entropy
Article
Advanced Exergy Analysis in the Dynamic
Framework for Assessing Building Thermal Systems
Ana Picallo-Perez 1,* , JoséM Sala 1, George Tsatsaronis 2and Saeed Sayadi 2
1Research Group Energy in Buildings (ENEDI), Department of Thermal Engineering, University of the
2Institute for Energy Engineering, Technische Universität Berlin, 10623 Berlin, Germany;
*Correspondence: [email protected]
Received: 13 November 2019; Accepted: 17 December 2019; Published: 25 December 2019
Abstract:
This work applies the Dynamic Advanced Exergy Analysis (DAEA) to a heating and
domestic hot water (DHW) facility supplied by a Stirling engine and a condensing boiler. For the
first time, an advanced exergy analysis using dynamic conditions is applied to a building energy
system. DAEA provides insights on the components’ exergy destruction (ED) by distinguishing the
inefficiencies that can be prevented by improving the quality (avoidable ED) and the ones constrained
because of technical limitations (unavoidable ED). ED is related to the inherent inefficiencies of
the considered element (endogenous ED) and those coming from the interconnections (exogenous
ED). That information cannot be obtained by any other approach. A dynamic calculation within
the experimental facility has been performed after a component characterization driven by a new
grey-box modelling technique, through TRNSYS and MATLAB. Novel solutions and terms of ED are
assessed for the rational implementation of the DAEA in building energy installations. The influence
of each component and their interconnections are valuated in terms of exergy destruction for further
diagnosis and optimization purposes.
Keywords:
dynamic advanced exergy analysis; grey box modeling; heating and DHW systems;
avoidable and unavoidable exergy destruction; endogenous and exogenous exergy destruction
1. Introduction
The worldwide awareness for reducing the per capita energy demand is well known since the
requirements of the world’s increasing population can lead to unsustainable situations. As reported
in Reference [
1
], if the current trend in energy use remains the same, the demand for oil from 2007
to 2035 is expected to grow by 30% and the demand for coal and natural gas is expected to rise by
50%. Therefore, there is some urgency for lowering the energy consumption, particularly in building
energy systems, since nearly one-third of the total primary energy supply in the world is used in the
building sector [
2
], mainly in Heating, Ventilation, and Air Conditioning (HVAC) systems [
3
]. Because
of that, significant energy savings can be achieved through proper operation of those systems [
4
].
Thus, the development of energy efficient facilities represents a great concern and has become the focus
of many research activities [
5
]. Notwithstanding the potential of these facilities, improvement of their
efficiencies is a complex and dynamic issue that needs special treatment.
In order to obtain more useful information from an energy system, an exergy analysis should be
conducted in addition to a conventional energy analysis, since the former measures the maximum
theoretical useful work that can be obtained [
6
] by accounting not only for the quantity of energy but
also for its quality [
7
]. Exergy, unlike energy, does not satisfy a conservation law, but it is destroyed
when the quality of energy is degraded because of the irreversibilities within different processes [
8
].
Entropy 2020,22, 32; doi:10.3390/e22010032 www.mdpi.com/journal/entropy
Entropy 2020,22, 32 2 of 23
In other words, the idea that something can be destroyed through a process is very useful in the
design, analysis, and optimization of energy systems [
7
]. An energy balance fails to identify the true
thermodynamic inefficiencies, and, thereby, an evaluation based exclusively on the energy concept
might be misleading.
In a conventional exergy analysis, the exergetic efficiency (
ε
) is used as an indicator to characterize
a component in terms of performance and compare it to similar components in other systems [
9
]. It is
defined as the ratio between the productive purpose (the goal) of the component, known as Product
(
EP
), and the resources required to achieve that objective, labelled as Fuel (
EF
) [
10
] (both of them
expressed in exergy terms). In addition, if no exergy losses are present, the difference between
EF
and
EP
is equal to the exergy destruction (
ED
) of the component [
11
]. However, this conventional exergetic
analysis cannot satisfactorily evaluate the mutual interdependencies among the system components,
and does not consider the real potential for improving every component [12].
Under these circumstances, to overcome those barriers, the Advanced Exergetic Analysis (AEA)
was developed. In this methodology, part of the inefficiencies caused by the component itself and
caused by the interactions with other components can be evaluated separately, as well as the fraction,
which can be avoided through technological improvements [
12
–
14
]. Consequently, the main purpose
of a plant analysis in the AEA is the identification of the causes of irreversibilities and their effects in
terms of
ED
and in terms of performance [
15
]. If the reader wants to explore other theories related to
the same objective, Reference [16] can be consulted.
As stated above, there are some irreversibilities that every component may have, which cannot be
reduced even using the best and current technical alternatives, due to physical, technological, and
economic constraints or limitations. They are known as unavoidable exergy destruction (
EUN
D
) [
17
,
18
],
whereas the remaining part is named as avoidable exergy destruction (
EAV
D
). Hence, the splitting up
of these two inefficiencies gives a realistic picture of the potential to improve the thermodynamic
efficiency of each component.
In addition to this, there is another way to distinguish the irreversibilities. Some exergy destructions
encountered in a component are due to the inefficiencies within other components. This means that
ED
occurring in one component of a system does not only depend on its performance, but it is also
influenced by the inefficiencies of the remaining components [
11
]. That part of the
ED
associated with
the exergy destruction in other components is called exogenous exergy destruction (
EEX
D
), while the
part caused only by internal irreversibities within the component itself is named as endogenous exergy
destruction (
EEN
D
). Thus, the separation of those two exergy destructions enables us to better understand
the interactions of the system components and to consider those interactions in optimization procedures.
Nonetheless, the calculation of
EEN
D
and
EEX
D
for a component is more difficult than that of
EUN
D
and
EAV
D. This is a major challenge of AEA.
Subsequently, the avoidable and unavoidable
ED
can be related to the endogenous and exogenous
ones. That information can be used to investigate: (1) which part of the exergy destruction within
a component can be decreased by improving the component itself (
EEN.AV
D
), (2) which part can be
reduced by a structural enhancement of the overall system or by improvements in other components
(
EEX.AV
D
), and (3) and (4) the exergy destructions, which cannot be prevented (reflected by
EEX.UN
D
and
EEN.UN
D
). In consequence, the information acquired by the AEA can be applied for system design,
control improvement, and maintenance purposes.
The novel aspects and originality of the present study are associated with the AEA application to a
building thermal facility and with proceeding from a steady-state analysis to a dynamic one. Although
the subtask A and C of the IEA ECBCS Annex 49 project was to focus on dynamic exergy analysis in
buildings [
19
], the AEA methodology was not expressly used. In this case, we implement it under a
dynamic point of view. For this reason, we call the proposed methodology Dynamic Advanced Exergy
Analysis (DAEA), which adds some new aspects to the steady-state AEA. Thus, one of the aims of the
paper is to present a guideline on how to apply a detailed DAEA.
Entropy 2020,22, 32 3 of 23
For instance, Reference [
20
] applies an AEA to an air conditioning system using average values to
evaluate the cooling process during the day and the accumulation process at night. Reference [
21
] applies
AEA to low-exergy analysis for existing building heating systems. In a similar way, Reference [
22
]
makes a comparison between two geothermal district heating systems based on an AEA. Although these
papers are related to a buildings framework, none of them (or any other similar paper) considers the
dynamic state of the system in the AEA. This makes the present paper, under the authors’ knowledge,
the first study of its kind in the application of DAEA.
On the other hand, an AEA has been applied in several research studies to different industrial
fields. References [
14
] and [
23
] apply this method to combined-cycle power plants. Reference [
11
]
performs a detailed AEA to an absorption refrigeration machine, and Reference [
24
] examines a
gas engine heat pump drying system. An AEA application to cogeneration systems is presented in
Reference [
25
]. Despite the abundance of studies about AEA, all of them have been carried out in a
steady-state context.
The work in this paper is presented as follows: initially, the heating and DHW experimental testing
facility is presented. Then, the procedure to obtain a grey-box model for the principal components
of the facility is explained. Afterward, a dynamic advanced exergetic analysis is conducted, and
the calculated avoidable and unavoidable exergy destructions for each component are discussed.
The following part focuses on the methodology for calculating the endogenous and exogenous
ED
in a
dynamic context. Moreover, some novel terms such as the endogenous exergy destruction based on
the real characteristic curves (EEN∗
D) are introduced.
The numerical results are presented and discussed. Lastly, some comments on the merits and
drawbacks of this new DAEA are made.
2. Dynamic Representation of the Building
Dynamic characterization of the studied building facility is performed as the first step since the
leap from the experimental data to the mathematical model is a key factor for the proper application of
DAEA. Every component taking part in the facility must be accurately and dynamically represented in
order to represent the reality as accurately as possible.
One of the problems with the detailed energy simulation of a building facility is the fact that many
inputs (some may not be practicably measurable) are required for model definition [
26
]. Therefore, the
characterization strongly depends on the availability and quality of the experimental data.
According to Reference [
27
], two types of models can be defined depending on the gathered data:
(1) The law-driven models and (2) the data-driven models. The last require prior data knowledge and
use system behavior to predict system properties.
The concerning case follows the second model characteristics since the data are taken from a
limited number of sensors and monitoring devices in the system. The model is built based on the
grey-box modeling approach, which is well-proven as a comprehensive and accurate method for
modeling dynamic systems [
28
] by identifying certain key parameters using a physical system model.
There are some building transient simulation tools based on these premises such as TRNSYS [
29
],
which implements a component-based simulation approach through a modular structure.
Likewise, system identification can be used for parameter estimation in a dynamic model
representation. It is used for building models based on the observed behavior of the system so that
variables like thermal inertia can be reflected. Consequently, the characterization of the facility under
study and the parameter adjustments were achieved by combining the TRNSYS v17 software-specific
components with the MATLAB System Identification Toolbox (R2014a) [30].
The representation of complex systems through necessary simplifications and simulation
constraints can be questioned since some information could be lost within that transition. As listed in
Reference [
26
], various sources of uncertainty can be found in the system identification, the modeling,
the numerical processing, and the scenario itself. In any modeling environment, the quality of the
outputs can only be as good as the quality of the available inputs.
Entropy 2020,22, 32 4 of 23
3. Case Study
This section deals with the detailed description of the methodology, according to the selected
case study.
3.1. Description of the Facility
The experimental facility of the Laboratory for the Quality Control in Buildings (LQCB) has been
used to obtain the needed data. This facility aims to test new energy technologies (that could be
incorporated in buildings) in order to obtain useful information that benefits different stakeholders of
the building sector. Through this plant, the operation of various types of equipment and pioneering
technologies can be analyzed, and different control strategies can be tested in order to reduce fuel
consumption and
CO2
emissions. This facility is based on a flexible concept, so that diverse types
of energy conversion equipment can be tested, with some based on fossil fuels and others based on
renewable energies [
31
]. Figure 1shows the general layout of the building’s thermal facility under
study including some of the energy conversion units.
The facility customized for the DAEA application is based on a micro-cogeneration Stirling engine
(S) and a condensing boiler (CB) (a Stirling was chosen in order to introduce a ground-breaking
component into a building system). That engine supplies 1 kW electricity, and 3.7–5 kW thermal energy
from the combustion gases, depending on the operating temperatures and modulation. Additional
20 kW thermal energy can be produced in an auxiliary boiler inside this unit. Another equipment used
in the energy conversion layer of the facility is a natural gas condensing boiler which provides 28 kW
thermal energy with a manufacturer’s energetic efficiency (based on the lower heating value) of 97%.
These components provide the required thermal energy and DHW equivalent to the demand of
three single-family dwellings located in Vitoria (Northern Spain). Additionally, there is a 351 hydraulic
compensator (HC), a plate heat exchanger (HX), a 1000 L storage tank (T), distribution pipes, hydraulic
pumps, three-way valves (V1, V2, V3), and a fan coil (FC), as shown in Figure 1.
Entropy 2020, 22, x FOR PEER REVIEW 4 of 23
3. Case Study
This section deals with the detailed description of the methodology, according to the selected
case study.
3.1. Description of the Facility
The experimental facility of the Laboratory for the Quality Control in Buildings (LQCB) has been
used to obtain the needed data. This facility aims to test new energy technologies (that could be
incorporated in buildings) in order to obtain useful information that benefits different stakeholders
of the building sector. Through this plant, the operation of various types of equipment and pioneering
technologies can be analyzed, and different control strategies can be tested in order to reduce fuel
consumption and CO emissions. This facility is based on a flexible concept, so that diverse types of
energy conversion equipment can be tested, with some based on fossil fuels and others based on
renewable energies [31]. Figure 1 shows the general layout of the building’s thermal facility under
study including some of the energy conversion units.
The facility customized for the DAEA application is based on a micro-cogeneration Stirling
engine (S) and a condensing boiler (CB) (a Stirling was chosen in order to introduce a ground-
breaking component into a building system). That engine supplies 1 kW electricity, and 3.7–5 kW
thermal energy from the combustion gases, depending on the operating temperatures and
modulation. Additional 20 kW thermal energy can be produced in an auxiliary boiler inside this unit.
Another equipment used in the energy conversion layer of the facility is a natural gas condensing
boiler which provides 28 kW thermal energy with a manufacturer’s energetic efficiency (based on the
lower heating value) of 97%.
These components provide the required thermal energy and DHW equivalent to the demand of
three single-family dwellings located in Vitoria (Northern Spain). Additionally, there is a 351
hydraulic compensator (HC), a plate heat exchanger (HX), a 1000 L storage tank (T), distribution
pipes, hydraulic pumps, three-way valves (V1, V2, V3), and a fan coil (FC), as shown in Figure 1.
Figure 1. Scheme of the building thermal facility under study.
On the one hand, the DHW demand profile was calculated using the Generation of Domestic
Hot Water Tool in Reference [32], which creates profiles based on a statistical analysis. Afterward, it
was discretized, programmed, and controlled by a high-accuracy flow meter. This profile uses 5-min
discrete values, which are continuously compared with the energy data obtained from the
temperature and flow meters associated with the facility.
Figure 1. Scheme of the building thermal facility under study.
On the one hand, the DHW demand profile was calculated using the Generation of Domestic
Hot Water Tool in Reference [
32
], which creates profiles based on a statistical analysis. Afterward,
it was discretized, programmed, and controlled by a high-accuracy flow meter. This profile uses 5-min
discrete values, which are continuously compared with the energy data obtained from the temperature
and flow meters associated with the facility.
Entropy 2020,22, 32 5 of 23
On the other hand, the heating profile was obtained from a TRNSYS simulation. The building
envelope characteristics were defined as well as the usage and the climate data, through the TMY2 type.
The emulation of the heating demand is done through a fan coil battery together with a three-way valve
so that the heating demand profile defined in advance is matched by its modulation and operation of
that component.
The control strategy is such that the Stirling engine has priority over the condensing boiler so that
it is switched when there is demand for thermal energy or when the average temperature of the DHW
tank falls below 60 ◦C.
The control is managed together with an expansion module and is connected via Ethernet to a PC.
The sensors distributed in the facility provide more than 120 signals and, thereby, enable engineers to
control the desired variables and to ensure proper operation of the plant. In this regard, 46 temperature
sensors Pt 100 are installed with 40 of them on the energy distribution system and the rest on the
deposits. Moreover, 11 electromagnetic flow meters with an uncertainty less than 0.1% are installed.
There are two pressure switches in the system as well, which function as sensors to measure the
ambient pressure and humidity, and some other measuring devices function to record the indoor
temperature and humidity inside the building containing the facility. Lastly, two gas meters of Class
1.5 are installed to measure fuel consumption in the condensing boiler and the micro-cogeneration unit,
and 1 electric meter of Class 1 is used to record the amount of generated electricity by the Stirling unit.
3.2. Selection of the Components
In order to properly conduct a DAEA, the next step requires the proper selection of every
subsystem, with respect to their productive final purpose. For instance, if the supply and return
collectors located above the hydraulic compensator are considered individually (driving mixer and
returning diverter separately), no productive final purpose can be defined for them. Conversely, if they
are jointly handled instead (C), the productive purpose of this component would be the coverage of
both the DHW and the heating demand. Similarly, the splitter and the mixer of the three-way valve
right before the fan coil should be considered inside the same component (V3). Then the goal would be
to supply the heating demand. Following those considerations, the components used for the analysis
are listed in Table 1, where their names and abbreviations are shown.
Table 1. List of components used for DAEA.
NAME DESCRIPTION
S Micro-cogeneration Stirling engine
CB Condensing boiler
ITF CB inlet temperature fixing
C Supply and return collectors
HC Hydraulic compensator
V1 DHW and heating mixer and splitter
V2 HX mixer and splitter
HX Heat exchanger
V3 Heating mixer and splitter
T Storage tank
FC Fan coil
3.3. Characterization of the Components
Once the components are selected, after collecting the experimental data from the corresponding
four-day test, the system was dynamically characterized (with a 5-min time step) by the grey-box
modeling technique and via the implementation of TRNSYS and MATLAB. The components were first
modeled individually and, then, the entire facility was simulated.
As stated above, the modeling of every component relied on TRNSYS. So, first of all, the appropriate
type from its libraries that best fits every component has to be chosen. In such a way, the characterization
Entropy 2020,22, 32 6 of 23
is performed based on the mathematical reference of the TRNSYS components. Therefore, the required
inputs to the software (which matched the actual measured values obtained from the facility) are
considered to be independent variables, and, accordingly, the acquired outputs from the TRNSYS
simulation are considered dependent ones. For instance, the variable
TTr
iDep
obtained from the TRNSYS
simulation and the real values measured in the LQCB experimental facility
TRe
iDep
might have a
deviation because TRNSYS does not consider the additional inertia encountered in the components
of the experimental facility. That refinement is performed using the MATLAB System Identification
Toolbox, by incorporating inertia and the consequent real behavior to adapt the outputs of TRNSYS to
reality TCalc
iDep . This is explained later in detail.
Figure 2serves as an example of how the individual characterization of the supply and return
collectors (C) and heat exchanger (HX), which have been programmed in the interface Simulation
Studio of TRNSYS.
Entropy 2020, 22, x FOR PEER REVIEW 6 of 23
characterization is performed based on the mathematical reference of the TRNSYS components.
Therefore, the required inputs to the software (which matched the actual measured values obtained
from the facility) are considered to be independent variables, and, accordingly, the acquired outputs
from the TRNSYS simulation are considered dependent ones. For instance, the variable 𝑇
obtained from the TRNSYS simulation and the real values measured in the LQCB experimental
facility 𝑇
might have a deviation because TRNSYS does not consider the additional inertia
encountered in the components of the experimental facility. That refinement is performed using the
MATLAB System Identification Toolbox, by incorporating inertia and the consequent real behavior
to adapt the outputs of TRNSYS to reality 𝑇
. This is explained later in detail.
Figure 2 serves as an example of how the individual characterization of the supply and return
collectors (C) and heat exchanger (HX), which have been programmed in the interface Simulation
Studio of TRNSYS.
As can be seen, different modules take part in the adaptation and improvement of the models,
as explained below.
Figure 2. Representative image for the C and HX characterization through the Simulation Studio
interface of TRNSYS.
• The component itself, chosen from the TRNSYS library, is located in the middle with its
abbreviated name, according to Table 2 (C or HX). First, the type needs to be chosen and then
adapted to the characteristics of the LQCB experimental facility. That is done by changing the
parameters of the selected TRNSYS Type.
• The user types, which appear in the component’s surrounding (labeled as 𝑇), correspond to
the external data readers containing the experimental values. In this case, the monitored data
from the LQCB experimental facility needs to be inserted, according to the chosen time step. The
number of the user types is equal to the number of recorded variables from the sensors.
• There are two types of user variables, which are the independent 𝑇
and dependent ones
𝑇
//, denoted by the subscripts “Ind” and “Dep,” respectively. The independent
variables correspond to the inputs of the component being analyzed and are located in the left
side of the component in Figure 2, while the dependent user variables that are the actual
measured values taken from the test facility are placed on the right side. These dependent
variables should be compared to other dependent variables, which resulted from the TRNSYS
simulation to obtain a model that is able to describe the real behavior of the component. To sum
up, there are three different dependent variables: those acquired from the TRNSYS simulation
𝑇
, the real ones provided by the sensors in the experimental facility 𝑇
, and the ones
calculated in MATLAB 𝑇
. Since the first two values are not the same 𝑇
≠𝑇
, a
mathematical relationship between the independent values ∑𝑇
and the dependent ones
Figure 2.
Representative image for the C and HX characterization through the Simulation Studio
interface of TRNSYS.
As can be seen, different modules take part in the adaptation and improvement of the models, as
explained below.
•
The component itself, chosen from the TRNSYS library, is located in the middle with its abbreviated
name, according to Table 2(C or HX). First, the type needs to be chosen and then adapted to the
characteristics of the LQCB experimental facility. That is done by changing the parameters of the
selected TRNSYS Type.
•
The user types, which appear in the component’s surrounding (labeled as
TRe
i
), correspond to the
external data readers containing the experimental values. In this case, the monitored data from the
LQCB experimental facility needs to be inserted, according to the chosen time step. The number
of the user types is equal to the number of recorded variables from the sensors.
•
There are two types of user variables, which are the independent
TRe
iInd
and dependent ones
TRe/Tr/Calc
iDep
, denoted by the subscripts “Ind” and “Dep,” respectively. The independent variables
correspond to the inputs of the component being analyzed and are located in the left side of
the component in Figure 2, while the dependent user variables that are the actual measured
values taken from the test facility are placed on the right side. These dependent variables should
be compared to other dependent variables, which resulted from the TRNSYS simulation to
obtain a model that is able to describe the real behavior of the component. To sum up, there
are three different dependent variables: those acquired from the TRNSYS simulation
TTr
iDep
,
the real ones provided by the sensors in the experimental facility
TRe
iDep
, and the ones calculated
Entropy 2020,22, 32 7 of 23
in MATLAB
TCalc
iDep
. Since the first two values are not the same
TTr
iDep
,TRe
iDep
, a mathematical
relationship between the independent values
PjTRe
jInd
and the dependent ones must be found
in order to represent reality (see Equation (1)). This step is conducted in the MATLAB System
Identification Toolbox.
TCalc
iDep =f
TTr
iDep ,X
j
TRe
jInd
=TRe
iDep +error (1)
•
For the reason mentioned above,
TRe
iDep
and
TTr
iDep
are connected to the MATLAB Type in Figure 2
(with the parameter identification tag). This type refers to the interconnection between both
software where the adjustment of dependent variables is carried out. To achieve that, the
experimental data have been compared to the values obtained from TRNSYS, so that the new
output from MATLAB is adjusted to the reality.
In this way, a mathematical model of every component of the system can be developed and
implemented in the simulation of the entire facility.
3.4. Conventional Exergy Analysis
Once the models of the individual components and the overall system are completed (and mass
and energy balances are fulfilled), the DAEA can be initiated. The first step is to conduct a conventional
exergy analysis in order to calculate the exergetic efficiency and exergy destruction for each component.
The definition of the dynamic exergetic efficiency is a delicate step and likely one of the most important
ones in completing this study correctly. As cited before, the variable that unambiguously characterizes
the performance of a component from the thermodynamic viewpoint is an appropriately defined
exergetic efficiency, i.e., the ratio between the product
EP
and the fuel
EF
in the studied component [
13
].
In this context, the Specific Exergy Costing (SPECO) approach [
33
] is used as a generic methodology to,
among other things, identify the exergies of fuel and product (
EF
and
EP
) for each subsystem. Even in
this systematization, the definitions of
EF
and
EP
must be carefully considered since special exceptions
can occur in dynamic situations.
Application to the Experimental Building Thermal Facility
In addition to the previously stated concerns, in the present case, a correct dynamic representation
is a key point since the definition of
EF
and
EP
in a component can vary over time, depending on
the actual productive structure of the component. As an example, different definitions of
EF
and
EP
exist for the storage tank T, and, consequently, for its exergetic efficiency
εT
, since this depends on
which flows are considered to be product and fuel. At any given time, the tank could be just charging
and, then,
EF
would be the incoming exergy supplied to the tank and
EP
would be the increase of
the accumulated exergy within the tank. Otherwise, it might be the case that only DHW demand
is activated. Therefore,
EF
would then be the decrease of the stored exergy within the tank and
EP
would be the exergy of the DHW leaving the tank, or we could have the situation that charging and
discharging go on concurrently and, then,
EF
is the exergy supplied to the tank plus the decrease of
the stored exergy, whereas
EP
would be the exergy of the DHW leaving the tank. Accordingly, in this
phase of the exergetic efficiency analysis, the inertia that arises in the system plays a significant role,
since it can alter the EFand EPassessment.
Taking into account the above considerations, a conventional dynamic exergetic analysis can be
performed. Accordingly, for all exergy analyses, the choice of the reference temperature is a crucial
and important part. Therefore, it is assumed that, for all the components, the system boundaries are at
the reference environment dynamic temperature. Thus, there are no exergy losses associated with heat
losses from the components [
34
]. Hence, exergy losses would only appear at the level of the overall
Entropy 2020,22, 32 8 of 23
facility, whereas, for every component, the difference between
EF
and
EP
corresponds to the exergy
destruction EDwithin this component.
3.5. Unavoidable and Avoidable Exergy Destructions
The unavoidable exergy destruction is constrained by technological limitations and is calculated
considering each component in isolation (i.e., separated from the system) assuming the most favorable
operating conditions. These conditions refer to the absolute minimum of exergy destruction when the
product remains unchanged. The conditions are associated with very low temperature differences
and very small losses of thermal and mechanical exergy within the component being analyzed [
14
,
17
].
Nevertheless, the assumptions for simulating unavoidable conditions depend on the engineers’
personal expertise and scope. Therefore, they are arbitrary to some extent.
The avoidable exergy destruction in the kth component of the system (
EAV
D,k
) is the difference
between the total and the unavoidable exergy destructions within the same component (Equation (2)).
EAV
D,k=ED,k−EUN
D,k(2)
Having reached this point, it is important to note that, even if the unavoidable and avoidable
exergy destructions are individually acquired, the behavior of the remaining components affects the
calculation of both exergy destructions. This happens because the independent variable values remain
the same as in reality or, in other words, when calculating avoidable exergy destruction. The real
input data are enforced to the component with the best attainable technology, and the effect of the
remaining components is included in those imposed input data. Consequently,
EAV
D,k
encompasses
both the inefficiencies that could be avoided if better quality equipment would be developed and the
inefficiencies that can be prevented by avoiding interactions among the components. For this reason,
the combinations of EUN·EN
D,k/EUN·EX
D,kand EAV·EN
D,k/EAV·EX
D,kmust be considered to separate these effects.
Application to the Experimental Building Thermal Facility
For calculating
EUN
D,k
, the major sources of inefficiency in each component need to be first identified
and, afterward, the minimum exergy destruction criterion should be applied. Different groups of
components are, hereafter, exposed and listed, according to their level of difficulty.
•
(C/V1/V2/V3) The exergy destructions in the mixers are mainly caused by mixing streams at
different temperatures and pressures. Thus, if the control system acts in a way that equal
temperatures and pressures are assumed, the unavoidable exergy destruction becomes zero.
•
(ITF) The aim of this component is to guarantee the best thermal conditions of the inlet flow to
the condensing boiler. Hence, all irreversibilities should be avoidable if that flow is already at its
nominal state.
•
(FC) The unavoidable exergy destruction within the fan coil is slightly lower than the exergy
destruction within the fan coil with the highest energetic efficiency in the market.
•
(HX) The exergy destruction within a heat exchanger can be reduced by: (1) matching streams
of similar heat capacity rates, which achieves parallel temperature profiles [
35
], (2) selecting
small temperature differences between the average temperatures of the hot and cold streams,
(3) considering an adiabatic heat exchanger, (4) neglecting pressure losses, and (5) choosing the
maximum available heat transfer coefficient in each zone of the heat exchanger.
•
(HC/T) The main cause of exergy destruction in those components is the mixing of the high
and low-temperature portions of the storage medium. To enhance the storage performance,
it is, therefore, necessary to decrease the mixing losses by inserting the heat transfer fluid in the
temperature layer, which is closer to the stream temperature. This process entails managing
the injection of heat into the corresponding temperature level by a correct stratification [
36
].
Moreover, it is shown that the exergy storage capacity increases as the degree of stratification arises.
Entropy 2020,22, 32 9 of 23
The exergy destruction is decreased by augmenting the thermal conductivity of the heat exchanger
inside the tank [37]. Additionally, the heat losses are reduced by improving the insulation.
Bearing all that in mind, the conditions assumed for calculating the
EUN
D
in HC and T are set out
below: (1) as the inlet and outlet positions of the heat transfer fluids are fixed, the incoming flows
cannot be inserted in different specific layers. Nevertheless, the maximum stratification profile should
be considered. (2) Due to legal regulations [
38
], the storage temperature should be greater than 60
◦
C
in order to avoid legionella formation and the same rule also influences the inlet fluid temperature,
(3) the DHW charging and discharging depend on the user demand profile, so no optimal heat process
periods can be enforced, (4) there is no heat exchanger inside the tank of the LQCB experimental facility,
and (5) lastly, thermal insulation should be added to the tank surface, so that it becomes adiabatic.
•
(S/CB) Systems including a combustion process are usually, by far, the components with the highest
exergy destruction. Hence, a detailed separated exergy analysis should be carried out. The main
causes of inefficiencies in a combustion process are friction, mixing, a chemical reaction, and heat
transfer. The
ED
caused by friction is significantly lower than the ones caused by a chemical reaction
and heat transfer. The
ED
due to isobaric mixing depends, once again, on the differences in temperature
and chemical composition of the streams that are mixed. That exergy destruction can be sometimes
reduced, but it is often entirely unavoidable. The
ED
resulting from chemical reactions can be reduced
by letting the reactions take place closer to their thermodynamic equilibrium. However, the exergy
destruction associated with chemical reactions will always be very high. The
ED
associated with
heat transfer depends on (1) the difference between the average thermodynamic temperatures of the
combustion gases and the heated fluid, and (2) the temperature level at which the heat transfer takes
place. It should be noted that four causes of
ED
are considered in this case by following the procedure
in Reference [39]. All these processes occur in real processes simultaneously and not successively.
According to the mentioned considerations,
EUN
D
was calculated under the assumptions that
(1) no pressure drop occurs during combustion, (2) the combustion is stoichiometric (
λ
=1) in order
to minimize the exergy destruction due to chemical reactions, even though this would increase the
adiabatic combustion temperature, and, thereby, the heat transfer inefficiencies, and (3) the minimum
temperature difference for the heat transfer is just unattainable. Incidentally, the composition of the
combustion gases in the unavoidable conditions would be different from that in the real case.
Table 2summarizes the above points.
Table 2. Justification and achievement of the unavoidable exergy destruction in every component.
n. CAUSES for EDUNAVOIDABLE EDAchievement
xC, V1, V2, V3 xMixing with different states xMixing at equal temperatures and pressures
are assumed
xITF xMixing for achieving the
required conditions
xFlow enters with the same thermodynamic
conditions as required CB’s inlet
xFC xThermal and pressure losses xHighest energetic efficiency +no pressure losses
xHX xTemperature difference, pressure
drop, and thermal losses
xMinimum ∆T of the average temperatures +
adiabatic HX +no pressure losses +constant and
maximum available heat transfer coefficient
xHC, T
xMixing, tank average T, charging
rate, heat losses to
the environment
xInsulation addition to the tank boundaries +
no pressure losses
S, CB
Friction, mixing, chemical reaction,
heat transfer
Stoichiometric combustion (λ=1) +minimum ∆Tª
for the heat transfer +no pressure losses
Along with the above conditions, it is worth highlighting that the
EUN
D,k
for each component must
be calculated dynamically in every time step. Then, different
EUN
D,k
values would emerge while the
productive conditions vary.
Entropy 2020,22, 32 10 of 23
3.6. Endogenous and Exogenous Exergy Destructions
The endogenous exergy destruction of the kth component (
EEN
D,k
) reflects that part of the overall
ED
is exclusively related to the intrinsic irreversibilities within the component itself.
As discussed in Reference [
34
], various methods can be used for splitting the exergy destruction
within system components into its endogenous and exogenous parts. Some of these approaches need
simulation and assessment of theoretical thermodynamic cycles. Therefore, one main disadvantage of
these methods is the complexity associated with the definition and the simulation of theoretical cycles
for some systems [
40
]. Others require several sensitivity analyses based on the exergy balances and the
fuel and product exergies [
41
]. Besides considerable effort required for doing mathematical calculations,
these approaches also fail to split exergy destruction in dissipative components. The main drawback
of the above-mentioned approaches is non-standard simulations required for the idealization of the
plant based on the second law of thermodynamics that cannot be easily conducted by using available
commercial software [
13
]. Nonetheless, a new straightforward and time-saving methodology has
recently been developed [
8
] based on a systematic approach derived from a general process design and
synthesis principles. Consequently, this methodology will be summarized and implemented below.
This methodological decomposition method is based on the idea that the exergy concept is
independent from the whole structure, so that
EEN
D,k
in every component can be individually evaluated,
according to its characteristics. In this way, the facility can be divided into reversible and irreversible
subgroups. The term
EEN
D,k
results from keeping the kth component operating at its current exergetic
efficiency (
εk
) while all the remaining components are assumed to be totally reversible, i.e., exhibiting
an exergetic efficiency of 100% [
8
]. Notwithstanding these simplifications, it must be noted that the
“idealization” of the remaining components should not change the organization and the structure of
the flowsheet. Likewise, the overall product stream(s) must remain the same as in the real facility. As a
result, it is possible to determine the productive contribution and the inefficiencies associated with
different components.
The graphical representation of this approach is depicted in Figure 3. The upper part of the figure
shows the facility under study where the real incoming resources and outgoing final products are
displayed. The other four pictures illustrate how the endogenous exergy destruction in components
S, V2, HC, and HX are calculated, while their
εk
as well as the outgoing final product stream(s)
(red arrows) are maintained the same as in the experimental facility.
Entropy 2020, 22, x FOR PEER REVIEW 11 of 23
Figure 3. Decomposition method for calculating the E
, adapted from Reference [42].
Application of the method to the experimental building thermal facility.
To begin with the calculation of 𝐸,
in our case study, the product of each component 𝐸,
needs to be defined first. That product expresses the reason for owning and operating the component
being considered under real conditions (i.e., with irreversibilities), while considering the rest of the
system under a hypothetical ideal operation (i.e., without irreversibilities). In this regard, attention
to the following issues is essential for the analysis of this building’s thermal facility.
• DHW is one of the outgoing products of the facility supplied by the storage tank T located at the
end of the production chain. That means that the conditions of DHW exclusively depend on the
storage thermal conditions instead of the activation or deactivation of the other components.
Two different situations are considered in this scenario as examples to make that clear. In one
case, the requested DHW is entirely covered by the tank discharge, while, in another situation,
there might be no demand for DHW. However, because of the temperature control strategy of
the tank, the heat generation units are turned on to achieve the set-point temperature within the
tank. Hence, the DHW demand should only be considered as the product of the tank
𝐸,=𝐸 whereas, for the remaining components of the system, the product (or part of the
product) is the flow of thermal energy supplied to the tank 𝐸,, as shown in Table 3.
Table 3. Description of the components and their final objective product used for
calculating the 𝐸,
.
𝐤 𝐄𝐏,𝐤 for 𝐄𝐃,𝐤
𝐄𝐍 Calculation
S 𝐸,+𝐸·%𝐸,
CB 𝐸,+𝐸·%𝐸,
ITF Not applicable
C 𝐸,+𝐸
HC 𝐸,+𝐸
V1 𝐸,+𝐸
V2 𝐸,
HX 𝐸,
V3 𝐸
T 𝐸
FC 𝐸
𝑬𝑯𝒆𝒂𝒕, Heating exergy demand; 𝑬𝑫𝑯𝑾, DHW exergy demand; 𝑬𝑭,𝑻, Exergy of the heating stream
supplied to the tank; %𝑬𝑷,𝑺, The share of S in satisfying the demand; %𝑬𝑷,𝑪𝑩, The share of CB in
satisfying the demand.
Figure 3. Decomposition method for calculating the EEN
D, adapted from Reference [35].
Entropy 2020,22, 32 11 of 23
Once the endogenous exergy destruction of the kth component is determined, the exogenous part
can be calculated by subtracting this value from the real ED,k, as shown in the following equation.
EEX
D,k=ED,k−EEN
D,k(3)
Accordingly,
EEX
D,k
represents part of the exergy destruction in component kthat exists because of
the inefficient operation of the remaining components in the given structure of the system.
Application of the method to the experimental building thermal facility.
To begin with the calculation of
EEN
D,k
in our case study, the product of each component
EP,k
needs
to be defined first. That product expresses the reason for owning and operating the component being
considered under real conditions (i.e., with irreversibilities), while considering the rest of the system
under a hypothetical ideal operation (i.e., without irreversibilities). In this regard, attention to the
following issues is essential for the analysis of this building’s thermal facility.
•
DHW is one of the outgoing products of the facility supplied by the storage tank T located at
the end of the production chain. That means that the conditions of DHW exclusively depend on
the storage thermal conditions instead of the activation or deactivation of the other components.
Two different situations are considered in this scenario as examples to make that clear. In one
case, the requested DHW is entirely covered by the tank discharge, while, in another situation,
there might be no demand for DHW. However, because of the temperature control strategy of the
tank, the heat generation units are turned on to achieve the set-point temperature within the tank.
Hence, the DHW demand should only be considered as the product of the tank
(EP,T=EDHW)
whereas, for the remaining components of the system, the product (or part of the product) is the
flow of thermal energy supplied to the tank (EF,T), as shown in Table 3.
Table 3.
Description of the components and their final objective product used for calculating the
EEN
D,k
.
kEP,kfor EEN
D,kCalculation
S(EF,T+EHeat)·%EP,S
CB (EF,T+EHeat)·%EP,CB
ITF Not applicable
CEF,T+EHeat
HC EF,T+EHeat
V1 EF,T+EHeat
V2 EF,T
HX EF,T
V3 EHeat
TEDHW
FC EHeat
EHeat
, Heating exergy demand;
EDHW
, DHW exergy demand;
EF,T
, Exergy of the heating stream supplied to the
tank; %EP,S, The share of S in satisfying the demand; %EP,CB, The share of CB in satisfying the demand.
•
The product associated with the heating demand needs to be carefully considered. One might
think that the exergetic value of the heating demand is the exergy of the flow of thermal energy at
the surface temperature of the fan coil. Nonetheless, the exergy of the delivered heat has to be
calculated at room air temperature (
≈
20
◦
) since the purpose of a heating device in a real facility is
to temper the room air, in order to satisfy the comfort conditions. Therefore, the heating exergy
demand is much lower than the supplied exergy by the fan coil, and, hence, the endogenous exergy
destruction in this component (
EEN
D,FC
) is very high. This high endogenous exergy destruction
within a downstream component of the system needs to be compensated by upstream ones, and,
therefore, it results in high exogenous exergy destructions in the rest of the system.
Some components of the system, such as the condensing boiler inlet temperature fixing (ITF) and
pumps, do not have productive purposes. Those components aim to satisfy some specific conditions
Entropy 2020,22, 32 12 of 23
for the boiler in order to provide the required mass flow by balancing the pressure losses, respectively.
They are merely used just to enable the operation of the facility. Hence, all their
ED
would correspond to
the exogenous part, since they are entirely caused by the operation of other components in the system.
3.6.1. Binary Exogenous Exergy Destructions
Once the exogenous exergy destruction (
EEX
D,k
) within every component is calculated, it can be
split into several parts with each one being generated by a different component in the system. That is
done by combining scenarios of two components working with their real exergetic efficiency
ε
while
all other components operate reversibly with an exergetic efficiency equal to 100%. In this situation,
the exergy destruction within the kth component (
E0D,k
) consists of two parts: the endogenous exergy
destruction that has already been calculated and the exogenous one caused only by the irreversibilities
within component i(
EEX
D,i→k
). The value of the latter is obtained by subtracting
EEN
D,k
from the new exergy
destruction of the kth component estimated in this new stage, as given by Equation (4).
∆EEX
D,i→k=E0
D,k−EEN
D,k(4)
Figure 4visualizes the methodology to obtain the binary exogenous exergy destruction caused
within component kby the irreversibilities within component i.
Entropy 2020, 22, x FOR PEER REVIEW 12 of 23
• The product associated with the heating demand needs to be carefully considered. One might
think that the exergetic value of the heating demand is the exergy of the flow of thermal energy
at the surface temperature of the fan coil. Nonetheless, the exergy of the delivered heat has to be
calculated at room air temperature (≈20 ℃) since the purpose of a heating device in a real
facility is to temper the room air, in order to satisfy the comfort conditions. Therefore, the heating
exergy demand is much lower than the supplied exergy by the fan coil, and, hence, the
endogenous exergy destruction in this component (𝐸,
) is very high. This high endogenous
exergy destruction within a downstream component of the system needs to be compensated by
upstream ones, and, therefore, it results in high exogenous exergy destructions in the rest of
the system.
Some components of the system, such as the condensing boiler inlet temperature fixing (ITF)
and pumps, do not have productive purposes. Those components aim to satisfy some specific
conditions for the boiler in order to provide the required mass flow by balancing the pressure losses,
respectively. They are merely used just to enable the operation of the facility. Hence, all their 𝐸
would correspond to the exogenous part, since they are entirely caused by the operation of other
components in the system.
3.6.1. Binary Exogenous Exergy Destructions
Once the exogenous exergy destruction (𝐸,
) within every component is calculated, it can be
split into several parts with each one being generated by a different component in the system. That
is done by combining scenarios of two components working with their real exergetic efficiency 𝜀
while all other components operate reversibly with an exergetic efficiency equal to 100%. In this
situation, the exergy destruction within the kth component ( 𝐸′,) consists of two parts: the
endogenous exergy destruction that has already been calculated and the exogenous one caused only
by the irreversibilities within component i (𝐸,→
). The value of the latter is obtained by subtracting
𝐸,
from the new exergy destruction of the kth component estimated in this new stage, as given by
Equation (4). ∆𝐸,→
=𝐸,
−𝐸,
(4)
Figure 4 visualizes the methodology to obtain the binary exogenous exergy destruction caused
within component k by the irreversibilities within component i.
Figure 4. Graphical explanation of the methodology to obtain 𝐸,→
.
The analysis of the binary interactions between upstream and downstream components of the
energy chain reveals that the latter are the ones which mainly cause 𝐸 in the upstream components.
In fact, if there is no energy recirculation within the system being considered, the exogenous part of
exergy destruction within component i due to thermodynamic inefficiencies occurring in the
Figure 4. Graphical explanation of the methodology to obtain EEX
D,i→k.
The analysis of the binary interactions between upstream and downstream components of the
energy chain reveals that the latter are the ones which mainly cause
ED
in the upstream components.
In fact, if there is no energy recirculation within the system being considered, the exogenous part of
exergy destruction within component idue to thermodynamic inefficiencies occurring in the upstream
component k(
EEX
D,k→i
) would be zero because, in this case,
E0D,i
would be exactly the same as the
EEN
D,i
(see Figure 5).
Entropy 2020, 22, x FOR PEER REVIEW 13 of 23
upstream component k (𝐸,→
) would be zero because, in this case, 𝐸′, would be exactly the same
as the 𝐸,
(see Figure 5).
Figure 5. Graphical justification for 𝐸′,=𝐸,
in the downstream component i.
3.6.2. Mexogenous Exergy Destructions
Besides endogenous and binary exogenous causes of exergy destruction within component k,
there is another source of exergy destruction in this component due to the simultaneous interactions
between the kth component and the rest of the system operating under its real efficiency. This is called
mexogenous (i.e., mixed exogenous) exergy destruction [14] and is calculated by subtracting the sum
of the binary exogenous exergy destructions from the total exogenous exergy destruction within the
kth component, as shown in the following equation.
𝐸,
=𝐸,
−𝐸,→
(5)
3.6.3. Considering Real Characteristic Curves
The decomposition method offers an appealing approach to obtain the endogenous exergy
destruction within different components of a system since the required mathematical effort and
calculation time are significantly lower than those by other methods. However, this approach deals
only with exergetic variables (such as 𝐸,, 𝐸,, and 𝜀), which should remain constant, without
considering the real physical characteristics of the components under different operating conditions.
Therefore, the approach could lead to some controversial results. For instance, when only one
component of the system is operating under its real conditions (with its real 𝜀) and the rest of the
system is assumed to be ideal 𝜀=1, the virtual product that this component is supposed to supply
𝐸, is inconsistent (e.g., outside of the component operating range, for example, too low demand
for CB that is not feasible). Moreover, the 𝜀 of the component under different operating conditions
does not remain the same.
Consequently, a similar standpoint can be carried out if, instead of working with a constant
exergetic efficiency, the real one under the new thermodynamic conditions (𝜀′ ) is considered, based
on the characteristic curves of each component. The endogenous exergy destruction obtained from
this approach (𝐸,
∗) represents the authentic 𝐸 that a component would have, when supplying the
corresponding 𝐸,.
The difference between the endogenous exergy destruction based on the real characteristic
curves of the components (𝐸,
∗) and the one obtained according to the decomposition method (𝐸,
)
refers to the irreversibilities due to the fact that the component needs to adapt itself to the new
thermodynamic conditions 𝜀′. ∆𝐸,
=𝐸,
∗−𝐸,
(6)
Figure 5. Graphical justification for E0D,i=EEN
D,iin the downstream component i.
Entropy 2020,22, 32 13 of 23
3.6.2. Mexogenous Exergy Destructions
Besides endogenous and binary exogenous causes of exergy destruction within component k,
there is another source of exergy destruction in this component due to the simultaneous interactions
between the kth component and the rest of the system operating under its real efficiency. This is called
mexogenous (i.e., mixed exogenous) exergy destruction [
14
] and is calculated by subtracting the sum
of the binary exogenous exergy destructions from the total exogenous exergy destruction within the
kth component, as shown in the following equation.
EMEX
D,K=EEX
D,K−
N
X
i
i,k
EEX
D,i→k(5)
3.6.3. Considering Real Characteristic Curves
The decomposition method offers an appealing approach to obtain the endogenous exergy
destruction within different components of a system since the required mathematical effort and
calculation time are significantly lower than those by other methods. However, this approach deals
only with exergetic variables (such as
EF,k
,
EP,k
, and
εk
), which should remain constant, without
considering the real physical characteristics of the components under different operating conditions.
Therefore, the approach could lead to some controversial results. For instance, when only one
component of the system is operating under its real conditions (with its real
εk
) and the rest of the
system is assumed to be ideal
(ε=1)
, the virtual product that this component is supposed to supply
EP,k
is inconsistent (e.g., outside of the component operating range, for example, too low demand for
CB that is not feasible). Moreover, the
ε
of the component under different operating conditions does
not remain the same.
Consequently, a similar standpoint can be carried out if, instead of working with a constant
exergetic efficiency, the real one under the new thermodynamic conditions (
ε0k
) is considered, based
on the characteristic curves of each component. The endogenous exergy destruction obtained from
this approach (
EEN∗
D,k
) represents the authentic
ED
that a component would have, when supplying the
corresponding EP,k.
The difference between the endogenous exergy destruction based on the real characteristic curves
of the components (
EEN∗
D,k
) and the one obtained according to the decomposition method (
EEN
D,k
) refers to
the irreversibilities due to the fact that the component needs to adapt itself to the new thermodynamic
conditions (ε0k).
∆EEN
D,k=EEN∗
D,k−EEN
D,k(6)
3.7. Combination of the UN/AV and EN/EX Parts of Exergy Destruction
Overviewing the general DAEA developed so far,
ED
in the kth component of the system has been
divided into its avoidable and unavoidable parts and into its endogenous and exogenous sections
in the present paper. Those parts of exergy destruction can be combined to calculate the following
four variables: (1)
EAV.EN
D,k
is the exergy destruction that can be reduced by the improvement of the
kth component itself, (2)
EAV.EX
D,k
is the exergy destruction within the kth component, which can be
decreased by enhancing the performance of the other components, (3)
EUN.EN
D,k
is the unavoidable
exergy destruction, which corresponds to the inherent limitations of the component being considered,
and (4)
EUN.EX
D,k
is the unavoidable exergy destruction that embodies the structural constraints and
component interactions. They are calculated as follows.
Entropy 2020,22, 32 14 of 23
4. Numerical Values and Results
Down below, the numerical results of the analysis are summarized.
EAV·EX
D,k=EAV
D,k·EEX
D,k
ED,k
(7)
EUN·EN
D,k=EUN
D,k·EEN
D,k
ED,k
(8)
EUN·EX
D,k=EUN
D,k·EEX
D,k
ED,k
(9)
EUN·EN
D,k=EUN
D,k·EEN
D,k
ED,k
(10)
4.1. Characterization of the Components
As previously mentioned, the LQCB experimental facility was used in a four-day test. In the
present analysis, 18 thermocouples (with an uncertainty of
±
0.15
◦
C) and seven flowmeters (with an
accuracy of ±0.1%) were used.
The DHW and heating demands were calculated with TRNSYS v17, and then the control system
was accordingly programmed. Those demands are illustrated in Figure 6. Although the data were
acquired every 10 s, the dynamic mathematical model was built based on a 5-min time step, since that
time step was considered sufficient for accurately representing the transient start-up and shut-down of
the components.
Entropy 2020, 22, x FOR PEER REVIEW 14 of 23
3.7. Combination of the UN/AV and EN/EX Parts of Exergy Destruction
Overviewing the general DAEA developed so far, 𝐸 in the kth component of the system has
been divided into its avoidable and unavoidable parts and into its endogenous and exogenous
sections in the present paper. Those parts of exergy destruction can be combined to calculate the
following four variables: (1) 𝐸,
. is the exergy destruction that can be reduced by the
improvement of the kth component itself, (2) 𝐸,
. is the exergy destruction within the kth
component, which can be decreased by enhancing the performance of the other components, (3)
𝐸,
. is the unavoidable exergy destruction, which corresponds to the inherent limitations of the
component being considered, and (4) 𝐸,
. is the unavoidable exergy destruction that embodies
the structural constraints and component interactions. They are calculated as follows.
4. Numerical Values and Results
Down below, the numerical results of the analysis are summarized.
𝐸,
·=𝐸,
·𝐸,
𝐸, (7)
𝐸,
·=𝐸,
·𝐸,
𝐸, (8)
𝐸,
·=𝐸,
·𝐸,
𝐸, (9)
𝐸,
·=𝐸,
·𝐸,
𝐸, (10)
4.1. Characterization of the Components
As previously mentioned, the LQCB experimental facility was used in a four-day test. In the
present analysis, 18 thermocouples (with an uncertainty of ±0.15 °C) and seven flowmeters (with an
accuracy of ±0.1%) were used.
Figure 6. Heating and DHW demand covered by the facility.
The DHW and heating demands were calculated with TRNSYS v17, and then the control system
was accordingly programmed. Those demands are illustrated in Figure 6. Although the data were
acquired every 10 s, the dynamic mathematical model was built based on a 5-min time step, since
that time step was considered sufficient for accurately representing the transient start-up and shut-
down of the components.
Figure 6. Heating and DHW demand covered by the facility.
As previously discussed, a mathematical characterization equation of every component has been
obtained. As an example, the calculation of the output variables of the component C (
TCalc
2Dep
,
TCalc
5Dep
, and
TCalc
6Dep
) is demonstrated. The variables obtained as TRNSYS outputs
TTr
iDep
are corrected to the actual
experimental facility measurements by means of the MATLAB System Identification Toolbox, which,
in this case, becomes the following.
TCalc
2Dep (t)=TRe
7Ind (t)(11)
TCalc
3Dep (t)=
TRe
7Ind (t)·0.9649 .
mCB =0
TTr
3Dep (t).
mCB ≥0(12)
TCalc
6Dep (t)=
.
mS(t)·TRe
1Ind (t)+.
mCB(t)·TRe
4Ind (t)
.
mS(t)+.
mCB
(13)
Entropy 2020,22, 32 15 of 23
Accordingly, it can be seen how the effects of the activation and deactivation of the pumps and
the hydraulic compensator inertia are taken into account (see the condition on .
mCB in Equation (12)).
The relative error between the experimental data and the simulation results shows the difference
among the real dependent values and the dependent values calculated from the TRNSYS and MATLAB
combination
TCalc
iDep
−TRe
iDep
is less that
±
3% for each individual component of the facility. However,
when all the subsystems are linked, the maximum error for the total facility is lower than
±
9%. This is
larger than the error for the individual components because the uncertainty increases when all the
components are modelled simultaneously.
4.2. Conventional Exergy Analysis
A conventional exergetic analysis calculates the exergy destruction within each component,
ED,k, in every time step.
Figure 7illustrates the total exergy destruction in the four-day period (
ETOT
D=
1259
kWh
) as well
as the percentages of the contribution of exergy destruction within different components to the total
exergy destruction. The causes of
ED,k
in all components are individually justified in Section 3.5 and
summarized in Table 4.
Entropy 2020, 22, x FOR PEER REVIEW 15 of 23
As previously discussed, a mathematical characterization equation of every component has been
obtained. As an example, the calculation of the output variables of the component C (𝑇
,𝑇
,
and 𝑇
) is demonstrated. The variables obtained as TRNSYS outputs 𝑇
are corrected to the
actual experimental facility measurements by means of the MATLAB System Identification Toolbox,
which, in this case, becomes the following.
T
t=T
t (11)
T
t=T
t· 0.9649 m=0
T
t m 0 (12)
T
t=mt·T
t+mt·T
t
mt+m (13)
Accordingly, it can be seen how the effects of the activation and deactivation of the pumps and
the hydraulic compensator inertia are taken into account (see the condition on 𝑚 in Equation (12)).
The relative error between the experimental data and the simulation results shows the difference
among the real dependent values and the dependent values calculated from the TRNSYS and
MATLAB combination 𝑇
−𝑇
is less that ±3% for each individual component of the facility.
However, when all the subsystems are linked, the maximum error for the total facility is lower than
±9%. This is larger than the error for the individual components because the uncertainty increases
when all the components are modelled simultaneously.
4.2. Conventional Exergy Analysis
A conventional exergetic analysis calculates the exergy destruction within each component,
𝐸,, in every time step.
Figure 7 illustrates the total exergy destruction in the four-day period (𝐸
=1259 𝑘𝑊ℎ) as well
as the percentages of the contribution of exergy destruction within different components to the total
exergy destruction. The causes of 𝐸, in all components are individually justified in Section 3.5 and
summarized in Table 4.
Figure 7. Average contribution of 𝐸
,
in each component to the overall exergy destruction.
Figure 7. Average contribution of ED,kin each component to the overall exergy destruction.
As expected, components including a combustion process have, by far, the highest exergy
destructions. Due to the previously explained control strategy, CB works as a backup device and its
operating hours are, thus, less than S. However, 46% of the overall exergy destruction occurs in CB and
only 27% in S. One reason that
ED,S
is much lower than
ED,CB
is because S generates heat and electricity
simultaneously, so that its exergetic efficiency is much higher than
εCB
. Another reason is that CB has a
higher nominal capacity than S.
Following the instructions written in Section 3.5, for the components CB and S, the exergy
destructions are separated into the following groups, according to their causes: (a) friction, (b) mixing,
(c) chemical reactions, and (d) heat transfer. The results show that almost all the exergy destructions
belong to the last two categories: 59.7% and 64.3% are caused by chemical reactions in S and CB
(comb), respectively, whereas 40.2% and 35.6% are due to heat transfer (HT) in S and CB, respectively
(see Figure 8).
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Entropy 2020, 22, x FOR PEER REVIEW 16 of 23
As expected, components including a combustion process have, by far, the highest exergy
destructions. Due to the previously explained control strategy, CB works as a backup device and its
operating hours are, thus, less than S. However, 46% of the overall exergy destruction occurs in CB
and only 27% in S. One reason that 𝐸, is much lower than 𝐸, is because S generates heat and
electricity simultaneously, so that its exergetic efficiency is much higher than 𝜀. Another reason is
that CB has a higher nominal capacity than S.
Following the instructions written in Section 3.5, for the components CB and S, the exergy
destructions are separated into the following groups, according to their causes: (a) friction, (b) mixing,
(c) chemical reactions, and (d) heat transfer. The results show that almost all the exergy destructions
belong to the last two categories: 59.7% and 64.3% are caused by chemical reactions in S and CB
(comb), respectively, whereas 40.2% and 35.6% are due to heat transfer (HT) in S and CB, respectively
(see Figure 8).
Figure 8. Exergy destruction distribution for the combustion devices based on Reference [37].
4.3. Unavoidable/Avoidable 𝐸
The unavoidable and avoidable 𝐸 of each component were dynamically calculated following
the guidelines outlined above and the average percentage results are presented in Figure 9.
Figure 9. Percentage of unavoidable and avoidable exergy destructions in each component of the
experimental facility.
As can be seen, the 𝐸
values within the most important components are much larger than the
avoidable ones (𝐸). For example, in S and CB, approximately 88% of the exergy destruction is
unavoidable because, when the destructions associated with chemical reactions are reduced, the
internal heat transfer irreversibilities increase due to the rise of the combustion temperature.
The average results of the conventional exergy analysis together with the DAEA are listed in
Table 4.
Figure 8. Exergy destruction distribution for the combustion devices based on Reference [37].
4.3. Unavoidable/Avoidable ED
The unavoidable and avoidable
ED
of each component were dynamically calculated following the
guidelines outlined above and the average percentage results are presented in Figure 9.
Entropy 2020, 22, x FOR PEER REVIEW 16 of 23
As expected, components including a combustion process have, by far, the highest exergy
destructions. Due to the previously explained control strategy, CB works as a backup device and its
operating hours are, thus, less than S. However, 46% of the overall exergy destruction occurs in CB
and only 27% in S. One reason that 𝐸, is much lower than 𝐸, is because S generates heat and
electricity simultaneously, so that its exergetic efficiency is much higher than 𝜀. Another reason is
that CB has a higher nominal capacity than S.
Following the instructions written in Section 3.5, for the components CB and S, the exergy
destructions are separated into the following groups, according to their causes: (a) friction, (b) mixing,
(c) chemical reactions, and (d) heat transfer. The results show that almost all the exergy destructions
belong to the last two categories: 59.7% and 64.3% are caused by chemical reactions in S and CB
(comb), respectively, whereas 40.2% and 35.6% are due to heat transfer (HT) in S and CB, respectively
(see Figure 8).
Figure 8. Exergy destruction distribution for the combustion devices based on Reference [37].
4.3. Unavoidable/Avoidable 𝐸
The unavoidable and avoidable 𝐸 of each component were dynamically calculated following
the guidelines outlined above and the average percentage results are presented in Figure 9.
Figure 9. Percentage of unavoidable and avoidable exergy destructions in each component of the
experimental facility.
As can be seen, the 𝐸
values within the most important components are much larger than the
avoidable ones (𝐸). For example, in S and CB, approximately 88% of the exergy destruction is
unavoidable because, when the destructions associated with chemical reactions are reduced, the
internal heat transfer irreversibilities increase due to the rise of the combustion temperature.
The average results of the conventional exergy analysis together with the DAEA are listed in
Table 4.
Figure 9.
Percentage of unavoidable and avoidable exergy destructions in each component of the
experimental facility.
As can be seen, the
EUN
D
values within the most important components are much larger than
the avoidable ones (
EAV
D
). For example, in S and CB, approximately 88% of the exergy destruction
is unavoidable because, when the destructions associated with chemical reactions are reduced, the
internal heat transfer irreversibilities increase due to the rise of the combustion temperature.
The average results of the conventional exergy analysis together with the DAEA are listed
in Table 4.
As a consequence of the facility’s physical model, the values of
ED
decrease significantly after the
HC component. The irreversibilities within the downstream components decrease plenty once the
energy passes through the HC component. This can be easily explained because, after that unit, the
downstream components are split into the DHW branch and the heating branch. Therefore, they are
dealing with a lower flow of energy (and exergy). Therefore, less exergy destruction takes place within
the downstream components.
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Table 4. Average results of the DAEA and the conventional exergy analysis.
Component kEF,k
[kWh]
EP,k
[kWh]
εk
[%]
ED,k
[kWh]
EUN
D,k
[kWh]
EAV
D,k
[kWh]
S 456.01 111.77 25% 344.24 302.67 41.56
CB 665.36 91.44 14% 573.92 542.62 31.30
ITF 116.75 59.31 51% 57.44 0.00 57.44
C 180.30 115.29 64% 65.01 0.00 65.01
HC 146.93 35.01 24% 111.92 63.99 47.93
V1 94.39 76.61 81% 17.78 0.00 17.78
V2 234.41 233.74 100% 0.68 0.00 0.68
HX 29.24 22.78 78% 6.46 1.47 4.99
V3 84.80 68.50 81% 16.30 0.00 16.30
T 32.77 14.97 46% 17.80 16.49 1.31
FC 65.33 12.34 19% 53.00 41.32 11.68
4.4. Endogenous/Exogenous ED
The contribution of endogenous and exogenous exergy destructions within different components
for the four-day test are illustrated in Figure 10.
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Table 4. Average results of the DAEA and the conventional exergy analysis.
Component 𝒌 𝐄𝐅,𝐤
[kWh] 𝐄𝐏,𝐤
[kWh] 𝛆𝐤
[%] 𝐄𝐃,𝐤
[kWh] 𝐄𝐃,𝐤
𝐔𝐍
[kWh] 𝐄𝐃,𝐤
𝐀𝐕
[kWh]
S 456.01 111.77 25% 344.24 302.67 41.56
CB 665.36 91.44 14% 573.92 542.62 31.30
ITF 116.75 59.31 51% 57.44 0.00 57.44
C 180.30 115.29 64% 65.01 0.00 65.01
HC 146.93 35.01 24% 111.92 63.99 47.93
V1 94.39 76.61 81% 17.78 0.00 17.78
V2 234.41 233.74 100% 0.68 0.00 0.68
HX 29.24 22.78 78% 6.46 1.47 4.99
V3 84.80 68.50 81% 16.30 0.00 16.30
T 32.77 14.97 46% 17.80 16.49 1.31
FC 65.33 12.34 19% 53.00 41.32 11.68
As a consequence of the facility’s physical model, the values of 𝐸 decrease significantly after
the HC component. The irreversibilities within the downstream components decrease plenty once
the energy passes through the HC component. This can be easily explained because, after that unit,
the downstream components are split into the DHW branch and the heating branch. Therefore, they
are dealing with a lower flow of energy (and exergy). Therefore, less exergy destruction takes place
within the downstream components.
4.4. Endogenous/ Exogenous 𝐸
The contribution of endogenous and exogenous exergy destructions within different
components for the four-day test are illustrated in Figure 10.
Figure 10. Share of endogenous and exogenous exergy destructions in each component.
As noted above, the closer the components are to the final products, the lower the amount of their
exogenous exergy destruction is. In other words, due to the fact that the main product of the system
remains constant 𝐸,=𝐸+𝐸, if the downstream components cause additional exergy
destruction, the upstream components need to produce a larger output to offset those additional
irreversibilities. This situation results in a larger 𝐸 in the respective upstream components. This is the
main reason that explains the high value of 𝐸
for both the CB and the S components.
Having no productive purpose, the exergy destruction in ITF is entirely exogenous. On the
contrary, the exergy destruction in the heat exchanger (HX), storage tank (T), and fan coil (FC) are
entirely endogenous because those components are directly linked to the final product of the overall
system.
The exogenous exergy destruction in every component can be split to consider the contributions
from each component by using the binary interrelation approach. Figure 11 displays those binary
Figure 10. Share of endogenous and exogenous exergy destructions in each component.
As noted above, the closer the components are to the final products, the lower the amount of
their exogenous exergy destruction is. In other words, due to the fact that the main product of the
system remains constant
(EP,TOT =EDHW +EHeat)
, if the downstream components cause additional
exergy destruction, the upstream components need to produce a larger output to offset those additional
irreversibilities. This situation results in a larger
ED
in the respective upstream components. This is the
main reason that explains the high value of EEX
Dfor both the CB and the S components.
Having no productive purpose, the exergy destruction in ITF is entirely exogenous. On the
contrary, the exergy destruction in the heat exchanger (HX), storage tank (T), and fan coil (FC)
are entirely endogenous because those components are directly linked to the final product of the
overall system.
The exogenous exergy destruction in every component can be split to consider the contributions
from each component by using the binary interrelation approach. Figure 11 displays those binary
interactions in terms of exergy destruction, which is colored according to the component associated
with its origin.
Entropy 2020,22, 32 18 of 23
Entropy 2020, 22, x FOR PEER REVIEW 18 of 23
interactions in terms of exergy destruction, which is colored according to the component associated
with its origin.
Figure 11. Average binary exogenous exergy destruction of every component.
As expected, FC is the component with a noticeable contribution to the exogenous 𝐸 in the
upstream components, not only because it is located at the end of the heating branch, but also because
of its very large endogenous exergy destruction.
4.5. Considering Real Characteristic Curves
A step forward in the application of DAEA is the calculation of endogenous exergy destruction
within every component based on the real exergetic efficiency of this component 𝜀′ instead of
having a constant one, where the thermodynamic state of the system changes at every time step. The
difference between the endogenous exergy destruction obtained from the previously mentioned
method and the one calculated based on the decomposition approach (∆𝐸,
) indicated that, in some
cases, dealing with constant ε for the calculation of 𝐸,
is a simplified assumption that might lead
to controversial results.
Figure 12. Endogenous exergy destruction of every component obtained from the decomposition
method (𝐸,
) and from the real characteristic curves (𝐸,
∗).
Figure 12 compares the values of 𝐸,
and 𝐸,
∗ for different components of the system.
The major difference is found in the condensing boiler because its real exergetic efficiency curve,
𝜀′, is not flat and decreases significantly when the demand decreases. Other components with
relatively large ∆𝐸,
are the supply and return collectors (C) and the hydraulic compensator (HC)
because their endogenous exergy destructions, caused mainly by mixing of fluids with different
temperatures, changes significantly at different operating conditions. For the remaining components,
the endogenous exergy destruction is similar in both methods.
Figure 11. Average binary exogenous exergy destruction of every component.
As expected, FC is the component with a noticeable contribution to the exogenous
ED
in the
upstream components, not only because it is located at the end of the heating branch, but also because
of its very large endogenous exergy destruction.
4.5. Considering Real Characteristic Curves
A step forward in the application of DAEA is the calculation of endogenous exergy destruction
within every component based on the real exergetic efficiency of this component
(ε0k)
instead of having
a constant one, where the thermodynamic state of the system changes at every time step. The difference
between the endogenous exergy destruction obtained from the previously mentioned method and the
one calculated based on the decomposition approach (
∆EEN
D,k
) indicated that, in some cases, dealing with
constant
ε
for the calculation of
EEN
D,k
is a simplified assumption that might lead to controversial results.
Figure 12 compares the values of EEN
D,kand EEN∗
D,kfor different components of the system.
Entropy 2020, 22, x FOR PEER REVIEW 18 of 23
interactions in terms of exergy destruction, which is colored according to the component associated
with its origin.
Figure 11. Average binary exogenous exergy destruction of every component.
As expected, FC is the component with a noticeable contribution to the exogenous 𝐸 in the
upstream components, not only because it is located at the end of the heating branch, but also because
of its very large endogenous exergy destruction.
4.5. Considering Real Characteristic Curves
A step forward in the application of DAEA is the calculation of endogenous exergy destruction
within every component based on the real exergetic efficiency of this component 𝜀′ instead of
having a constant one, where the thermodynamic state of the system changes at every time step. The
difference between the endogenous exergy destruction obtained from the previously mentioned
method and the one calculated based on the decomposition approach (∆𝐸,
) indicated that, in some
cases, dealing with constant ε for the calculation of 𝐸,
is a simplified assumption that might lead
to controversial results.
Figure 12. Endogenous exergy destruction of every component obtained from the decomposition
method (𝐸,
) and from the real characteristic curves (𝐸,
∗).
Figure 12 compares the values of 𝐸,
and 𝐸,
∗ for different components of the system.
The major difference is found in the condensing boiler because its real exergetic efficiency curve,
𝜀′, is not flat and decreases significantly when the demand decreases. Other components with
relatively large ∆𝐸,
are the supply and return collectors (C) and the hydraulic compensator (HC)
because their endogenous exergy destructions, caused mainly by mixing of fluids with different
temperatures, changes significantly at different operating conditions. For the remaining components,
the endogenous exergy destruction is similar in both methods.
Figure 12.
Endogenous exergy destruction of every component obtained from the decomposition
method (EEN
D,k) and from the real characteristic curves (EEN∗
D,k).
The major difference is found in the condensing boiler because its real exergetic efficiency curve,
ε0CB
, is not flat and decreases significantly when the demand decreases. Other components with
relatively large
∆EEN
D,k
are the supply and return collectors (C) and the hydraulic compensator (HC)
because their endogenous exergy destructions, caused mainly by mixing of fluids with different
temperatures, changes significantly at different operating conditions. For the remaining components,
the endogenous exergy destruction is similar in both methods.
Entropy 2020,22, 32 19 of 23
4.6. Combination of the UN/AV, EN/EX Parts of Exergy Destruction
Lastly, new findings can be identified when unavoidable and avoidable exergy destructions are
combined with the endogenous and exogenous exergy destructions. Detailed results from the DAEA
application to the experimental building’s thermal facility for a period of four days are given in Table 5.
The upgrading prospective of each component can be detected there.
Table 5. Detailed aggregated results obtained from the DAEA.
Component kED[kWh] Unavoidable Avoidable
EUN,EN
D[kWh] EUN,EX
D[kWh] EAV,EN
D[kWh] EAV,EX
D[kWh]
S 302.67 149.25 153.43 5.67 35.96
CB 542.62 125.39 417.23 8.41 22.28
ITF 0.00 0.00 0.00 0.00 57.16
C 0.00 0.00 0.00 15.36 49.13
HC 63.99 48.41 15.58 25.58 22.29
V1 0.00 0.00 0.00 16.87 0.91
V2 0.00 0.00 0.00 0.40 0.25
HX 1.47 1.49 0.00 4.97 0.00
V3 0.00 0.00 0.00 2.11 14.21
T 16.49 16.13 0.00 1.67 0.00
FC 41.32 39.55 0.00 13.44 0.00
Similarly, Figure 13 summarizes the contributions of the four possible combinations to the
entire system.
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4.6. Combination of the UN/AV, EN/EX Parts of Exergy Destruction
Lastly, new findings can be identified when unavoidable and avoidable exergy destructions are
combined with the endogenous and exogenous exergy destructions. Detailed results from the DAEA
application to the experimental building’s thermal facility for a period of four days are given in
Table 5. The upgrading prospective of each component can be detected there.
Table 5. Detailed aggregated results obtained from the DAEA.
Component 𝒌 𝐄𝐃 [kWh] Unavoidable Avoidable
𝐄𝐃
𝐔𝐍,𝐄𝐍 [kWh] 𝐄𝐃
𝐔𝐍,𝐄𝐗 [kWh] 𝐄𝐃
𝐀𝐕,𝐄𝐍 [kWh] 𝐄𝐃
𝐀𝐕,𝐄𝐗 [kWh]
S 302.67 149.25 153.43 5.67 35.96
CB 542.62 125.39 417.23 8.41 22.28
ITF 0.00 0.00 0.00 0.00 57.16
C 0.00 0.00 0.00 15.36 49.13
HC 63.99 48.41 15.58 25.58 22.29
V1 0.00 0.00 0.00 16.87 0.91
V2 0.00 0.00 0.00 0.40 0.25
HX 1.47 1.49 0.00 4.97 0.00
V3 0.00 0.00 0.00 2.11 14.21
T 16.49 16.13 0.00 1.67 0.00
FC 41.32 39.55 0.00 13.44 0.00
Similarly, Figure 13 summarizes the contributions of the four possible combinations to the entire
system.
Figure 13. Contributions of E
.
, E
.
, E
.
, and E
.
to the total exergy destruction
in the entire system.
It can be seen that more than three-quarters of the overall exergy destruction is unavoidable,
with 39% of it being due to the components’ internal limitations, while the remaining 61% is due to
the interactions among components and to system structural restrictions.
Concerning the avoidable exergy destruction, only 8% of the total 𝐸 can be reduced by using
the best technological alternatives currently available in the market, whereas 15% of the global exergy
destruction can be avoided by improving the interrelations among components of the system by
customizing and improving the control system.
In summary, according to the results of the DAEA, the improvement potential of the overall
system is rather low and limited. Likewise, the fact that 𝐸. is higher than 𝐸. proves that
components of the system are strongly interconnected. Thus, a better control strategy can improve
the overall efficiency of the system. Nevertheless, it must be noted that 𝐸. considers both the
Figure 13.
Contributions of
EUN.EN
D
,
EUN.EX
D
,
EAV.EN
D
, and
EAV.EX
D
to the total exergy destruction in the
entire system.
It can be seen that more than three-quarters of the overall exergy destruction is unavoidable,
with 39% of it being due to the components’ internal limitations, while the remaining 61% is due to the
interactions among components and to system structural restrictions.
Concerning the avoidable exergy destruction, only 8% of the total
ED
can be reduced by using the
best technological alternatives currently available in the market, whereas 15% of the global exergy
destruction can be avoided by improving the interrelations among components of the system by
customizing and improving the control system.
In summary, according to the results of the DAEA, the improvement potential of the overall
system is rather low and limited. Likewise, the fact that
EAV.EX
D
is higher than
EAV.EN
D
proves that
components of the system are strongly interconnected. Thus, a better control strategy can improve
the overall efficiency of the system. Nevertheless, it must be noted that
EAV.EX
D
considers both the
interconnections between components as well as the imperfections coming from the others because
they are not using the best equipment available in the current market.
As a whole, DAEA analysis gives good insight on the optimisation possibilities. On the other
hand, a heating system based on a heat pump with a floor heating system would have a much better
Entropy 2020,22, 32 20 of 23
performance compared to the described Stirling engine/gas boiler and fain coil unit system. Even so,
this comparison is not within the frame of this study, but further analysis can be done for project
design optimization.
Therefore, the obtained information can be used for control-strategy optimization, a fault detection
approach, or even design optimization.
5. Discussion
A Dynamic Advanced Exergy Analysis (DAEA) is applied to a building thermal energy system.
Buildings are major contributors to the primary energy demand so that the awareness of their
improvement potential is an essential requirement for reducing energy demand and
CO2
emissions.
That assessment can be made through a DAEA application, as presented in this article.
A DAEA allows engineers to determine which inefficiencies could be avoided in the current
technical limitations by splitting the exergy destruction into avoidable and unavoidable parts. Moreover,
a DAEA, using the concepts of endogenous and exogenous exergy destructions, identifies the
inefficiencies caused by the component itself as well as those coming from the imperfections of the
remaining components. Consequently, it provides very useful information that cannot be supplied
through a conventional exergetic analysis.
Nevertheless, even with the suitability of that analysis, some shortcomings need to be mentioned.
First, the calculation of unavoidable exergy destruction is associated with some subjectivity during
its estimation. Even so, this standpoint depends on the engineers’ judgment. Therefore, accordingly,
the chosen criteria are explained in detail and justified throughout this article.
Furthermore, when endogenous and exogenous
ED
are calculated, some information might be
lost if some real thermodynamic quantities, such as a varying exergetic efficiency, are not considered.
However, this can be overcome by the incorporation of the real characteristic curves of the components.
Lastly, apart from the insight that a detailed distribution of the exergy destruction
ED
can provide,
one of the advantages in the application of DAEA is that there is no need to predefine any reference
conditions to evaluate the performance of a system. Hence, it is a generic method that can be used for
control, diagnosis, or even design purposes. In addition to that, since exergy destruction is employed
as the base parameter, the real involvement of every component within the overall system is regarded.
This implication should not be noticed if exergetic efficiency (
ε
) would have been taken instead. Even if
the upstream components have higher efficiencies than the downstream ones, the exergy destruction
is much higher in the group of the former than the latter, due to the bigger amount of exergy those
components deal with. That is the case, for example, of the supply and return collector (C) and the fan
coil (FC). As a result, some information can be misinterpreted if the EDis not used.
Moreover, one of the innovative features of this paper is associated with the dynamism used in
the DAEA, since a steady state can never be related to building energy supply facilities. Therefore,
before any calculation, the development of a reliable dynamic model for every component and for
the entire facility is of crucial importance. This was achieved on the basis of recorded data from an
experimental plant and the grey-box modeling, by the combination of TRNSYS models and MATLAB
System Identification Toolbox for the parameter adjustment, with an overall error below ±9%.
Despite that, certain issues arise when an AEA is dynamically applied. In the first instance, since
thermal parameters are continuously time-varying, special care needs to be given to the Fuel and
Product definition for every component. In addition, the inertia over the system plays a relevant role,
which must be taken into account. Furthermore, the dynamic operating conditions also introduce
non-flat exergetic efficiency curves. However, those complexities have been overcome during the
development of this paper.
6. Conclusions
To conclude, a DAEA elaborately resolves the way to allocate the inefficiencies of a system within
its components, by considering both the internal irreversibilities as well as the interconnections between
Entropy 2020,22, 32 21 of 23
components. Due to the dynamic character, its application in building facilities seems to be more
complicated than in systems where a steady state operation can be assumed. Despite that, a DAEA can
be equally applied by merely adjusting some assumptions. Therefore, a step forward on the reduction
of the energy use can be achieved by using the information provided by this analysis.
The future steps should include the economic quantification of those results as well as the
environmental impact calculation or the translation from the exergetic units to the monetary ones
and to units of environmental impacts. That can be performed with the aid of exergoeconomic and
exergoenvironmental analysis.
Author Contributions:
Conceptualization, G.T. and S.S.; Investigation, A.P.-P.; Writing—original draft, A.P.-P.;
Writing—review & editing, J.M.S., G.T. and S.S. All authors have read and agreed to the published version of
the manuscript.
Funding: This research received no external funding.
Acknowledgments:
The author, A.P., acknowledges the support provided to her by the Ministry of Education of
the Spanish Government through a scholarship granted to her to complete her Ph.D. degree. The authors G.T. and
S.S. appreciate the financial support provided for this work by the German Federal Ministry for Economic Affairs
and Energy (BMWi), promotional reference 03ET1218B. The authors also acknowledge the support provided by
the Laboratory for the Quality Control in Buildings of the Basque Government. This work would not have been
possible without the help of Mathias Penkuhn and Andreas Christidis from the Technische Universität Berlin.
Conflicts of Interest: The authors declare no conflict of interest.
Nomenclature
AEA Advanced Exergy Analysis
CSupply and Return Collectors
CB Condensing Boiler
DAEA Dynamic Advanced Exergy Analysis
DHW Domestic Hot Water
FC Fan Coil
HC Hydraulic Compensator
HX Heat Exchanger
ITF CB Inlet Temperature Fixing
LQCB Laboratory for the Quality Control in Buildings
SMicro-Cogeneration Stirling Engine
TStorage Tank
VMixer and Splitter
TRe
iInd Real experimental value of the independent variable i
TTr
iDep Output value taken from TRNSYS of the dependent variable i
TCalc
iDep Calculated dependent variable i
TRe
iDep Real experimental value of the dependent variable i
EF,kFuel for the kth component
EP,kProduct for the kth component
εkExergetic efficiency within the kth component
ε0kExergetic efficiency within the kth component in new thermodynamic conditions
ED,kTotal exergy destruction within the kth component
E0D,kTotal exergy destruction within the kth component in new thermodynamic conditions
EAV
D,kAvoidable exergy destruction within the kth component
EUN
D,kUnavoidable exergy destruction within the kth component
EEN
D,kEndogenous exergy destruction within the kth component, based on the decomposition method
EEN∗
D,k
Endogenous exergy destruction within the kth component, based on the real characteristic curves
EEX
D,kExogenous exergy destruction within the kth component
EEX
D,i→kExogenous exergy destruction that component icauses within component k
EAV·EN
D,kAvoidable endogenous exergy destruction within the kth component
Entropy 2020,22, 32 22 of 23
EAV·EX
D,kAvoidable exogenous exergy destruction within the kth component
EUN·EN
D,kUnavoidable endogenous exergy destruction within the kth component
EUN·EX
D,kUnavoidable exogenous exergy destruction within the kth component
EAV·EN
D,kAvoidable endogenous exergy destruction within the kth component
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