
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"v_boundary_tur = np.zeros_like(t_vec)\n",
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"p_boundary_res = np.zeros_like(t_vec)\n",
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"p_boundary_tur = np.zeros_like(t_vec)\n",
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"\n",
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"# prepare the vectors that store the temporal evolution of the level in the reservoir\n",
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"level_vec = np.full(nt+1,initial_level) # level at the end of each pipeline timestep\n",
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"\n",
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"# set the boundary conditions for the first timestep\n",
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"v_boundary_res[0] = v_old[0]\n",
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"v_boundary_tur[0] = v_old[-1] \n",
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"p_boundary_res[0] = p_old[0]\n",
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"p_boundary_tur[0] = p_old[-1]\n",
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"\n",
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"LA_soll_vec = np.full_like(t_vec,T1.get_current_LA())\n",
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"LA_ist_vec = np.full_like(t_vec,T1.get_current_LA())\n",
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"\n",
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"LA_soll_vec2 = np.full_like(t_vec,T_in.get_current_LA())\n",
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"LA_soll_vec2[500:1000] = 0.\n",
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"LA_soll_vec2[1000:1500] = 1. \n",
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"LA_soll_vec2[1500:2000] = 0.\n",
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"LA_soll_vec2[2000:2500] = 0.5 \n"
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"# level controll\n",
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"level_control = PI_controller_class(Con_targetLevel,Con_deadbandRange,Con_K_p,Con_T_i,Pip_dt)\n",
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"level_control.set_control_variable(turbine.get_current_LA(),display_warning=False)\n"
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]
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},
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{
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@@ -155,21 +112,74 @@
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"execution_count": 5,
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"metadata": {},
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"outputs": [],
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"source": [
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"# initialization for Timeloop\n",
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"\n",
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"v_old = pipe.get_current_velocity_distribution()\n",
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"v_min = pipe.get_current_velocity_distribution()\n",
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"v_max = pipe.get_current_velocity_distribution()\n",
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"Q_old = pipe.get_current_flux_distribution()\n",
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"Q_min = pipe.get_current_flux_distribution()\n",
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"Q_max = pipe.get_current_flux_distribution()\n",
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"p_old = pipe.get_current_pressure_distribution()\n",
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"p_min = pipe.get_current_pressure_distribution()\n",
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"p_max = pipe.get_current_pressure_distribution()\n",
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"\n",
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"Q_in_vec = np.zeros_like(t_vec)\n",
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"Q_in_vec[0] = flux_init\n",
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"\n",
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"v_boundary_res = np.zeros_like(t_vec)\n",
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"v_boundary_tur = np.zeros_like(t_vec)\n",
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"Q_boundary_res = np.zeros_like(t_vec)\n",
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"Q_boundary_tur = np.zeros_like(t_vec)\n",
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"p_boundary_res = np.zeros_like(t_vec)\n",
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"p_boundary_tur = np.zeros_like(t_vec)\n",
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"\n",
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"level_vec = np.full_like(t_vec,level_init) # level at the end of each pipeline timestep\n",
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"volume_vec = np.full_like(t_vec,reservoir.get_current_volume()) # volume at the end of each pipeline timestep\n",
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"\n",
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"v_boundary_res[0] = v_old[0]\n",
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"v_boundary_tur[0] = v_old[-1] \n",
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"Q_boundary_res[0] = Q_old[0]\n",
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"Q_boundary_tur[0] = Q_old[-1]\n",
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"p_boundary_res[0] = p_old[0]\n",
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"p_boundary_tur[0] = p_old[-1]\n",
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"\n",
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"LA_soll_vec = np.full_like(t_vec,turbine.get_current_LA())\n",
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"LA_ist_vec = np.full_like(t_vec,turbine.get_current_LA())\n",
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"\n",
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"LA_soll_vec2 = np.full_like(t_vec,turbine_in.get_current_LA())\n",
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"LA_soll_vec2[500:1000] = 0.\n",
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"LA_soll_vec2[1000:1500] = 1. \n",
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"LA_soll_vec2[1500:2000] = 0.\n",
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"LA_soll_vec2[2000:2500] = 0.5 \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": 6,
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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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"# time loop\n",
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"# Con_T_ime loop\n",
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"\n",
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"# create a figure and subplots to display the velocity and pressure distribution across the pipeline in each pipeline step\n",
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"fig1,axs1 = plt.subplots(2,1)\n",
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"fig1.suptitle(str(0) +' s / '+str(round(t_vec[-1],2)) + ' s' )\n",
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"axs1[0].set_title('Pressure distribution in pipeline')\n",
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"axs1[1].set_title('Velocity distribution in pipeline')\n",
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"axs1[0].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
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"axs1[0].set_ylabel(r'$p$ ['+conversion_pressure_unit+']')\n",
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"axs1[0].set_ylabel(r'$p$ ['+pUnit_conv+']')\n",
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"axs1[1].set_title('Flux distribution in pipeline')\n",
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"axs1[1].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
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"axs1[1].set_ylabel(r'$v$ [$\\mathrm{m} / \\mathrm{s}$]')\n",
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"lo_00, = axs1[0].plot(pl_vec,pressure_conversion(p_old,initial_pressure_unit, conversion_pressure_unit),marker='.')\n",
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"lo_01, = axs1[1].plot(pl_vec,v_old,marker='.')\n",
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"axs1[1].set_ylabel(r'$Q$ [$\\mathrm{m}^3 / \\mathrm{s}$]')\n",
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"lo_p, = axs1[0].plot(Pip_x_vec,pressure_conversion(p_old,pUnit_calc, pUnit_conv),marker='.')\n",
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"lo_q, = axs1[1].plot(Pip_x_vec,Q_old,marker='.')\n",
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"lo_pmin, = axs1[0].plot(Pip_x_vec,pipe.get_lowest_pressure_per_node(disp=True),c='red')\n",
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"lo_pmax, = axs1[0].plot(Pip_x_vec,pipe.get_highest_pressure_per_node(disp=True),c='red')\n",
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"lo_qmin, = axs1[1].plot(Pip_x_vec,pipe.get_lowest_flux_per_node(),c='red')\n",
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"lo_qmax, = axs1[1].plot(Pip_x_vec,pipe.get_highest_flux_per_node(),c='red')\n",
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"\n",
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"axs1[0].autoscale()\n",
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"axs1[1].autoscale()\n",
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"\n",
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@@ -180,136 +190,153 @@
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"execution_count": 7,
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"metadata": {},
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"outputs": [],
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"source": [
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"error_vec = np.zeros_like(t_vec)\n",
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"# loop through time steps of the pipeline\n",
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"for it_pipe in range(1,pipe.nt+1):\n",
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"convergence_parameters = [p_old[-2],v_old[-2],Pip_dia,Pip_area,Pip_angle,Pip_f_D,Pip_pw_vel,rho,Pip_dt]\n",
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"\n",
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" T_in.update_LA(LA_soll_vec2[it_pipe])\n",
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" T_in.set_pressure(p_nenn)\n",
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" V.set_influx(T_in.get_current_Q())\n",
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"# loop through Con_T_ime steps of the pipeline\n",
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"for it_pipe in range(1,nt+1):\n",
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"\n",
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" turbine_in.update_LA(LA_soll_vec2[it_pipe])\n",
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" turbine_in.set_pressure(Tur_p_nenn)\n",
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" Q_in_vec[it_pipe] = turbine_in.get_current_Q()\n",
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" reservoir.set_influx(Q_in_vec[it_pipe])\n",
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"\n",
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"# for each pipeline timestep, execute nt_eRK4 timesteps of the reservoir code\n",
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" # set initial conditions for the reservoir time evolution calculted with e-RK4\n",
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" V.set_pressure(p_old[0])\n",
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" V.set_outflux(v_old[0]*area_outflux)\n",
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" # calculate the time evolution of the reservoir level within each pipeline timestep to avoid runaway numerical error\n",
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" for it_res in range(nt_eRK4):\n",
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" V.timestep_reservoir_evolution() \n",
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" level_vec[it_pipe] = V.get_current_level() \n",
|
||||
" # set initial condition for the reservoir Con_T_ime evolution calculted with e-RK4\n",
|
||||
" reservoir.set_pressure(p_old[0],display_warning=False)\n",
|
||||
" reservoir.set_outflux(Q_old[0],display_warning=False)\n",
|
||||
" # calculate the Con_T_ime 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",
|
||||
" # get the control variable\n",
|
||||
" Pegelregler.update_control_variable(level_vec[it_pipe])\n",
|
||||
" LA_soll_vec[it_pipe] = Pegelregler.get_current_control_variable()\n",
|
||||
" level_control.update_control_variable(level_vec[it_pipe])\n",
|
||||
" LA_soll_vec[it_pipe] = level_control.get_current_control_variable()\n",
|
||||
" \n",
|
||||
" # change the Leitapparatöffnung based on the target value\n",
|
||||
" T1.update_LA(LA_soll_vec[it_pipe])\n",
|
||||
" LA_ist_vec[it_pipe] = T1.get_current_LA()\n",
|
||||
" turbine.update_LA(LA_soll_vec[it_pipe])\n",
|
||||
" LA_ist_vec[it_pipe] = turbine.get_current_LA()\n",
|
||||
"\n",
|
||||
" T1.set_pressure(p_old[-1])\n",
|
||||
" # set boundary conditions for the next timestep of the characteristic method\n",
|
||||
" p_boundary_res[it_pipe] = V.get_current_pressure()\n",
|
||||
" v_boundary_tur[it_pipe] = 1/A_pipe*T1.get_current_Q()\n",
|
||||
" # set boundary condition for the next timestep of the characterisCon_T_ic method\n",
|
||||
" turbine.set_pressure(p_old[-1])\n",
|
||||
" convergence_parameters[0] = p_old[-2]\n",
|
||||
" convergence_parameters[1] = v_old[-2]\n",
|
||||
" turbine.converge(convergence_parameters)\n",
|
||||
" p_boundary_res[it_pipe] = reservoir.get_current_pressure()\n",
|
||||
" v_boundary_tur[it_pipe] = 1/Pip_area*turbine.get_current_Q()\n",
|
||||
" Q_boundary_tur[it_pipe] = turbine.get_current_Q()\n",
|
||||
"\n",
|
||||
" # the the boundary conditions in the pipe.object and thereby calculate boundary pressure at turbine\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)\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",
|
||||
" error_vec[it_pipe] = abs(v_boundary_res[it_pipe]-V.get_current_outflux()/A_pipe)\n",
|
||||
"\n",
|
||||
" # perform the next timestep via the characteristic method\n",
|
||||
" # perform the next timestep via the characterisCon_T_ic method\n",
|
||||
" pipe.timestep_characteristic_method()\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",
|
||||
"\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",
|
||||
" lo_p.remove()\n",
|
||||
" lo_pmin.remove()\n",
|
||||
" lo_pmax.remove()\n",
|
||||
" lo_q.remove()\n",
|
||||
" lo_qmin.remove()\n",
|
||||
" lo_qmax.remove()\n",
|
||||
" # plot new pressure and velocity distribution in the pipeline\n",
|
||||
" lo_00, = axs1[0].plot(pl_vec,pressure_conversion(p_old,initial_pressure_unit, conversion_pressure_unit),marker='.',c='blue')\n",
|
||||
" lo_01, = axs1[1].plot(pl_vec,v_old,marker='.',c='blue')\n",
|
||||
" # lo_02, = axs1[2].plot(level_vec_2,c='blue')\n",
|
||||
" lo_p, = axs1[0].plot(Pip_x_vec,pipe.get_current_pressure_distribution(disp=True),marker='.',c='blue')\n",
|
||||
" lo_pmin, = axs1[0].plot(Pip_x_vec,pipe.get_lowest_pressure_per_node(disp=True),c='red')\n",
|
||||
" lo_pmax, = axs1[0].plot(Pip_x_vec,pipe.get_highest_pressure_per_node(disp=True),c='red')\n",
|
||||
" lo_q, = axs1[1].plot(Pip_x_vec,pipe.get_current_flux_distribution(),marker='.',c='blue')\n",
|
||||
" lo_qmin, = axs1[1].plot(Pip_x_vec,pipe.get_lowest_flux_per_node(),c='red')\n",
|
||||
" lo_qmax, = axs1[1].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(0.001) \n",
|
||||
"\n",
|
||||
" \n",
|
||||
" "
|
||||
" plt.pause(0.001) "
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 7,
|
||||
"execution_count": 13,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"# plot time evolution of boundary pressure and velocity as well as the reservoir level\n",
|
||||
"# plot Con_T_ime evolution of boundary pressure and velocity as well as the reservoir level\n",
|
||||
"\n",
|
||||
"fig2,axs2 = plt.subplots(3,2)\n",
|
||||
"axs2[0,0].set_title('Pressure reservoir')\n",
|
||||
"axs2[0,0].plot(t_vec,pressure_conversion(p_boundary_res,initial_pressure_unit, conversion_pressure_unit))\n",
|
||||
"axs2[0,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
|
||||
"axs2[0,0].set_ylabel(r'$p$ ['+conversion_pressure_unit+']')\n",
|
||||
"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",
|
||||
"axs2[0,1].set_title('Velocity reservoir')\n",
|
||||
"axs2[0,1].plot(t_vec,v_boundary_res)\n",
|
||||
"axs2[0,1].set_ylim(-2*Q_nenn,+2*Q_nenn)\n",
|
||||
"axs2[0,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
|
||||
"axs2[0,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n",
|
||||
"fig2,axs2 = plt.subplots(1,1)\n",
|
||||
"axs2.set_title('LA')\n",
|
||||
"axs2.plot(t_vec,100*LA_soll_vec,label='Target')\n",
|
||||
"axs2.plot(t_vec,100*LA_ist_vec,label='Actual')\n",
|
||||
"axs2.set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
|
||||
"axs2.set_ylabel(r'$LA$ [%]')\n",
|
||||
"axs2.legend()\n",
|
||||
"\n",
|
||||
"axs2[1,0].set_title('Pressure turbine')\n",
|
||||
"axs2[1,0].plot(t_vec,pressure_conversion(p_boundary_tur,initial_pressure_unit, conversion_pressure_unit))\n",
|
||||
"axs2[1,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
|
||||
"axs2[1,0].set_ylabel(r'$p$ ['+conversion_pressure_unit+']')\n",
|
||||
"fig2,axs2 = plt.subplots(1,1)\n",
|
||||
"axs2.set_title('Pressure reservoir and turbine')\n",
|
||||
"axs2.plot(t_vec,pressure_conversion(p_boundary_res,pUnit_calc, pUnit_conv),label='Reservoir')\n",
|
||||
"axs2.plot(t_vec,pressure_conversion(p_boundary_tur,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",
|
||||
"axs2[1,1].set_title('Velocity turbine')\n",
|
||||
"axs2[1,1].plot(t_vec,v_boundary_tur)\n",
|
||||
"axs2[1,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
|
||||
"axs2[1,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n",
|
||||
"fig2,axs2 = plt.subplots(1,1)\n",
|
||||
"axs2.set_title('Fluxes')\n",
|
||||
"axs2.plot(t_vec,Q_boundary_res,label='Outflux')\n",
|
||||
"axs2.plot(t_vec,Q_in_vec,label='Influx')\n",
|
||||
"axs2.plot(t_vec,Q_boundary_tur,label='Flux Turbine')\n",
|
||||
"axs2.set_ylim(-2*Tur_Q_nenn,+2*Tur_Q_nenn)\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=True),c='red')\n",
|
||||
"axs2.plot(Pip_x_vec,pipe.get_highest_pressure_per_node(disp=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",
|
||||
"# axs2[0,1].legend()\n",
|
||||
"# axs2[1,0].legend()\n",
|
||||
"# axs2[1,1].legend()\n",
|
||||
"# # axs2[2,0].legend()\n",
|
||||
"# # axs2[2,1].legend()\n",
|
||||
"\n",
|
||||
"axs2[2,0].set_title('Level reservoir')\n",
|
||||
"axs2[2,0].plot(t_vec,level_vec)\n",
|
||||
"axs2[2,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
|
||||
"axs2[2,0].set_ylabel(r'$h$ [m]')\n",
|
||||
"\n",
|
||||
"axs2[2,1].set_title('LA')\n",
|
||||
"axs2[2,1].plot(t_vec,100*LA_soll_vec)\n",
|
||||
"axs2[2,1].plot(t_vec,100*LA_ist_vec)\n",
|
||||
"axs2[2,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
|
||||
"axs2[2,1].set_ylabel(r'$LA$ [%]')\n",
|
||||
"fig2.tight_layout()\n",
|
||||
"plt.show()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 10,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"[<matplotlib.lines.Line2D at 0x1ac81d70af0>]"
|
||||
]
|
||||
},
|
||||
"execution_count": 10,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"plt.semilogy(t_vec,error_vec)"
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
|
||||
Reference in New Issue
Block a user