#!/usr/bin/env python # -*- coding: utf-8 -*- """ *********************************************************************************** tutorial5.py DAE Tools: pyDAE module, www.daetools.com Copyright (C) Dragan Nikolic *********************************************************************************** DAE Tools is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License version 3 as published by the Free Software Foundation. DAE Tools is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with the DAE Tools software; if not, see <http://www.gnu.org/licenses/>. ************************************************************************************ """ __doc__ = """ This tutorial introduces the following concepts: - Discontinuous equations (non-symmetrical state transition networks: daeSTN statements) In this example we use the same heat transfer problem as in the tutorial 4. Again we have a piece of copper which is at one side exposed to the source of heat and at the other to the surroundings. The process starts at the temperature of 283K. The metal is allowed to warm up, and then its temperature is kept in the interval (320K - 340K) for 350 seconds. This is performed by switching the heater on when the temperature drops to 320K and by switching the heater off when the temperature reaches 340K. After 350s the heat source is permanently switched off and the metal is allowed to slowly cool down to the ambient temperature. This can be modelled using the following non-symmetrical state transition network: .. code-block:: none STN Regulator case Heating: Qin = 1500 W on condition T > 340K switch to Regulator.Cooling on condition t > 350s switch to Regulator.HeaterOff case Cooling: Qin = 0 W on condition T < 320K switch to Regulator.Heating on condition t > 350s switch to Regulator.HeaterOff case HeaterOff: Qin = 0 W The temperature plot: .. image:: _static/tutorial5-results.png :width: 500px """ import sys from time import localtime, strftime from daetools.pyDAE import * # Standard variable types are defined in variable_types.py from pyUnits import m, kg, s, K, Pa, mol, J, W class modTutorial(daeModel): def __init__(self, Name, Parent = None, Description = ""): daeModel.__init__(self, Name, Parent, Description) self.m = daeParameter("m", kg, self, "Mass of the copper plate") self.cp = daeParameter("c_p", J/(kg*K), self, "Specific heat capacity of the plate") self.alpha = daeParameter("α", W/((m**2)*K), self, "Heat transfer coefficient") self.A = daeParameter("A", m**2, self, "Area of the plate") self.Tsurr = daeParameter("T_surr", K, self, "Temperature of the surroundings") self.Qin = daeVariable("Q_in", power_t, self, "Power of the heater") self.T = daeVariable("T", temperature_t, self, "Temperature of the plate") def DeclareEquations(self): daeModel.DeclareEquations(self) eq = self.CreateEquation("HeatBalance", "Integral heat balance equation") eq.Residual = self.m() * self.cp() * dt(self.T()) - self.Qin() + self.alpha() * self.A() * (self.T() - self.Tsurr()) """ Non-symmetrical STNs in DAE Tools can be created by using STN/STATE/END_STN statements. Again, states MUST contain the SAME NUMBER OF EQUATIONS. First start with the call to STN("STN_Name") function from daeModel class. If you need to change active states in operating procedure in function Run() store the stn reference (here in the stnRegulator object). After that call, define your states by calling the function STATE("State1") and write equations that will be active if this state (called 'State1') is active. Models and states can contain OnConditionActions and OnEventActions. OnConditionActions are trigerred when a specified logical condition is satisfied. OnEventActions are trigerred when a specified EventPort receives an event (more info in tutorial13.py). There are different types of actions that can be executed by a logical condition. In this example, we want to change the active states subject to given conditions and ON_CONDITION(logical_condition, switchToStates = [list_of_actions]) function will be used. Again, there is an optional argument eventTolerance, as explained in tutorial 4. Repeat this procedure for all states in the state transition network. Finally call the function END_STN() to finalize the state transition network. """ self.stnRegulator = self.STN("Regulator") self.STATE("Heating") eq = self.CreateEquation("Q_in", "The heater is on") eq.Residual = self.Qin() - Constant(1500 * W) """ ON_CONDITION() function Arguments: - Condition that triggers the actions - 'switchToStates' is a list of python tuples (STN-name-relative-to-model, State-name) that will be set active when the condition is satisified - 'triggerEvents' is a list of python tuples (outlet-event-port, expression), where the first part is the event-port object and the second a value to be sent when the event is trigerred - 'setVariableValues' is a list of python tuples (variable, expression); if the variable is differential it will be reinitialized (using ReInitialize() function), otherwise it will be reassigned (using ReAssign() function) - 'userDefinedActions' is a list of user defined daeAction-derived objects (see tutorial13.py for more information) """ # Here the built-in Time() function is used to get the current time (time elapsed) in the simulation self.ON_CONDITION(self.T() > Constant(340*K), switchToStates = [ ('Regulator', 'Cooling') ], setVariableValues = [], triggerEvents = [], userDefinedActions = [] ) self.ON_CONDITION(Time() > Constant(350*s), switchToStates = [ ('Regulator', 'HeaterOff') ], setVariableValues = [], triggerEvents = [], userDefinedActions = [] ) self.STATE("Cooling") eq = self.CreateEquation("Q_in", "The heater is off") eq.Residual = self.Qin() self.ON_CONDITION(self.T() < Constant(320*K), switchToStates = [ ('Regulator', 'Heating') ], setVariableValues = [], triggerEvents = [], userDefinedActions = [] ) self.ON_CONDITION(Time() > Constant(350*s), switchToStates = [ ('Regulator', 'HeaterOff') ], setVariableValues = [], triggerEvents = [], userDefinedActions = [] ) self.STATE("HeaterOff") eq = self.CreateEquation("Q_in", "The heater is off") eq.Residual = self.Qin() self.END_STN() class simTutorial(daeSimulation): def __init__(self): daeSimulation.__init__(self) self.m = modTutorial("tutorial5") self.m.Description = __doc__ def SetUpParametersAndDomains(self): self.m.cp.SetValue(385 * J/(kg*K)) self.m.m.SetValue(1 * kg) self.m.alpha.SetValue(200 * W/((m**2)*K)) self.m.A.SetValue(0.1 * m**2) self.m.Tsurr.SetValue(283 * K) def SetUpVariables(self): # Set the state active at the beginning (the default is the first declared state; here 'Heating') self.m.stnRegulator.ActiveState = "Heating" self.m.T.SetInitialCondition(283 * K) def run(**kwargs): simulation = simTutorial() return daeActivity.simulate(simulation, reportingInterval = 2, timeHorizon = 500, **kwargs) if __name__ == "__main__": guiRun = False if (len(sys.argv) > 1 and sys.argv[1] == 'console') else True run(guiRun = guiRun)