Source code for tespy.components.heat_exchangers.parabolic_trough

# -*- 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 HeatExchangerSimple
from tespy.tools.data_containers import ComponentProperties as dc_cp
from tespy.tools.data_containers import DataContainerSimple as dc_simple
from tespy.tools.data_containers import GroupedComponentProperties as dc_gcp
from tespy.tools.document_models import generate_latex_eq
from tespy.tools.fluid_properties import T_mix_ph


[docs]class ParabolicTrough(HeatExchangerSimple): 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.HeatExchangerSimple.energy_balance_func` - :py:meth:`tespy.components.heat_exchangers.simple.HeatExchangerSimple.hydro_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"` Tube's roughness, :math:`ks/\text{m}` for darcy friction, :math:`ks/\text{1}` for hazen-williams equation. hydro_group : str, dict Parametergroup for pressure drop calculation based on pipes dimensions. Choose 'HW' for hazen-williams equation, else darcy friction factor is used. 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 >>> fluids = ['INCOMP::S800'] >>> nw = Network(fluids=fluids) >>> 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={'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_variables(self): return { 'Q': dc_cp( deriv=self.energy_balance_deriv, latex=self.energy_balance_func_doc, num_eq=1, func=self.energy_balance_func), 'pr': 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': 'pr'}), 'zeta': dc_cp( min_val=0, max_val=1e15, num_eq=1, deriv=self.zeta_deriv, func=self.zeta_func, latex=self.zeta_func_doc, func_params={'zeta': 'zeta'}), 'D': dc_cp(min_val=1e-2, max_val=2, d=1e-4), 'L': dc_cp(min_val=1e-1, d=1e-3), 'ks': dc_cp(val=1e-4, min_val=1e-7, max_val=1e-3, d=1e-8), '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), 'dissipative': dc_simple(val=True), 'hydro_group': dc_gcp( elements=['L', 'ks', 'D'], num_eq=1, latex=self.hydro_group_func_doc, func=self.hydro_group_func, deriv=self.hydro_group_deriv), '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) }
[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].get_flow() o = self.outl[0].get_flow() T_m = (T_mix_ph(i, T0=self.inl[0].T.val_SI) + T_mix_ph(o, T0=self.outl[0].T.val_SI)) / 2 iam = ( 1 - self.iam_1.val * abs(self.aoi.val) - self.iam_2.val * self.aoi.val ** 2) return ( i[0] * (o[2] - i[2]) - 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 self.jacobian[k, 0, 0] = ( self.outl[0].h.val_SI - self.inl[0].h.val_SI) if not increment_filter[0, 1]: self.jacobian[k, 0, 1] = self.numeric_deriv(f, 'p', 0) if not increment_filter[0, 2]: self.jacobian[k, 0, 2] = self.numeric_deriv(f, 'h', 0) if not increment_filter[1, 1]: self.jacobian[k, 1, 1] = self.numeric_deriv(f, 'p', 1) if not increment_filter[1, 2]: self.jacobian[k, 1, 2] = self.numeric_deriv(f, 'h', 1) # custom variables for the energy-group for var in self.energy_group.elements: var = self.get_attr(var) if var == self.Tamb: continue if var.is_var: self.jacobian[k, 2 + var.var_pos, 0] = ( self.numeric_deriv(f, self.vars[var], 2))
[docs] def calc_parameters(self): r"""Postprocessing parameter calculation.""" i = self.inl[0].get_flow() o = self.outl[0].get_flow() self.Q.val = i[0] * (o[2] - i[2]) self.pr.val = o[1] / i[1] self.zeta.val = ((i[1] - o[1]) * np.pi ** 2 / ( 4 * i[0] ** 2 * (self.inl[0].vol.val_SI + self.outl[0].vol.val_SI) )) 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