Evaluation of Virtual Refrigerant Mass Flow Sensors

Transcription

1 Purdu Univrsity Purdu -Pubs Intrnational Rfrigration and Air Conditioning Confrnc School of Mchanical Enginring 01 Evaluation of Virtual Rfrigrant Mass Flow Snsors Woohyun Kim Jams E. Braun Follow this and additional works at: Kim, Woohyun and Braun, Jams E., "Evaluation of Virtual Rfrigrant Mass Flow Snsors" (01). Intrnational Rfrigration and Air Conditioning Confrnc. Papr This documnt has bn mad availabl through Purdu -Pubs, a srvic of th Purdu Univrsity Libraris. Plas contact pubs@purdu.du for additional information. Complt procdings may b acquird in print and on CD-ROM dirctly from th Ray W. Hrrick Laboratoris at Hrrick/Evnts/ordrlit.html

2 99, Pag 1 Evaluation of Virtual Rfrigrant Mass Flow Snsors Woohyun Kim, Jams E. Braun* Hrrick Laboratory, Purdu Univrsity, Mchanical Enginring, Wst Lafaytt, IN, 7906, USA * Corronding Author: jbraun@purdu.du ABSTRACT Rfrigrant mass flow rat is an important masurmnt for monitoring quipmnt prformanc and nabling fault dtction and diagnostics. Howvr, a traditional mass flow mtr is xpnsiv to purchas and install. A virtual rfrigrant mass flow snsor (VRMF) uss a mathmatical modl to stimat flow rat using low-cost masurmnts and can potntially b implmntd at low cost. This study valuats thr VRMFs for stimating rfrigrant mass flow rat. Th first modl uss a comprssor map that rlats rfrigrant flow rat to masurmnts of inlt and outlt prssur, and inlt tmpratur masurmnts. Th scond modl uss an nrgy-balanc mthod on th comprssor that uss a comprssor map for powr consumption, which is rlativly indpndnt of comprssor faults that influnc mass flow rat. Th third modl is dvlopd using an mpirical corrlation for an lctronic xpansion valv (EEV) basd on an orific quation. Th thr VRMFs ar shown to work wll in stimating rfrigrant mass flow rat for various systms undr fault-fr conditions with lss than 5% RMS rror. Each of th thr mass flow rat stimats can b utilizd to diagnos and track th following faults: 1) loss of comprssor prformanc, ) fould condnsr or vaporator filtr, 3) faulty xpansion dvic, rctivly. For xampl, a comprssor rfrigrant flow map modl only provids an accurat stimation whn th comprssor oprats normally. Whn a comprssor suction or discharg valv is laking and th comprssor is not dlivring th xpctd flow, th nrgy-balanc or EEV modl can provid accurat flow stimats. In this cas, th flow diffrncs provid an indication of loss of comprssor prformanc and can b usd for fault dtction and diagnostics, as will b dmonstratd in this papr. 1. Introduction Spac hating, vntilation and air conditioning (HVAC) account for 0% of rsidntial primary nrgy us, and for 30% of primary nrgy us in commrcial buildings (DOE,010). Ovr half of all conditiond floor ac in th U.S. incorporats packagd HVAC quipmnt in thir systm dsign (Brodrick, 000). Th study conductd by Mssngr (008) indicats unitary air conditionrs typically do not achiv ratd fficincy bcaus of impropr installation or lack of srvicing in th fild. This papr suggstd that srvic and rplacmnt programs can yild nrgy savings on th ordr of 30 to 50%. Th othr study from ADM (009) valuatd 109 units in th fild and found that 89 had fault conditions, with 31having two or mor faults. Th avrag EER for th units incrasd from 6.6 bfor srvicing to 7.0 aftr srvicing, an avrag incras of 6.1%. Anothr invstigation (Katipamula, 005) suggstd that faults or non-optimal control can caus th malfunction of quipmnt or prformanc dgradation from 15 to 50%. Automatd diagnostics has th potntial to addrss ths fild prformanc problms and produc significant nrgy savings. Rfrigrant mass flow rat is an important masurmnt for monitoring HVAC systms and nabling Automatd Fault Dtction and Diagnostics (AFDD) to sav nrgy and xtnd quipmnt lif. Thr diffrnt virtual rfrigrant mass flow (VRMF) snsors wr dvlopd and valuatd in this study that us mathmatical modls to stimat flow rat using low cost masurmnts. Th thr approachs us: 1) a comprssor map for rfrigrant mass flow rat that uss inlt prssur and tmpratur and outlt prssur as inputs; ) an nrgy-balanc mthod mploys a virtual snsor for powr consumption basd on a comprssor map; 3) smi-mpirical corrlations for EEV and thrmostatic xpansion valvs (TXV) that ar basd on an orific quation. Th modls wr traind and tstd using data obtaind from arlir laboratory studis. Th application of th virtual snsors for diagnosing comprssor valv faults and insnsitivity to othr faults ar also dmonstratd using th availabl data. Intrnational Rfrigration and Air Conditioning Confrnc at Purdu, July 16-19, 01

3 99, Pag. Systm dscriptions and tst conditions Laboratory tst data from a varity of sourcs wr usd to dvlop and valuat VRMF snsors. Tabl 1 givs cifications for quipmnt whr data wr obtaind through laboratory tsting. Th systms includ a watr-towatr hat pump with a variabl-d comprssor, a rsidntial air lit systm, and light commrcial packagd systms with fixd and variabl-d comprssors. Th systms usd ithr a TXV or EEV as an xpansion dvic and R- or R-10A as a rfrigrant. Som of th units includd low-sid accumulators. Tabl prsnts th rang of oprating tst conditions for ach unit, including th rang of rfrigrant flow rats ncountrd. Th laboratory tst data wr obtaind with variations in both indoor and ambint tmpratur. Thr of four systms wr tstd with diffrnt condnsr and vaporator airflow rats, which could rprsnt faults associatd with a dirty air filtr or coil fouling. All of th systms xcpt for systm II wr tstd at diffrnt rfrigrant charg lvls to simulat impropr charg srvic and rfrigrant lakag. Systms I and III includd simulatd comprssor valv lakag faults whr a portion of th discharg flow from th comprssor was bypassd to th comprssor suction. Systm II was a laboratory stup for tsting lctronic xpansion valvs ovr a vry wid rang of rfrigrant flows. Two diffrnt valvs (B0B and B1F in th Tabl 1) wr tstd with two diffrnt rfrigrants (R-10A and R-0A in Tabl ). Th B1F valv has a ratd rfrigrant flow (also cooling capacity and associatd air/watr flow) that is thr tims highr than that for th B0B valv with a 10 bar prssur diffrnc across th imum valv opning, basd on th cification in th manufacturr s catalog. During th cours of tsting for systm II, it was discovrd that th comprssor was not oprating normally and was dlivring significantly lss than th ratd flow. Thus, this data st could also b usd to rprsnt faulty comprssor bhavior. Systm III also includd fault tsting for a liquid lin rstriction (additional prssur drop incras through liquid lin) and th prsnc of non-condnsabl gas (injction of nitrogn gas into th systm). In gnral, only normal oprating (i.., no-fault) data wr usd to larn paramtrs of th VRMF snsors, whras all of th data wr usd for assssing VRMF snsor prformanc. Tabl 1 Systm dscriptions for laboratory tst data Systm Siz (kw) Rfrigrant Comprssor Expansion Dvic Accumulator Systm Typ Variabl-d I (Kim,005) 3 R- EEV No comprssor Watr to Watr R-10A EEV II (Bach, 010) 7.0 Fixd-d Ys R-0A (B0B/B1F) comprssors III (Payn, 008) 8.8 R-10A TXV Ys Air Split Typ Systm Indoor Tmpratur Dry Wt Tabl Tst conditions for laboratory tsting data Prcntag of Ambint Indoor air/ rat rfrigrant tmpratur watr flow rat mass flow rat Outdoor air/ watr flow rat Rfrigrant charg ( C ) ( C) ( F ) [ % ] [ % ] [%] [ % ] I //3/0 65~100 35~100 5~100 60~100 II / 8 0~100 (R10A) 10~100 (R0A) III 6.7 / 1 19 / 15/ Dry 3.1 Dvlopmnt of VRMF snsor I 8/ 35/ 39 60~100 70~ VRMF snsor I basd on a comprssor flow map 50~100 (Coil Block) 70~130 A comprssor map is usd to stimat rfrigrant mass flow rat using input masurmnts of inlt and outlt prssur. Basd on ARI Standard 50, rfrigrant mass flow rat for a fixd d comprssor can b rprsntd using a 10-cofficint polynomial quation for a cifid amount of suprhat. Th map at th cifid suprhat is typically corrctd using th ratio of th comprssor suction dnsity at th actual suprhat to th dnsity at th Intrnational Rfrigration and Air Conditioning Confrnc at Purdu, July 16-19, 01

4 99, Pag 3 tstd suprhat. Basd on th ARI modl form, th VRMF Snsor I for a fixd-d comprssor is dtrmind using quation 1. m a a T a T a T a T 3 a T T a T 3 6 a T 3 7 a T T a T T map suc 0 1 c c 5 c c c (1) whr m map is th stimatd rfrigrant mass flow rat, th a s ar mpirical cofficints, T is vaporating saturation tmpratur, T c is condnsing saturation tmpratur, and ρ suc is th dnsity at th suction (inlt) of th comprssor. Th dvlopmnt of VRMF snsor I for a variabl-d comprssor is xplaind in Kim and Braun (01). Equation 1 is usd to map th mass flow rat for a ratd frquncy and this is corrctd for othr frquncis using a scond-ordr polynomial as givn in quation. Th c and b cofficints ar stimatd using rgrssion analysis applid to xprimntal data. map suc 8 9 c c 1 f fratd c f fratd c3 b 0 bt 1 c bt c b3t bt b5t c Tc ratd, frquncy m () whr th b s and c s ar mpirical cofficints, f is comprssor frquncy, and f ratd is th ratd comprssor frquncy. 3. Prformanc of VRMF snsor I Figurs 1 and show th prformanc of VRMF Snsor I that is basd on a comprssor map. Th trms Normal, Comp Fault, Cond Fault, Evap Fault, Liquid Fault, Charg Fault, and NonCond Fault stand for no fault, comprssor lakag fault, condnsr fouling fault, vaporator fouling fault, liquid-lin rstriction fault, rfrigrant lakag fault, and non-condnsabl gas fault, rctivly To valuat prformanc of th VRMF snsor, th prdictd ratio of rfrigrant mass flow rat to ratd flow is compard to th valu dtrmind using masurmnts. Th VRMF modls wr dvlopd using only th normal data but usd to prdict flow rats for all of th fault tsts. Figur 1: Prformanc of VRMF snsor basd on fixd-d comprssor map for systm III undr no fault and fault conditions (RMS of snsor rrors shown for ach fault typ) Figur : Prformanc of VRMF snsor basd on variabl d comprssor map for systm I undr no fault and fault conditions (RMS of snsor rrors shown for ach fault typ) Figur 1 shows th prformanc of VRMF snsor I for systm III with a fixd-d comprssor undr no fault and various faulty conditions. Th RMS rror is gnrally lss than % for normal opration and with a varity of faults xcpt for comprssor valv lakag. For th rang of comprssor lakag conditions considrd, th RMS rror for th VRMF snsor I was 19%. In gnral, th rror incrass with th svrity of th comprssor lakag fault. As a rsult, diffrncs btwn rfrigrant flow dtrmind using VRMF snsor I and othr VRMF snsors can b usd to diagnos a fault associatd with th comprssor not dlivring th propr rfrigrant flow. Intrnational Rfrigration and Air Conditioning Confrnc at Purdu, July 16-19, 01

5 99, Pag Figur shows th prformanc of VRMF snsor I for systm I with a variabl-d comprssor undr no fault and various fault conditions. Although th VRMF snsor I was traind using only no-fault data, it accuratly stimats mass flow rat for faulty conditions ovr th rang of oprating frquncis, xcpt for th comprssor valv lakag fault. Th RMS rrors for VRMF snsor I wr lss than 3% for condnsr fouling, rfrigrant charg, and vaporator fouling conditions, rctivly. Howvr, VRMF snsor I prdictions wr about 16% highr than masurmnts for th rang of comprssor fault conditions considrd, with th rrors incrasing with fault lvl..1 Dvlopmnt of VRMF snsor II. VRMF snsor II basd on a comprssor nrgy balanc In ordr to diagnos comprssor flow problms, it is ncssary to hav an altrnativ VRMF snsor. On altrnativ approach is to us an nrgy balanc on th comprssor to stimat flow rat as shown in quation 3. Li (006) dmonstratd that this mthod provids accurat flow prdictions whn using a virtual comprssor snsor for powr consumption, vn in th prsnc of a comprssor valv lakag fault or othr faults. Compard to th map-basd mthod, th nrgy balanc modl is much simplr and can b usd for both fixd-d and variabl-d comprssors. m nrgy h ( T, P W 1 ) h dis dis dis suc suc suc (3) whr α loss is comprssor hat loss ratio, W is comprssor powr consumption, and h dis (T dis,p dis ) and h suc (T suc,p suc ) ar th discharg lin and suction lin rfrigrant nthalpy. Th comprssor powr consumption, discharg prssur (P dis ) and suction prssur (P suc ) can b stimatd using othr virtual snsors. α loss is gnrally vry small (undr 5%) for quipmnt having a fixd-d comprssor oprating normally. Howvr, it can b mor significant at low comprssor ds for variabl-d quipmnt or with faults for fixdd quipmnt. For xampl, dcrasing th comprssor frquncy from 60Hz to 30Hz almost doubls th hat loss as a fraction of th powr input. To provid mor accurat mass flow rats prdictions undr various faulty conditions and/or ds, an mpirical modl for α loss was dvlopd that is traind using rgrssion applid to data. Th modl for fixd-d quipmnt is givn in quation, whil a function for variabl-d quipmnt is shown in quation 5. loss ( T, P loss, prd c0 c1pdis cpsuc c3tdis ctsuc loss, prd c0 c1p dis cpsuc c3t dis ct suc c5 ) () f (5) whr th c s ar mpirical cofficints, P suc is suction prssur, P dis is discharg prssur, T amb is comprssor ambint tmpratur, T suc is suction tmpratur, and f is d of th comprssor motor.. Prformanc of VRMF snsor II Figur 3 shows th prformanc of VRMF snsor II for systm III with a fixd-d comprssor. Th mass flow rat prdiction was dtrmind using hat loss stimats and prdictions of othr virtual snsors. Th hat loss modl was dtrmind using data for normal opration whr th hat loss was dtrmind from an nrgy balanc on th comprssor with th flow masurd. Th powr consumption was dtrmind using a map in trms of suction prssur and tmpratur and discharg prssur as outlind in Kim and Braun (01). Th RMS rror for th VRMF snsor was lss than 3% for all of th data, including both normal and faulty conditions. Th largr rrors for th vaporator fouling occurrd whn th suprhat at th comprssor inlt was blow 1.5F. Th incorrct comprssor suction nthalpy du to a two-phas rfrigrant inlt stat ld to th inaccurat stimat of mass flow rat. Th VRMF snsor II is rlativly indpndnt of comprssor faults compard to th VRMF snsor I. Figur shows th prformanc of VRMF snsor II for systm II with a variabl-d comprssor. Th mass flow rat stimats wr compard to masurmnts for a rang of diffrnt faults at diffrnt fault lvls. Th RMS rror for th VRMF snsor II is lss than 5%. Excpt for svral low comprssor d conditions, th VRMF works wll rgardlss of th fault conditions. Howvr, thr wr som significant rrors (10%) at low frquncis. Additional Intrnational Rfrigration and Air Conditioning Confrnc at Purdu, July 16-19, 01

6 99, Pag 5 work is ncssary to accuratly dtrmin hat loss for variabl-d comprssors whn oprating at low frquncis. Figur 3: Prformanc of VRMF snsor II basd on nrgy balanc for systm III undr no fault and fault conditions (RMS of rrors shown for ach fault typ) Figur : Prformanc of VRMF snsor II basd on nrgy balanc for systm I undr no fault and fault conditions (RMS of rrors shown for ach fault typ) 5. VRMF snsor III basd on an xpansion valv modl Expansion dvics ar usd to drop th prssur of th rfrigrant and to rgulat th rfrigrant mass flow rat in rons to a variabl load. Thr ar thr typs of xpansion dvics usd in air conditionrs: fixd-orific (FXO), thrmostatic xpansion valv (TXV), and lctronic xpansion valv (EEV). Evn though an FXO has advantags of simplicity and low cost, it is not appropriat for a systm that rquirs prcis flow control for a wid rang of flow rat rquirmnts. TXV and EEV dvics ar adjustabl throat-ara xpansion valvs. Th TXV adopts a mchanical control mthod to obtain rlativly constant suprhat at th vaporator outlt. Th EEV provids a mor prcis control of suprhat and fast flow control for a wid rang of mass flow rats bcaus it uss lctronic actuation and snsor information along with a digital fdback controllr. Most of th prvious litratur on modling of xpansion dvics has focusd on constant-ara xpansion dvics, such as FXO. Modls for prdicting th mass flow charactristics of TXVs and EEVs ar limitd. Li (008) dvlopd gnralizd xprssions for TXV mass flow as a function of suprhat and valv. Shanwi t al. (005) and Park t al. (007) dvlopd mpirical corrlations for mass flow rat through an EEV by prforming th dimnsionlss analysis basd on a powr law form. Howvr, ths xisting modls rquir ithr dtaild gomtric paramtrs or many masurmnts to rprsnt prformanc. This papr prsnts VRMF snsors for TXV and EEV dvics basd on a smi-mpirical modl that can b traind using a rlativly small amount of data and thn can stimat rfrigrant mass flow rat as part of an automatd diagnostic systm. 5.1 Dvlopmnt of VRMF snsor III for TXV Th valv opning for a TXV is dtrmind by a forc balanc on a diaphragm, as dpictd in Figur 5. Th bulb and suction-lin prssur act on opposit sids of th diaphragm and coupld with th ring forc, control th ffctiv orific ara. Th vaporator inlt and condnsr prssur influnc th flow rat through th orific for a givn opning. Th bulb typically contains a two-phas mixtur of th sam rfrigrant that is mployd within th systm. Thrfor, whn a positiv suprhat xists at th vaporator outlt thn thr is a positiv diffrnc btwn th bulb and vaporator outlt prssurs acting th diaphragm. Th ring is usd to nsur a positiv suprhat at th vaporator xit sinc th bulb prssur must b gratr than th vaporator xit prssur in ordr to ovrcom th forc of th ring. Intrnational Rfrigration and Air Conditioning Confrnc at Purdu, July 16-19, 01

7 99, Pag 6 As dpictd in Figur 5, a conical pin movs up and down to chang th opn ara for rfrigrant flow in rons to th valv control. Th mass flow rat through th TXV is assumd to b linar function of th opn ara as givn in quation 6. Aorific Apin mtxv m (6) A orific whr A orific = ((D orific ) π)/ is th ara at th full opning, A pin = ((D pin ) π)/ is closd ara associatd with th pin, and m is th rfrigrant mass flow rat associatd with a full opn condition. Figur 5: Diagram of TXV Th imum flow rat for a givn valv is a function of th prssur drop across th valv and th siz of th orific. Th imum flow rat for a givn orific is calculatd using th mpirical corrlation givn in quations 7 and 8, as dvlopd by Hmjak (1989). P P K C P P K m C A (7) 0 orific f c 1 3 SC C Pcri P K C C C5 (8) TCri Pcri whr th C s ar mpirical cofficints, ( P c -P ) is th diffrnc btwn th valv inlt prssur and th vaporating prssur, ρ f is th dnsity of th rfrigrant at th valv inlt, SC is th subcooling of th rfrigrant at th valv inlt, T cri and P cri ar th critical tmpratur and prssur. Th ring dflction, δ nds to known in ordr to find th ffctiv orific ara. Th dflction of th ring can b found using quation 9. F F, cl (9) k whr F is th ring forc, F,cl is th ring forc whn th valv is closd and k is th ring constant. Both F,cl and k ar fixd for a givn xpansion valv. F is calculatd from a quasi-static forc balanc on th diaphragm, as shown in quation 10. F diaph P P A P P A (10) b suc whr ( P b -P suc ) is th prssur diffrnc btwn bulb and suction lin, and A diaph is th ara of diaphragm. F,cl, A diaph and k ar constants basd on th valv dsign and initial stting. Sinc th ring forc is a linar function of th dflction, th ring dflction can b xprssd using mpirical cofficints a s, as shown in quation 11. diaph suc f c Intrnational Rfrigration and Air Conditioning Confrnc at Purdu, July 16-19, 01

8 99, Pag 7 Adiaph P Psuc F, cl a1p Psuc a (11) k If th pin dflction is zro, no rfrigrant flows through th orific, and if th pin dflction is at som imum valu, th pin will not obstruct th flow and th valv will oprat at th imum flow rat. Th ffctiv orific ara is calculatd by subtracting th obstructing ara of th pin from th ara of th valv orific. Th VRMF snsor for a TXV is dvlopd by substituting δ from quation 11 into quation 6 and xprssing th rsult in trms of nw mpirical cofficints that ar dtrmind through rgrssion. m TXV A orific A A orific pin m m C m a 3P Psuc a P Psuc a5 m (1) 5. Prformanc of VRMF snsor III for TXV Th mpirical cofficints C 1, C, C 3, C and C 5 within orific quations 7 and 8 wr stimatd by minimizing mass flow rat prdiction rrors using fully opn TXV tst data and non-linar rgrssion. Fully opn TXV tst data wr collctd from th conditions whr suprhat of th comprssor inlt was highr than th ratd suprhat. Th mpirical cofficints a 3, a, and a 5 within th TXV modl quation 1 wr stimatd basd on th availabl normal tst data with suprhat undr control using linar rgrssion. Th data includs variations in ambint tmpratur, and indoor dry bulb tmpratur with positiv subcooling ntring th valv. Sinc quation 8 uss subcooling as an input, zro subcooling data wr disrgardd for training and tsting. Th paramtr stimation mthods minimizd th rrors btwn prdictd and known mass flow rats. Th rsulting modl with mpirical cofficints dtrmind from normal data was applid to prdict rfrigrant mass flow rat for all of th availabl data including various fault conditions. Figur 6: Prformanc of VRMF snsor III basd on TXV for systm III undr no fault and fault conditions (RMS of snsor rrors shown for ach fault typ) Figur 7: Prformanc of VRMF snsor III basd on EEV for systm I undr no fault and fault conditions (RMS of snsor rrors shown for ach fault typ) Figur 6 shows rfrigrant mass flow rat stimatd from th VRMF snsor III for TXV applid to systm III with six diffrnt kinds of faults individually implmntd. Th ovrall RMS rrors wr about 1% for no fault conditions and 3% of actual mass flow rat for all fault conditions. Th prformanc of th VRMF snsor is vry good ovr a wid rang of rfrigrant mass flow rats and oprating conditions rgardlss of th fault. Thr wr som significant rrors of about 10% for low rfrigrant charg lvls whn th ntring subcooling was almost zro. With zro subcooling and two-phas conditions ntring th TXV, th VRMF snsor III may not b rliabl. Intrnational Rfrigration and Air Conditioning Confrnc at Purdu, July 16-19, 01

9 99, Pag Dvlopmnt of VRMF snsor III for EEV Elctronic xpansion valvs (EEV) wr dvlopd in th 1980s to provid tightr and mor stabl control of suprhat with fastr rons. Th applications of EEV for high fficincy air conditionr and multi-vaporator hat pump systms hav incrasd in rcnt yars. Howvr, mass flow modls of EEV for fault dtction and diagnosis ar vry limitd. In this study, th VRMF snsor basd on an mpirical corrlation can prdict rfrigrant mass flow rats through EEV. Th mpirical mass flow corrlation was dvlopd by incorporating a dimnsionlss cofficint in trms of EEV gomtris and oprating conditions into th orific quations 6 and 7 bcaus th only diffrnc btwn th EEV and TXV modl is how th ara opns and closs. Th mpirical corrlation for VRMF snsor is givn in quation 13. Th variation of th actual orific diamtr controls th rfrigrant flow ara for flow rstriction. Th mass flow rat proportionally incrass with th ris of th flow ara. C3 D acutal Pcri P SC meev Aactual m C1 f Pc P C C C 5 (13) TCri P cri whr th C s ar mpirical cofficints, D actual is actual orific diamtr (s Figur 8), ρ f is th dnsity of rfrigrant at th valv inlt, P c and P ar th inlt prssur and vaporator prssur. Figur 8 shows th flow passag structur and gomtric rprsntation for an EEV. A ndl valv movs up and down to chang th flow ara, typically using a stppr motor to maintain prcis control of th rfrigrant suprhat at th vaporator xit. At a crtain pin tip position h, th rfrigrant flow ara A actual can b calculatd by subtracting th obstructing ara of th ndl from th ara of th valv orific as dvlopd by Li (008) and givn in quation 1. A actual D actual D D D tan H h orific pin orific (1) whr D pin =( tanθ (H-h)) is th currnt ndl diamtr that is within th plan of th flow orific, and D orific = H tanθ is th orific diamtr. Th currnt ndl diamtr can thn b xprssd in trms of th orific diamtr and ndl position as shown in quation 15. D Dorific h H h Dorific (15) H H pin 1 Equations 1 and 15 can b combind to xprss th rfrigrant flow ara for any ndl position, A actual, as h h h h Aactual Dorific Dorific 1 Dorific (16) H H H H Th rfrigrant mass flow rat through th EEV can b obtaind by substituting th rfrigrant flow ara, quation 16, into th gnral modl quation 13. D orific h h m EEV C 1 f Pc P K (17) H H Th flow ara of th EEV varis with th up-and-down movmnt of th ndl valv that is drivn by a stp motor. Th ndl position (h) is linarly proportional to th motor stp of EEV, as givn in quation 18. EEVSTEP h EEVSTEP currnt H (18) Intrnational Rfrigration and Air Conditioning Confrnc at Purdu, July 16-19, 01

10 99, Pag 9 Figur 8: Flow passag structur and gomtric modls for EEV In this study, th VRMF snsor for an EEV was dvlopd by substituting th ratio of motor stp, quation 18, into th EEV rfrigrant mass flow rat quation 17. Th corrction cofficint in 19 can b dtrmind using linar rgrssion basd on normal tst data. EEVSTEP EEVSTEP D currnt currnt orific m EEV C C f Pc P K EEVSTEP 3 EEVSTEP (19) 5. Prformanc of th VRMF snsor III for EEV Th mpirical cofficints within orific quation 8 wr dtrmind using non-linar rgrssion applid to fully opn EEV data. Fully opn EEV data wr collctd from th conditions whr th motor stp was at a imum. Lik th TXV, quation 8 uss subcooling as in input, and thus zro subcooling data wr disrgardd for training and tsting. Onc th mpirical cofficints of orific quation ar obtaind, th EEV quation 19 was thn fit to normal oprating (i.., no-fault) data using linar rgrssion. Th bst fit quation was thn usd to prdict th rfrigrant mass flow rat through th EEV for all availabl tst data including various fault conditions. Figur 7 shows prformanc of th VRMF snsor III for EEV approach applid to systm I. Th modl provids rsults that ar gnrally within 6% ovr a wid rang of mass flow rats and oprating conditions. Largr rrors for low rfrigrant charg and condnsr fouling occurrd whn th subcooling at th condnsr outlt was blow F. Figurs 9 and 10 show prformanc of th VRMF snsor III for EEV applid to systm II with R-10A and R-0A as rfrigrant. Rsults ar prsntd for two diffrnt EEVs that wr tstd in this systm. Ovrall, th RMS rrors of th VRMF snsor III wr 6% and 5% for R-10A and R-0A, rctivly. Som of th largr rrors may b associatd with two-phas rfrigrant conditions at th EEV inlt with nar-zro subcooling. 6. Application of VRMF snsors for fault dtction and diagnosis Outputs from th thr VRMF snsors can b compard in ordr to dtct a fault and localiz faults within a systm, including: 1) loss of comprssor prformanc, ) faulty comprssor motor, and 3) faulty xpansion dvic. Figurs 11 to 1 dmonstrat th us of th VRMF snsors for isolating a fault condition whr th comprssor is not providing xpctd flow. Figur 11 shows comparisons of th thr VRMF snsors with mass flow masurmnts for systm III oprating at fixd d with a simulatd comprssor valv lakag fault. With this fault, th rfrigrant mass flow rat is rducd compard to normal opration. As a rsult, th comprssor map ovr-prdicts rfrigrant mass flow rat whras th othr VRMF snsors provid accurat flow stimats. Th RMS rrors for comprssor nrgy balanc Intrnational Rfrigration and Air Conditioning Confrnc at Purdu, July 16-19, 01

11 99, Pag 10 modl and TXV modls wr about %, whras th RMS rror for th fixd-d comprssor modl was 19 %. Thus, a comprssor flow fault could b isolatd through comparison of th VRMF snsors for this cas. Figur 1 similar rsults for systm I having a variabl-d comprssor and EEV. Th RMS rrors for th VRMF snsors wr about 5 % basd on a comprssor nrgy balanc and 3 % basd on th EEV modl, but wr approximatly 16 % for th variabl-d comprssor map. Figurs 13 and 1 show rsults for systm II with B1F and B0B as xpansion dvics and th two diffrnt rfrigrant typs, R-10A and R-0a. Th data did not includ information that could b usd to valuat th nrgy balanc mthod. Th tsts covrd a wid rang of comprssor fault lvls from 10 to 100%. For ithr st of tst data, a comprssor fault could b radily idntifid by comparing prdictions of th comprssor map with thos from th EEV modl. Figur 9: Prformanc of VRMF snsor III basd on EEV with R10a as rfrigrant for systm II Figur 10: Prformanc of VRMF snsor III basd on EEV with R10a as rfrigrant for systm II Figur 11: Comparison of VRMF snsor outputs for systm III with comprssor flow fault Figur 1: Comparison of VRMF snsor outputs for systm I with comprssor flow fault 7. CONCLUSIONS Intrnational Rfrigration and Air Conditioning Confrnc at Purdu, July 16-19, 01

12 99, Pag 11 Figur 13: Comparison of VRMF snsor outputs for systm II (R10A) with comprssor flow fault Figur 1: Comparison of VRMF snsor outputs for systm II (R0A) with comprssor flow fault Rfrigrant mass flow rat is an important masurmnt for quipmnt prformanc monitoring, fault dtction, and diagnostics. Howvr, a typical rfrigrant mass flow mtr is xpnsiv and installation for xisting fild quipmnt is complicatd bcaus it rquirs an quipmnt modification that can lad to rfrigrant lakag. To nabl low-cost implmntations for on-lin prformanc monitoring and automatd diagnostics, thr diffrnt virtual rfrigrant mass flow (VRMF) snsors wr dvlopd for stimating rfrigrant mass flow rat from lowcost masurmnts that ar basd on: 1) a comprssor map, ) a comprssor nrgy balanc, and 3) a smimpirical corrlation for th xpansion dvic (TXV or EEV). Th VRMF snsors prsntd in this papr wr validatd for systms having fixd and variabl-d comprssors, diffrnt rfrigrants, and diffrnt xpansion dvics (TXV/EXV) oprating ovr a wid rang of oprating conditions both with and without faults. Th thr VRMFs work wll in stimating th rfrigrant mass flow rat for th various systms undr fault-fr conditions with lss than a 5% RMS rror. Prdictions from th VRMF snsor basd on a comprssor map dviat from th othr VRMF snsors in th prsnc of a comprssor fault with th dviations growing with th magnitud of th fault. Ths diffrncs can b usd within a diagnostic systm to isolat this particular fault sinc th accuracy of th nrgy balanc modl and xpansion dvic modls ar indpndnt of comprssor flow faults. NOMENCLATURE A ara m Subscripts a, b, c Empirical constants actual Actual C d,v Corrction cofficint for EEV modl b Bulb C d,v,pi Corrction cofficint for PI thorm c Condnsr D Diamtr m cri Critical d Currnt ndl diamtr m diaph Diagram EEV Elctronic xpansion valv dis Discharg EEVSTEP Opning of EEV Stp Evaporator F Forc N dis Discharg f Comprssor d Hz f Liquid FDD Fault Dtction and Diagnostics g Gas H Maximum ndl position m Maximum Intrnational Rfrigration and Air Conditioning Confrnc at Purdu, July 16-19, 01

13 99, Pag 1 h Crtain ndl position m orific Orific h Enthalpy kj/kg Ratd Ratd condition k Spring constant N/m Spring m map m nrgy m TXV m EEV Rfrigrant mass flow rat basd on comprssor map Rfrigrant mass flow rat basd on comprssor nrgy balanc Rfrigrant mass flow rat basd on TXV modl Rfrigrant mass flow rat basd on EEV modl kg/s,cl Closd ring kg/s suc Suction kg/s TXV Thrmostatic valv xpansion P Prssur Pa Grk kg/s W Comprssor input Powr W ρ Dsnsity SC Subcooling C α loss Comprssor hat loss ratio TXV Thrmostatic valv xpansion δ Spring dflction T Tmpratur C Viscosity VRMF Virtual rfrigrant mass flow snsor θ Angl of pin REFERENCES ADM Associats, 009, Markt assssmnt and fild M&V study for comprhnsiv packagd A/C systms program, SCE086, July, 009. Amrican Rfrigration Institut (ARI), 1999, Positiv dilacmnt rfrigrant comprssors and comprssor units. Bach, C. 010, Prsonal communication, Ray W. Hrrick Laboratoris, Purdu Univrsity. Brodrick, J., 000, Ar fans blowing your nrgy budgt?, HPAC Hating/Piping/Air Conditioning Enginring, p Hrnjak, P.S., Lngr, M.J., and Jacobi, A.M., 1998, Suprhat stability of an vaporator and thrmostatic xpansion valv, air conditioning and rfrigration cntr., Univrsity of Illinois at Urbana-Champaign Katipamula, S. and Brambly, M.R., 005. Mthods for fault dtction, diagnostics, and prognostics for vapor comprssion quipmnt Systms, A Rviw, Part I, HVAR&R Rsarch, Vol. 11(1), p Kim, M. and Kim, M.S., 003, Prformanc invstigation of a variabl d vapor comprssion systm for fault dtction and diagnosis, Intrnational Journal of Rfrigrant, Vol. 8, p Kim, W.H and Braun, J.E., 01, Virtual rfrigrant mass flow and powr snsors for variabl-d comprssors, Intrnational Rfrigrant and Air conditioning Confrnc, No. 99. Li, H. and Braun, J.E., 008, A mthod for modling adjustabl throat-ara xpansion valvs using manufacturrs' rating data, HVAC&R Rsarch, Vol. 1(), p Mssngr, M., Stratgic Plan to Rduc th Enrgy Impact of Air Conditionrs, CEC , Jun, 008. Payn, W. V., Kim, M. S., Yoon, S. H., and Domanski, P. A., 008, Cooling mod fault dtction and diagnosis mthod for a rsidntial Hat Pump., NIST SP 1087; NIST Spcial Publication p.1087; 98 Park, C., Cho, H. and Kim, Y., 007, Mass flow charactristics and mpirical modling of R AND R10A flowing through lctronic xpansion valvs, Intrnational Journal of Rfrigration, Vol. 03, p Shanwi, M., Chuan, Z., Jiangping, C., and Zhiujiu, C., 005, Exprimntal rsarch on rfrigrant mass flow cofficint of lctronic xpansion valv, Applid Thrmal Eng., Vol. 5, p U.S. Dpartmnt of Enrgy, 010, Enrgy fficincy trnds in rsidntial and commrcial buildings, August, 010. ACKNOWLEDGEMENT This work was supportd by th Dpartmnt of Enrgy through th Enrgy Efficint Buildings Hub. Intrnational Rfrigration and Air Conditioning Confrnc at Purdu, July 16-19, 01