CrossFlowHeatExchanger1D ======================== .. index:: pair: idaes.models_extra.power_generation.unit_models.cross_flow_heat_exchanger_1D;CrossFlowHeatExchanger1D .. module:: idaes.models_extra.power_generation.unit_models.cross_flow_heat_exchanger_1D This model is for a cross flow heat exchanger between two gases. The gas in the shell has a straight path, while the gas in the tubes snakes back and forth across the shell's path. Note that the ``finite_elements`` option in the shell and tube control volume configs should be set to an integer factor of ``number_passes`` in order for the discretization equations to make sense as a cross-flow heat exchanger. Example ------- .. code-block:: python import pyomo.environ as pyo from idaes.core import FlowsheetBlock import idaes.core.util.scaling as iscale from idaes.models.unit_models import HeatExchangerFlowPattern from idaes.models.properties.modular_properties import GenericParameterBlock from idaes.models_extra.power_generation.properties.natural_gas_PR import ( get_prop, EosType, ) from idaes.models_extra.power_generation.unit_models import CrossFlowHeatExchanger1D from idaes.core.util.model_statistics import degrees_of_freedom optarg = { "constr_viol_tol": 1e-8, "nlp_scaling_method": "user-scaling", "linear_solver": "ma57", "OF_ma57_automatic_scaling": "yes", "max_iter": 350, "tol": 1e-8, "halt_on_ampl_error": "no", } m = pyo.ConcreteModel() m.fs = pyo.FlowsheetBlock(dynamic=False) m.fs.properties = GenericParameterBlock( **get_prop(["H2", "H2O", "Ar", "N2"], {"Vap"}, eos=EosType.IDEAL), doc="H2O + H2 gas property parameters", ) m.fs.heat_exchanger = CrossFlowHeatExchanger1D( has_holdup=True, dynamic=False, cold_side={ "property_package": m.fs.h2_side_prop_params, "has_holdup": False, "dynamic": False, "has_pressure_change": pressure_drop, "transformation_method": "dae.finite_difference", "transformation_scheme": "FORWARD", }, hot_side={ "property_package": m.fs.h2_side_prop_params, "has_holdup": False, "dynamic": False, "has_pressure_change": pressure_drop, "transformation_method": "dae.finite_difference", "transformation_scheme": "BACKWARD", }, shell_is_hot=True, flow_type=HeatExchangerFlowPattern.countercurrent, finite_elements=12, tube_arrangement="staggered", ) hx = m.fs.heat_exchanger hx.hot_side_inlet.flow_mol.fix(2619.7) hx.hot_side_inlet.temperature.fix(971.6) hx.hot_side_inlet.pressure.fix(1.2e5) hx.hot_side_inlet.mole_frac_comp[0, "H2"].fix(0.79715) hx.hot_side_inlet.mole_frac_comp[0, "H2O"].fix(0.20177) hx.hot_side_inlet.mole_frac_comp[0, "Ar"].fix(0.00086358) hx.hot_side_inlet.mole_frac_comp[0, "N2"].fix(0.00021589) hx.cold_side_inlet.flow_mol.fix(2619.7) hx.cold_side_inlet.temperature.fix(446.21) hx.cold_side_inlet.pressure.fix(1.2e5) hx.cold_side_inlet.mole_frac_comp[0, "H2"].fix(0.36203) hx.cold_side_inlet.mole_frac_comp[0, "H2O"].fix(0.63689) hx.cold_side_inlet.mole_frac_comp[0, "Ar"].fix(0.00086358) hx.cold_side_inlet.mole_frac_comp[0, "N2"].fix(0.00021589) hx.di_tube.fix(0.0525018) hx.thickness_tube.fix(0.0039116) hx.length_tube_seg.fix(4.3) hx.number_passes.fix(12) hx.number_columns_per_pass.fix(50) hx.number_rows_per_pass.fix(25) hx.pitch_x.fix(0.1) hx.pitch_y.fix(0.1) hx.therm_cond_wall = 43.0 hx.rfouling_tube = 0.0001 hx.rfouling_shell = 0.0001 hx.fcorrection_htc_tube.fix(1) hx.fcorrection_htc_shell.fix(1) hx.cp_wall.value = 502.4 pp = m.fs.properties pp.set_default_scaling("enth_mol_phase", 1e-3) pp.set_default_scaling("pressure", 1e-5) pp.set_default_scaling("temperature", 1e-2) pp.set_default_scaling("flow_mol", 1e-3) _mf_scale = { "H2": 1, "H2O": 1, "N2": 10, "Ar": 10, } for comp, s in _mf_scale.items(): pp.set_default_scaling("mole_frac_comp", s, index=comp) pp.set_default_scaling("mole_frac_phase_comp", s, index=("Vap", comp)) pp.set_default_scaling("flow_mol_phase_comp", s * 1e-3, index=("Vap", comp)) shell = hx.hot_side tube = hx.cold_side iscale.set_scaling_factor(shell.area, 1e-1) iscale.set_scaling_factor(shell.heat, 1e-6) iscale.set_scaling_factor(tube.area, 1) iscale.set_scaling_factor(tube.heat, 1e-6) iscale.set_scaling_factor(shell._enthalpy_flow, 1e-8) # pylint: disable=W0212 iscale.set_scaling_factor(tube._enthalpy_flow, 1e-8) # pylint: disable=W0212 iscale.set_scaling_factor(shell.enthalpy_flow_dx, 1e-7) iscale.set_scaling_factor(tube.enthalpy_flow_dx, 1e-7) iscale.set_scaling_factor(hx.heat_holdup, 1e-8) iscale.calculate_scaling_factors(m) initializer = m.fs.heat_exchanger.default_initializer( solver="ipopt", solver_options=optarg ) initializer.initialize(m.fs.heat_exchanger) Heat Exchanger Geometry ----------------------- =========================== =========== =================================================================================================== Variable Index Sets Doc =========================== =========== =================================================================================================== ``number_columns_per_pass`` None Number of columns of tube per pass ``number_rows_per_pass`` None Number of rows of tube per pass ``number_passes`` None Number of tube banks of ``nrow_tube * ncol_inlet`` tubes ``pitch_x`` None Distance between tubes parallel to shell flow, measured from center-of-tube to center-of-tube ``pitch_y`` None Distance between tubes perpendicular to shell flow, measured from center-of-tube to center-of-tube ``length_tube_seg`` None Length of tube segment perpendicular to flow in each pass ``area_flow_shell`` None Reference to flow area on shell control volume ``length_flow_shell`` None Reference to flow length on shell control volume ``area_flow_shell_min`` None Minimum flow area on shell side ``di_tube`` None Inner diameter of tubes ``thickness_tube`` None Thickness of tube wall. ``area_flow_tube`` None Reference to flow area on tube control volume ``length_flow_tube`` None Reference to flow length on tube control volume =========================== =========== =================================================================================================== ============================ =========== =========================================================================== Expression Index Sets Doc ============================ =========== =========================================================================== ``nrow_tube`` None Total number of rows of tube ``do_tube`` None Outer diameter of tube (equal to ``di_tube+2*thickness_tube``) ``pitch_x_to_do`` None Ratio of ``pitch_x`` to ``do_tube`` ``pitch_y_to_do`` None Ratio of ``pitch_y`` to ``do_tube`` ``area_wall_seg`` None Total cross-sectional area of tube per pass ``total_heat_transfer_area`` None Total heat transfer area, as measured on outer surface of tubes ============================ =========== =========================================================================== =========================== =========== ================================================================================================= Constraint Index Sets Doc =========================== =========== ================================================================================================= ``length_flow_shell_eqn`` None Constrains shell flow length from control volume to equal value implied by geometry ``area_flow_shell_eqn`` None Constrains shell flow cross-sectional area from control volume to equal value implied by geometry ``area_flow_shell_min_eqn`` None Constraints ``area_flow_shell_min`` to equal value determined by geometry ``length_flow_tube_eqn`` None Constrains tube flow length from control volume to equal value implied by geometry ``area_flow_tube_eqn`` None Constrains tube flow cross-sectional area from control volume to equal value implied by geometry =========================== =========== ================================================================================================= Performance Equations ----------------------- ================================== ============ ================================================================================= Variable Index Sets Doc ================================== ============ ================================================================================= ``fcorrection_htc_shell`` time, length Correction factor for shell convective heat transfer ``conv_heat_transfer_coeff_shell`` time, length Shell-side convective heat transfer coefficient ``temp_wall_shell`` time, length Shell-side wall temperature of tube ``temp_wall_center`` time, length Temperature at center of tube wall ``v_shell`` time, length Flow velocity on shell side through minimum area ``N_Re_shell`` time, length Reynolds number on shell side ``N_Nu_shell`` time, length Nusselt number on shell side ``heat_transfer_coeff_tube`` time, length Tube-side heat transfer coefficient ``temp_wall_tube`` time, length Tube-side wall temperature of tube ``v_tube`` time, length Flow velocity of gas in tube ``N_Re_tube`` time, length Reynolds number in tube ``N_Nu_tube`` time, length Nusselt number on tube side ================================== ============ ================================================================================= =========================== =========== ================================================================================= Parameter Index Sets Doc =========================== =========== ================================================================================= ``therm_cond_wall`` None Thermal conductivity of tube wall ``density_wall`` None Mass density of tube wall metal ``cp_wall`` None Tube wall heat capacity (mass basis) ``rfouling_shell`` None Fouling resistance on shell side ``f_arrangement`` None Adjustment factor depending on ``tube_arrangement`` in config =========================== =========== ================================================================================= ====================================== ============ ================================================================================= Constraint Index Sets Doc ====================================== ============ ================================================================================= ``v_shell_eqn`` time, length Calculates velocity of flow through shell using ``area_flow_shell_min`` ``N_Re_shell_eqn`` time, length Calculates the shell-side Reynolds number ``conv_heat_transfer_coeff_shell_eqn`` time, length Calculates the shell-side convective heat transfer coefficient ``v_tube_eqn`` time, length Calculates gas velocity in tube ``N_Re_tube_eqn`` time, length Calculates the tube-side Reynolds number ``heat_transfer_coeff_tube_eqn`` time, length Calculates the tube-side heat transfer coefficient ``N_Nu_shell_eqn`` time, length Calculate the shell-side Nusselt number ``N_Nu_tube_eqn`` time, length Calculate the tube-side Nusselt number ``heat_tube_eqn`` time, length Calculates heat transfer per unit length ``heat_shell_eqn`` time, length Calculates heat transfer per unit length ``temp_wall_tube_eqn`` time, length Calculate the wall temperature of the inner tube ``temp_wall_shell_eqn`` time, length Calculate the wall temperature of the outer tube ``temp_wall_center_eqn`` time, length Overall energy balance on tube metal ====================================== ============ ================================================================================= ====================================== ============ =================================================================================== Expression Index Sets Doc ====================================== ============ =================================================================================== ``total_heat_transfer_coeff_shell`` time Returns ``conv_heat_transfer_coeff_shell``. Could be extended to include radiation. ``total_heat_duty`` time Created only if not ``dynamic``. Gives total heat transferred over entire exchanger ``log_mean_delta_temperature`` time Created only if not ``dynamic``. Gives the log mean temperature difference (LMTD). ``overall_heat_transfer_coefficient`` time Created only if not ``dynamic``. Calculated from total heat transfer, area, and LMTD. ====================================== ============ =================================================================================== Pressure Change Equations ------------------------- =========================== ============ ================================================================================= Parameter Index Sets Doc =========================== ============ ================================================================================= ``fcorrection_dp_shell`` None Correction factor for shell side pressure drop ``kloss_uturn`` None Loss coefficient of a tube u-turn ``fcorrection_dp_tube`` None Correction factor for tube side pressure drop =========================== ============ ================================================================================= =========================== ============ ================================================================================= Variable Index Sets Doc =========================== ============ ================================================================================= ``fcorrection_dp_shell`` None Correction factor for shell side pressure drop ``friction_factor_shell`` time, length Friction factor on shell side ``friction_factor_tube`` time, length Friction factor on tube side ``deltaP_tube_friction`` time, length Change of pressure in tube due to friction ``deltaP_tube_uturn`` time, length Change of pressure in tube due to U turns =========================== ============ ================================================================================= ================================== ============ ================================================================================== Constraint Index Sets Doc ================================== ============ ================================================================================== ``friction_factor_shell_eqn`` time, length Calculates the shell-side friction factor ``deltaP_shell_eqn`` time, length Sets ``deltaP_shell`` based on the friction factor and shell properties ``friction_factor_tube_eqn`` time, length Calculates the tube-side friction factor ``deltaP_tube_friction_eqn`` time, length Sets ``deltaP_tube_friction`` based on friction factor ``deltaP_tube_uturn_eqn`` time, length Sets ``deltaP_tube_uturn`` based on ``kloss_uturn`` ``deltaP_tube_eqn`` time, length Sets ``deltaP_tube`` by summing ``deltaP_tube_friction`` and ``deltaP_tube_uturn`` ================================== ============ ================================================================================== Holdup Equations ---------------- Created when ``has_holdup=True`` in the config. =========================== ============ ================================================================================= Variable Index Sets Doc =========================== ============ ================================================================================= ``heat_holdup`` time, length Energy holdup per unit length of shell flow path =========================== ============ ================================================================================= =========================== ============ ================================================================================= Constraint Index Sets Doc =========================== ============ ================================================================================= ``heat_holdup_eqn`` time, length Defines heat holdup in terms of geometry and physical properties =========================== ============ ================================================================================= Dynamic Equations ----------------- Created when ``dynamic=True`` in the config. =========================== ============ ================================================================================= Derivative Variable Index Sets Doc =========================== ============ ================================================================================= ``heat_accumulation`` time, length Energy accumulation in tube wall per unit length of shell flow path per unit time =========================== ============ ================================================================================= CrossFlowHeatExchanger1D Class ------------------------------ .. autoclass:: CrossFlowHeatExchanger1D :members: CrossFlowHeatExchanger1DData Class ---------------------------------- .. autoclass:: CrossFlowHeatExchanger1DData :members: CrossFlowHeatExchanger1DInitializer Class ----------------------------------------- .. autoclass:: CrossFlowHeatExchanger1DInitializer :members: