# -*- coding: utf-8
"""Module of class Turbine.
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/turbomachinery/turbine.py
SPDX-License-Identifier: MIT
"""
import numpy as np
from tespy.components.turbomachinery.base import Turbomachine
from tespy.tools import logger
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 SimpleDataContainer as dc_simple
from tespy.tools.document_models import generate_latex_eq
from tespy.tools.fluid_properties import isentropic
[docs]
class Turbine(Turbomachine):
r"""
Class for gas or steam turbines.
**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.turbomachinery.base.Turbomachine.energy_balance_func`
- :py:meth:`tespy.components.turbomachinery.turbine.Turbine.eta_s_func`
- :py:meth:`tespy.components.turbomachinery.turbine.Turbine.eta_s_char_func`
- :py:meth:`tespy.components.turbomachinery.turbine.Turbine.cone_func`
Inlets/Outlets
- in1
- out1
Image
.. image:: /api/_images/Turbine.svg
:alt: flowsheet of the turbine
:align: center
:class: only-light
.. image:: /api/_images/Turbine_darkmode.svg
:alt: flowsheet of the turbine
: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.
P : float, dict
Power, :math:`P/\text{W}`
eta_s : float, dict
Isentropic efficiency, :math:`\eta_s/1`
pr : float, dict, :code:`"var"`
Outlet to inlet pressure ratio, :math:`pr/1`
eta_s_char : tespy.tools.characteristics.CharLine, dict
Characteristic curve for isentropic efficiency, provide CharLine as
function :code:`func`.
cone : dict
Apply Stodola's cone law (works in offdesign only).
Example
-------
A steam turbine expands 10 kg/s of superheated steam at 550 °C and 110 bar
to 0,5 bar at the outlet. For example, it is possible to calulate the power
output and vapour content at the outlet for a given isentropic efficiency.
>>> from tespy.components import Sink, Source, Turbine
>>> from tespy.connections import Connection
>>> from tespy.networks import Network
>>> from tespy.tools import ComponentCharacteristics as dc_cc
>>> import shutil
>>> nw = Network(p_unit='bar', T_unit='C', h_unit='kJ / kg', iterinfo=False)
>>> si = Sink('sink')
>>> so = Source('source')
>>> t = Turbine('turbine')
>>> t.component()
'turbine'
>>> inc = Connection(so, 'out1', t, 'in1')
>>> outg = Connection(t, 'out1', si, 'in1')
>>> nw.add_conns(inc, outg)
In design conditions the isentropic efficiency is specified. For offdesign
a characteristic function will be applied, together with Stodola's cone
law coupling the turbine mass flow to inlet pressure.
>>> t.set_attr(eta_s=0.9, design=['eta_s'],
... offdesign=['eta_s_char', 'cone'])
>>> inc.set_attr(fluid={'water': 1}, m=10, T=550, p=110, design=['p'])
>>> outg.set_attr(p=0.5)
>>> nw.solve('design')
>>> nw.save('tmp')
>>> round(t.P.val, 0)
-10452574.0
>>> round(outg.x.val, 3)
0.914
>>> inc.set_attr(m=8)
>>> nw.solve('offdesign', design_path='tmp')
>>> round(t.eta_s.val, 3)
0.898
>>> round(inc.p.val, 1)
88.6
>>> shutil.rmtree('./tmp', ignore_errors=True)
"""
[docs]
@staticmethod
def component():
return 'turbine'
[docs]
def get_parameters(self):
return {
'P': dc_cp(
max_val=0, num_eq=1,
deriv=self.energy_balance_deriv,
func=self.energy_balance_func,
latex=self.energy_balance_func_doc),
'eta_s': dc_cp(
min_val=0, max_val=1, num_eq=1,
deriv=self.eta_s_deriv,
func=self.eta_s_func, latex=self.eta_s_func_doc),
'eta_s_char': dc_cc(
param='m', num_eq=1,
deriv=self.eta_s_char_deriv,
func=self.eta_s_char_func, latex=self.eta_s_char_func_doc),
'pr': dc_cp(
min_val=0, max_val=1, num_eq=1,
deriv=self.pr_deriv,
func=self.pr_func, func_params={'pr': 'pr'},
latex=self.pr_func_doc),
'cone': dc_simple(
deriv=self.cone_deriv, num_eq=1,
func=self.cone_func, latex=self.cone_func_doc)
}
[docs]
def eta_s_func(self):
r"""
Equation for given isentropic efficiency of a turbine.
Returns
-------
residual : float
Residual value of equation.
.. math::
0 = -\left( h_{out} - h_{in} \right) +
\left( h_{out,s} - h_{in} \right) \cdot \eta_{s,e}
"""
inl = self.inl[0]
outl = self.outl[0]
return (
-(outl.h.val_SI - inl.h.val_SI)
+ (
isentropic(
inl.p.val_SI,
inl.h.val_SI,
outl.p.val_SI,
inl.fluid_data,
inl.mixing_rule,
T0=inl.T.val_SI
)
- inl.h.val_SI
) * self.eta_s.val
)
[docs]
def eta_s_func_doc(self, label):
r"""
Equation for given isentropic efficiency of a turbine.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (
r'0=-\left(h_\mathrm{out}-h_\mathrm{in}\right)+\left('
r'h_\mathrm{out,s}-h_\mathrm{in}\right)\cdot\eta_\mathrm{s}')
return generate_latex_eq(self, latex, label)
[docs]
def eta_s_deriv(self, increment_filter, k):
r"""
Partial derivatives for isentropic efficiency function.
Parameters
----------
increment_filter : ndarray
Matrix for filtering non-changing variables.
k : int
Position of derivatives in Jacobian matrix (k-th equation).
"""
f = self.eta_s_func
i = self.inl[0]
o = self.outl[0]
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(o.p, increment_filter):
self.jacobian[k, o.p.J_col] = self.numeric_deriv(f, "p", o)
if self.is_variable(i.h, increment_filter):
self.jacobian[k, i.h.J_col] = self.numeric_deriv(f, "h", i)
if o.h.is_var and self.it == 0:
self.jacobian[k, o.h.J_col] = -1
[docs]
def cone_func(self):
r"""
Equation for stodolas cone law.
Returns
-------
residual : float
Residual value of equation.
.. math::
0 = \frac{\dot{m}_{in,ref} \cdot p_{in}}{p_{in,ref}} \cdot
\sqrt{\frac{p_{in,ref} \cdot v_{in}}{p_{in} \cdot v_{in,ref}}}
\cdot \sqrt{\frac{1 - \left(\frac{p_{out}}{p_{in}} \right)^{2}}
{1 - \left(\frac{p_{out,ref}}{p_{in,ref}} \right)^{2}}} -
\dot{m}_{in}
"""
n = 1
i = self.inl[0]
o = self.outl[0]
vol = i.calc_vol(T0=i.T.val_SI)
return (
- i.m.val_SI + i.m.design * i.p.val_SI / i.p.design
* np.sqrt(i.p.design * i.vol.design / (i.p.val_SI * vol))
* np.sqrt(
abs(
(1 - (o.p.val_SI / i.p.val_SI) ** ((n + 1) / n))
/ (1 - (self.pr.design) ** ((n + 1) / n))
)
)
)
[docs]
def cone_func_doc(self, label):
r"""
Equation for stodolas cone law.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (
r'0 = \frac{\dot{m}_\mathrm{in,design}\cdot p_\mathrm{in}}'
r'{p_\mathrm{in,design}}\cdot\sqrt{\frac{p_\mathrm{in,design}'
r'\cdot v_\mathrm{in}}{p_\mathrm{in}\cdot '
r'v_\mathrm{in,design}}\cdot\frac{1-\left('
r'\frac{p_\mathrm{out}}{p_\mathrm{in}} \right)^{2}}'
r'{1-\left(\frac{p_\mathrm{out,design}}{p_\mathrm{in,design}}'
r'\right)^{2}}} -\dot{m}_\mathrm{in}')
return generate_latex_eq(self, latex, label)
[docs]
def cone_deriv(self, increment_filter, k):
r"""
Partial derivatives for stodolas cone law.
Parameters
----------
increment_filter : ndarray
Matrix for filtering non-changing variables.
k : int
Position of derivatives in Jacobian matrix (k-th equation).
"""
f = self.cone_func
i = self.inl[0]
o = self.outl[0]
if i.m.is_var:
self.jacobian[k, i.m.J_col] = -1
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)
[docs]
def eta_s_char_func(self):
r"""
Equation for given isentropic efficiency characteristic.
Returns
-------
residual : float
Residual value of equation.
.. math::
0 = - \left( h_\mathrm{out} - h_\mathrm{in} \right) +
\eta_\mathrm{s,design} \cdot f\left( expr \right) \cdot
\left(h_\mathrm{out,s}-h_\mathrm{in}\right)
"""
p = self.eta_s_char.param
expr = self.get_char_expr(p)
if not expr:
msg = (
"Please choose a valid parameter, you want to link the "
f"isentropic efficiency to at component {self.label}."
)
logger.error(msg)
raise ValueError(msg)
inl = self.inl[0]
outl = self.outl[0]
return (
-(outl.h.val_SI - inl.h.val_SI)
+ self.eta_s.design * self.eta_s_char.char_func.evaluate(expr)
* (
isentropic(
inl.p.val_SI,
inl.h.val_SI,
outl.p.val_SI,
inl.fluid_data,
inl.mixing_rule,
T0=inl.T.val_SI
) - inl.h.val_SI
)
)
[docs]
def eta_s_char_func_doc(self, label):
r"""
Equation for given isentropic efficiency characteristic.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (
r'0=-\left(h_\mathrm{out}-h_\mathrm{in}\right)+'
r'\eta_\mathrm{s,design}\cdot f \left(X\right)'
r'\cdot\left(h_\mathrm{out,s}-h_\mathrm{in}\right)')
return generate_latex_eq(self, latex, label)
[docs]
def eta_s_char_deriv(self, increment_filter, k):
r"""
Partial derivatives for isentropic efficiency characteristic.
Parameters
----------
increment_filter : ndarray
Matrix for filtering non-changing variables.
k : int
Position of derivatives in Jacobian matrix (k-th equation).
"""
f = self.eta_s_char_func
i = self.inl[0]
o = self.outl[0]
if self.is_variable(i.m, increment_filter):
self.jacobian[k, i.m.J_col] = self.numeric_deriv(f, 'm', i)
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)
[docs]
def convergence_check(self):
r"""
Perform a convergence check.
Note
----
Manipulate enthalpies/pressure at inlet and outlet if not specified by
user to match physically feasible constraints.
"""
i, o = self.inl[0], self.outl[0]
if not i.good_starting_values:
if i.p.val_SI <= 1e5 and i.p.is_var:
i.p.val_SI = 1e5
if i.h.val_SI < 10e5 and i.h.is_var:
i.h.val_SI = 10e5
if o.h.val_SI < 5e5 and o.h.is_var:
o.h.val_SI = 5e5
if i.h.val_SI <= o.h.val_SI and o.h.is_var:
o.h.val_SI = i.h.val_SI * 0.9
if i.p.val_SI <= o.p.val_SI and o.p.is_var:
o.p.val_SI = i.p.val_SI * 0.9
[docs]
@staticmethod
def initialise_Source(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}
5 \cdot 10^4 & \text{key = 'p'}\\
1.5 \cdot 10^6 & \text{key = 'h'}
\end{cases}
"""
if key == 'p':
return 0.5e5
elif key == 'h':
return 1.5e6
[docs]
@staticmethod
def initialise_target(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}
2.5 \cdot 10^6 & \text{key = 'p'}\\
2 \cdot 10^6 & \text{key = 'h'}
\end{cases}
"""
if key == 'p':
return 2.5e6
elif key == 'h':
return 2e6
[docs]
def calc_parameters(self):
r"""Postprocessing parameter calculation."""
super().calc_parameters()
inl = self.inl[0]
outl = self.outl[0]
self.eta_s.val = (
(outl.h.val_SI - inl.h.val_SI)
/ (
isentropic(
inl.p.val_SI,
inl.h.val_SI,
outl.p.val_SI,
inl.fluid_data,
inl.mixing_rule,
T0=inl.T.val_SI
)
- inl.h.val_SI
)
)
[docs]
def exergy_balance(self, T0):
r"""
Calculate exergy balance of a turbine.
Parameters
----------
T0 : float
Ambient temperature T0 / K.
Note
----
.. math::
\dot{E}_\mathrm{P} =
\begin{cases}
-P & T_\mathrm{in}, T_\mathrm{out} \geq T_0\\
-P + \dot{E}_\mathrm{out}^\mathrm{T}
& T_\mathrm{in} > T_0 \geq T_\mathrm{out}\\
-P +\dot{E}_\mathrm{out}^\mathrm{T}- \dot{E}_\mathrm{in}^\mathrm{T}
& T_0 \geq T_\mathrm{in}, T_\mathrm{out}\\
\end{cases}
\dot{E}_\mathrm{F} =
\begin{cases}
\dot{E}_\mathrm{in}^\mathrm{PH} - \dot{E}_\mathrm{out}^\mathrm{PH}
& T_\mathrm{in}, T_\mathrm{out} \geq T_0\\
\dot{E}_\mathrm{in}^\mathrm{T} + \dot{E}_\mathrm{in}^\mathrm{M} -
\dot{E}_\mathrm{out}^\mathrm{M}
& T_\mathrm{in} > T_0 \geq T_\mathrm{out}\\
\dot{E}_\mathrm{in}^\mathrm{M} - \dot{E}_\mathrm{out}^\mathrm{M}
& T_0 \geq T_\mathrm{in}, T_\mathrm{out}\\
\end{cases}
\dot{E}_\mathrm{bus} = -P
"""
if self.inl[0].T.val_SI >= T0 and self.outl[0].T.val_SI >= T0:
self.E_P = -self.P.val
self.E_F = self.inl[0].Ex_physical - self.outl[0].Ex_physical
elif self.inl[0].T.val_SI > T0 and self.outl[0].T.val_SI <= T0:
self.E_P = -self.P.val + self.outl[0].Ex_therm
self.E_F = self.inl[0].Ex_therm + (
self.inl[0].Ex_mech - self.outl[0].Ex_mech)
elif self.inl[0].T.val_SI <= T0 and self.outl[0].T.val_SI <= T0:
self.E_P = -self.P.val + (
self.outl[0].Ex_therm - self.inl[0].Ex_therm)
self.E_F = self.inl[0].Ex_mech - self.outl[0].Ex_mech
else:
msg = ('Exergy balance of a turbine, where outlet temperature is '
'larger than inlet temperature is not implmented.')
logger.warning(msg)
self.E_P = np.nan
self.E_F = np.nan
self.E_bus = {"chemical": 0, "physical": 0, "massless": -self.P.val}
self.E_D = self.E_F - self.E_P
self.epsilon = self._calc_epsilon()