MODELING OF COMPONENTS IN ABSORPTION REFRIGERATION SYSTEMS DURING TRANSIENT OPERATION

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1 MODELING OF COMPONENTS IN ABSORPTION REFRIGERATION SYSTEMS DURING TRANSIENT OPERATION A. Nouri-Borujrdi, A. Mirzai Islamic Azad Univrsity, South Thran Branch Jamal-Zadh Strt, Thrah, Iran Tl: , Fax: , anouri@shari.du Abstract In this study, two modls hav bn dvlopd to simulat th dynamic bhavior o an oriic in an absorption chillr. Thy ar dvlopd basd on homognous as wll as sparatd low modls. Svral two-phas low modls hav bn dmd to anticipat th prormanc o th oriic in th absorption chillr. Th dynamic bhavior o th oriic in th transint stag rigorously dpnds on som low variabls such as vapor quality, void raction, prssur loss and two-phas mass low rat. Rsults show that th homognous modl prdicts mor prssur drops than that th sparatd modl during transint throttling procss o working luid. KEY WORDS: absorption chillr, xpansion dvic; two-phas low; rrigrant; prssur drop INTRODUCTION Bcaus o tim-consuming o th absorption chillr during start up opration, th study o th dynamic simulation will b important. Th ovrall prormanc o th absorption chillrs ar rlatd to th dynamic bhavior o thir xpansion dvics during start up opration. Short and long-tub oriics ar commonly usd bcaus o asy manuacturing, rliability and cost ctivnss. Dspit o simplicity in shap, oriic shows som complicatd bhavior during th xpansions procss. Kim and O Nal [1] drivd a smi-mpirical modl to ind out th mass low rat through a shorttub oriic as a unction o tub gomtry, inlt conditions and downstram prssur. Zhang and Yang [] dvlopd a non-quilibrium two-luid modl (TFM) or rrigrant two-phas critical low insid a short-tub oriic. Thy took into account both intr-phas vlocity and tmpratur dirncs in thir modl. Thy ultimatly dmonstratd th applicability o TFM to rrigrant twophas low in a short tub. This vriis th xistnc o thrmodynamic and hydraulic nonquilibrium charactristics o two-phas low in a short tub as wll as non-quilibrium cts on mass low rat. Kim t al. [3] by assuming a critical low through an oriic dvlopd a two-phas low modl to simulat dynamic bhavior o a small-scal absorption chillr. Som prvious works hav ocusd on dynamic simulation o absorption chillrs without using any spcial modl [4, 5]. This papr highlights th importanc o th throttling simulation o a short-tub oriic btwn th condnsr and vaporator sctions during th transint procss by using both homognous as wll as sparatd low modls. Th rsults o th short-tub oriic throttling by using dirnt low modls ar also compard. MATHEMATICAL MODELING Atr boiling o LiBr-H O solution in th gnrator o an absorption chillr, th watr vapor is condnsd by a watr-coold hat xchangr in th condnsr. Subsquntly, th mixtur o liquidvapor as a rrigrant substanc lows through th oriic and bing throttld btwn condnsr and vaporator sctions rom high to low prssur rspctivly.

2 Fig.1. Evaporation o rrigrant in an annular low rom th lt to right dirction during xpansion through an oriic In an idal situation, th prssurs o th gnrator and condnsr sctions ar assumd to b idntical and ar dtrmind by thir corrsponding saturation tmpratur. Tmpratur and concntration o th LiBr-H O solution ar dtrmind by numrical solution o mass and nrgy quations. NTU approach is also usd or hat xchangr and mass low rat in th condnsr. apor Quality Th vapor quality in th vaporator as a rrigrant substanc is irst obtaind by th adiabatic procss whn th two-phas low xpands btwn th condnsr and vaporator as: 1 u x = ( hc hc ) (1) ( hg ) whr th vlocity is radily obtaind by mass continuity as: u = G ( υ + x υ ) () g x is irst gussd by th isnthalpic procss as th two-phas low xpands btwn th sam prssurs as: hc h x = (3) ( g ) Thr ar traditionally two modls to dtrmin prssur drop in a two-phas low: (i) Th homognous low modl, (ii) th sparatd low modl. Ths modls ar prsntd blow. Prssur Drop Th two-phas low prssur drop through a vrtical oriic up to down can b obtaind by a homognous modl, [6]. In this modl, th two-phas mixtur is simulatd as a singl phas luid lowing with th man luid proprtis and thrmodynamic quilibrium btwn two phass. υ υ θ υ P = (1 + ) + G υ x + (1 + x ) LG x g glsin g g D υ xυg υ whr th two-phas Fanning riction actor is stimatd as blow. (4)

3 0.079 = GD 0.5 ( ) µ Whr th two-phas viscosity is dtrmind by: (5a) µ 1 x x = + µ µ 1 (5b) In this quation th physical proprty o th luid is calculatd basd on th man prssur btwn downstram and upstram sctions. In th transint priod, it is also practic to assum that th two phass low annularly through th oriic. A similar modl has bn invstigatd by Kim t al. [1]. Anothr modl or th two-phas prssur drop is suggstd by Chisholm [7] basd on th liquid low which is only lowing alon insid th oriic as: C 1 P = (1 + + ) P X X or basd on th vapor low which is only lowing alon as: (6) = (1 + + ) P CX X P (7) X is namd th Lockart-Martinlli paramtr and dind as: dp ( F ) = dz x µ υ X = ( ) ( ) ( ) (8) dp ( F ) x µ υ dz and C is a constant and yilds. C υ 1 υ = k( ) + ( ) υ k υ (9) whr k = ( υ / υ ) i X 1and k = ( υ / υ ) i X Th prssur drop o th liquid and vapor ar rspctivly dtrmind by: L P = G (1 x) υ D (10a) P L G x υ D = (10b) Assuming no shar orc btwn phass, Murdock [8] has suggstd th ollowing corrlation, basd on th sparatd modl, or th prssur drop as: P = (1+ 1.6X) P (11) Anothr corrlation xtractd rom th continuity quation or on-phas low has bn suggstd or two-phas low as blow, [8]:

4 P = 1.6 P + P (1) In all abov quations, th quality o rrigrant is to b dtrmind in upstram. Th rquird void raction is suggstd by Zivi [9] as: 1 x υ 3 α = 1 + ( ) x υ And or an annular low, it can b obtaind by th ollowing corrlation. 1 C 1 1 φ = 1+ + = X X (1 α) (13) (14) SOLUTION METHOD In th procdur dvlopd or th two-phas throttling modl, th condnsr prssur as wll as th low rat is known. On th othr hand, th prssur drop and th vapor quality bor and atr th throttling ar unknown. Atr dtrmining th quality bor xpansion, downstram prssur is assumd and rom which vapor quality is valuatd at this location. Thn, prssur drop across th oriic will b dtrmind using on o th aormntiond modls. Th procdur is rpatd until th gussd and calculatd prssur drop ar th sam or th dirnc btwn thm is within accptabl rang. In this procdur, th prssur drop accuracy is 0.1 Kpa. RESULTS AND DISCUSSION In a commrcial absorption chillr with 150 ton rrigration, th pip nominal diamtr carrying rrigrant rom th condnsr to th vaporator is assumd to b D =.5inch. Th condnsr prssur is varid in th rang o 1.5 < PC < 7.5 Kpa, [10]. Fig. shows th prssur drop o th rrigrant across th oriic against th inlt vapor quality or dirnt two-phas mass low rats by Chisholm modl. It can b inrrd that by lapsing tim during th start-up, th prssur drop will b incrasd du to mor rrigrant bing condnsd in th condnsr. Thror, mor liquid and wr vapors pass through th xpansion dvic. In all igurs th inlt vapor quality is usually high, bcaus th condnsation rat o th vapor coming rom th gnrator is low and mor vapor rmains in th condnsr at th arly stag o th opration. For m & > 004. kg/s thr is a critical quality blow that th prssur drop incrass with quality and abov that th opposit action occurs. Morovr, th slop o th curv is vry stp and limitd to a vry small rang o quality. Fig. 3 again dpicts th two-phas mixtur prssur drop across th oriic vrsus inlt vapor quality or dirnt mixtur mass low rat basd on th homognous modl. Similar to th prvious igur, at ach mass low rat, P drops against th inlt vapor quality but with modrat slop. In addition, th igur xhibits lss snsitivity rlativ to th inlt vapor quality at low mass rat. Fig. 4 compars th prssur drop against inlt vapor quality or dirnt modls whn m & =. 04 kg/s. It is sn that th homognous modl prdicts mor prssur drop in comparison with th othr ons but thy hav narly a similar slop. It is clar that th irst part o th curv has a highr slop than th scond part. This nhancmnt o th slop may b attributd to th two-phas low ct. Fig. 5 illustrats th two-phas low prssur drop against th two-phas mixtur mass low rat. Each P C curv approachs toward th on corrsponding to PC = 7Kpa as th mass low rat o th

5 mixtur bcoms small. Th rsults show that th prssur drop across th oriic is suddnly riss atr a crtain valu o th mixtur mass low rat. Fig. 6 prsnts th prssur drop against mass low or dirnt condnsr prssur in homognous modl. Th rsults show that all th curvs hav a similar trnd and th prssur loss is narly constant and qual to about P = 15. Kpa whn. 015 < m <. 055 kg/s and all P C curvs hav th sam asymptots. Fig. 7 compars th prssur drop against th mass low rat o th dirnt modls at PC = 7Kpa.. Th discrpancy btwn th homognous modl rsults and th othr ons bcoms largr as th mass low rat incrass. In othr words, this dirnc is rlatd to th physical proprtis cts o th mixtur which hav dirnt cts in th homognous as wll as th sparatd modls. CONCLUSION Th dynamic bhavior o an xpansion dvic btwn th condnsr and vaporator has bn studid by a homognous as wll as a sparatd modl. Svral two-phas prssur drop modls hav bn dvlopd to simulat th dynamic bhavior o th rrigrant low through th oriic in th transint procss. Thy prdict th prssur and quality o th rrigrant atr th xpansion dvic. Th thr sparatd two-phas modls hav almost th sam rsults whras th homognous rsults ar dirnt and with highr valus rlativ to th thr sparatd modls. Th rsults show that at any givn condnsr prssur, thr xists a mass low o th two-phas mixtur that th slop o th prssur drop riss sharply. NOMENCLATURE C constant liquid D diamtr c condnsr liquid saturation riction actor Evaporator liquid saturation G mass vlocity g latnt hat h nthalpy riction K constant in inlt L lngth Two-phas P prssur v vapor u vlocity Grk Lttrs x quality α void raction X Lockart-Martinlli paramtr dirnc Subscripts φ two-phas prssur ratio c condnsr θ vrtical angl vaporator υ spciic volum

6 REFERENCES [1] Kim Y., O Nal D.L., A smi-mpirical modl o two-phas low o rrigrant-134-a through short tub oriics// Exprimntal Thrmal and Fluid Scinc; 9(4). 1994, pp [] Zhang Ch. L., Yang L., Two-luid modl o rrigrant two-phas low through short tub oriic// Int. J. o Rrigration, 8,005, pp [3] Kim D.S., Wang L., Machilsn C.H.M., Dynamic modling o a small-scal NH3-HO absorption chillr// Intrnational Congrss o Rrigration, Washington, D.C., USA, 003. [4] Kim B., Park J., Dynamic simulation o a singl-ct Ammonia-watr absorption chillr// Int. J. Rrigration, 30, 007, pp [5] Bian J., Radrmachr R., Moran D., Transint simulation o an absorption chillr in a CHP systm// Procdings o Int. Sorption Hat Pump Conrnc, Dnvr, USA, 005. [6] Collir G.C., Thom J.R., Convctiv boiling and condnsation, third d., Clarndon Prss, Oxord, [7] Chisholm D., Flow o incomprssibl two-phas mixtur through sharp-dgd oriic// J. Mch. Enginring Sinc., 9(1), 1967, pp [8] Murdock J.W., Two-phas low masurmnt with oriics, J. Basic Enginring, 84(4), , in Collir G..C., Thm J.R., Convctiv boiling and condnsation, third d., chap 3, Clarndon Prss, Oxord, [9] Zivi S.M., Estimation o stady-stat stam void raction by mans o th principl o minimum ntropy production// ASME Journal o Hat Transr, 86, 1964, pp [10] ASHRAE Handbook-rrigration, Chaptr 41, Atlanta: Amrican socity o hating, rrigrating and air-conditioning nginrs, Inc. ASHRAE, 00.

7 Fig. Two-phas low prssur drop against inlt vapor quality basd on Chisholm modl or dirnt two-phas mass low rats Fig. 3 Two-phas low prssur drop against inlt vapor quality basd on homognous modl or dirnt two-phas mass low rats

8 Fig. 4 Prssur drop vrsus inlt quality or dirnt modls at m & = 004. kg/s Fig. 5 Two-phas low prssur drop against to-phas mass low rat basd on Chisholm modl or dirnt condnsr prssurs

9 Fig. 6 Two-phas prssur drop against two-phas mass low rat basd on homognous modl or dirnt condnsr prssurs Fig. 7 Prssur drop vrsus mixtur mass low rat or dirnt Modls at condnsr prssur P = 7 Kpa C