HeatExchanger (0D) ================== .. index:: pair: idaes.models.unit_models.heat_exchanger;HeatExchanger .. currentmodule:: idaes.models.unit_models.heat_exchanger The HeatExchanger model can be imported from :code:`idaes.models.unit_models`, while additional rules and utility functions can be imported from ``idaes.models.unit_models.heat_exchanger``. Example ------- The example below demonstrates how to initialize the HeatExchanger model, and override the default temperature difference calculation. This example also demonstrates how to assign custom names to the hot and cold sides of the heat exchanger. .. testcode:: import pyomo.environ as pe # Pyomo environment from idaes.core import FlowsheetBlock, StateBlock from idaes.models.unit_models import HeatExchanger from idaes.models.unit_models.heat_exchanger import HX0DInitializer from idaes.models.unit_models.heat_exchanger import delta_temperature_amtd_callback from idaes.models.properties import iapws95 # Create an empty flowsheet and steam property parameter block. model = pe.ConcreteModel() model.fs = FlowsheetBlock(dynamic=False) model.fs.properties = iapws95.Iapws95ParameterBlock() # Add a Heater model to the flowsheet. model.fs.heat_exchanger = HeatExchanger( delta_temperature_callback=delta_temperature_amtd_callback, hot_side_name="shell", cold_side_name="tube", shell={"property_package": model.fs.properties}, tube={"property_package": model.fs.properties} ) model.fs.heat_exchanger.area.fix(1000) model.fs.heat_exchanger.overall_heat_transfer_coefficient[0].fix(100) model.fs.heat_exchanger.shell_inlet.flow_mol.fix(100) model.fs.heat_exchanger.shell_inlet.pressure.fix(101325) model.fs.heat_exchanger.shell_inlet.enth_mol.fix(4000) model.fs.heat_exchanger.tube_inlet.flow_mol.fix(100) model.fs.heat_exchanger.tube_inlet.pressure.fix(101325) model.fs.heat_exchanger.tube_inlet.enth_mol.fix(3000) # Initialize the model initializer = HX0DInitializer() initializer.initialize(model.fs.heat_exchanger) Degrees of Freedom ------------------ Aside from the inlet conditions, a heat exchanger model usually has two degrees of freedom, which can be fixed for it to be fully specified. Things that are frequently fixed are two of: * heat transfer area, * heat transfer coefficient, or * temperature approach. The user may also provide constraints to calculate the heat transfer coefficient. .. note:: For model initialization, the in-built routine currently only supports defining two of area, heat transfer coefficient and heat duty as fixed variables. Fixing of temperature differences or driving forces is not currently supported. Also note that it is assumed that if a time-indexed variable (i.e. heat duty) is fixed that it will be fixed at all points in time during initialization. Users wishing to solve models with alternative specifications should first initialize the model using one of the supported options, or write a custom initialization routine for their specification. Model Structure --------------- The ``HeatExchanger`` model contains two ``ControlVolume0DBlock`` blocks which are named ``hot_side`` and ``cold_side``. These names are configurable using the ``hot_side_name`` and ``cold_side_name`` configuration arguments, in which case aliases are assigned to the control volumes and associated Ports using the names provided (note that ``hot_side`` and ``cold_side`` will always work). The sign convention is that duty is positive for heat flowing from the hot side to the cold side. Aside from the sign convention there is no requirement that the hot side be hotter than the cold side, however some formulations for the average temperature driving force may require that the hot side be hotter than the cold side. The control volumes are configured the same as the ``ControlVolume0DBlock`` in the :ref:`Heater model `. The ``HeatExchanger`` model contains additional constraints that calculate the amount of heat transferred from the hot side to the cold side. The ``HeatExchanger`` has two inlet ports and two outlet ports. By default these are ``hot_side_inlet``, ``cold_side_inlet``, ``hot_side_outlet``, and ``cold_side_outlet``. If the user supplies different hot and cold side names the inlet and outlets are named accordingly. Variables --------- =========================== ================== =========== ============================================================================= Variable Symbol Index Sets Doc =========================== ================== =========== ============================================================================= heat_duty :math:`Q` t Heat transferred from hot side to the cold side area :math:`A` None Heat transfer area heat_transfer_coefficient :math:`U` t Heat transfer coefficient delta_temperature :math:`\Delta T` t Temperature difference, defaults to LMTD =========================== ================== =========== ============================================================================= Note: ``delta_temperature`` may be either a variable or expression depending on the callback used. If the specified cold side is hotter than the specified hot side this value will be negative. Constraints ----------- The default constants can be overridden by providing :ref:`alternative rules ` for the heat transfer equation, temperature difference, and heat transfer coefficient. The section describes the default constraints. Heat transfer from shell to tube: .. math:: Q = UA\Delta T Temperature difference is an expression: .. math:: \Delta T = \frac{\Delta T_1 - \Delta T_2}{\log_e\left(\frac{\Delta T_1}{\Delta T_2}\right)} The heat transfer coefficient is a variable with no associated constraints by default. Initialization -------------- .. autoclass:: HX0DInitializer :members: initialization_routine Class Documentation ------------------- .. Note:: The ``hot_side`` and ``cold_side`` can also be supplied using the name of the hot and cold sides as in :ref:`the example `. .. autoclass:: HeatExchanger :members: .. autoclass:: HeatExchangerData :members: Callbacks --------- A selection of functions for constructing the ``delta_temperature`` variable or expression are provided in the ``idaes.models.unit_models.heat_exchanger`` module. The user may also provide their own function. These callbacks should all take one argument (the HeatExchanger block). With the block argument, the function can add any additional variables, constraints, and expressions needed. The only requirement is that either a variable or expression called ``delta_temperature`` must be added to the block. Defined Callbacks for the ``delta_temperature_callback`` Option ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ These callbacks provide expressions for the temperature difference used in the heat transfer equations. There is a choice of three forms for the LMTD calculation. Depending on the expected approach temperatures, one form may be more favorable. The first two forms do not require one side or the other to be the hot side, while the third form requires the hot side to be the hot side to avoid an evaluation error in the log function. .. autofunction:: delta_temperature_lmtd_callback .. autofunction:: delta_temperature_lmtd2_callback .. autofunction:: delta_temperature_lmtd3_callback .. autofunction:: delta_temperature_amtd_callback .. autofunction:: delta_temperature_underwood_callback .. autofunction:: delta_temperature_lmtd_smooth_callback