# -*- coding: utf-8
"""Module of class ParabolicTrough.
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/parabolic_trough.py
SPDX-License-Identifier: MIT
"""
import numpy as np
from tespy.components.heat_exchangers.simple import SimpleHeatExchanger
from tespy.tools.data_containers import ComponentProperties as dc_cp
from tespy.tools.data_containers import GroupedComponentProperties as dc_gcp
from tespy.tools.data_containers import SimpleDataContainer as dc_simple
from tespy.tools.document_models import generate_latex_eq
[docs]
class ParabolicTrough(SimpleHeatExchanger):
r"""
The ParabolicTrough calculates heat output from irradiance.
**Mandatory Equations**
- :py:meth:`tespy.components.component.Component.fluid_func`
- :py:meth:`tespy.components.component.Component.mass_flow_func`
**Optional Equations**
- :py:meth:`tespy.components.component.Component.pr_func`
- :py:meth:`tespy.components.component.Component.zeta_func`
- :py:meth:`tespy.components.heat_exchangers.simple.SimpleHeatExchanger.energy_balance_func`
- :py:meth:`tespy.components.heat_exchangers.simple.SimpleHeatExchanger.darcy_group_func`
- :py:meth:`tespy.components.heat_exchangers.simple.SimpleHeatExchanger.hw_group_func`
- :py:meth:`tespy.components.heat_exchangers.parabolic_trough.ParabolicTrough.energy_group_func`
Inlets/Outlets
- in1
- out1
Image
.. image:: /api/_images/ParabolicTrough.svg
:alt: flowsheet of the parabolic trough
:align: center
:class: only-light
.. image:: /api/_images/ParabolicTrough_darkmode.svg
:alt: flowsheet of the parabolic trough
: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, :code:`"var"`
Heat transfer, :math:`Q/\text{W}`.
pr : float, dict, :code:`"var"`
Outlet to inlet pressure ratio, :math:`pr/1`.
zeta : float, dict, :code:`"var"`
Geometry independent friction coefficient,
:math:`\frac{\zeta}{D^4}/\frac{1}{\text{m}^4}`.
D : float, dict, :code:`"var"`
Diameter of the absorber tube, :math:`D/\text{m}`.
L : float, dict, :code:`"var"`
Length of the absorber tube, :math:`L/\text{m}`.
ks : float, dict, :code:`"var"`
Pipe's roughness, :math:`ks/\text{m}`.
darcy_group : str, dict
Parametergroup for pressure drop calculation based on pipes dimensions
using darcy weissbach equation.
ks_HW : float, dict, :code:`"var"`
Pipe's roughness, :math:`ks/\text{1}`.
hw_group : str, dict
Parametergroup for pressure drop calculation based on pipes dimensions
using hazen williams equation.
E : float, dict, :code:`"var"`
Direct irradiance to tilted collector,
:math:`E/\frac{\text{W}}{\text{m}^2}`.
aoi : float, dict, :code:`"var"`
Angle of incidience, :math:`aoi/^\circ`.
doc : float, dict, :code:`"var"`
Degree of cleanliness (1: full absorption, 0: no absorption),
:math:`X`.
eta_opt : float, dict, :code:`"var"`
(constant) optical losses due to surface reflection,
:math:`\eta_{opt}`.
c_1 : float, dict, :code:`"var"`
Linear thermal loss key figure,
:math:`c_1/\frac{\text{W}}{\text{K} \cdot \text{m}^2}`.
c_2 : float, dict, :code:`"var"`
Quadratic thermal loss key figure,
:math:`c_2/\frac{\text{W}}{\text{K}^2 \cdot \text{m}^2}`.
iam_1 : float, dict, :code:`"var"`
Linear incidence angle modifier,
:math:`iam_1/\frac{1}{^\circ}`.
iam_2 : float, dict, :code:`"var"`
Quadratic incidence angle modifier,
:math:`iam_2/\left(\frac{1}{^\circ}\right)^2`.
A : float, dict, :code:`"var"`
Collector aperture surface area :math:`A/\text{m}^2`.
Tamb : float, dict
Ambient temperature, provide parameter in network's temperature unit.
energy_group : str, dict
Parametergroup for energy balance of solarthermal collector.
Example
-------
A parabolic trough is installed using S800 as thermo-fluid.
First, the operation conditions from :cite:`Janotte2014` are reproduced.
Therefore, the direct normal irradiance :math:`\dot{E}_\mathrm{DNI}` is at
1000 :math:`\frac{\text{W}}{\text{m}^2}` at an angle of incidence
:math:`aoi` at 20 °. This means, the direct irradiance to the parabolic
trough :math:`E` is at
:math:`\dot{E}_{DNI} \cdot cos\left(20^\circ\right)`.
>>> from tespy.components import Sink, Source, ParabolicTrough
>>> from tespy.connections import Connection
>>> from tespy.networks import Network
>>> import numpy as np
>>> import shutil
>>> nw = Network()
>>> nw.set_attr(p_unit='bar', T_unit='C', h_unit='kJ / kg', iterinfo=False)
>>> so = Source('source')
>>> si = Sink('sink')
>>> pt = ParabolicTrough('parabolic trough collector')
>>> pt.component()
'parabolic trough'
>>> inc = Connection(so, 'out1', pt, 'in1')
>>> outg = Connection(pt, 'out1', si, 'in1')
>>> nw.add_conns(inc, outg)
The pressure ratio is at a constant level of 1. However, it is possible to
specify the pressure losses from the absorber tube length, roughness and
diameter, too. The aperture surface :math:`A` is specified to 1
:math:`\text{m}^2` for simplicity reasons.
>>> aoi = 20
>>> E = 1000 * np.cos(aoi / 180 * np.pi)
>>> pt.set_attr(pr=1, aoi=aoi, doc=1,
... Tamb=20, A=1, eta_opt=0.816, c_1=0.0622, c_2=0.00023, E=E,
... iam_1=-1.59e-3, iam_2=9.77e-5)
>>> inc.set_attr(fluid={'INCOMP::S800': 1}, T=220, p=2)
>>> outg.set_attr(T=260)
>>> nw.solve('design')
>>> round(pt.Q.val, 0)
736.0
For example, it is possible to calculate the aperture area of the parabolic
trough given the total heat production, outflow temperature and mass flow.
>>> pt.set_attr(A='var', Q=5e6, Tamb=25)
>>> inc.set_attr(T=None)
>>> outg.set_attr(T=350, m=20)
>>> nw.solve('design')
>>> round(inc.T.val, 0)
229.0
>>> round(pt.A.val, 0)
6862.0
Given this design, it is possible to calculate the outlet temperature as
well as the heat transfer at different operating points.
>>> aoi = 30
>>> E = 800 * np.cos(aoi / 180 * np.pi)
>>> pt.set_attr(A=pt.A.val, aoi=aoi, Q=None, E=E)
>>> inc.set_attr(T=150)
>>> outg.set_attr(T=None)
>>> nw.solve('design')
>>> round(outg.T.val, 0)
244.0
>>> round(pt.Q.val, 0)
3603027.0
"""
[docs]
@staticmethod
def component():
return 'parabolic trough'
[docs]
def get_parameters(self):
data = super().get_parameters()
for k in ["kA_group", "kA_char_group", "kA", "kA_char"]:
del data[k]
data.update({
'E': dc_cp(min_val=0), 'A': dc_cp(min_val=0),
'eta_opt': dc_cp(min_val=0, max_val=1),
'c_1': dc_cp(min_val=0), 'c_2': dc_cp(min_val=0),
'iam_1': dc_cp(), 'iam_2': dc_cp(),
'aoi': dc_cp(min_val=-90, max_val=90),
'doc': dc_cp(min_val=0, max_val=1),
'Tamb': dc_cp(),
'Q_loss': dc_cp(max_val=0, val=0),
'energy_group': dc_gcp(
elements=['E', 'eta_opt', 'aoi', 'doc', 'c_1', 'c_2', 'iam_1',
'iam_2', 'A', 'Tamb'], num_eq=1,
latex=self.energy_group_func_doc,
func=self.energy_group_func, deriv=self.energy_group_deriv
)
})
return data
[docs]
def energy_group_func(self):
r"""
Equation for solar collector energy balance.
Returns
-------
residual : float
Residual value of equation.
.. math::
\begin{split}
T_m = & \frac{T_{out} + T_{in}}{2}\\
iam = & 1 - iam_1 \cdot |aoi| - iam_2 \cdot aoi^2\\
0 = & \dot{m} \cdot \left( h_{out} - h_{in} \right)\\
& - A \cdot \left[E \cdot \eta_{opt} \cdot doc^{1.5} \cdot
iam \right. \\
& \left. - c_1 \cdot \left(T_m - T_{amb} \right) -
c_2 \cdot \left(T_m - T_{amb}\right)^2
\vphantom{ \eta_{opt} \cdot doc^{1.5}} \right]
\end{split}
Reference: :cite:`Janotte2014`.
"""
i = self.inl[0]
o = self.outl[0]
T_m = 0.5 * (i.calc_T() + o.calc_T())
iam = (
1 - self.iam_1.val * abs(self.aoi.val)
- self.iam_2.val * self.aoi.val ** 2
)
return (
i.m.val_SI * (o.h.val_SI - i.h.val_SI) - self.A.val * (
self.E.val * self.eta_opt.val * self.doc.val ** 1.5 * iam
- (T_m - self.Tamb.val_SI) * self.c_1.val
- self.c_2.val * (T_m - self.Tamb.val_SI) ** 2
)
)
[docs]
def energy_group_func_doc(self, label):
r"""
Equation for solar collector energy balance.
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} \cdot \left( h_\mathrm{out} - '
r'h_\mathrm{in} \right)\\' + '\n'
r'& - A \cdot \left[E \cdot \eta_\mathrm{opt} \cdot doc^{1.5}'
r'\cdot iam \right. \\' + '\n'
r'&\left. -c_1\cdot\left(T_\mathrm{m}-T_\mathrm{amb}\right) -'
r'c_2 \cdot \left(T_\mathrm{m} - T_\mathrm{amb}\right)^2'
r'\vphantom{\eta_\mathrm{opt}\cdot doc^{1.5}}\right]\\' + '\n'
r'T_\mathrm{m}=&\frac{T_\mathrm{out}+T_\mathrm{in}}{2}\\' +
'\n'
r'iam = & 1 - iam_1 \cdot |aoi| - iam_2 \cdot aoi^2\\' + '\n'
r'\end{split}'
)
return generate_latex_eq(self, latex, label)
[docs]
def energy_group_deriv(self, increment_filter, k):
r"""
Calculate partial derivatives of energy group function.
Parameters
----------
increment_filter : ndarray
Matrix for filtering non-changing variables.
k : int
Position of derivatives in Jacobian matrix (k-th equation).
"""
f = self.energy_group_func
i = self.inl[0]
o = self.outl[0]
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.p, increment_filter):
self.jacobian[k, i.p.J_col] = self.numeric_deriv(f, 'p', i)
if self.is_variable(i.h, increment_filter):
self.jacobian[k, i.h.J_col] = self.numeric_deriv(f, 'h', i)
if self.is_variable(o.p, increment_filter):
self.jacobian[k, o.p.J_col] = self.numeric_deriv(f, 'p', o)
if self.is_variable(o.h, increment_filter):
self.jacobian[k, o.h.J_col] = self.numeric_deriv(f, 'h', o)
# custom variables for the energy-group
for variable_name in self.energy_group.elements:
parameter = self.get_attr(variable_name)
if parameter == self.Tamb:
continue
if parameter.is_var:
self.jacobian[k, parameter.J_col] = (
self.numeric_deriv(f, variable_name, None)
)
[docs]
def calc_parameters(self):
r"""Postprocessing parameter calculation."""
i = self.inl[0]
o = self.outl[0]
self.Q.val = i.m.val_SI * (o.h.val_SI - i.h.val_SI)
self.pr.val = o.p.val_SI / i.p.val_SI
self.zeta.val = self.calc_zeta(i, o)
if self.energy_group.is_set:
self.Q_loss.val = - self.E.val * self.A.val + self.Q.val
self.Q_loss.is_result = True
else:
self.Q_loss.is_result = False