On Thermoeconomic Diagnosis of a Fouled Direct Expansion Coil: Effects of Induced Malfunctions on Quantitative Performance of the Diagnostic Technique

Transcription

1 ISSN Journal of Sustanable Development of Energy, Water Journal of Sustanable Development of Energy, Water and Envronment Systems On Thermoeconomc Dagnoss of a Fouled Drect Expanson Col: Effects of Induced Malfunctons on Quanttatve Performance of the Dagnostc Technque Antono Pacentno *1, Petro Catrn 2 1 Department of Energy, Informaton Engneerng and Mathematcal Models, Unversty of Palermo, Vale delle Scenze, Edfco 9, Palermo, Italy e-mal: antono.pacentno@dream.unpa.t 2 Department of Energy, Informaton Engneerng and Mathematcal Models, Unversty of Palermo, Vale delle Scenze, Edfco 9, Palermo, Italy e-mal: catrnpetro@gmal.com Cte as: Pacentno, A., Catrn, P., On Thermoeconomc Dagnoss of a Fouled Drect Expanson Col: Effects of Induced Malfunctons on Quanttatve Performance of the Dagnostc Technque, J. sustan. dev. energy water envron. syst., 5(2), pp , 2017, DOI: ABSTRACT Thermoeconomc dagnoss represents a promsng technque for the detecton of common faults n refrgeraton systems, whch are responsble of degradaton n ther energetc performance. Recently, the authors have carred out a senstvty analyss of the performance of ths method to the thermodynamc condtons of nlet ar and to the geometry of the drect expanson col, n case of degradaton nduced by evaporator foulng. The analyss showed that the method s able to detect ths fault, but sometmes ts quanttatve assessments are not satsfactory. In order to understand more n-depth the orgn of such results and dentfy margns for refnement of the technque, ths paper s amed at evaluatng at what extent changes n the exergetc performance of faults-free components may negatvely nfluence the model capablty to detect the fouled evaporator and quantfy the consequent addtonal exergy consumpton. The results suggest that the method s partcularly senstve to the cost of nduced malfunctons on the compressor and the condenser, especally when low col depth or hgh relatve humdty of nlet ar are consdered. KEYWORDS Thermoeconomc dagnoss, Evaporator foulng, Drect expanson col, Exergy, Malfuncton cost, Fuel mpact, Induced malfuncton, Intrnsc malfuncton. INTRODUCTION In last few decades, thermoeconomc dagnoss has been shown to represent a promsng nstrument for the detecton of malfunctons occurrng n energy systems. Most of the works avalable n lterature have been focused on dagnoss n power plants, wth a focus on coal fred plants n [1] and [2], cogeneraton plants n [3] and combned cycles n [4]; for such applcatons, the method has been proven to furnsh promsng results. Only n the last few years the dea to extend ts applcaton to refrgeraton system has been emergng as a research trend. As shown n several studes [5], large energy * Correspondng author 177

2 consumpton s related wth space coolng n buldngs, where the poor mantenance of ar condtonng plants frequently nduces relevant degradaton of ther performance [6] and a consequent ncrease n ther energy consumpton. Havng a relable tool whch nforms on any devaton occurrng n plant performance and dentfes ts causes would be very helpful to schedule preventve mantenance program and thus acheve energy savngs. Exergy and cost represent the key concepts of thermoeconomc dagnoss; exergy, s a measure of thermodynamc qualty of energy flows [7], and t allows to evaluate the ratonale of energy converson process by assessng the exergy destructon occurrng at each stage [8]. As regards exergy applcaton n bult envronment, useful methods were developed n [9] n order to estmate exergy/energy consumpton; furthermore, practcal desgn-support nstruments have been defned n COST Acton C24 n order to facltate the applcaton of the exergy concept n ths sector [10]. As regards HVAC systems, n [11] the authors showed that these components are characterzed by very poor exergetc effcency, snce they are suppled wth hgh qualty energy, fossl fuel or electrcty, n order to produce thermal energy flows at low temperature (.e. low exergy content) as requred by heatng and coolng processes. As t was outlned n Annex 37 [12], and n the followng developments acheved n Annex 49 [13], exergy analyss suggests that the most ratonal way to use energy n HVAC systems conssts of supplyng them wth low qualty energy sources as process waste heat or renewable sources (solar thermal heat, geothermal heat), thus leadng to economc and envronmental benefts from substtuton of non-renewable energy sources to renewable ones [14]. Some examples of buldngs whch are already equpped wth such systems can be found n [15]. Other promsng solutons are presented n [16], where dfferent typologes of solar trgeneraton systems for HVAC are proposed, and n [17] where economc assessment for a trgeneraton plant for HVAC systems n Italy are presented. The above analyses were carred out consderng systems whch operate n desgn condton: when faults occur n a component [these faults beng assocated wth poor performance of the unt, ether n terms of decreased capacty or Coeffcent of Performance (COP)], ts exergy consumpton ncreases due to hgher generaton of rreversblty, thus reducng the exergy effcency. In order to mantan ts producton rate constant (as usually mposed by the control system), the plant consumes more fuel (to be ntended as nput resource, ether beng represented by fossl combustbles, electrcty, etc.); thermoeconomc dagnoss ams at dsaggregatng ths addtonal fuel consumpton (caused by the presence of faults) nto contrbutons assocated wth the malfunctons occurrng n each specfc component, based on rgorous nstruments such as cost balances and approprate cost allocaton rules [18]. As a frst step, t s necessary to defne for each component the exergy of ts consumed resources [.e. ts fuels (F)] and ts useful outputs [.e. ts products (P)]; then, based on an analyss of the nteractons between plant components and wth the external envronment, a productve structure of the examned system s developed. Dependng on the expertse of the analyst and on the dsaggregaton level adopted for the thermoeconomc representaton of the plant, t s clear that dfferent productve structures of a same energy system can be defned, whch could lead to more or less accurate results even when dagnosng a unque faulty operatng condton. In a recent paper [19] the classcal thermoeconomc approaches have been tested wth a set of multple faults scenaros n ar-cooled drect expanson ar condtonng unt: the results ndcated that conventonal thermoeconomc dagnoss s not a relable technque when appled to refrgeraton systems because: t cannot effcently deal wth system level faults,.e., wth faults not assocated wth any specfc component lke refrgerant under- or over-charge, and the usually adopted productve model for the expanson valve erroneously leads to dentfy ths component as faulty even when ts operaton 178

3 has no anomales. In order to overcome these lmts, an nnovatve thermoeconomc model has been proposed n [20], whch was proven to be suffcently relable when the effects of system level faults lke refrgerant undercharge are fltered. More recently the authors of the present paper have nvestgated the robustness of ths nnovatve dagnostc technque for the detecton of evaporator foulng n drect-expanson ar-condtonng unts [21]. In partcular, the senstvty of the performance of the method to a number of dfferent varables was assessed, focusng the attenton on the col geometry and on the thermodynamc condtons of the nlet ar at the evaporator col, whch evdently nfluence the ntensty of ts coolng and dehumdfcaton process. From a qualtatve pont of vew, the method was very effcent n detectng the evaporator as the faulty component n almost all the examned cases; conversely, from a quanttatve pont of vew, the technque was effcent n quantfyng the addtonal energy consumpton nduced by evaporator foulng only when the nlet ar had a low absolute humdty (.e. not partcularly hgh values of temperature and relatve humdty) and when cols wth hgher depth were concerned (.e. col wth a hgh number of rows and a consequently hgh dehumdfyng capacty). The lmted capablty of ths method to localze anomales wthn a system and to quantfy ther effects manly derves from the fact that under faulty condton not only the exergetc performance of the malfunctonng component changes, but also varatons n the performance of fault-free components occur due to change n ther operatng condtons (and/or n the thermodynamc states of the workng fluds). As a consequence, there s a strong rsk that a dagnostc technque erroneously dentfes possble malfunctons located n fault-free components. If the dagnoss technque s not able to flter all these nduced effects,.e. effects generated by the faulty components on the other ones, msleadng results mght be acheved. In the scentfc lterature several works have already focused on ths topc; wth reference to a gas turbne-based cogeneraton plant, for nstance, n [22] a method was proposed to flter the malfunctons nduced by the control system and by the specfc behavour of each plant component. In the present paper, startng from the dagnostc results obtaned n [21], the authors focus ther attenton on those cases where the method dd not properly quantfy the effects provoked (n terms of addtonal electrcty consumpton) by evaporator foulng and, based on n-depth analyses, attempt to dentfy the causes of these erroneous/msleadng results. In partcular, the present work attempts to clarfy at whch extent the nduced malfunctons nfluence the quanttatve performance of ths dagnoss technque, and under what condtons the thermoeconomc model adopted may be able to reduce ther mpact. Although the scope of the study mght appear of nterest only for expert thermoeconomc analysts, t must be observed that: Developng effcent dagnostc technques for refrgeraton and ar condtonng systems has been emergng as a challengng but very promsng research lne, as proven by the dozens of scentfc artcles publshed on ths topc n the last few years; The scope for such sgnfcant research efforts s absolutely justfed by the hgh energy savng potental related wth the adopton of ratonal mantenance schedules n ar condtonng systems, whch have been proven to be often poorly mantaned both n the commercal and n the resdental sectors. ON THE METHOD OF THERMOECONOMIC DIAGNOSIS In ths secton a bref overvew on thermoeconomc dagnoss s gven, n order to clarfy some man features and crtcsms of ths technque; a detaled descrpton of the 179

4 fundamentals of ths method s out of the scopes of ths paper. The reader may refer to the referenced works [3] and [4] for a comprehensve explanaton of ths technque. The frst step n any thermoeconomc analyss conssts of the defnton of the exergy of the Fuel F consumed, as an nput, by each generc -th plant component, and of ts useful output P (.e., ts Product ); both these flows must be evaluated n exergy unts. Applyng the exergy balance to the generc -th component, F = P + I, the rreversblty I generated durng ts operaton may be easly obtaned. Once the fuel(s) and the product(s) are defned for each component, t must be clarfed how each component nteracts wth other components wthn the system and wth the external envronment, n terms of exergy flows exchange. The representaton (alternatve to the physcal plant scheme) where all components are nterconnected on the bass of ther functonal relaton (that means, each -th component s connected only wth the components that supply ts fuels or consume ts products) s named productve structure. In some cases the aforementoned Fuels/Products representaton s not suffcent to reflect the operaton of the components, snce t s not possble to dentfy a productve scope of the components (.e. a useful product) to be measured n exergy terms. As an example, when we consder the condenser of an ar condtonng unt, t evdently dsspates the thermal exergy of the refrgerant to the external coolng ar, wthout producng any useful exergy flow. In order to model such components, the theory of Thermoeconomcs defnes such exergy flows (dsspated wth no apparent scope) as resdues, suggestng to consder them as a sort of product of the component where they are physcally dsspated, and then to allocate them as addtonal nputs to the dfferent plant components whch had contrbuted to ther formaton process [23]. For a generc -th component an overall unt exergy consumpton k and an overall unt resdue consumpton r, are defned as follows: F k = (1a) P R r = (1b) P The overall ncrease of exergy destructon n a generc -th component due to presence of faults s determned as sum of addtonal local exergy destructon due to rreversblty ΔI (where I = F P) and addtonal resdue consumpton ΔR [3], eq. (2): 0 0 [( k 1) P ] + Δ( r P ) = Δ k P X + [ k ( X ) 1Δ ] P + Δ r P X r ( X ) P (2) ΔI + Δ R = Δ + Δ In eq. (2), X and X 0 represent two sets of thermodynamc varables, respectvely ndcatng the system operatng under desgn (.e. fault-free) and faulty condtons. Basng on eq. (2), we may dstngush between: Malfuncton (or endogenous rreversblty), represented by the terms ΔkP (X 0 ) and ΔrP (X 0 ) n eq. (2) and assocated wth ncreases n unt exergy consumptons or unt consumpton of resdues n the -th component: 0 0 ( X ) Δ ( X ) (k) (r) MF = MF + MF = Δk P + r P (3) 180

5 Dysfuncton (or exogenous rreversblty), nduced n the -th component by the malfuncton of other components that provoke a varaton ΔP n the producton rate of component : DF N = = 1 (k) (r) ( DF + DF ) = k ( X ) j j [ 1Δ ] P + r ( X ) ΔP (4) The method ams at dstngushng the addtonal exergy destructon n each component provoked by faults occurrng n the same component and those nduced by malfunctons occurrng n other components; at ths purpose, a malfuncton cost MF * s ntroduced: MF * = MF + N (k) (r) ( DFj + DFj ) j = 1 (5) where MF * represents the addtonal fuel consumpton provoked by faults occurrng n component, and s calculated summng up the addtonal exergy destructon MF that these faults nduce on the same component [see eq. (3)] and the dysfunctons that these faults generate n other components j (for j = 1 to N, wth j ) [24]. The second term on the rght hand sde of eq. (5) s synthetcally ndcated as DI [11]. As can be seen from eq. (4), the dysfunctons represent the extra rreversblty occurrng n the component when they are forced to vary ther product n order to satsfy the ncreased fuel consumpton of the faulty unts; snce they represent a secondary phenomenon related to the propagaton on all the plant components of the malfuncton occurrng n a specfc component, quantfcaton of ther cost has no meanng. The overall fuel mpact ΔFT s the addtonal overall exergy consumpton nduced by the faults occurrng n the N plant components, and t can be fnally calculated as: = N * Δ FT MF (6) = 0 In order to assess whether the method quantfes properly the mpact of malfuncton on the addtonal fuel consumpton, an approprate ndcator Ѱ fault, s defned: MF * fault, j j Ψ = (7) fault, j ΔFT As can be seen from eq. (7), Ѱ fault, j s defned as rato between the malfuncton cost (.e. the addtonal energy consumpton nduced by fault j, accordng to the estmaton provded by the dagnostc technque) and the fuel mpact ΔFT,.e. the actual addtonal energy consumpton nduced by fault j, calculated as dfference between the energy consumpton evaluated expermentally (or by the use of a smulator, as n the case of the referenced paper [9]) n presence of fault j and that evaluated n absence of fault j. Obvously, when Ѱ fault, j = 1, the dagnostc technque exactly quantfes the addtonal energy consumpton provoked by the fault; conversely, when Ѱ fault, j > 1 or Ѱ fault, j < 1 the dagnostc procedure respectvely over- or under-estmates the addtonal energy consumpton provoked by fault j. As stated n the prevous secton, the man reasons for the scarce relablty of the dagnostc technque n detectng the malfunctonng component s related wth the fact that n presence of faults the unt exergy consumpton ncreases (or the exergy effcency 181

6 decreases) not only n the component where malfunctons are located, but also n the remanng faults-free components, due to the changes nduced n ther operatng pont. As a consequence, accordng to eq. (3), a malfuncton MF arses not only n the actually malfunctonng components but also n those components where no anomales are occurrng. It s thus mportant to dstngush between ntrnsc malfunctons, whch are related to the varaton of unt exergy consumpton occurrng n the actual faulty component, and nduced malfunctons, whch are related to the varaton of unt exergy consumpton occurrng n faults-free component. It s clear that f a faults-free component was characterzed by a constant value of unt exergy consumpton (.e. f nduced malfunctons were absent), the extra rreversblty generated n t would be entrely classfed as a dysfuncton nduced by the faults occurrng n other components; partcularly ths ncrease of rreversblty generaton [as quantfed by eq. (4)] would only derve from the greater amount of product necessary to satsfy the ncreasng consumpton of the faulty components. The presence of nduced malfunctons s related wth the non-flat exergy effcency curves of components (at dfferent producton rates). Induced malfunctons also derve from the nterventon of the control system whch, amng at restorng the values of controlled parameters n a plant, further modfes the operatng pont of each component and consequently ts exergy unt consumpton [22]. Accordng to eq. (5), the presence of nduced malfuncton mples that a non-null malfuncton cost s obtaned for fault-free components; as a consequence, due to the presence of several smultaneous postve malfuncton costs, the analyst could not dentfy the components that are actually experencng performance degradaton due to the presence of local faults. The elmnaton of these nduced effects s complex and requres the use of a thermodynamc model for each component, n order to predct ts response to changes n the operatng condtons; as an example, n [25] some thermodynamc models were developed n order to predct changes of component exergetc performance when anomales occur. In [26] t has been shown how the accuracy of a dagnostc procedure mproves when flterng respectvely the effect of nduced malfunctons caused by the control system and by the dependence of component effcency curves from the operatng condton. ON THE REFERENCE PLANT AND ITS PRODUCTIVE STRUCTURE In ths secton only the man features of the reference plant adopted n [21] and servng as a bass for the present analyss are gven; a more detaled descrpton can be found n the referenced paper. The plant conssts of a 120 kw ar-cooled ar condtonng rooftop unt, usng R407C as refrgerant, equpped wth a Thermal Expanson Valve (TXV) whch mposes a fxed 6 C superheatng at evaporator outlet, and a thermostatc control to start and swtch-off the compressor. In the referenced paper, several scenaros were nvestgated, each dfferng from the other for the evaporator geometry (.e. the col depth expressed n terms of number of rows ) and for the nlet ar condtons at the evaporator. In partcular: Three dfferent col depths were analysed, equal to 3-rows, 5-rows and 7-rows respectvely; Fve values of ar nlet temperature (.e. 22 C, 25 C, 28 C, 31 C and 34 C) and three values of ar nlet relatve humdty (.e. 45%, 60% and 75%) were consdered. The faulty operatng condton on the evaporator was mplemented by mposng for all the scenaros and col geometres a heavy foulng condton, correspondng to a decrease n the ar face velocty to the col from 2.7 m/s down to 2.1 m/s. Followng a well-establshed approach already adopted n prevous papers [19] and [20], accurate 1-D smulatons were performed usng the tool IMST-ART verson 3.60 [27]. 182

7 In ths work, the same productve structure defned and presented n [20] was adopted, as shown n Fgure 1; as can be seen from the fgure, the physcal exergy of refrgerant s splt n a thermal fracton (ndcated as, ΔB T see red contnuous lnes n the fgure) and a mechancal fracton, (ndcated as ΔB M, see blue lnes n the fgure), whch are respectvely related to thermal and mechancal dsequlbrum between the refrgerant state and the reference dead state [28]. Splttng exergy flows n these two fractons allows the analyst to defne more accurately the consumed resource and the productve functon of each plant component: for nstance, as can be seen n Fgure 1, t s very ntutve that the only component producng mechancal exergy (.e. ncreasng the pressure dsequlbrum between the refrgerant and the ambent) s the compressor, whle all the other components (.e. evaporator, TXV and condenser) only consume mechancal exergy. A complete understandng of the productve structure and all the formulas presented n Fgure 1 would requre long methodologcal premses, whch are not formulated here for the sake of brevty. In fact, an accurate descrpton of the productve structure can be found n [20]; below only some further elements are gven, to clarfy some key aspects. Fgure 1. Productve structure of the examned drect expanson refrgeraton system In [20] two knds of resdues have been defned for an ar-condtonng system: Conventonal resdues (see red dotted lnes n Fgure 1) refer to the refrgerant exergy dsspated even n case of plant operatng n optmal mantenance condtons (.e., n the absence of faults). As an example, the exergy destroyed at the condenser 183

8 184 n the heat exchange wth the coolng ar at ambent condton represents a conventonal resdue; Margnal resdues (see green dotted lnes n Fgure 1) are related to the addtonal exergy destructons occurrng n the TXV and n the condenser when the plant works under faulty condtons. These flows are allocated as addtonal nputs to the compressor, the condenser and the evaporator, by means of approprate dstrbuton factors a1, a2, a4 (for the TXV) and c1, c2, c4 (for the condenser). Ths qute complex approach, dscussed n detal n [20], s needed to address the followng crtcsm: when faults occur n components other than the TXV, the hgh malfunctons nduced on the valve do not allow localzng the anomales takng place n other components, thus leadng always to detect the TXV as faulty, even though t s operatng correctly. Modellng the addtonal exergy destructon at the TXV as a margnal resdue and reallocatng t to the other components allows to overcome ths dffculty. The referenced paper provdes further detals about ths approach. Fnally, the product of the whole plant s the exergy varaton of the cooled and dehumdfed ar n the col; a detaled descrpton on exergy calculatons s provded n [21]. In ths cted paper, no procedure was adopted to flter the effects nduced by nterventon of the control system, snce a thermostatc control s used to start and shut-off the compressor: then, flterng the effects of the control system s unnecessary because the plant s not forced to modfy ts nstantaneous operatng condtons, beng only the duraton of on-cycles adjusted to match the load. ANALYSIS OF RESULTS In the paper that nspred the present study [21], t was shown that for all the examned scenaros the method allowed to correctly detect the evaporator as fouled, snce ts malfuncton cost (.e. MF4 * ) always assumed the hghest postve values among the plant components. However, n the same paper the quanttatve assessments of the addtonal exergy consumpton provoked by evaporator foulng were not satsfactory, especally when low-depth cols or hgh values of absolute humdty of nlet ar were concerned. As prevously stated, ths paper ntroduces advances wth respect to a prevous work by the same authors [21]: n the cted work, the authors only presented the results of the thermoeconomc dagnoss of evaporator foulng, n order to hghlght the operatng condtons (.e. nlet-ar temperature and humdty at the drect expanson col) for whch the dagnostc performance was good from both a quanttatve and a qualtatve pont of vew. In the present paper, how the nduced malfunctons on the compressor and the condenser nfluence the poor quanttatve performance of the method n the operatng condtons when the technque acheved the poorest performance s nvestgated. To acheve ths goal, a detaled zoom on the thermoeconomc quanttes (malfunctons, dysfunctons, malfuncton costs) s made, so as to understand whch components and at whch extent are affected by the mposed fault. The proposed analyss thus offers some nsghts on the thermoeconomc model adopted and suggests eventual solutons for future mprovement of the dagnostc technque. In Fgure 2 (a-c), the malfuncton costs MF *, the malfunctons MF, and the dysfunctons DI are presented respectvely for the 3-, 5- and 7-rows cols; furthermore, the performance ndcator Ѱ fault,4 s shown nsde green or red boxes below n each fgure. The two colours dstngush the cases of good and poor dagnostc performance, accordng to the approach proposed n [21]: When the condton 0.5 < Ψ fault,4 < 1.5 s satsfed, the dagnostc performance s good, snce the technque provdes a reasonable quanttatve estmaton of the addtonal consumpton provoked by the fouled evaporator. In such cases green boxes are used;

9 Conversely, when the former condton s not fulflled, the results of the dagnoss are consdered unsatsfactory snce the dagnostc technque sgnfcantly underor over-estmates the addtonal consumpton provoked by foulng. These cases are dentfed by the use of red boxes n Fgure 2. [kw ex ] MF1 DI1 MF2 DI2 MF4 DI4 MF1* MF2* MF4* Δ FT C-60% C-45% 2.06 (a) 25 C-60% C-45% 2.89 [kw ex ] 3.00 MF1 DI1 MF1* MF2 DI2 MF2* MF4 DI4 MF4* ΔFT C-45% C-75% C-45% C-60% C-45% C-45% 1.28 (b) [kw ex ] 4.00 MF1 DI1 MF1* MF2 DI2 MF2* C-45% C-75% C-45% C-75% C-45% C-45% 1.04 Fgure 2. Malfuncton cost MF *, fuel mpact ΔF T and performance ndcator of the dagnostc technque Ψ fault,4, for 3 rows (a); 5 rows (b); 7 rows (c) For the sake of brevty, n the secton below only the most llustratve cases are presented, among the large number of scenaros smulated n [21]. 185

10 The nfluence of the nduced malfunctons on the performance of the dagnostc procedure s evaluated by examnng the magntude of the related malfuncton cost, keepng n mnd that: The method recognzes as faulty the components characterzed by the hghest postve malfuncton cost; The malfuncton cost for a faults-free component would be null f nduced malfunctons were absent: n such condtons the dagnostc technque would acheve a very good performance. Beng malfuncton costs represented by algebrac values (.e. they can be ether postve or negatve), any hgh absolute value (.e., any hgh postve or negatve value) of the malfuncton cost for a fault-free component wll sgnfcantly affect the relablty of the dagnostc procedure n quantfyng the mpact of each fault. The results are shown n Fgure 2, and the components have been enumerated as follows: Compressor = Component 1, Condenser = Component 2, TXV = Component 3 and Evaporator col = Component 4. In all the subfgures no bars for the thermal expanson valve are shown (.e. no values for MF3, DI3 and MF3 * are presented), havng been the addtonal exergy destructon at the valve allocated as margnal resdues to the other three components. It can be observed that: For a 3-row cols, see Fgure 2a, the method s not able to estmate correctly the addtonal exergy consumpton provoked by the fouled evaporator. As can be seen from the fgure, under all the examned scenaros the exergetc effcency of the compressor ncreased (.e. the unt exergy consumpton decreased) as an nduced effect of the fouled evaporator, as testfed by the negatve values of MF1 resulted. The cost of ths nduced malfuncton (.e. MF1 * ) s not neglgble. Conversely, the exergetc effcency of the condenser s rather senstve to the ar nlet condtons, oscllatng between postve and negatve values MF2 values; however, n terms of malfuncton costs, n most cases negatve values of MF2 * were obtaned, suggestng that also the condenser seems to beneft of the presence of foulng at the evaporator. Drawng some conclusons, the sgnfcant over-estmaton of the addtonal consumpton provoked by evaporator foulng (see Ψ fault,4 >> 1!) s due to a smple fact: as an exergy-based dagnostc technque, the thermoeconomc model erroneously propagates the effects of the fouled evaporator on the compressor (prmarly) and the condenser (secondarly), detectng a msleadng mprovement n ther performance. Ths effect s partcularly evdent for ths col geometry, whle t wll be mtgated when examnng deeper cols (wth 5 and 7 rows), as clarfed below; As evdent n Fgures 2b and 2c, respectvely for 5-rows and the 7-rows cols, the performance method here s satsfactory n most of the examned scenaros, but when a very hgh relatve humdty (.e., 75%) of nlet ar s consdered: n these last cases, n fact, the cost of the nduced malfuncton on the compressor (whch s the most affected component for the 5-rows col case) and the condenser (whch s the most affected for the 7-rows col case) s not neglgble compared to the evaporator one. Only n these scenaros the method s not able to flter the effect of nduced malfunctons on these components, leadng to an unsatsfactory performance of the dagnostc technque. An explanaton of ths trend may be found n reference [21], where a detaled exergy analyss has shown that sgnfcant changes n the chemcal exergy of dehumdfed ar may nduce dstortons n the exergetc representaton of the plant. Dehumfcaton s obvously prevalent when the relatve humdty of nlet ar to the col s hgher; n such scenaros most of the col tubes operate n wet condtons. Conversely, when low relatve humdty s consdered (.e., values between 45% and 60%, see cases wth green boxes n Fgures 2b and 2c), the col 186

11 tubes prevalently operate under dry coolng condton, and the ntensty of dehumdfcaton decreases (thus makng the nfluence of chemcal exergy of cooled ar neglgble). In these last condtons, the dagnostc technque acheves very good performance, provdng a reasonable estmaton of the addtonal power consumpton provoked by evaporator foulng (as evdent from the Ψ fault,4 values, very close to 1). In these cases, although the malfunctons MF1 and MF2 nduced on both the compressor and the condenser are sometme hgh, ther mpact n terms of malfuncton costs MF1 * and MF2 * s very low, thus allowng for a relable use of the dagnostc method. From the dscusson above, t can be stated that the method performance s partcularly senstve to the nduced malfuncton cost when low-depth cols or hgh humdty of nlet ar are consdered; n these cases, the costs of nduced malfunctons on the compressor and the condenser are not neglgble and consequently the quanttatve assessments of addtonal exergy consumpton provoked by evaporator foulng are not satsfactory. It s clear that the senstveness of the dagnostc performance to the nduced malfunctons lmt the potental of ths technque at the present tme; one possblty to solve these dscrepances can arse from further mprovements n the thermoeconomc model. Some possble research lnes for the future refnements of the technque can be dentfed: More promsng results could be obtaned by the dentfcaton of optmal values of the dstrbuton factors a and c for each specfc col geometry or operatng condton. In the present analyss, n fact, fxed values of these constant were adopted, as derved for the same plant from reference [20]; t may be expected that the performance of the dagnostc technque wll beneft from the adopton of case-orented values of these factors ntroduced to flter the nduced malfunctons; Improvements could also be acheved by the prelmnary development of approprate characterstc equatons of the exergetc performance of each component, to better characterze ther behavour (n terms of varaton n the unt exergy consumpton) when devatons from the desgn workng condtons occur and thus flter the nduced malfunctons more effcently. CONCLUSION In ths paper a crtcal analyss of the performance of thermoeconomc dagnoss for an ar condtonng unt wth a fouled evaporator was carred out. Based on the results obtaned by the same authors n a prevous work, a zoomed analyss on the nduced malfunctons on compressor and condenser was performed, n order to understand the orgn of the unsatsfactory dagnostc performance occurred n some of the examned scenaros. It was shown that when hgh col depths or low nlet ar relatve humdtes are consdered, the costs of the nduced malfunctons on fault-free components do not nfluence the quanttatve assessments of the thermoeconomc dagnoss, suggestng that the thermoeconomc model s capable to reduce the mpact of these malfunctons even when no flterng technques are appled. Ths s no more vald when low depth cols or hgh relatve humdtes of nlet ar are consdered: n such cases, the method s very senstve to the nduced malfunctons and relevant overestmaton of the addtonal exergy consumpton provoked by evaporator foulng s obtaned. Future studes wll be focused on the possble mprovements of the thermoeconomc model of the examned system n order to address crtcsms that eventually lead to msleadng results, thus lmtng the applcablty of ths technque and the current potental for ndustral mplementaton of thermoeconomcs-based dagnostc systems. 187

12 NOMENCLATURE a dstrbuton rato on component of valve s addtonal exergy destructon [-] c dstrbuton rato on component of condenser s addtonal exergy destructon [-] DF dysfuncton generated n -th component [kwex] DI dysfuncton generated by malfuncton occurrng n -th component [kwex] F fuel of component [kwex] ΔFT fuel mpact [kwex] k overall unt exergy consumpton of component (dmensonless) I exergy destructon n component due to rreversblty [kwex] MF malfuncton [kwex] MF * malfuncton cost [kwex] N numbers of component [-] P product of component [kwex] R resdue exergy flow [kwex] r overall unt resdue generaton of component (dmensonless) T temperature [ C or K] Vectors and matrces X set of thermodynamc varables that dentfy an operatng condton Greek letters Δ ndcates varaton of the preceded term Ψ performance ndcator of the dagnoss technque Superscrpts 0 referrng to the desgn/no faults condton M referrng to mechancal exergy (the fracton related to pressure) T referrng to thermal exergy (the fracton related to temperature) (k) referrng to exergy destructon n the generaton of products (r) referrng to exergy destructon n generaton of resdues Abbrevatons COP Coeffcent Of Performance TXV Thermostatc Expanson Valve REFERENCES 1. Valero, A., Lerch, F., Serra, L. and Royo, J., Structural Theory and Thermoeconomc Dagnoss: Part II, On Malfuncton and Dysfuncton Analyss, Energy Converson and Management, Vol. 43, No. 9-12, pp , 2002, 2. Zhang, C., Chen, S., Zheng, C. and Lou, X., Thermoeconomc Dagnoss of Coal Fred Plant, Energy Converson and Management, Vol. 48, No. 2, pp , 2007, 3. Torres, C., Valero, A., Serra, L. and Royo, J., Structural Theory and Thermoeconomc Dagnoss: Part I, On Malfuncton and Dysfuncton Analyss, Energy Converson and Management, Vol. 43, No. 9-12, pp , 2002, 4. Lazzaretto, A., Toffolo, A., Ren, M., Taccan, R., Zaleta-Agular, A., Rangel-Hernandez, V. and Verda, V., Four Approaches compared on the TADEUS 188

13 (Thermoeconomc Approach to the Dagnoss of Energy Utlty Systems) Test Case, Energy, Vol. 31, No , pp , 2006, 5. Seo, S., Wang, C. H. and Grozev, G., Coolng Energy Consumpton and Reducton Effect for Resdental Buldngs n South East Queensland, Australa, Buldng and Envronment, Vol. 59, pp , 2013, 6. Breuker, M. S. and Braun, J. E., Common Faults and Ther Impacts for Rooftop Ar Condtoners, HVAC&R Research, Vol. 4, No. 3, pp , Shukuya, M. and Hammache, A., Introducton to the Concept of Exergy, IEA ANNEX 37, Low Exergy Systems for Heatng Coolng of Buldng, Kotas, T. J., Exergy Crtera of Performance for Thermal Plant, Int. J. Heat and Flud Flow, Vol. 2, No. 4, pp , 2001, 9. COST Acton C24 Analyss and Desgn of Innovatve SYstems for Low-EXergy n the Bult Envronment: COSTeXergy, [Accessed: 17-August-2016] 10. Tronchn, L. and Fabbr, K., Analyss of Buldngs Energy Consumpton by means of Exergy Method, Int. J. Exergy, Vol. 5, No. 5/6, 2008, Marletta, L., Ar Condtonng Systems from a 2 nd Law Perspectve, Entropy, Vol. 12, No. 4, pp , 2010, Annex 37, Energy Conservaton n Buldngs and Communty Systems Low Exergy Systems for Heatng and Coolng of Buldngs, , [Accessed: 17-August-2016] 13. Annex 49, Energy Conservaton n Buldngs and Communty Systems Low Exergy Systems for Hgh Performance Buldngs and Communtes, , [Accessed: 17-August-2016] 14. Kozoł, J. and Mendecka, B., Evaluaton of Economc, Energy-envronmental and Socologcal Effects of Substtutng Non-renewable Energy wth Renewable Energy Sources, Journal of Sustanable Development of Energy, Water and Envronment Systems, Vol. 3, No. 4, pp , 2015, Schmdt, D. and Ala-Juusela, M., Low Exergy Systems for Heatng and Coolng of Buldngs, Proceedngs of 21 st PLEA Conference, pp , Del Amo Sancho, A., Lar Trgeneraton: A Transtory Smulaton of HVAC Systems usng Dfferent Typologes of Hybrd Panels, Journal of Sustanable Development of Energy, Water, Vol. 2, No. 1, pp 1-14, 2014, D Palma, D., Lucentn, M. and Rottenberg, F., Trgeneraton Plants n Italan Large Retal Sector: A Calculaton Model for the TPF Projects wth Evaluaton of all the Incentvzng Mechansms, Journal of Sustanable Development of Energy, Water and Envronment Systems, Vol. 1, No. 4, pp , 2013, Valero, A., Correas, L., Zaleta, A., Lazzaretto, A., Verda, V., Ren, M. and Rangel, V., On the Thermoeconomc approach to the Dagnoss of Energy System Malfunctons: Part 2, Malfuncton Defntons and Assessment, Energy, Vol. 29, No , pp , 2004, Pacentno, A. and Talamo, M., Crtcal Analyss of Conventonal Thermoeconomc Approaches to the Dagnoss of Multple Faults n Ar Condtonng Unts: Capabltes, Drawbacks and Improvement Drectons, a Case Study for an Ar Cooled System wth 120 kw Capacty, Internatonal Journal of Refrgeraton, Vol. 36, No. 8, pp 24-44, 2013, 189

14 20. Pacentno, A. and Talamo, M., Innovatve Thermoeconomc Dagnoss of Multple Faults n Ar Condtonng Unts: Methodologcal Improvements and Increased Relablty of Results, Internatonal Journal of Refrgeraton, Vol. 36, No. 8, pp , 2013, Pacentno, A. and Catrn, P., Assessng the Robustness of Thermoeconomc Dagnoss of Fouled Evaporators: Senstvty Analyss of Exergetc Performance of Drect Expanson Cols, Entropy, Vol. 18, No. 3, 2016, Verda, V., Serra, L. and Valero, A., The Effects of the Control System on the Thermoeconomc Dagnoss of a Power Plant, Energy, Vol. 29, No. 3, pp , 2004, Torres, C., Valero, A., Rangel, V. and Zaleta, A., On the Cost Formaton Process of the Resdues, Energy, Vol. 33, No. 2, pp , 2008, Uson, S. and Valero, A., Thermoeconomc Dagnoss of Energy Systems, Prensa, Unversdad de Zaragoza, Zaragoza, Span, Verda, V., Accuracy Level n Thermoeconomc Dagnoss of Energy Systems, Energy, Vol. 31, No. 15, pp , 2006, Xua, J.-Q., Yang, T., Zhou, K.-Y. and Sh, Y. F., Malfuncton Dagnoss Method for the Thermal System of a Power Plant based on Thermoeconomc Analyss, Energy Sources, Part A: Recovery, Utlzaton, and Envronmental Effects, Vol. 38, No. 1, pp , 2016, IMST-Group Insttuto de Ingenería Energétca Unversdad Poltécnca de Valenca, Advanced Refrgeraton Technologes Software IMST-ART, Release 3.60, 2014, [Accessed: 17-August-2016] 28. Perez-del-Notaro, P. and Leo, T. J., A Dvson of the Thermomechancal Exergy nto Two Components wth very dfferent Economc Values, Energy, Vol. 32, No. 4, pp , 2007, Paper submtted: Paper revsed: Paper accepted: