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fix for numerical runaway of rounding errors

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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
2022-08-03 15:56:56 +02:00
parent 84631ee4cc
commit ba696444bb
13 changed files with 1257 additions and 1198 deletions
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207
Ausgleichsbecken/Ausgleichsbecken_test_steady_state.ipynb
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@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
"execution_count": 7,
"execution_count": 29,
"metadata": {},
"outputs": [],
"source": [
@@ -21,151 +21,142 @@
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"L = 1000.\n",
"n = 10000 # number of pipe segments in discretization\n",
"c = 400. \n",
"dx = L/n # length of each pipe segment\n",
"dt = dx/c \n",
"\n",
"# # define constants\n",
"# initial_level = 10.1 # m\n",
"# initial_influx = 0.8 # m³/s\n",
"# conversion_pressure_unit = 'mWS'\n",
"\n",
"# area_base = 75. # m²\n",
"# area_outflux = (0.9/2)**2*np.pi # m²\n",
"# critical_level_low = 0. # m\n",
"# critical_level_high = 10. # m\n",
"# simulation_timestep = dt # s\n",
"\n",
"# # for while loop\n",
"# total_min_level = 0.01 # m\n",
"# total_max_time = 100 # s\n",
"\n",
"# nt = int(total_max_time//simulation_timestep)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"execution_count": 30,
"metadata": {},
"outputs": [],
"source": [
"# define constants\n",
"initial_level = 10.1 # m\n",
"initial_influx = 1. # m³/s\n",
"# initial_outflux = 1. # m³/s\n",
"# initial_pipeline_pressure = 10.\n",
"# initial_pressure_unit = 'mWS'\n",
"conversion_pressure_unit = 'mWS'\n",
"\n",
"area_base = 75. # m²\n",
"area_outflux = 2. # m²\n",
"critical_level_low = 0. # m\n",
"critical_level_high = 10. # m\n",
"simulation_timestep = dt # s\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 while loop\n",
"total_min_level = 0.01 # m\n",
"total_max_time = 1000 # s\n",
"\n",
"nt = int(total_max_time//simulation_timestep)"
" # for Turbine\n",
"Tur_Q_nenn = 0.85 # [m³/s] nominal flux of turbine \n",
"Tur_p_nenn = pressure_conversion(10.6,'bar',pUnit_calc) # [Pa] nominal pressure of turbine \n",
"Tur_closingTime = 90. # [s] closing time of turbine\n",
"\n",
"\n",
" # for PI controller\n",
"Con_targetLevel = 8. # [m]\n",
"Con_K_p = 0.1 # [-] proportional constant of PI controller\n",
"Con_T_i = 10. # [s] timespan in which a steady state error is corrected by the intergal term\n",
"Con_deadbandRange = 0.05 # [m] Deadband range around targetLevel for which the controller does NOT intervene\n",
"\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",
"\n",
" # for reservoir\n",
"Res_area_base = 5. # [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 = 600. # [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": 10,
"execution_count": 31,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib qt\n",
"# 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_initial_pressure(pressure_conversion(initial_pipeline_pressure,input_unit = initial_pressure_unit, target_unit = 'Pa'),conversion_pressure_unit)\n",
"# V.pressure = converted_pressure\n",
"V.set_steady_state(initial_influx,initial_level,conversion_pressure_unit)\n",
"# Upstream reservoir\n",
"reservoir = Ausgleichsbecken_class(Res_area_base,Res_area_out,Res_dt,Res_level_crit_lo,Res_level_crit_hi,rho)\n",
"reservoir.set_steady_state(flux_init,level_init)\n",
"\n",
"time_vec = np.arange(0,nt+1,1)*simulation_timestep\n",
"outflux_vec = np.zeros_like(time_vec)\n",
"outflux_vec[0] = V.get_current_outflux()\n",
"level_vec = np.zeros_like(time_vec)\n",
"level_vec[0] = V.get_current_level()\n",
"pressure_vec = np.zeros_like(time_vec)\n",
"pressure_vec[0] = V.get_current_pressure()\n",
"\n",
"# pressure_vec = np.full_like(time_vec,converted_pressure)*((np.sin(time_vec)+1)*np.exp(-time_vec/50))\n",
" \n",
"i_max = -1\n",
"reservoir.get_info(full=True)\n",
"\n",
"# initialize vectors\n",
"outflux_vec = np.zeros_like(t_vec)\n",
"outflux_vec[0] = reservoir.get_current_outflux()\n",
"level_vec = np.zeros_like(t_vec)\n",
"level_vec[0] = reservoir.get_current_level()\n",
"volume_vec = np.zeros_like(t_vec)\n",
"volume_vec[0] = reservoir.get_current_volume()\n",
"pressure_vec = np.zeros_like(t_vec)\n",
"pressure_vec[0] = reservoir.get_current_pressure()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# time loop\n",
"for i in range(1,nt+1):\n",
" V.set_pressure(pressure_vec[i-1])\n",
" V.set_outflux(outflux_vec[i-1])\n",
" V.timestep_reservoir_evolution()\n",
" outflux_vec[i] = V.get_current_outflux()\n",
" level_vec[i] = V.get_current_level()\n",
" pressure_vec[i] = V.get_current_pressure()\n",
" if V.level < total_min_level:\n",
" i_max = i\n",
" break\n",
"\n"
" # if i == 500:\n",
" # reservoir.set_influx(0.)\n",
" reservoir.set_pressure(pressure_vec[i-1],display_warning=False)\n",
" reservoir.set_outflux(outflux_vec[i-1],display_warning=False)\n",
" for it_res in range(Res_nt):\n",
" reservoir.timestep_reservoir_evolution() \n",
" \n",
" outflux_vec[i] = reservoir.get_current_outflux()\n",
" level_vec[i] = reservoir.get_current_level()\n",
" pressure_vec[i] = reservoir.get_current_pressure()\n",
"\n",
" reservoir.get_info()"
]
},
{
"cell_type": "code",
"execution_count": 11,
"execution_count": 32,
"metadata": {},
"outputs": [],
"source": [
"\n",
"%matplotlib qt5\n",
"fig1, (ax1, ax2, ax3) = plt.subplots(3, 1)\n",
"fig1.set_figheight(10)\n",
"fig1.suptitle('Ausgleichsbecken')\n",
"\n",
"ax1.plot(time_vec[:i_max],level_vec[:i_max], label='Water level')\n",
"ax1.set_ylabel(r'$h$ ['+V.level_unit+']')\n",
"ax1.set_xlabel(r'$t$ ['+V.time_unit+']')\n",
"ax1.plot(t_vec,level_vec, label='Water level')\n",
"ax1.set_ylabel(r'$h$ ['+reservoir.level_unit+']')\n",
"ax1.set_xlabel(r'$t$ ['+reservoir.time_unit+']')\n",
"ax1.legend()\n",
"\n",
"ax2.plot(time_vec[:i_max],outflux_vec[:i_max], label='Outflux')\n",
"ax2.set_ylabel(r'$Q_{out}$ ['+V.flux_unit+']')\n",
"ax2.set_xlabel(r'$t$ ['+V.time_unit+']')\n",
"ax2.plot(t_vec,outflux_vec, label='Outflux')\n",
"ax2.set_ylabel(r'$Q_{out}$ ['+reservoir.flux_unit+']')\n",
"ax2.set_xlabel(r'$t$ ['+reservoir.time_unit+']')\n",
"ax2.legend()\n",
"\n",
"ax3.plot(time_vec[:i_max],pressure_conversion(pressure_vec[:i_max],'Pa',conversion_pressure_unit), label='Pipeline pressure at reservoir')\n",
"ax3.set_ylabel(r'$p_{pipeline}$ ['+conversion_pressure_unit+']')\n",
"ax3.set_xlabel(r'$t$ ['+V.time_unit+']')\n",
"ax3.plot(t_vec,pressure_conversion(pressure_vec,'Pa',pUnit_conv), label='Pipeline pressure at reservoir')\n",
"ax3.set_ylabel(r'$p_{pipeline}$ ['+pUnit_conv+']')\n",
"ax3.set_xlabel(r'$t$ ['+reservoir.time_unit+']')\n",
"ax3.legend()\n",
"\n",
"\n",
"fig1.tight_layout() "
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"10.1"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"V.get_current_level()"
]
}
],
"metadata": {