# -*- coding: utf-8
"""Module of class HeatExchanger.
This file is part of project TESPy (github.com/oemof/tespy). It's copyrighted
by the contributors recorded in the version control history of the file,
available from its original location
tespy/components/heat_exchangers/base.py
SPDX-License-Identifier: MIT
"""
import numpy as np
from tespy.components.component import Component
from tespy.tools.data_containers import ComponentCharacteristics as dc_cc
from tespy.tools.data_containers import ComponentProperties as dc_cp
from tespy.tools.data_containers import GroupedComponentCharacteristics as dc_gcc
from tespy.tools.document_models import generate_latex_eq
from tespy.tools.fluid_properties import h_mix_pT
from tespy.tools.fluid_properties import s_mix_ph
[docs]
class HeatExchanger(Component):
r"""
Class for counter current heat exchanger.
The component HeatExchanger is the parent class for the components:
- :py:class:`tespy.components.heat_exchangers.condenser.Condenser`
- :py:class:`tespy.components.heat_exchangers.desuperheater.Desuperheater`
**Mandatory Equations**
- :py:meth:`tespy.components.component.Component.fluid_func`
- :py:meth:`tespy.components.component.Component.mass_flow_func`
- :py:meth:`tespy.components.heat_exchangers.base.HeatExchanger.energy_balance_func`
**Optional Equations**
- :py:meth:`tespy.components.heat_exchangers.base.HeatExchanger.energy_balance_hot_func`
- :py:meth:`tespy.components.heat_exchangers.base.HeatExchanger.kA_func`
- :py:meth:`tespy.components.heat_exchangers.base.HeatExchanger.kA_char_func`
- :py:meth:`tespy.components.heat_exchangers.base.HeatExchanger.ttd_u_func`
- :py:meth:`tespy.components.heat_exchangers.base.HeatExchanger.ttd_l_func`
- hot side :py:meth:`tespy.components.component.Component.pr_func`
- cold side :py:meth:`tespy.components.component.Component.pr_func`
- hot side :py:meth:`tespy.components.component.Component.zeta_func`
- cold side :py:meth:`tespy.components.component.Component.zeta_func`
Inlets/Outlets
- in1, in2 (index 1: hot side, index 2: cold side)
- out1, out2 (index 1: hot side, index 2: cold side)
Image
.. image:: /api/_images/HeatExchanger.svg
:alt: flowsheet of the heat exchanger
:align: center
:class: only-light
.. image:: /api/_images/HeatExchanger_darkmode.svg
:alt: flowsheet of the heat exchanger
:align: center
:class: only-dark
Parameters
----------
label : str
The label of the component.
design : list
List containing design parameters (stated as String).
offdesign : list
List containing offdesign parameters (stated as String).
design_path : str
Path to the components design case.
local_offdesign : boolean
Treat this component in offdesign mode in a design calculation.
local_design : boolean
Treat this component in design mode in an offdesign calculation.
char_warnings : boolean
Ignore warnings on default characteristics usage for this component.
printout : boolean
Include this component in the network's results printout.
Q : float, dict
Heat transfer, :math:`Q/\text{W}`.
pr1 : float, dict, :code:`"var"`
Outlet to inlet pressure ratio at hot side, :math:`pr/1`.
pr2 : float, dict, :code:`"var"`
Outlet to inlet pressure ratio at cold side, :math:`pr/1`.
zeta1 : float, dict, :code:`"var"`
Geometry independent friction coefficient at hot side,
:math:`\frac{\zeta}{D^4}/\frac{1}{\text{m}^4}`.
zeta2 : float, dict, :code:`"var"`
Geometry independent friction coefficient at cold side,
:math:`\frac{\zeta}{D^4}/\frac{1}{\text{m}^4}`.
ttd_l : float, dict
Lower terminal temperature difference :math:`ttd_\mathrm{l}/\text{K}`.
ttd_u : float, dict
Upper terminal temperature difference :math:`ttd_\mathrm{u}/\text{K}`.
kA : float, dict
Area independent heat transfer coefficient,
:math:`kA/\frac{\text{W}}{\text{K}}`.
kA_char : dict
Area independent heat transfer coefficient characteristic.
kA_char1 : tespy.tools.characteristics.CharLine, dict
Characteristic line for hot side heat transfer coefficient.
kA_char2 : tespy.tools.characteristics.CharLine, dict
Characteristic line for cold side heat transfer coefficient.
Note
----
The HeatExchanger and subclasses (
:py:class:`tespy.components.heat_exchangers.condenser.Condenser`,
:py:class:`tespy.components.heat_exchangers.desuperheater.Desuperheater`)
are countercurrent heat exchangers. Equations (:code:`kA`, :code:`ttd_u`,
:code:`ttd_l`) do not work for directcurrent and crosscurrent or
combinations of different types.
Example
-------
A water cooling is installed to transfer heat from hot exhaust air. The
heat exchanger is designed for a terminal temperature difference of 5 K.
From this, it is possible to calculate the heat transfer coefficient and
predict water and air outlet temperature in offdesign operation.
>>> from tespy.components import Sink, Source, HeatExchanger
>>> from tespy.connections import Connection
>>> from tespy.networks import Network
>>> from tespy.tools import document_model
>>> import shutil
>>> nw = Network(T_unit='C', p_unit='bar', h_unit='kJ / kg', iterinfo=False)
>>> exhaust_hot = Source('Exhaust air outlet')
>>> exhaust_cold = Sink('Exhaust air inlet')
>>> cw_cold = Source('cooling water inlet')
>>> cw_hot = Sink('cooling water outlet')
>>> he = HeatExchanger('waste heat exchanger')
>>> he.component()
'heat exchanger'
>>> ex_he = Connection(exhaust_hot, 'out1', he, 'in1')
>>> he_ex = Connection(he, 'out1', exhaust_cold, 'in1')
>>> cw_he = Connection(cw_cold, 'out1', he, 'in2')
>>> he_cw = Connection(he, 'out2', cw_hot, 'in1')
>>> nw.add_conns(ex_he, he_ex, cw_he, he_cw)
The volumetric flow of the air is at 100 l/s. After designing the component
it is possible to predict the temperature at different flow rates or
different inlet temperatures of the exhaust air.
>>> he.set_attr(pr1=0.98, pr2=0.98, ttd_u=5,
... design=['pr1', 'pr2', 'ttd_u'], offdesign=['zeta1', 'zeta2', 'kA_char'])
>>> cw_he.set_attr(fluid={'water': 1}, T=10, p=3,
... offdesign=['m'])
>>> ex_he.set_attr(fluid={'air': 1}, v=0.1, T=35)
>>> he_ex.set_attr(T=17.5, p=1, design=['T'])
>>> nw.solve('design')
>>> nw.save('tmp')
>>> round(ex_he.T.val - he_cw.T.val, 0)
5.0
>>> ex_he.set_attr(v=0.075)
>>> nw.solve('offdesign', design_path='tmp')
>>> round(he_cw.T.val, 1)
27.5
>>> round(he_ex.T.val, 1)
14.4
>>> ex_he.set_attr(v=0.1, T=40)
>>> nw.solve('offdesign', design_path='tmp')
>>> document_model(nw)
>>> round(he_cw.T.val, 1)
33.9
>>> round(he_ex.T.val, 1)
18.8
>>> shutil.rmtree('./tmp', ignore_errors=True)
"""
[docs]
@staticmethod
def component():
return 'heat exchanger'
[docs]
def get_parameters(self):
return {
'Q': dc_cp(
max_val=0, func=self.energy_balance_hot_func, num_eq=1,
deriv=self.energy_balance_hot_deriv,
latex=self.energy_balance_hot_func_doc),
'kA': dc_cp(
min_val=0, num_eq=1, func=self.kA_func, latex=self.kA_func_doc,
deriv=self.kA_deriv),
'td_log': dc_cp(min_val=0, is_result=True),
'ttd_u': dc_cp(
min_val=0, num_eq=1, func=self.ttd_u_func,
deriv=self.ttd_u_deriv, latex=self.ttd_u_func_doc),
'ttd_l': dc_cp(
min_val=0, num_eq=1, func=self.ttd_l_func,
deriv=self.ttd_l_deriv, latex=self.ttd_l_func_doc),
'pr1': dc_cp(
min_val=1e-4, max_val=1, num_eq=1, deriv=self.pr_deriv,
latex=self.pr_func_doc,
func=self.pr_func, func_params={'pr': 'pr1'}),
'pr2': dc_cp(
min_val=1e-4, max_val=1, num_eq=1, latex=self.pr_func_doc,
deriv=self.pr_deriv, func=self.pr_func,
func_params={'pr': 'pr2', 'inconn': 1, 'outconn': 1}),
'zeta1': dc_cp(
min_val=0, max_val=1e15, num_eq=1, latex=self.zeta_func_doc,
deriv=self.zeta_deriv, func=self.zeta_func,
func_params={'zeta': 'zeta1'}),
'zeta2': dc_cp(
min_val=0, max_val=1e15, num_eq=1, latex=self.zeta_func_doc,
deriv=self.zeta_deriv, func=self.zeta_func,
func_params={'zeta': 'zeta2', 'inconn': 1, 'outconn': 1}),
'kA_char': dc_gcc(
elements=['kA_char1', 'kA_char2'],
num_eq=1, latex=self.kA_char_func_doc, func=self.kA_char_func,
deriv=self.kA_char_deriv),
'kA_char1': dc_cc(param='m'),
'kA_char2': dc_cc(
param='m', char_params={
'type': 'rel', 'inconn': 1, 'outconn': 1})
}
[docs]
def get_mandatory_constraints(self):
return {
'energy_balance_constraints': {
'func': self.energy_balance_func,
'deriv': self.energy_balance_deriv,
'constant_deriv': False, 'latex': self.energy_balance_func_doc,
'num_eq': 1}
}
[docs]
@staticmethod
def inlets():
return ['in1', 'in2']
[docs]
@staticmethod
def outlets():
return ['out1', 'out2']
[docs]
def energy_balance_func(self):
r"""
Equation for heat exchanger energy balance.
Returns
-------
residual : float
Residual value of equation.
.. math::
0 = \dot{m}_{in,1} \cdot \left(h_{out,1} - h_{in,1} \right) +
\dot{m}_{in,2} \cdot \left(h_{out,2} - h_{in,2} \right)
"""
return (
self.inl[0].m.val_SI
* (self.outl[0].h.val_SI - self.inl[0].h.val_SI)
+ self.inl[1].m.val_SI
* (self.outl[1].h.val_SI - self.inl[1].h.val_SI)
)
[docs]
def energy_balance_func_doc(self, label):
r"""
Equation for heat exchanger energy balance.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (
r'0 = \dot{m}_\mathrm{in,1} \cdot \left(h_\mathrm{out,1} -'
r' h_\mathrm{in,1} \right) +\dot{m}_\mathrm{in,2} \cdot '
r'\left(h_\mathrm{out,2} - h_\mathrm{in,2} \right)')
return generate_latex_eq(self, latex, label)
[docs]
def energy_balance_deriv(self, increment_filter, k):
r"""
Partial derivatives of energy balance function.
Parameters
----------
increment_filter : ndarray
Matrix for filtering non-changing variables.
k : int
Position of derivatives in Jacobian matrix (k-th equation).
"""
for _c_num, i in enumerate(self.inl):
o = self.outl[_c_num]
if self.is_variable(i.m, increment_filter):
self.jacobian[k, i.m.J_col] = o.h.val_SI - i.h.val_SI
if self.is_variable(i.h, increment_filter):
self.jacobian[k, i.h.J_col] = -i.m.val_SI
if self.is_variable(o.h, increment_filter):
self.jacobian[k, o.h.J_col] = i.m.val_SI
[docs]
def energy_balance_hot_func(self):
r"""
Equation for hot side heat exchanger energy balance.
Returns
-------
residual : float
Residual value of equation.
.. math::
0 =\dot{m}_{in,1} \cdot \left(h_{out,1}-h_{in,1}\right)-\dot{Q}
"""
return self.inl[0].m.val_SI * (
self.outl[0].h.val_SI - self.inl[0].h.val_SI
) - self.Q.val
[docs]
def energy_balance_hot_func_doc(self, label):
r"""
Equation for hot side heat exchanger energy balance.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (
r'0 =\dot{m}_{in,1} \cdot \left(h_{out,1}-'
r'h_{in,1}\right)-\dot{Q}')
return generate_latex_eq(self, latex, label)
[docs]
def energy_balance_hot_deriv(self, increment_filter, k):
r"""
Partial derivatives for hot side heat exchanger energy balance.
Parameters
----------
increment_filter : ndarray
Matrix for filtering non-changing variables.
k : int
Position of derivatives in Jacobian matrix (k-th equation).
"""
i = self.inl[0]
o = self.outl[0]
if self.is_variable(i.m):
self.jacobian[k, i.m.J_col] = o.h.val_SI - i.h.val_SI
if self.is_variable(i.h):
self.jacobian[k, i.h.J_col] = -i.m.val_SI
if self.is_variable(o.h):
self.jacobian[k, o.h.J_col] = i.m.val_SI
[docs]
def calculate_td_log(self):
i1 = self.inl[0]
i2 = self.inl[1]
o1 = self.outl[0]
o2 = self.outl[1]
# temperature value manipulation for convergence stability
T_i1 = i1.calc_T()
T_i2 = i2.calc_T()
T_o1 = o1.calc_T()
T_o2 = o2.calc_T()
if T_i1 <= T_o2:
T_i1 = T_o2 + 0.01
if T_i1 <= T_o2:
T_o2 = T_i1 - 0.01
if T_i1 <= T_o2:
T_o1 = T_i2 + 0.02
if T_o1 <= T_i2:
T_i2 = T_o1 - 0.02
ttd_u = T_i1 - T_o2
ttd_l = T_o1 - T_i2
if ttd_u == ttd_l:
td_log = ttd_l
else:
td_log = (ttd_l - ttd_u) / np.log((ttd_l) / (ttd_u))
return td_log
[docs]
def kA_func(self):
r"""
Calculate heat transfer from heat transfer coefficient.
Returns
-------
residual : float
Residual value of equation.
.. math::
0 = \dot{m}_{in,1} \cdot \left( h_{out,1} - h_{in,1}\right) +
kA \cdot \frac{T_{out,1} -
T_{in,2} - T_{in,1} + T_{out,2}}
{\ln{\frac{T_{out,1} - T_{in,2}}{T_{in,1} - T_{out,2}}}}
"""
return (
self.inl[0].m.val_SI * (
self.outl[0].h.val_SI - self.inl[0].h.val_SI
) + self.kA.val * self.calculate_td_log()
)
[docs]
def kA_func_doc(self, label):
r"""
Calculate heat transfer from heat transfer coefficient.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (
r'0 = \dot{m}_\mathrm{in,1} \cdot \left( h_\mathrm{out,1} - '
r'h_\mathrm{in,1}\right)+ kA \cdot \frac{T_\mathrm{out,1} - '
r'T_\mathrm{in,2} - T_\mathrm{in,1} + T_\mathrm{out,2}}'
r'{\ln{\frac{T_\mathrm{out,1} - T_\mathrm{in,2}}'
r'{T_\mathrm{in,1} - T_\mathrm{out,2}}}}'
)
return generate_latex_eq(self, latex, label)
[docs]
def kA_deriv(self, increment_filter, k):
r"""
Partial derivatives of heat transfer coefficient function.
Parameters
----------
increment_filter : ndarray
Matrix for filtering non-changing variables.
k : int
Position of derivatives in Jacobian matrix (k-th equation).
"""
f = self.kA_func
i = self.inl[0]
o = self.outl[0]
if self.is_variable(i.m):
self.jacobian[k, i.m.J_col] = o.h.val_SI - i.h.val_SI
for c in self.inl + self.outl:
if self.is_variable(c.p):
self.jacobian[k, c.p.J_col] = self.numeric_deriv(f, 'p', c)
if self.is_variable(c.h):
self.jacobian[k, c.h.J_col] = self.numeric_deriv(f, 'h', c)
[docs]
def kA_char_func(self):
r"""
Calculate heat transfer from heat transfer coefficient characteristic.
Returns
-------
residual : float
Residual value of equation.
.. math::
0 = \dot{m}_{in,1} \cdot \left( h_{out,1} - h_{in,1}\right) +
kA_{design} \cdot f_{kA} \cdot \frac{T_{out,1} -
T_{in,2} - T_{in,1} + T_{out,2}}
{\ln{\frac{T_{out,1} - T_{in,2}}{T_{in,1} - T_{out,2}}}}
f_{kA} = \frac{2}{\frac{1}{f_1\left( expr_1\right)} +
\frac{1}{f_2\left( expr_2\right)}}
Note
----
For standard functions f\ :subscript:`1` \ and f\ :subscript:`2` \ see
module :py:mod:`tespy.data`.
"""
p1 = self.kA_char1.param
p2 = self.kA_char2.param
f1 = self.get_char_expr(p1, **self.kA_char1.char_params)
f2 = self.get_char_expr(p2, **self.kA_char2.char_params)
fkA1 = self.kA_char1.char_func.evaluate(f1)
fkA2 = self.kA_char2.char_func.evaluate(f2)
fkA = 2 / (1 / fkA1 + 1 / fkA2)
td_log = self.calculate_td_log()
return (
self.inl[0].m.val_SI * (
self.outl[0].h.val_SI - self.inl[0].h.val_SI
) + self.kA.design * fkA * td_log
)
[docs]
def kA_char_func_doc(self, label):
r"""
Calculate heat transfer from heat transfer coefficient characteristic.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (
r'\begin{split}' + '\n'
r'0 = & \dot{m}_\mathrm{in,1} \cdot \left( h_\mathrm{out,1} - '
r'h_\mathrm{in,1}\right)\\' + '\n'
r'&+kA_\mathrm{design} \cdot '
r'f_\mathrm{kA} \cdot \frac{T_\mathrm{out,1} - T_\mathrm{in,2}'
r' - T_\mathrm{in,1} + T_\mathrm{out,2}}{\ln{'
r'\frac{T_\mathrm{out,1} - T_\mathrm{in,2}}{T_\mathrm{in,1} -'
r' T_\mathrm{out,2}}}}\\' + '\n'
r'f_\mathrm{kA}=&\frac{2}{\frac{1}{f\left(X_1\right)}+'
r'\frac{1}{f\left(X_2\right)}}\\' + '\n'
r'\end{split}'
)
return generate_latex_eq(self, latex, label)
[docs]
def kA_char_deriv(self, increment_filter, k):
r"""
Partial derivatives of heat transfer coefficient characteristic.
Parameters
----------
increment_filter : ndarray
Matrix for filtering non-changing variables.
k : int
Position of derivatives in Jacobian matrix (k-th equation).
"""
f = self.kA_char_func
for i in self.inl:
if self.is_variable(i.m):
self.jacobian[k, i.m.J_col] = self.numeric_deriv(f, 'm', i)
for c in self.inl + self.outl:
if self.is_variable(c.p):
self.jacobian[k, c.p.J_col] = self.numeric_deriv(f, 'p', c)
if self.is_variable(c.h):
self.jacobian[k, c.h.J_col] = self.numeric_deriv(f, 'h', c)
[docs]
def ttd_u_func(self):
r"""
Equation for upper terminal temperature difference.
Returns
-------
residual : float
Residual value of equation.
.. math::
0 = ttd_{u} - T_{in,1} + T_{out,2}
"""
i = self.inl[0]
o = self.outl[1]
T_i1 = i.calc_T()
T_o2 = o.calc_T()
return self.ttd_u.val - T_i1 + T_o2
[docs]
def ttd_u_func_doc(self, label):
r"""
Equation for upper terminal temperature difference.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = r'0 = ttd_\mathrm{u} - T_\mathrm{in,1} + T_\mathrm{out,2}'
return generate_latex_eq(self, latex, label)
[docs]
def ttd_u_deriv(self, increment_filter, k):
"""
Calculate partial derivates of upper terminal temperature function.
Parameters
----------
increment_filter : ndarray
Matrix for filtering non-changing variables.
k : int
Position of derivatives in Jacobian matrix (k-th equation).
"""
f = self.ttd_u_func
for c in [self.inl[0], self.outl[1]]:
if self.is_variable(c.p, increment_filter):
self.jacobian[k, c.p.J_col] = self.numeric_deriv(f, 'p', c)
if self.is_variable(c.h, increment_filter):
self.jacobian[k, c.h.J_col] = self.numeric_deriv(f, 'h', c)
[docs]
def ttd_l_func(self):
r"""
Equation for upper terminal temperature difference.
Returns
-------
residual : float
Residual value of equation.
.. math::
0 = ttd_{l} - T_{out,1} + T_{in,2}
"""
i = self.inl[1]
o = self.outl[0]
T_i2 = i.calc_T()
T_o1 = o.calc_T()
return self.ttd_l.val - T_o1 + T_i2
[docs]
def ttd_l_func_doc(self, label):
r"""
Equation for upper terminal temperature difference.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = r'0 = ttd_\mathrm{l} - T_\mathrm{out,1} + T_\mathrm{in,2}'
return generate_latex_eq(self, latex, label)
[docs]
def ttd_l_deriv(self, increment_filter, k):
"""
Calculate partial derivates of upper terminal temperature function.
Parameters
----------
increment_filter : ndarray
Matrix for filtering non-changing variables.
k : int
Position of derivatives in Jacobian matrix (k-th equation).
"""
f = self.ttd_l_func
for c in [self.inl[1], self.outl[0]]:
if self.is_variable(c.p, increment_filter):
self.jacobian[k, c.p.J_col] = self.numeric_deriv(f, 'p', c)
if self.is_variable(c.h, increment_filter):
self.jacobian[k, c.h.J_col] = self.numeric_deriv(f, 'h', c)
[docs]
def bus_func(self, bus):
r"""
Calculate the value of the bus function.
Parameters
----------
bus : tespy.connections.bus.Bus
TESPy bus object.
Returns
-------
val : float
Value of energy transfer :math:`\dot{E}`. This value is passed to
:py:meth:`tespy.components.component.Component.calc_bus_value`
for value manipulation according to the specified characteristic
line of the bus.
.. math::
\dot{E} = \dot{m}_{in,1} \cdot \left(
h_{out,1} - h_{in,1} \right)
"""
return self.inl[0].m.val_SI * (
self.outl[0].h.val_SI - self.inl[0].h.val_SI
)
[docs]
def bus_func_doc(self, bus):
r"""
Return LaTeX string of the bus function.
Parameters
----------
bus : tespy.connections.bus.Bus
TESPy bus object.
Returns
-------
latex : str
LaTeX string of bus function.
"""
return (
r'\dot{m}_\mathrm{in,1} \cdot \left(h_\mathrm{out,1} - '
r'h_\mathrm{in,1} \right)')
[docs]
def bus_deriv(self, bus):
r"""
Calculate partial derivatives of the bus function.
Parameters
----------
bus : tespy.connections.bus.Bus
TESPy bus object.
Returns
-------
deriv : ndarray
Matrix of partial derivatives.
"""
f = self.calc_bus_value
if self.inl[0].m.is_var:
if self.inl[0].m.J_col not in bus.jacobian:
bus.jacobian[self.inl[0].m.J_col] = 0
bus.jacobian[self.inl[0].m.J_col] -= self.numeric_deriv(f, 'm', self.inl[0], bus=bus)
if self.inl[0].h.is_var:
if self.inl[0].h.J_col not in bus.jacobian:
bus.jacobian[self.inl[0].h.J_col] = 0
bus.jacobian[self.inl[0].h.J_col] -= self.numeric_deriv(f, 'h', self.inl[0], bus=bus)
if self.outl[0].h.is_var:
if self.outl[0].h.J_col not in bus.jacobian:
bus.jacobian[self.outl[0].h.J_col] = 0
bus.jacobian[self.outl[0].h.J_col] -= self.numeric_deriv(f, 'h', self.outl[0], bus=bus)
[docs]
def initialise_source(self, c, key):
r"""
Return a starting value for pressure and enthalpy at outlet.
Parameters
----------
c : tespy.connections.connection.Connection
Connection to perform initialisation on.
key : str
Fluid property to retrieve.
Returns
-------
val : float
Starting value for pressure/enthalpy in SI units.
.. math::
val = \begin{cases}
4 \cdot 10^5 & \text{key = 'p'}\\
h\left(p, 200 \text{K} \right) & \text{key = 'h' at outlet 1}\\
h\left(p, 250 \text{K} \right) & \text{key = 'h' at outlet 2}
\end{cases}
"""
if key == 'p':
return 50e5
elif key == 'h':
if c.source_id == 'out1':
T = 200 + 273.15
else:
T = 250 + 273.15
return h_mix_pT(c.p.val_SI, T, c.fluid_data, c.mixing_rule)
[docs]
def initialise_target(self, c, key):
r"""
Return a starting value for pressure and enthalpy at inlet.
Parameters
----------
c : tespy.connections.connection.Connection
Connection to perform initialisation on.
key : str
Fluid property to retrieve.
Returns
-------
val : float
Starting value for pressure/enthalpy in SI units.
.. math::
val = \begin{cases}
4 \cdot 10^5 & \text{key = 'p'}\\
h\left(p, 300 \text{K} \right) & \text{key = 'h' at inlet 1}\\
h\left(p, 220 \text{K} \right) & \text{key = 'h' at outlet 2}
\end{cases}
"""
if key == 'p':
return 50e5
elif key == 'h':
if c.target_id == 'in1':
T = 300 + 273.15
else:
T = 220 + 273.15
return h_mix_pT(c.p.val_SI, T, c.fluid_data, c.mixing_rule)
[docs]
def calc_parameters(self):
r"""Postprocessing parameter calculation."""
# component parameters
self.Q.val = self.inl[0].m.val_SI * (
self.outl[0].h.val_SI - self.inl[0].h.val_SI)
self.ttd_u.val = self.inl[0].T.val_SI - self.outl[1].T.val_SI
self.ttd_l.val = self.outl[0].T.val_SI - self.inl[1].T.val_SI
# pr and zeta
for i in range(2):
self.get_attr('pr' + str(i + 1)).val = (
self.outl[i].p.val_SI / self.inl[i].p.val_SI)
self.get_attr('zeta' + str(i + 1)).val = self.calc_zeta(
self.inl[i], self.outl[i]
)
# kA and logarithmic temperature difference
if self.ttd_u.val < 0 or self.ttd_l.val < 0:
self.td_log.val = np.nan
elif self.ttd_l.val == self.ttd_u.val:
self.td_log.val = self.ttd_l.val
else:
self.td_log.val = (
(self.ttd_l.val - self.ttd_u.val)
/ np.log(self.ttd_l.val / self.ttd_u.val)
)
self.kA.val = -self.Q.val / self.td_log.val
[docs]
def entropy_balance(self):
r"""
Calculate entropy balance of a heat exchanger.
The allocation of the entropy streams due to heat exchanged and due to
irreversibility is performed by solving for T on both sides of the heat
exchanger:
.. math::
h_\mathrm{out} - h_\mathrm{in} = \int_\mathrm{in}^\mathrm{out} v
\cdot dp - \int_\mathrm{in}^\mathrm{out} T \cdot ds
As solving :math:`\int_\mathrm{in}^\mathrm{out} v \cdot dp` for non
isobaric processes would require perfect process knowledge (the path)
on how specific volume and pressure change throught the component, the
heat transfer is splitted into three separate virtual processes for
both sides:
- in->in*: decrease pressure to
:math:`p_\mathrm{in*}=p_\mathrm{in}\cdot\sqrt{\frac{p_\mathrm{out}}{p_\mathrm{in}}}`
without changing enthalpy.
- in*->out* transfer heat without changing pressure.
:math:`h_\mathrm{out*}-h_\mathrm{in*}=h_\mathrm{out}-h_\mathrm{in}`
- out*->out decrease pressure to outlet pressure :math:`p_\mathrm{out}`
without changing enthalpy.
Note
----
The entropy balance makes the follwing parameter available:
.. math::
\text{S\_Q1}=\dot{m} \cdot \left(s_\mathrm{out*,1}-s_\mathrm{in*,1}
\right)\\
\text{S\_Q2}=\dot{m} \cdot \left(s_\mathrm{out*,2}-s_\mathrm{in*,2}
\right)\\
\text{S\_Qirr}=\text{S\_Q2} - \text{S\_Q1}\\
\text{S\_irr1}=\dot{m} \cdot \left(s_\mathrm{out,1}-s_\mathrm{in,1}
\right) - \text{S\_Q1}\\
\text{S\_irr2}=\dot{m} \cdot \left(s_\mathrm{out,2}-s_\mathrm{in,2}
\right) - \text{S\_Q2}\\
\text{S\_irr}=\sum \dot{S}_\mathrm{irr}\\
\text{T\_mQ1}=\frac{\dot{Q}}{\text{S\_Q1}}\\
\text{T\_mQ2}=\frac{\dot{Q}}{\text{S\_Q2}}
"""
self.S_irr = 0
for i in range(2):
inl = self.inl[i]
out = self.outl[i]
p_star = inl.p.val_SI * (
self.get_attr('pr' + str(i + 1)).val) ** 0.5
s_i_star = s_mix_ph(
p_star, inl.h.val_SI, inl.fluid_data, inl.mixing_rule,
T0=inl.T.val_SI
)
s_o_star = s_mix_ph(
p_star, out.h.val_SI, out.fluid_data, out.mixing_rule,
T0=out.T.val_SI
)
setattr(
self, 'S_Q' + str(i + 1),
inl.m.val_SI * (s_o_star - s_i_star)
)
S_Q = self.get_attr('S_Q' + str(i + 1))
setattr(
self, 'S_irr' + str(i + 1),
inl.m.val_SI * (out.s.val_SI - inl.s.val_SI) - S_Q
)
setattr(
self, 'T_mQ' + str(i + 1),
inl.m.val_SI * (out.h.val_SI - inl.h.val_SI) / S_Q
)
self.S_irr += self.get_attr('S_irr' + str(i + 1))
self.S_irr += self.S_Q1 + self.S_Q2
[docs]
def exergy_balance(self, T0):
r"""
Calculate exergy balance of a heat exchanger.
Parameters
----------
T0 : float
Ambient temperature T0 / K.
Note
----
.. math::
\dot{E}_\mathrm{P} =
\begin{cases}
\dot{E}_\mathrm{out,2}^\mathrm{T} -
\dot{E}_\mathrm{in,2}^\mathrm{T}
& T_\mathrm{in,1}, T_\mathrm{in,2}, T_\mathrm{out,1},
T_\mathrm{out,2} > T_0\\
\dot{E}_\mathrm{out,1}^\mathrm{T} -
\dot{E}_\mathrm{in,1}^\mathrm{T}
& T_0 \geq T_\mathrm{in,1}, T_\mathrm{in,2}, T_\mathrm{out,1},
T_\mathrm{out,2}\\
\dot{E}_\mathrm{out,1}^\mathrm{T} +
\dot{E}_\mathrm{out,2}^\mathrm{T}
& T_\mathrm{in,1}, T_\mathrm{out,2} > T_0 \geq
T_\mathrm{in,2}, T_\mathrm{out,1}\\
\dot{E}_\mathrm{out,1}^\mathrm{T}
& T_\mathrm{in,1} > T_0 \geq
T_\mathrm{in,2}, T_\mathrm{out,1}, T_\mathrm{out,2}\\
\text{not defined (nan)}
& T_\mathrm{in,1}, T_\mathrm{out,1} > T_0 \geq
T_\mathrm{in,2}, T_\mathrm{out,2}\\
\dot{E}_\mathrm{out,2}^\mathrm{T}
& T_\mathrm{in,1}, T_\mathrm{out,1},
T_\mathrm{out,2} \geq T_0 > T_\mathrm{in,2}\\
\end{cases}
\dot{E}_\mathrm{F} =
\begin{cases}
\dot{E}_\mathrm{in,1}^\mathrm{PH} -
\dot{E}_\mathrm{out,1}^\mathrm{PH} +
\dot{E}_\mathrm{in,2}^\mathrm{M} -
\dot{E}_\mathrm{out,2}^\mathrm{M}
& T_\mathrm{in,1}, T_\mathrm{in,2}, T_\mathrm{out,1},
T_\mathrm{out,2} > T_0\\
\dot{E}_\mathrm{in,2}^\mathrm{PH} -
\dot{E}_\mathrm{out,2}^\mathrm{PH} +
\dot{E}_\mathrm{in,1}^\mathrm{M} -
\dot{E}_\mathrm{out,1}^\mathrm{M}
& T_0 \geq T_\mathrm{in,1}, T_\mathrm{in,2}, T_\mathrm{out,1},
T_\mathrm{out,2}\\
\dot{E}_\mathrm{in,1}^\mathrm{PH} +
\dot{E}_\mathrm{in,2}^\mathrm{PH} -
\dot{E}_\mathrm{out,1}^\mathrm{M} -
\dot{E}_\mathrm{out,2}^\mathrm{M}
& T_\mathrm{in,1}, T_\mathrm{out,2} > T_0 \geq
T_\mathrm{in,2}, T_\mathrm{out,1}\\
\dot{E}_\mathrm{in,1}^\mathrm{PH} +
\dot{E}_\mathrm{in,2}^\mathrm{PH} -
\dot{E}_\mathrm{out,2}^\mathrm{PH} -
\dot{E}_\mathrm{out,1}^\mathrm{M}
& T_\mathrm{in,1} > T_0 \geq
T_\mathrm{in,2}, T_\mathrm{out,1}, T_\mathrm{out,2}\\
\dot{E}_\mathrm{in,1}^\mathrm{PH} -
\dot{E}_\mathrm{out,1}^\mathrm{PH} +
\dot{E}_\mathrm{in,2}^\mathrm{PH} -
\dot{E}_\mathrm{out,2}^\mathrm{PH}
& T_\mathrm{in,1}, T_\mathrm{out,1} > T_0 \geq
T_\mathrm{in,2}, T_\mathrm{out,2}\\
\dot{E}_\mathrm{in,1}^\mathrm{PH} -
\dot{E}_\mathrm{out,1}^\mathrm{PH} +
\dot{E}_\mathrm{in,2}^\mathrm{PH} -
\dot{E}_\mathrm{out,2}^\mathrm{M}
& T_\mathrm{in,1}, T_\mathrm{out,1},
T_\mathrm{out,2} \geq T_0 > T_\mathrm{in,2}\\
\end{cases}
"""
if all([c.T.val_SI > T0 for c in self.inl + self.outl]):
self.E_P = self.outl[1].Ex_therm - self.inl[1].Ex_therm
self.E_F = self.inl[0].Ex_physical - self.outl[0].Ex_physical + (
self.inl[1].Ex_mech - self.outl[1].Ex_mech)
elif all([c.T.val_SI <= T0 for c in self.inl + self.outl]):
self.E_P = self.outl[0].Ex_therm - self.inl[0].Ex_therm
self.E_F = self.inl[1].Ex_physical - self.outl[1].Ex_physical + (
self.inl[0].Ex_mech - self.outl[0].Ex_mech)
elif (self.inl[0].T.val_SI > T0 and self.outl[1].T.val_SI > T0 and
self.outl[0].T.val_SI <= T0 and self.inl[1].T.val_SI <= T0):
self.E_P = self.outl[0].Ex_therm + self.outl[1].Ex_therm
self.E_F = self.inl[0].Ex_physical + self.inl[1].Ex_physical - (
self.outl[0].Ex_mech + self.outl[1].Ex_mech)
elif (self.inl[0].T.val_SI > T0 and self.inl[1].T.val_SI <= T0 and
self.outl[0].T.val_SI <= T0 and self.outl[1].T.val_SI <= T0):
self.E_P = self.outl[0].Ex_therm
self.E_F = self.inl[0].Ex_physical + self.inl[1].Ex_physical - (
self.outl[1].Ex_physical + self.outl[0].Ex_mech)
elif (self.inl[0].T.val_SI > T0 and self.outl[0].T.val_SI > T0 and
self.inl[1].T.val_SI <= T0 and self.outl[1].T.val_SI <= T0):
self.E_P = np.nan
self.E_F = self.inl[0].Ex_physical - self.outl[0].Ex_physical + (
self.inl[1].Ex_physical - self.outl[1].Ex_physical)
else:
self.E_P = self.outl[1].Ex_therm
self.E_F = self.inl[0].Ex_physical - self.outl[0].Ex_physical + (
self.inl[1].Ex_physical - self.outl[1].Ex_mech)
self.E_bus = {"chemical": np.nan, "physical": np.nan, "massless": np.nan}
if np.isnan(self.E_P):
self.E_D = self.E_F
else:
self.E_D = self.E_F - self.E_P
self.epsilon = self._calc_epsilon()
[docs]
def get_plotting_data(self):
"""Generate a dictionary containing FluProDia plotting information.
Returns
-------
data : dict
A nested dictionary containing the keywords required by the
:code:`calc_individual_isoline` method of the
:code:`FluidPropertyDiagram` class. First level keys are the
connection index ('in1' -> 'out1', therefore :code:`1` etc.).
"""
return {
i + 1: {
'isoline_property': 'p',
'isoline_value': self.inl[i].p.val,
'isoline_value_end': self.outl[i].p.val,
'starting_point_property': 'v',
'starting_point_value': self.inl[i].vol.val,
'ending_point_property': 'v',
'ending_point_value': self.outl[i].vol.val
} for i in range(2)}