1. Introduction
In the last decades great efforts have been made to improve the efficiency of air-conditioning units, as proven by the growth of Certification Programmes [
1], both in terms of coverage among manufacturers and refinements in standard ratings, and by the wide research activities concerning the new refrigerants [
2] and the technological solutions for enhanced heat transfer [
3].
Unfortunately, despite this great effort in developing components and systems with higher nominal efficiency, less attention has been paid to the problem of improper/insufficient system maintenance. Extensive surveys have revealed that refrigeration units integrated in air conditioning systems are often poorly maintained and experience dramatic degradation of performance due to the presence of malfunctions or “faults” [
4]. Among the most commonly detected faults, despite all electrical failures, the authors identified the frequent presence of dirty coils, refrigerant leakages from the high to the low pressure side of the compressor and refrigerant leakages to the ambient eventually resulting in undercharge. Efficient troubleshooting is not sufficient, since repairs are often invoked when the system is already experiencing the presence of “heavy faults” that eventually lead it out-of-service; conversely, the attention should be more and more focused on the detection of “soft faults”, that do not cause the unit stop functioning, but only induce degradation in plant performance provoking a decrease in the cooling capacity and a reduction in the Coefficient Of Performance (COP).
Actually, the the has been already addressed in literature. The scientific community has been developing more and more refined Faults Detection and Diagnosis (FDD) techniques, oriented to identifying faults affecting plant performance, thus allowing for maintenance aimed at restoring efficient operating conditions. Earlier studies were oriented to develop a “symptom matrix”, where for each fault the expected changes of different thermodynamic parameters were qualitatively recorded, in terms of either increase (↑) or decrease (↓) [
5]. More recent works, however, have proposed new model-based FDD techniques for systems not heavily instrumented; in general, the diagnostic capability resulted from the evaluation of “residuals”,
i.e., differences between the measured values of some thermodynamic parameters and their “expected values” [
6].
The aforementioned diagnostic approaches suffer the possible presence of multiple faults, which is a quite common condition in refrigeration systems, especially for air conditioning applications. Then, an interesting approach has been proposed in [
7], based on the use of “decoupling features”,
i.e., thermodynamic variables (or their combinations) that are prevalently influenced by a unique fault and thus suitable for problem decomposition in multi-faults systems.
All the above described FDD techniques, however, share in common a limit that is essentially related with the qualitative nature of their results: even when a fault is correctly identified, the procedure does not allow one to assess whether we are in presence of a “light” or a “heavy” fault nor, in case of multiple simultaneous faults, to quantify the degradation of plant performance induced by any individual fault.
Then, a growing interest has been emerging for possible applications of thermoeconomic diagnosis, due to its intrinsically quantitative nature; thermoeconomic diagnosis is aimed at detecting efficiency deviations and evaluating their economic worth to identify the main causes that originated the performance degradation. The “fuel impact approach”, in particular, assumes a “productive structure” of the energy system (a representation alternative to its physical lay-out) where the interactions between components are identified basing on their functional relation. The resources consumed by each component (namely, its “fuels” F) and its useful outputs (namely, its “products” P) are preliminarily evaluated in exergy terms; then, a peculiar syntax based on cost balances and appropriate cost allocation rules [
8] allows the analyst to disaggregate the additional fuel consumption into contributes associated with the malfunctions occurring in each component. Thermoeconomic diagnosis has been rarely applied to refrigeration systems for several reasons:
- -
The application of thermoeconomic diagnosis to vapour compression cycles is quite difficult and the reliability of results hasn’t been proven yet. The performance of any plant component, in fact, is heavily influenced by all other components (due to system balancing); then, the effects of any fault will propagate to the whole plant, according to quite complex relationships. This problem has been addressed in literature [
9,
10], decomposing the additional exergy destructions observed at component level (due to local decrease of exergy efficiency) into “intrinsic malfunctions”, directly provoked by anomalies on the component, and “induced malfunctions”,
i.e., malfunctions induced by changes in the operating point of the component (eventually provoked by intervention of the control system) [
11] and consequent variations in its efficiency;
- -
Difficulties are encountered when developing the “productive structure”, which requires any component to be modelled as a consumer of a fuel “F” and producer of a product “P”. The conceptual ambiguities are mainly related with the “condenser” and the “throttling valve”. The former represents a “dissipative component”,
i.e., a device whose productive purpose (to discharge heat allowing to close the thermodynamic cycle of refrigerant) can be hardly expressed as a useful exergetic product. Several approaches have been proposed in literature, allocating the cost of the “residues” generated on the different components proportionally to their “negentropy” consumption [
12,
13] or to the exergy of the flows processed in the dissipative units according to the productive structure of the plant [
14]. As concerns the expansion valve, the conventional thermoeconomic approach assumes this component to represent a productive unit, which consumes “mechanical exergy” to produce an increase of refrigerant “thermal exergy” [
15]; however, this approach has been proven controversial [
16].
A first example of comprehensive thermoeconomic diagnosis of refrigeration plants has been presented in [
13], adopting the “fuel impact” approach. However, in this paper lacks controversial arguments, since the diagnosis is performed for a generic off-design state, not providing details about the set of faults that led to the abnormal operating condition.
In a recent paper by Piacentino and Talamo [
17] some innovative solutions have been proposed, consisting of an original approach to model the dissipative components (the expansion valve and the condenser) and on an improvement in the diagnostic performance achievable by preliminarily filtering the effects of “system level” faults like refrigerant undercharge. The proposed approach has been tested for several combinations of multiple faults, in case of light and heavy performance (
i.e., COP) degradation, achieving very promising results both in qualitative (capability of the technique to identify the faulty components) and quantitative (estimation of the increased energy consumption induced by each fault) terms. Analysing in details the methodological fundamentals of the improved thermoeconomic approach adopted in [
17] is beyond the scope of the present paper.
Being this diagnostic method based on exergy flows, however, it’s worthwhile verifying whether (and at what extent) its performance is sensitive to boundary conditions; in fact, the very good performance achieved in the referenced paper was obtained for a specific operating condition, and it is evident that the exergy values may experience very high fluctuations when changing some thermodynamic parameters of the operating fluids. From this perspective the evaporator is probably the most critical component, due to the contemporary air cooling and dehumidification processes occurring across it, that induce significant variations in both the chemical and thermal fractions of air exergy. For this reason, the aim of this work is to investigate the sensitivity of the performance of the diagnostic technique proposed in [
17] to the parameters that mostly influence the exergetic performance of the evaporator, assuming different operating conditions in terms of:
- -
temperature and relative humidity of the air entering the direct expansion (DX) coil;
- -
coil depth (modified by assuming different number of rows), since this parameter influences the dehumidification capacity of the coil and the sensible/latent heat ratio.
3. Definition of the Reference Scheme and of the Examined Scenarios
The plant consists of a 120 kW air-cooled air conditioning rooftop unit that includes:
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Two Copeland D4SA-200X reciprocating compressors (322 cm3 displacement each).
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A finned condenser with 15.9 mm tube diameter, 14 fins per inch spacing and a compactness ratio of 913.8 m2/m3.
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A thermal expansion valve (TXV) that imposes a fixed 6 °C superheating at the evaporator outlet.
As concerns the design of the evaporator, a fixed 1.92 m
2 face area was assumed (resulting from the 2400 × 800 mm size), while in the present paper three different coil depth were examined, characterized by a fixed 25 mm transversal spacing between consecutive rows. All the geometrical details of the main components and piping (
i.e., discharge, liquid and suction lines) have been provided in [
18]; the refrigerant is R407C. The reader is referred to the cited article for a detailed description of all the geometrical specifications of the plant.
As concerns the examined scenarios, an ambient temperature T
0 = 307.15 K (t
0 = 34 °C) was assumed, while different values of ambient relative humidities ϕ
0 (40%, 70% and 100%) were selected. In order to perform simulations, different conditions were assumed:
- -
Five different air inlet temperatures at the evaporator coils, equal to 22 °C, 25 °C, 28 °C, 31 °C and 34 °C. While the former three values (22, 25 and 28 °C) may be conceived as more or less realistic set-point conditions for indoor comfort (depending on the clothing level and internal activity performed in the cooled ambient), the last two values (31 and 34 °C) represent possible inlet temperatures in case that the remote cooling units threats only “external air” or that a very low air recirculation rate is considered;
- -
Three different air inlet relative humidities, equal to 45%, 60% and 75%;
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Three different coil depths, respectively equal to 3, 5 and 7 rows [
19]. The scope for examining these three different geometries is evident in
Figure 1, where the results obtained for the particular air inlet conditions T
E-inlet = 25 °C and ϕ
E-inlet = 60% are presented for the clean coils; from an analysis of
Figure 1 we may observe that the dehumidification capacity increases with coil depth, as testified by the increasing relative humidity of the cold air exiting the coil. This is obviously due to the reduction of the by-pass factor of coils when the number of rows increases;
- -
Two general operating conditions, related with the presence or the absence of the evaporator fouling (i.e., dirty or clean coil).
Therefore, the total number of plant simulations performed is 5 × 3 × 3 × 2 = 90 (referring to 45 combinations of inlet air conditions and coil geometries and two operating conditions, i.e., “dirty coil” and “design”).
As any thermoeconomic model requires the material streams and the components to be easily identified, the main plant components and the material streams were numbered consecutively, respectively by Arabic numerals (from 1 to 4) and by letters (from A to D for the refrigerant and by E and G for air), according to the simple notation presented in
Figure 2. No “line faults” were considered in this study, and then the thermodynamic state of the refrigerant exiting a component were assimilated with that of the fluid entering the successive one (
i.e., A ≡ A', B ≡ B', C ≡ C', D ≡ D').
4. Plant Simulations of the Examined Scenarios
The simulations were performed using the tool IMST-ART Version 3.60 [
20], that implements the Finite Volume Method (FVM) to produce a discretization of coils’ surface and simulate the heat and mass transfer processes. Performance maps of the compressor and the fans were also adopted. The tool has been proven highly reliable, basing on comparisons with experimental data [
21].
The tool does not include specific options to simulate a fouled evaporator; however, it allows for introducing “an enhancement factor” of pressure drops through the coil on the air-side, that is the largely prevalent effect of fouling on coils (since it implies a significant reduction in the air-velocity across the coil). In Ref. [
19], in fact, it has been shown that while a heavy fouling induces increases in the air-side pressure drop in the order of 30%–50% compared to the clean coil (for a given air velocity), the induced change in the heat transfer coefficient is much lower (reduction in the order of 3%–5% is observed, for a given air velocity). IMST-ART implements a detailed heat exchangers model that determines heat transfer coefficients by built-in correlations and solves heat and mass transfer equations by FVM, discretizing the surfaces into a series of one dimensional paths of 1D-cells. Then, in order to simulate the effects of the examined fault, appropriate adjustments were made to the “pressure drop enhancement factor”, so as to simulate clean coils (corresponding to average air face velocity w
air equal to 2.7 m/s) and dirty/fouled coils (achieving a w
air = 2.1 m/s); the changes induced on the heat transfer coefficient due to the lower air velocity were determined by the routine.
The convenience of using thermodynamic data derived from plant simulations, rather than from experimental campaigns, is largely proven in the literature for such kind of problems. In fact, complex experimental campaigns would have been needed to acquire data on systems with clean and dirty coils, over such a wide range of possible operating conditions. Also, the use of a simulator is particularly appropriate for “what-if analyses” [
8], since it yields flexibility in developing “faulty operation” scenarios, thus allowing for an efficient testing of the diagnosis technique; finally, in a recent work [
22] the use of numerical-based diagnosis has been validated as an option to perform the diagnosis of a refrigeration system. Below in the paper all the thermodynamic parameters obtained by plant simulation had been preliminarily compared with experimental trends available in literature to ensure that they were realistic. In order to give a synthetic view of the effects induced by coil fouling, in
Table 1 the results are shown for the 5-rows coil and the 15 examined scenarios in terms of air inlet conditions, both for the cases of clean and dirty coil. The simulation tool provided detailed thermodynamic results on both the air-side and the refrigerant-side and for all the components; such results are not presented, being associated with hundreds of numerical values.
5. Exergy Analysis for All the Examined Scenarios
Due to the very high number of thermodynamic data to process, in order to calculate the exergy flows and significant parameters such as the unit exergy consumptions
k of components (inverse of their exergetic efficiencies η
ex), a convenient file was developed in Engineering Equations Solver Version 9.810 [
23].
As concerns the refrigerant side, the reference expression of the total exergy (sum of a physical and a chemical fraction) is:
where h and s represent the specific enthalpy and entropy, while μ
i,
mfi and M
i respectively indicate the chemical potential, the molar fraction and the molar mass of the i-th constituent species. However, since plant operation did not involve any change in the chemical composition of the refrigerant, only its physical exergy fraction was calculated. Also, due to the need to identify a productive scope for each plant components in order to perform the thermoeconomic diagnosis, the physical exergy was split into its “thermal” and “mechanical” fractions, b
T and b
P (with b
T + b
P = b
phys), related with the temperature and pressure disequilibria between any examined thermodynamic state and the ambient dead state, respectively [
15,
24]. Different from the physical exergy, which represents a co-property of the fluid and the dead-ambient states (
i.e., that represents a state function once the ambient dead state has been specified), the “thermal” and “mechanical” fractions of exergy depend on the specific path defined to move from the “equilibrium with ambient” to the specified state point. In a recent paper [
17] a convenient path has been defined, which was proven efficient for the thermoeconomic diagnosis of refrigeration systems; for further details on the approach followed to calculate b
T and b
P for the refrigerant the reader is invited to examine the cited reference work.
On the air side, both the thermal and the chemical exergy fractions had to be calculated, since at the evaporator coil the air undergoes a simultaneous cooling and dehumidification process, thus modifying also its composition and chemical exergy. Conversely, it was not necessary to calculate the mechanical exergy of air, related to pressure, since in the thermoeconomic model the evaporator and its fans were dealt with as a single component (and then it was not necessary to follow individually the increase of air mechanical exergy across the fan and its successive reduction due to pressure drops across the coil).
Below are the expressions adopted to calculate the specific exergy of air streams:
In the following of the analysis the main focus was given to the exergetic performance of the evaporator, since the paper is aimed at investigating the efficiency of thermoeconomic diagnosis (
i.e., an exergy-based technique) to detect a fouled evaporator coil. Then, some results are now presented in terms of exergetic efficiency of the evaporator, defined as follows (the notation presented in
Figure 2 is used to identify components and fluids’ state):
Equation (4) expresses the exergetic efficiency as ratio between the useful exergy output (
i.e., the increase in thermal and chemical exergy of the air being cooled and dehumidified) and the exergy consumption (
i.e., the reduction in the thermal and mechanical exergy of refrigerant, passing from state C to state D, plus the electric consumption to drive the fan). As an example, in
Figure 3 the results obtained for a number of different scenarios are shown for the five rows coil, simulated as “clean”; results are plotted
versus the relative humidity assumed for the ambient dead state, ϕ
0: in fact, according to Equation (3) the chemical fraction of air exergy (that increases across the coil due to the dehumidification) is highly sensitive to this parameter.
Looking at
Figure 3, we may observe that:
- -
When ϕ
0 increases from 40% to 100%, the exergetic performance also increases due to the higher value of chemical exergy of the dehumidified air: in fact, the higher the vapour content of the ambient “dead state” air, the higher the deviation from chemical equilibrium and the chemical exergy content of the low humidity air exiting at state “E-out” (see
Figure 2);
- -
At a given value of ϕ0, the exergetic performance of the evaporator decreases for higher air inlet temperatures, because both the thermal exergy of the cooled air and the latent capacity of the coil decrease;
- -
Negative values of the exergy efficiency were surprisingly obtained for low values of ϕ0, when inlet air is very warm and humid (TE-inl = 34 °C and ϕE-inl = 75%). This result is a consequence of the reduction in the chemical exergy of the cooled air, when moving across the coil: in fact, being dehumidified, the vapour content of air ω becomes closer to the reference vapour content ω0 of ambient air and, according to Equation (3), the chemical exergy content of air decreases.
7. Analysis of the Results Achieved by Thermoeconomic Diagnosis
Once presented in the previous sections all the methodological aspects and some crucial settings needed to make the procedure potentially reliable, the thermoeconomic diagnosis was performed by imposing for all the scenarios and coil geometries a “heavy fouling” condition (corresponding to a decrease in the air face velocity from 2.7 m/s down to 2.1 m/s) and verifying whether or not the diagnostic procedure was able to correctly identify the evaporator coil as “dirty or fouled”. In this section the results obtained for all the examined scenarios will be presented and discussed.
In
Figure 4a–c three series of results are shown, respectively for the three, five and seven row coils and for all the examined scenarios as concerns the coil air inlet conditions:
- -
The term
indicates the estimation of additional exergy consumption induced by evaporator fouling, according to the diagnostic procedure proposed in [
17] and described by the tabular productive structure presented in
Table 2;
- -
The term ΔFT represents the actual additional exergy consumption provoked by evaporator fouling (at a fixed exergy production rate). This term, that usually represents an unknown value when diagnosing a real plant, is in our case known because the “faulty” scenarios have been numerically simulated, thus making available the correct value to benchmark the performance of the diagnostic technique;
- -
The performance indicator Ψfault 4 represents the ratio between the two above terms, which assesses the reliability of the technique in quantifying the additional consumption.
Looking at
Figure 4a–c, we may observe that:
- (1)
the vast majority of cases, i.e., for most of the combinations of boundary conditions (inlet air temperature and humidity) and geometry (i.e., coil depth), the term is positive; in all these cases the thermoeconomic diagnosis provides a correct response “from a qualitative viewpoint”, since due to the resulting positive malfunction cost it can provide an alert signal for the apparent presence of fouling at the evaporator (component “4”). Only in three cases, and in particular for the three row coil and in presence of very high air inlet temperature and relative humidity (i.e., in case of very high absolute humidity of the inlet air), the technique fails in detecting the evaporator as “probably fouled”, as evident from the < 0;
- (2)
In a number of cases (more frequently for the three row coil, rarely for the five and seven row ones) the term ΔF
T is negative, thus resulting in a consequently negative value of the performance indicator Ψ
fault 4. In such conditions the use of “exergy” as a basis to identify malfunctions reveals inadequate, since the dirty/fouled coil appears “more exergetically efficient” than the clean coil, thus leading to an evident inconsistency. This condition may be observed to occur for the same set of conditions that in
Table 5 had been observed to achieve the unsatisfactory condition
. Since most of these cases occur (for any coil geometry) at high relative humidities of inlet air (
i.e., when a large fraction of the coil is wet), we may conclude that the use of “exergy-based” diagnostic techniques is favoured (even when chemical exergy of dehumidified air is excluded from the analysis, as in our case) when air with a quite low relative humidity enters the coil,
i.e., when most of the rows operate in dry conditions;
- (3)
Once excluded the aforementioned cases where ΔF
T < 0 occurs, let us look at the numerical value assumed by the performance indicator Ψ
fault 4, in order to assess whether or not the diagnostic technique is efficient in quantifying the additional consumption induced by evaporator fouling. Let us assume as a good performance indication, from a “quantitative viewpoint”, the condition “0.5 < Ψ
fault 4 < 1.5”, identified by the hatched bold line contour in
Figure 3a–c; in fact, in such cases we are sure that
and that
(the output value of the diagnostic technique) represents a more or less reasonable estimation of the actual additional consumption
induced by the dirty coil (this value being, as said above, unknown in any real world application). The cases where the above condition is satisfied and the technique achieves a quite appreciable “quantitative” performance are identified by a red circle and numerated consecutively in
Figure 4a–c. It is evident that for the five and seven row coils the diagnostic technique performs well in a high number of cases, and in particular in most of the cases with relative humidity between 45% and 60% (which represent the largely most common situation in civil uses of air conditioning); for a 75% relative humidity, the diagnostic procedure has a much poorer performance, with a relevant overestimation of the additional exergy consumption provoked by evaporator fouling. On the contrary, the performance of the diagnostic technique is always poor for the system with a three row coil, with frequent overestimation of the impact of evaporator fouling.
The relation between the sensitivity of performance of the diagnostic technique to the coil geometry and to the inlet air conditions appears much more clear and intuitive in
Figure 5a–c. Here the three aforementioned levels of performance, based on a qualitative aspect (related with the capability to detect the dirty coil condition) and a quantitative aspect (related with the capability of the technique to provide a reasonable estimation of the additional energy consumption induced by the dirty coil), are mapped over a psychrometric chart.
This representation allows to observe much more intuitively that the thermoeconomic diagnostic technique performs worse whenever the air entering the cooling coil has a high absolute humidity.
An interpretation of the poor performance of the diagnostic technique in certain operating conditions is here provided. As stated in
Section 6.2, the effectiveness of the technique used to filter
induced malfunctions (so as to focus only on
intrinsic ones) is of utmost importance for the reliability of thermoeconomic diagnosis of refrigeration systems. The adopted filtering technique, that uses two sets of distribution ratios (“
a1,
a2,
a4” and “
c1,
c2,
c4”) to allocate respectively the effects induced by malfunctions on the expansion valve and the condenser, was implemented using specific values of these ratios calculated in [
17] for a specific geometry (five row coil) and a specific set of operating conditions (in particular assuming t = 27 °C and ϕ = 65% as air inlet conditions to the evaporator coil). One of the limits of the method can be related with the poor performance of the technique used to filter these induced malfunctions, whenever the diagnosed geometry and operating condition significantly differ from the reference geometry/condition used in [
17] to fix the distribution ratios. From this perspective, future advances of the technique could be aimed at calibrating the optimal values of the distribution ratios to be used for each specific coil geometry and interval of operating conditions (
i.e., for each specific region of the psychrometric chart in
Figure 5). Another possible limit of the technique is related with the volatility of the exergy function when air is intensely dehumidified across the coil,
i.e., when most of its surface operates in wet conditions; in order to overcome this limit, more accurate thermodynamic models will be probably needed to filter efficiently the malfunctions induced by changes in the exergy performance.
The proposed analysis revealed that in general the performance of the diagnosis is very sensitive to all the examined parameters. This result is very relevant; in fact, the particular operating conditions tested in [
17] had led to an excellent diagnostic performance of the technique, thus making this pioneering technique seem a ready-to-use and reliable methodology, which could be expected to have potential for testing in industrial components. Conversely, the results of this study verified that: (i) the methodology is not robust, since its performance is extremely sensitive to the operating conditions (due to the particular behaviour of the function “exergy”) and (ii) it is very likely that exergy-based diagnostic techniques should necessarily be designed, in the field of refrigeration and air-conditioning, paying great attention to the specific conditions expected during the plant lifetime operation.
8. Conclusions
In this paper the robustness of thermoeconomic diagnosis for the detection of malfunctions in direct-expansion air-conditioning units was investigated. The sensitivity of performance to a number of different variables was assessed, focusing the attention on the thermodynamic conditions of the coil inlet air to be cooled and dehumidified, the “dead state” humidity assumed and the coil geometry.
The preliminary exergy analysis revealed that due to the analytical expression of chemical and thermal exergy, the assumption of the “total exergy of the cooled air” as useful output of the evaporator coil can lead to misleading result; in particular, based on the total exergy performance, the unit may erroneously appear to work more efficiently with a dirty coil, compared to the “reference case” of clean coil.
Once properly implemented the diagnostic technique on the basis of the “thermal fraction only” of air exergy, the performance of the methodology revealed highly sensitive to both the inlet air conditions and to the coil geometry. In particular, it resulted very efficient both in detecting the faulty unit and in quantifying the additional energy consumption induced by fouling when the air entering the coils has a low absolute humidity (i.e., not to high values of temperature and relative humidity); also, the efficiency of the technique resulted to increase when coils with higher depth are considered. These results, mapped on a psychrometric chart, allowed to distinguish between regions where a performance of the diagnosis can be expected and other regions where the thermoeconomic diagnosis performs poorly.
As a general conclusion, it can be said that the pioneering use of thermoeconomic diagnosis for air-conditioning applications requires great expertise of the analyst, which should in general design the whole procedure being aware of the conditions the plant will most likely encounter during its operation.