tespy.components.combustion package

tespy.components.combustion.base module

Module of class CombustionChamber.

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/combustion/base.py

SPDX-License-Identifier: MIT

class tespy.components.combustion.base.CombustionChamber(label, **kwargs)

Bases: Component

The class CombustionChamber is parent class of all combustion components.

Ports

• Fluid inlets: in1, in2

• Fluid outlets: out1

Mandatory Equations

• mass flow balance over all inflows and outflows: mass_flow_func

• pressure equality constraints: combustion_pressure_structure_matrix

• constraints for stoichiometry of the reaction: stoichiometry_func

• constraint for energy balance: energy_balance_func

Parameters:

• char_warnings (bool) – Ignore warnings on default characteristics usage for this component.

• design (list) – List containing design parameters (stated as String).

• design_path (str) – Path to the components design case.

• f_nox (float, dict) – Mass-based nitric oxide (NO) generation rate in flue gas in mass of created NO per mass of fuel and air input. Only active if value is explicitly set. Quantity: ratio.

• label (str) – The label of the component.

• lamb (float, dict) – Available oxygen to stoichiometric oxygen ratio. Quantity: ratio. Equation: lambda_func.

• local_design (bool) – Treat this component in design mode in an offdesign calculation.

• local_offdesign (bool) – Treat this component in offdesign mode in a design calculation.

• offdesign (list) – List containing offdesign parameters (stated as String).

• printout (bool) – Include this component in the network’s results printout.

• ti (float, dict) – Thermal input of fuel: lower heating value multiplied with mass flow. Quantity: heat. Equation: ti_func.

Notes

Tip

You can add more fluids by importing COMBUSTION_FLUIDS from the tespy.tools module and passing the respective information. See in the example below, how to do that. To retrieve the fluids available by default run:

from tespy.tools.global_vars import COMBUSTION_FLUIDS
COMBUSTION_FLUIDS.fluids.keys()

Note

The fuel and the air components can be connected to either of the inlets.

Example

The combustion chamber calculates energy input due to combustion as well as the flue gas composition based on the type of fuel and the amount of oxygen supplied. In this example a mixture of methane, hydrogen and carbon dioxide is used as fuel.

>>> from tespy.components import Sink, Source, CombustionChamber
>>> from tespy.connections import Connection
>>> from tespy.networks import Network
>>> from tespy.tools.fluid_properties import T_sat_p
>>> nw = Network(iterinfo=False)
>>> nw.units.set_defaults(**{
...     "pressure": "bar", "pressure_difference": "bar",
...     "temperature": "degC"
... })
>>> amb = Source("ambient air")
>>> sf = Source("fuel")
>>> fg = Sink("flue gas outlet")
>>> comb = CombustionChamber("combustion chamber")
>>> amb_comb = Connection(amb, "out1", comb, "in1")
>>> sf_comb = Connection(sf, "out1", comb, "in2")
>>> comb_fg = Connection(comb, "out1", fg, "in1")
>>> nw.add_conns(sf_comb, amb_comb, comb_fg)

Specify the thermal input of the combustion chamber. At the given fluid compositions this determines the mass flow of the fuel. The outlet temperature of the flue gas determines the ratio of oxygen to fuel mass flow.

>>> comb.set_attr(ti=500000)
>>> amb_comb.set_attr(
...     p=1, T=20,
...     fluid={"Ar": 0.0129, "N2": 0.7553, "CO2": 0.0004, "O2": 0.2314}
... )
>>> sf_comb.set_attr(T=25, fluid={"CO2": 0.03, "H2": 0.01, "CH4": 0.96})
>>> comb_fg.set_attr(T=1200)
>>> nw.solve("design")
>>> round(comb.lamb.val, 3)
2.014
>>> comb.set_attr(lamb=2)
>>> comb_fg.set_attr(T=None)
>>> nw.solve("design")
>>> round(comb_fg.T.val, 1)
1206.6

You can add a custom combustion fluid if you need. The combustion gas must be available in fluid property back-end and you need to provide the name of the fluid as well as its formation enthalpy hf in kJ/mol or the lower heating value LHV in J/kg. For example, let’s use ethanol and acetone as examples:

>>> from tespy.tools import COMBUSTION_FLUIDS
>>> COMBUSTION_FLUIDS.add_fluid("ethanol", hf=-234.95)
>>> COMBUSTION_FLUIDS.add_fluid("acetone", LHV=28.603e6)

>>> sf_comb.set_attr(fluid={"acetone": 1})
>>> nw.solve("design")
>>> round(comb_fg.T.val, 1)
1232.3
>>> sf_comb.set_attr(fluid={"ethanol": 1})
>>> nw.solve("design")
>>> round(comb_fg.T.val, 1)
1241.7

calc_lhv(f)

Calculate the lower heating value of the combustion chamber’s fuel.

• Source for fluids O2, H2O and CO2: [29]

• Source for all other fluids: [30]

Parameters:

f (str) – Alias of the fuel.

Returns:

val (float) – Lower heating value of the combustion chambers fuel.

\[\begin{split}LHV = -\frac{\sum_i {\Delta H_f^0}_i - \sum_j {\Delta H_f^0}_j } {M_{fuel}}\\ \forall i \in \text{reation products},\\ \forall j \in \text{reation educts},\\ \Delta H_f^0: \text{molar formation enthalpy}\end{split}\]

combustion_pressure_structure_matrix(k)

Equations for reactor pressure balance.

Returns:

residual (list) – Residual values of equations.

\[\begin{split}0 = p_\text{in,1} - p_\text{out,1}\\ 0 = p_\text{in,2} - p_\text{out,1}\end{split}\]

convergence_check()

Perform a convergence check.

Note

Manipulate enthalpies/pressure at inlet and outlet if not specified by user to match physically feasible constraints, keep fluid composition within feasible range and then propagates it towards the outlet.

energy_balance_dependents()

energy_balance_func()

Calculate the energy balance of the adiabatic combustion chamber.

Returns:

residual (float) – Residual value of equation.

\[ \begin{align}\begin{aligned}\begin{split}\begin{split} 0 = & \sum_i \dot{m}_{in,i} \cdot \left( h_{in,i} - h_{in,i,ref} \right)\\ & -\dot{m}_{out,2}\cdot\left( h_{out,1}-h_{out,1,ref} \right)\\ & + LHV_{fuel} \cdot\left(\sum_i\dot{m}_{in,i}\cdot x_{fuel,in,i}- \dot{m}_{out,1} \cdot x_{fuel} \right) \end{split}\\\end{split}\\\forall i \in \text{inlets}\end{aligned}\end{align} \]

Note

The temperature for the reference state is set to 25 °C, thus the water may be liquid. In order to make sure, the state is referring to the lower heating value, the state of the water in the flue gas is forced to gaseous.

• Reference temperature: 298.15 K.

• Reference pressure: 1 bar.

entropy_balance()

Calculate entropy balance of combustion chamber.

Note

The entropy balance makes the following parameter available:

• T_mcomb: Thermodynamic temperature of heat of combustion

• S_comb: Entropy production due to combustion

• S_irr: Entropy production due to irreversibilty

The methodology for entropy analysis of combustion processes is derived from [31]. Similar to the energy balance of a combustion reaction, we need to define the same reference state for the entropy balance of the combustion. The temperature for the reference state is set to 25 °C and reference pressure is 1 bar. As the water in the flue gas may be liquid but the thermodynamic temperature of heat of combustion refers to the lower heating value, the water is forced to gas at the reference point by considering evaporation.

• Reference temperature: 298.15 K.

• Reference pressure: 1 bar.

\[\begin{split}T_\text{m,comb}= \frac{\dot{m}_\text{fuel} \cdot LHV} {\dot{S}_\text{comb}}\\ \dot{S}_\text{comb}= \dot{m}_\text{fluegas} \cdot \left(s_\text{fluegas}-s_\text{fluegas,ref}\right) - \sum_{i=1}^2 \dot{m}_{\text{in,}i} \cdot \left( s_{\text{in,}i} - s_{\text{in,ref,}i} \right)\\ \dot{S}_\text{irr}= 0\\\end{split}\]

get_mandatory_constraints()

get_parameters()

static initialise_source(c, key)

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.

\[\begin{split}val = \begin{cases} 5 \cdot 10^5 & \text{key = 'p'}\\ 10^6 & \text{key = 'h'} \end{cases}\end{split}\]

static initialise_target(c, key)

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.

\[\begin{split}val = \begin{cases} 5 \cdot 10^5 & \text{key = 'p'}\\ 5 \cdot 10^5 & \text{key = 'h'} \end{cases}\end{split}\]

static inlets()

lambda_dependents()

lambda_func()

Calculate the residual for specified lambda.

Returns:

residual (float) – Residual value of equation.

\[ \begin{align}\begin{aligned}0 = \frac{\dot{m}_{f,m}}{\dot{m}_{O_2,m} \cdot \left(n_{C,fuel} + 0.25 \cdot n_{H,fuel}\right)} - \lambda\\\begin{split}\dot{m}_{fluid,m} = \sum_i \frac{x_{fluid,i} \cdot \dot{m}_{i}} {M_{fluid}}\\ \forall i \in inlets\end{split}\end{aligned}\end{align} \]

mass_flow_dependents()

mass_flow_func()

Calculate the residual value for component’s mass flow balance.

Returns:

residual (list) – Vector with residual value for component’s mass flow balance.

\[0 = \dot{m}_{in,1} + \dot{m}_{in,2} - \dot{m}_{out,1}\]

static outlets()

propagate_wrapper_to_target(branch)

setup_reaction_parameters()

Setup parameters for reaction (gas name aliases and LHV).

stoichiometry_dependents()

stoichiometry_func()

Calculate residual values for all fluids in stoichiometry.

Shared intermediate quantities (molar flows of fuel atoms, oxygen, lambda, excess fuel) are computed once and reused for every fluid equation, instead of being recomputed per fluid.

Returns:

residual (list) – Vector with residual values of equations.

General equation for each fluid:

\[\begin{split}res = \sum_i \left(x_{fluid,i} \cdot \dot{m}_{i}\right) - \sum_j \left(x_{fluid,j} \cdot \dot{m}_{j}\right) + dm\\ \forall i \in \text{combustion inlets},\; \forall j \in \text{flue gas outlet}\end{split}\]

where \(dm\) accounts for the production or consumption of reactive species (see stoichiometry for the per-species expressions).

ti_dependents()

ti_func()

Calculate the residual for specified thermal input.

Returns:

residual (float) – Residual value of function.

\[0 = \dot{m}_{fuel} \cdot LHV - ti\]

tespy.components.combustion.diabatic module

Module of class DiabaticCombustionChamber.

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/combustion/diabatic.py

SPDX-License-Identifier: MIT

class tespy.components.combustion.diabatic.DiabaticCombustionChamber(label, **kwargs)

Bases: CombustionChamber

An extension of the adiabatic combustion chamber with pressure drop and heat loss.

Ports

• Fluid inlets: in1, in2

• Fluid outlets: out1

Mandatory Equations

• mass flow balance over all inflows and outflows: mass_flow_func

• constraints for stoichiometry of the reaction: stoichiometry_func

Parameters:

• char_warnings (bool) – Ignore warnings on default characteristics usage for this component.

• design (list) – List containing design parameters (stated as String).

• design_path (str) – Path to the components design case.

• dp (float, dict) – Inlet 0 to outlet 0 absolute pressure change. Quantity: pressure_difference. Equation: dp_structure_matrix.

• eta (float, dict) – Heat dissipation ratio relative to thermal input. Quantity: efficiency. Equation: energy_balance_func.

• f_nox (float, dict) – Mass-based nitric oxide (NO) generation rate in flue gas in mass of created NO per mass of fuel and air input. Only active if value is explicitly set. Quantity: ratio.

• label (str) – The label of the component.

• lamb (float, dict) – Available oxygen to stoichiometric oxygen ratio. Quantity: ratio. Equation: lambda_func.

• local_design (bool) – Treat this component in design mode in an offdesign calculation.

• local_offdesign (bool) – Treat this component in offdesign mode in a design calculation.

• offdesign (list) – List containing offdesign parameters (stated as String).

• pr (float, dict) – Outlet 0 to inlet 0 pressure ratio. Quantity: ratio. Equation: pr_structure_matrix.

• printout (bool) – Include this component in the network’s results printout.

• Qloss (float, dict) – Heat dissipation. Quantity: heat.

• ti (float, dict) – Thermal input of fuel: lower heating value multiplied with mass flow. Quantity: heat. Equation: ti_func.

Notes

Tip

You can add more fluids by importing COMBUSTION_FLUIDS from the tespy.tools module and passing the respective information. See in the example of tespy.components.combustion.base.CombustionChamber, how to do that. To retrieve the fluids available by default run:

from tespy.tools.global_vars import COMBUSTION_FLUIDS
COMBUSTION_FLUIDS.fluids.keys()

Note

The fuel and the air components can be connected to either of the inlets. The pressure of inlet 2 is disconnected from the pressure of inlet 1. A warning is prompted, if the pressure at inlet 2 is lower than the pressure at inlet 1.

Example

The combustion chamber calculates energy input due to combustion as well as the flue gas composition based on the type of fuel and the amount of oxygen supplied. In this example a mixture of methane, hydrogen and carbon dioxide is used as fuel.

>>> from tespy.components import Sink, Source, DiabaticCombustionChamber
>>> from tespy.connections import Connection
>>> from tespy.networks import Network
>>> from tespy.tools.fluid_properties import T_sat_p
>>> nw = Network(iterinfo=False)
>>> nw.units.set_defaults(**{
...     "pressure": "bar", "pressure_difference": "bar",
...     "temperature": "degC"
... })
>>> amb = Source('ambient air')
>>> sf = Source('fuel')
>>> fg = Sink('flue gas outlet')
>>> comb = DiabaticCombustionChamber('combustion chamber')
>>> amb_comb = Connection(amb, 'out1', comb, 'in1')
>>> sf_comb = Connection(sf, 'out1', comb, 'in2')
>>> comb_fg = Connection(comb, 'out1', fg, 'in1')
>>> nw.add_conns(sf_comb, amb_comb, comb_fg)

Specify the thermal input of the combustion chamber. At the given fluid compositions this determines the mass flow of the fuel. The outlet temperature of the flue gas determines the ratio of oxygen to fuel mass flow. In contrast to the simple combustion chamber, this component does allow for a pressure drop. Therefore the outlet pressure or the pressure ratio of the combustion chamber must be specified. Since the component is not adiabatic, an efficiency value eta can be supplied to account for heat loss to the ambient. First, we specify eta=1 and expect identical lambda or outlet temperature as in an adiabatic combustion chamber.

>>> comb.set_attr(ti=500000, pr=0.95, eta=1)
>>> amb_comb.set_attr(
...     p=1.2, T=20,
...     fluid={'Ar': 0.0129, 'N2': 0.7553, 'CO2': 0.0004, 'O2': 0.2314}
... )
>>> sf_comb.set_attr(
...     p=1.3, T=25, fluid={'CO2': 0.03, 'H2': 0.01, 'CH4': 0.96}
... )
>>> comb_fg.set_attr(T=1200)
>>> nw.solve('design')
>>> round(comb.lamb.val, 3)
2.014
>>> round(comb_fg.p.val, 2)
1.14

Instead of the pressure ratio, we can also specify the outlet pressure. The pressure ratio is the ratio of pressure at the outlet to the pressure at the inlet 1 (ambient air inlet in this example).

>>> comb.set_attr(pr=None)
>>> comb_fg.set_attr(p=1)
>>> nw.solve('design')
>>> round(comb.pr.val, 3)
0.833

We can change lambda to a specific value and unset the flue gas temperature:

>>> comb.set_attr(lamb=2)
>>> comb_fg.set_attr(T=None)
>>> nw.solve('design')
>>> round(comb_fg.T.val, 1)
1206.5

Now, if we change the efficiency value, e.g. to 0.9, a total of 10 % of heat respective to the thermal input will be transferred to the ambient. Note, that the heat loss Qloss has a negative value as it is extracted from the system.

>>> eta = 0.9
>>> comb.set_attr(eta=eta)
>>> nw.solve('design')
>>> round(comb.Qloss.val, 0)
-50000.0
>>> round(comb.ti.val * comb.eta.val, 0)
450000.0

calc_parameters()

Postprocessing parameter calculation.

energy_balance_func()

Calculate the energy balance of the diabatic combustion chamber.

Returns:

residual (float) – Residual value of equation.

\[ \begin{align}\begin{aligned}\begin{split}\begin{split} 0 = & \sum_i \dot{m}_{in,i} \cdot \left( h_{in,i} - h_{in,i,ref} \right)\\ & -\dot{m}_{out,2}\cdot\left( h_{out,1}-h_{out,1,ref} \right)\\ & + LHV_{fuel} \cdot\left(\sum_i\dot{m}_{in,i}\cdot x_{fuel,in,i}- \dot{m}_{out,1} \cdot x_{fuel} \right) \cdot \eta \end{split}\\\end{split}\\\forall i \in \text{inlets}\end{aligned}\end{align} \]

Note

The temperature for the reference state is set to 25 °C, thus the water may be liquid. In order to make sure, the state is referring to the lower heating value, the state of the water in the flue gas is forced to gaseous.

• Reference temperature: 298.15 K.

• Reference pressure: 1 bar.

get_mandatory_constraints()

get_parameters()

tespy.components.combustion.engine module

Module of class CombustionEngine.

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/combustion/engine.py

SPDX-License-Identifier: MIT

class tespy.components.combustion.engine.CombustionEngine(label, **kwargs)

Bases: CombustionChamber

An internal combustion engine supplies power and heat cogeneration.

The combustion engine produces power and heat in cogeneration from fuel combustion. The combustion properties are identical to the combustion chamber. Thermal input and power output, heat output and heat losses are linked with an individual characteristic line for each property.

Ports

• Fluid inlets: in1, in2, in3, in4

• Fluid outlets: out1, out2, out3

• Power outlets: power

Mandatory Equations

• mass flow balance over all inflows and outflows: mass_flow_func

• pressure equality constraints: combustion_pressure_structure_matrix

• constraints for stoichiometry of the reaction: stoichiometry_func

• constraint for energy balance: energy_balance_func

• equation for thermal input to power generation relation: tiP_char_func

• equation for thermal input to heating port 1 heat generation relation: Q1_char_func

• equation for thermal input to heating port 2 heat generation relation: Q2_char_func

• equation for thermal input to heat dissipation relation: Qloss_char_func

• equation for mass flow equality at heating ports: variable_equality_structure_matrix

• equation for fluid composition equality at heating ports: variable_equality_structure_matrix

When a power or heat connector is attached:

• energy_connector_balance: energy_connector_balance_func

Parameters:

• char_warnings (bool) – Ignore warnings on default characteristics usage for this component.

• design (list) – List containing design parameters (stated as String).

• design_path (str) – Path to the components design case.

• dp1 (float, dict) – Heating port 1 inlet to outlet absolute pressure change. Quantity: pressure_difference. Equation: dp_structure_matrix.

• dp2 (float, dict) – Heating port 2 inlet to outlet absolute pressure change. Quantity: pressure_difference. Equation: dp_structure_matrix.

• eta_mech (float) – Description missing.

• f_nox (float, dict) – Mass-based nitric oxide (NO) generation rate in flue gas in mass of created NO per mass of fuel and air input. Only active if value is explicitly set. Quantity: ratio.

• label (str) – The label of the component.

• lamb (float, dict) – Available oxygen to stoichiometric oxygen ratio. Quantity: ratio. Equation: lambda_func.

• local_design (bool) – Treat this component in design mode in an offdesign calculation.

• local_offdesign (bool) – Treat this component in offdesign mode in a design calculation.

• offdesign (list) – List containing offdesign parameters (stated as String).

• P (float, dict, "var") – Mechanical power generated by the engine. Quantity: power. Can be set as a system variable by passing "var" as its value.

• pr1 (float, dict) – Heating port 1 outlet to inlet pressure ratio. Quantity: ratio. Equation: pr_structure_matrix.

• pr2 (float, dict) – Heating port 2 outlet to inlet pressure ratio. Quantity: ratio. Equation: pr_structure_matrix.

• printout (bool) – Include this component in the network’s results printout.

• Q1 (float, dict) – Heating port 1 heat production. Quantity: heat. Equation: Q1_func.

• Q1_char (tespy.tools.characteristics.CharLine, dict) – Thermal input to heat production of port 1 lookup table.

• Q2 (float, dict) – Heating port 2 heat production. Quantity: heat. Equation: Q2_func.

• Q2_char (tespy.tools.characteristics.CharLine, dict) – Thermal input to heat production of port 2 lookup table.

• Qloss (float, dict, "var") – Heat dissipation. Quantity: heat. Can be set as a system variable by passing "var" as its value.

• Qloss_char (tespy.tools.characteristics.CharLine, dict) – Thermal input to heat dissipation lookup table.

• T_v_inner (float) – Description missing.

• ti (float, dict) – Thermal input of fuel: lower heating value multiplied with mass flow. Quantity: heat. Equation: ti_func.

• tiP_char (tespy.tools.characteristics.CharLine, dict) – Thermal input to power lookup table.

• zeta1 (float, dict) – Deprecated, use zeta1_d4 instead.

• zeta1_d4 (float, dict) – Heating port 1 geometry-independent friction coefficient zeta/D^4 for pressure loss calculation. Equation: zeta_d4_func.

• zeta2 (float, dict) – Deprecated, use zeta2_d4 instead.

• zeta2_d4 (float, dict) – Heating port 2 geometry-independent friction coefficient zeta/D^4 for pressure loss calculation. Equation: zeta_d4_func.

Notes

Tip

You can add more fluids by importing COMBUSTION_FLUIDS from the tespy.tools module and passing the respective information. See in the example of tespy.components.combustion.base.CombustionChamber, how to do that. To retrieve the fluids available by default run:

from tespy.tools.global_vars import COMBUSTION_FLUIDS
COMBUSTION_FLUIDS.fluids.keys()

Note

The fuel and the air components can be connected to either of the inlets.

Example

The combustion chamber calculates energy input due to combustion as well as the flue gas composition based on the type of fuel and the amount of oxygen supplied. In this example a mixture of methane, hydrogen and carbon dioxide is used as fuel. There are two cooling ports, the cooling water will flow through them in parallel.

>>> from tespy.components import (Sink, Source, CombustionEngine, Merge,
... Splitter)
>>> from tespy.connections import Connection, Ref
>>> from tespy.networks import Network
>>> nw = Network(iterinfo=False)
>>> nw.units.set_defaults(**{
...     "pressure": "bar", "pressure_difference": "bar",
...     "temperature": "degC"
... })
>>> amb = Source('ambient')
>>> sf = Source('fuel')
>>> fg = Sink('flue gas outlet')
>>> cw_in = Source('cooling water inlet')
>>> sp = Splitter('cooling water splitter', num_out=2)
>>> me = Merge('cooling water merge', num_in=2)
>>> cw_out = Sink('cooling water outlet')
>>> chp = CombustionEngine(label='internal combustion engine')
>>> amb_comb = Connection(amb, 'out1', chp, 'in3')
>>> sf_comb = Connection(sf, 'out1', chp, 'in4')
>>> comb_fg = Connection(chp, 'out3', fg, 'in1')
>>> nw.add_conns(sf_comb, amb_comb, comb_fg)
>>> cw_sp = Connection(cw_in, 'out1', sp, 'in1')
>>> sp_chp1 = Connection(sp, 'out1', chp, 'in1')
>>> sp_chp2 = Connection(sp, 'out2', chp, 'in2')
>>> chp1_me = Connection(chp, 'out1', me, 'in1')
>>> chp2_me = Connection(chp, 'out2', me, 'in2')
>>> me_cw = Connection(me, 'out1', cw_out, 'in1')
>>> nw.add_conns(cw_sp, sp_chp1, sp_chp2, chp1_me, chp2_me, me_cw)

The combustion engine produces a power output of 10 MW the oxygen to stoichiometric oxygen ratio is set to 1. Only pressure ratio 1 is set as we reconnect both cooling water streams. At the merge all pressure values will be identical automatically. Reference the mass flow at the splitter to be split in half.

>>> chp.set_attr(pr1=0.99, P=-10e6, lamb=1.0,
... design=['pr1'], offdesign=['zeta1_d4'])
>>> amb_comb.set_attr(p=5, T=30, fluid={'Ar': 0.0129, 'N2': 0.7553,
... 'CO2': 0.0004, 'O2': 0.2314})
>>> sf_comb.set_attr(T=30, fluid={'CH4': 1})
>>> cw_sp.set_attr(p=3, T=60, m=50, fluid={'H2O': 1})
>>> sp_chp2.set_attr(m=Ref(sp_chp1, 1, 0))
>>> mode = 'design'
>>> nw.solve(mode=mode)
>>> design_state = nw.save(as_dict=True)
>>> round(chp.ti.val, 0)
25300000.0
>>> round(chp.Q1.val, 0)
-4980000.0
>>> chp.set_attr(Q1=-4e6, P=None)
>>> mode = 'offdesign'
>>> nw.solve(mode=mode, init_path=design_state, design_path=design_state)
>>> round(chp.ti.val, 0)
17794554.0
>>> round(chp.P.val / chp.P.design, 3)
0.617
>>> chp.set_attr(P=chp.P.design * 0.75, Q1=None)
>>> mode = 'offdesign'
>>> nw.solve(mode=mode, init_path=design_state, design_path=design_state)
>>> round(chp.ti.val, 0)
20550000.0
>>> round(chp.P.val / chp.P.design, 3)
0.75

Q1_char_dependents()

Q1_char_func()

Calculate the relation of heat output 1 and thermal input.

Returns:

residual (float) – Residual value of equation.

\[\begin{split}\begin{split} 0 = & \dot{m}_1 \cdot \left(h_{out,1} - h_{in,1} \right) \cdot f_{TI}\left(\frac{P}{P_{design}}\right) \\ & - LHV \cdot \left[\sum_i \left(\dot{m}_{in,i} \cdot x_{f,i}\right) - \dot{m}_{out,3} \cdot x_{f,3} \right] \cdot f_{Q1}\left(\frac{P}{P_{ref}}\right)\\ \end{split}\\ \forall i \in [3,4]\end{split}\]

Q1_dependents()

Q1_func()

Calculate residual value of primary heat loop function.

Returns:

residual (float) – Residual value of equation.

\[0 = \dot{m}_1 \cdot \left(h_{out,1} + h_{in,1} \right) - \dot{Q}_1\]

Q2_char_dependents()

Q2_char_func()

Calculate the relation of heat output 2 and thermal input.

Returns:

residual (float) – Residual value of equation.

\[\begin{split}\begin{split} 0 = & \dot{m}_2 \cdot \left(h_{out,2} - h_{in,2} \right) \cdot f_{TI}\left(\frac{P}{P_{design}}\right) \\ & - LHV \cdot \left[\sum_i \left(\dot{m}_{in,i} \cdot x_{f,i}\right) - \dot{m}_{out,3} \cdot x_{f,3} \right] \cdot f_{Q2}\left(\frac{P}{P_{ref}}\right)\\ \end{split}\\ \forall i \in [3,4]\end{split}\]

Q2_dependents()

Q2_func()

Calculate residual value of secondary heat loop function.

Returns:

residual (float) – Residual value of equation.

\[0 = \dot{m}_2 \cdot \left(h_{out,2} - h_{in,2} \right) - \dot{Q}_2\]

Qloss_char_dependents()

Qloss_char_func()

Calculate the relation of heat loss and thermal input.

Returns:

residual (float) – Residual value of equation.

\[\begin{split}\begin{split} 0 = & \dot{Q}_{loss} \cdot f_{TI}\left(\frac{P}{P_{design}}\right) \\ & + LHV \cdot \left[\sum_i \left(\dot{m}_{in,i} \cdot x_{f,i}\right) - \dot{m}_{out,3} \cdot x_{f,3} \right] \cdot f_{QLOSS}\left(\frac{P}{P_{ref}}\right)\\ \end{split}\\ \forall i \in [3,4]\end{split}\]

check_parameter_bounds()

Check parameter value limits.

energy_balance_dependents()

energy_balance_deriv(increment_filter, k, dependents=None)

Calculate partial derivatives of energy balance function.

Parameters:

• increment_filter (ndarray) – Matrix for filtering non-changing variables.

• k (int) – Position of equation in Jacobian matrix.

energy_balance_func()

Calculate the energy balance of the combustion engine.

Returns:

residual (float) – Residual value of equation.

\[\begin{split}\begin{split} 0 = & \sum_i \dot{m}_{in,i} \cdot \left( h_{in,i} - h_{in,i,ref} \right)\\ & - \dot{m}_{out,3} \cdot \left( h_{out,3} - h_{out,3,ref} \right)\\ & + LHV_{fuel} \cdot \left(\sum_j \left(\dot{m}_{in,j} \cdot x_{fuel,j} \right)- \dot{m}_{out,3} \cdot x_{fuel,3} \right)\\ & - \dot{Q}_1 - \dot{Q}_2 - P - \dot{Q}_{loss}\\ \end{split}\\ \forall i \in [1,2] j \in [3,4]\end{split}\]

Note

The temperature for the reference state is set to 25 °C, thus the water may be liquid. In order to make sure, the state is referring to the lower heating value, the necessary enthalpy difference for evaporation is added.

• Reference temperature: 298.15 K.

• Reference pressure: 1 bar.

energy_connector_balance_func()

energy_connector_dependents()

entropy_balance()

Calculate entropy balance of combustion engine.

For the entropy balance of a combustion engine two additional parameters need to be specified:

• virtual inner temperature T_v_inner that is used to determine the entropy of heat transferred from the hot side.

• mechanical efficiency eta_mech describing the ratio of power output P to reversible power of the motor [32]. It is used to determine the irreversibilty inside the motor.

  \[P_\text{irr,inner}=\left(1 - \frac{1}{\eta_\text{mech}} \right) \cdot P\]

The default values are:

• T_v_inner: flue gas temperature (result of calculation)

• eta_mech: 0.85

Note

The entropy balance makes the following parameter available:

• T_mcomb: Thermodynamic temperature of heat of combustion

• S_comb: Entropy production due to combustion

• T_mQ1: Thermodynamic temperature of heat at cold side of heater 1

• S_Q11: Entropy transport at hot side of heater 1

• S_Q12: Entropy transport at cold side of heater 1

• S_Q1irr: Entropy production due to heat transfer at heater 1

• S_irr1: Entropy production due to pressure losses at heater 1

• T_mQ2: Thermodynamic temperature of heat at cold side of heater 2

• S_Q21: Entropy transport at hot side of heater 2

• S_Q22: Entropy transport at cold side of heater 2

• S_Q2irr: Entropy production due to heat transfer at heater 2

• S_irr2: Entropy production due to pressure losses at heater 2

• S_irr_i: Entropy production due to internal irreversibilty

• S_Qloss: Entropy transport with heat loss to ambient

• S_Qcomb: Virtual entropy transport of heat to revert combustion gases to reference state

• S_irr: Total entropy production due to irreversibilty

The methodology for entropy analysis of combustion processes is derived from [31]. Similar to the energy balance of a combustion reaction, we need to define the same reference state for the entropy balance of the combustion. The temperature for the reference state is set to 25 °C and reference pressure is 1 bar. As the water in the flue gas may be liquid but the thermodynamic temperature of heat of combustion refers to the lower heating value, the water is forced to gas at the reference point by considering evaporation.

• Reference temperature: 298.15 K.

• Reference pressure: 1 bar.

\[\begin{split}\begin{split} T_\text{m,comb}= & \frac{\dot{m}_\text{fuel} \cdot LHV} {\dot{S}_\text{comb}}\\ \dot{S}_\text{comb} =&\dot{S}_\text{Q,comb}-\left( \dot{S}_\text{Q,11} + \dot{S}_\text{Q,21} + \dot{S}_\text{Q,loss} +\dot{S}_\text{irr,i}\right)\\ \dot{S}_\text{Q,comb}= & \dot{m}_\text{fluegas} \cdot \left(s_\text{fluegas}-s_\text{fluegas,ref}\right)\\ & - \sum_{i=3}^4 \dot{m}_{\text{in,}i} \cdot \left( s_{\text{in,}i} - s_{\text{in,ref,}i} \right)\\ \dot{S}_\text{Q,11}= & \frac{\dot{Q}_1}{T_\text{v,inner}}\\ \dot{S}_\text{Q,21}= & \frac{\dot{Q}_2}{T_\text{v,inner}}\\ \dot{S}_\text{Q,loss}= & \frac{\dot{Q}_\text{loss}} {T_\text{v,inner}}\\ \dot{S}_\text{irr,i}= & \frac{\left(1 - \frac{1}{\eta_\text{mech}}\right) \cdot P}{T_\text{v,inner}}\\ T_\text{Q,12} = &\frac{-\dot{Q}_1}{\dot{m}_1 \cdot \left( s_\text{out,1} - s_\text{in,1}\right)}\\ T_\text{Q,22} = &\frac{-\dot{Q}_2}{\dot{m}_2 \cdot \left( s_\text{out,2} - s_\text{in,2}\right)}\\ \dot{S}_\text{irr} = &\sum \dot{S}_\text{irr}\\ \end{split}\\\end{split}\]

get_mandatory_constraints()

get_parameters()

get_variables()

static initialise_source(c, key)

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.

\[\begin{split}val = \begin{cases} 5 \cdot 10^5 & \text{key = 'p'}\\ 10^6 & \text{key = 'h'} \end{cases}\end{split}\]

static initialise_target(c, key)

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.

\[\begin{split}val = \begin{cases} 5 \cdot 10^5 & \text{key = 'p'}\\ 5 \cdot 10^5 & \text{key = 'h'} \end{cases}\end{split}\]

static inlets()

static outlets()

static poweroutlets()

propagate_wrapper_to_target(branch)

tiP_char_dependents()

tiP_char_func()

Calculate the relation of output power and thermal input.

Returns:

residual (float) – Residual value of equation.

\[0 = P \cdot f_{TI}\left(\frac{P}{P_{design}}\right)+ LHV \cdot \left[\sum_i \left(\dot{m}_{in,i} \cdot x_{f,i}\right) - \dot{m}_{out,3} \cdot x_{f,3} \right] \; \forall i \in [3,4]\]

variable_equality_structure_matrix(k, **kwargs)

Create pairwise linear relationship between two variables var for all inlets and the respective outlets. This usually is applied to mass flow, pressure, enthalpy and fluid composition.

\[var_\text{in,i} = var_\text{out,i}\]

Parameters:

• k (int) – equation number in systems of equations

• variable (str) – Connection variable name, e.g. h.