Design optimal of refrigeration insulations

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1 Issu 5, Volum 7, Dsign optimal of rfrigration insulations Ioan Sarbu, Emilian Stfan Vala, and Gabril Ostaf Abstract Economic opration with minimal nrgy consumption and low costs of a coold room or a rfrigrant piping systm dpnds largly on th quality and thicknss of thir insulation. h classical mthod of insulation rating for rfrigration systms is basd on rspct of th condition to prvnt condnsation of watr vapours in th air on th surfac of insulation or on limiting hat gain, but rarly lads to optimum in trms of a tchnical and conomic critrion. In this papr ar dscribd som typs of insulation for rfrigration applications and is dvlopd a rating optimation modl of ths insulations with a high lvl of gnrality. It uss multipl dynamic optimation critria simpl or compound, which bttr rflcts th conomic and nrgy complx aspcts, prsnt and futur. Basd on this modl wr laboratd two computr programs implmntd on PC microsystms. Numrical xampls will b prsntd to dmonstrat th accuracy and fficincy of th proposd optimation modl. hs show th good prformanc of th nw modl. Kywords Coold rooms, Rfrigrant piping, Insulation rating, Optimation modl, Comparativ analysis. I. INRODUCION HE rol of rfrigration systm insulation is to rduc hat flow to coold spacs or to cold dvics and pips in which th rfrigrant tmpratur blow ambint tmpratur (fr air, soil or nighbouring rooms). hrfor, rfrigration insulation is commonly usd to rduc nrgy consumption of rfrigrating systms and quipmnt. Economic opration of a coold room or a cold pip dpnds largly on th quality and thicknss of thir insulation. Hnc th propr slction importanc of th insu-lation matrial and rating of thir rfrigration insulations, lading to judicious us of invstmnt funds, to normal opration with minimal nrgy consumption and low costs. Cllular glass, flxibl lastomric, minral wool, polyisocyanurat, and xpandd or xtrudd polystyrn ar insulation matrials commonly usd in rfrigrant applications. h classical mthod of insulation rating for rfrigration systms is basd on rspct of th condition to prvnt condnsation of watr vapours in th air on th surfac of insulation, but rarly lads to optimum in trms of a tchnical and conomic rason. In cas of flat surfacs is usd hat Ioan Sarbu is currntly a Profssor and Dpartmnt Had at th Building Srvics Enginring Dpartmnt, Polithnica Univrsity of imisoara, ROMANIA, -mail addrss: ioan.sarbu@ct.upt.ro Emilian Stfan Vala is currntly a Lcturr at th Building Srvics Enginring Dpartmnt, Polithnica Univrsity of imisoara, ROMANIA, -mail addrss: milian.vala@ct.upt.ro Gabril Ostaf is currntly a Assistant Profssor at th Building Srvics Enginring Dpartmnt, Polithnica Univrsity of imisoara, ROMANIA, -mail addrss: gabril.ostaf@ct.upt.ro transfr quation which admits a hat gain so that nithr rsults too thick xpnsiv insulation, nor vry high cool consumption. In spcialty litratur [2], [11] ar rcommndd thicknsss for rfrigration insulation basd on condnsation control or for limiting hat gain. h most conomical insulation thicknss can b dtrmind by considring both initial costs and long-trm nrgy savings. Optimal computation of th insulations applid to coold rooms and to cold pips basd on conomic critria of minimum total lif-cycl cost lads to insulation thicknss that applid in practic bcom incorrct at som point aftr th xcution, bcaus pric volution in tim. h nrgy costs ar volatil, and a ful cost inflation factor may incras mor quickly than gnral inflation. In this papr is dvlopd a computational modl of th optimal thicknss of ths insulations, with a high lvl of gnrality. his modl uss multipl dynamic optimation critria simpl or compound, which bttr rflcts th conomic and nrgy complx aspcts, prsnt and futur. Basd on this optimation modl ar laboratd two computr programs implmntd on PC microsystms. II. YPES OF INSULAION FOR REFRIGERAION APPLICAIONS Rfrigration systms covr a broad spctrum of application tmpraturs and nvironmnts. But thy all fac th sam issus rlating to both condnsation control and moistur. Sinc moistur is a good thrmal conductor, its prsnc in an insulation systm is highly dtrimntal. Unlik hot systms, whr marginal insulation may rsult in incrasd nrgy us (and addd cost), rfrigration systms fac condnsation, which oftn lads to complt systm failur. Evn with today s high nrgy costs, th dsign thicknss in most rfrigration applications is dictatd by what is ndd to prvnt condnsation, rathr than by conomic payback. Rfrigration systms typically oprat in th rang of 5 C (for Fron systms) to as low as 45 C (for ammonia systms). hy can us a varity of rfrigrants and fluids in addition to Fron and ammonia, including glycol, brin, and othr spcialty fluids. Coppr, iron, stainlss stl, or othr piping matrials may b usd to carry th cooling mdium. ypical applications includ thos in suprmarkts, bvrag dispnsing lins, chillrs, and food procssing, frzing, and storag facilitis. Othr applications includ thos at ic rinks and various uniqu applications. All of ths applications shar common concrns rgarding condnsation control and long-trm rliability, but thy also hav particular issus with installation, rquird thicknss, and th nvironmntal conditions in which thy oprat.

2 Issu 5, Volum 7, Rliability should b th primary concrn whn considring th dsign and installation for any application. Dsign must considr factors including th application tmpratur, nvironmntal considrations, consquncs if a failur occurs, and xpctations of th job by th ownrs (longvity of th systm, asthtics, tc.). h following ar som important faturs of th insulation in various rfrigration applications: thrmal conductivity; watr vapor transmission (WV) proprtis; watr absorption proprtis; cofficint of thrmal xpansion; moistur wicking. hr ar rcommndd th following insulation matrials for rfrigration applications [2]: cllular glass, closd-cll phnolic, flxibl lastomric, polyisocyurant, and polystyrn. All of ths matrials ar closd-cll foam matrials, which mans thy will hav good WV and low watr absorption charactristics. In all cass, th ntir systm (sams, butt joints, and trmination points) must b compltly sald with adhsivs to protct against air intrusion into th systm, which would carry moistur and rsult in condnsation btwn th cold pip and th insulation. Rlying on a singl, concntratd vapor rtardr is not rcommndd. Gnrally, closd-cll foam insulations ar usd for ths applications. Sams should b minimd. On multilayr systms, th sams should b staggrd. apd sams ar only allowd as a complimntary closur systm. Suprmarkts ar on of th biggst and most noticabl applications for rfrigration systms. hy fac svral issus, including changs in rfrigrant, coldr lin tmpraturs, highr tmpratur hot gas dfrost cycls, changing stor dsigns, and prssurs to rduc installation tim to dcras stor build tim. In [2] ar dtaild many of th issus rlatd to this markt sgmnt. Using prinsulatd pip hangrs is a concpt that is gaining accptanc in suprmarkts bcaus it savs tim and improvs rliability by rducing condnsation at hangr locations. h majority of piping on a suprmarkt is indoors, but for th outdoor and rooftop sctions, th us of flxibl jacktingpolyvinyl chlorid (PVC), AL laminats, tc., is bing valuatd, ithr installd at th job sit or factory applid to improv th longvity and apparanc of th job. Us of protctiv coatings that nd priodic maintnanc is bcoming lss spcifid. Rfrigration piping on most suprmarkts is found insid, but som stors ar dsignd with 90% of th piping on th roof. Som lastomric insulation products ar bing promotd as ultraviolt (UV) rsistant and accptabl for us outdoors without th additional protction of coatings, jackts, or cladding matrials. But UV protction is not th only issu whn it coms to outdoor applications. Mchanical abus (by birds, cats, popl, tc.) and nvironmntal abus (by hail, sand, dirt, wind, rain, tc.) play a rol in th rliability and longvity of th insulation systm. For optimum prformanc, coatings, jackting, or cladding should b usd for outdoor applications. h insulation systm installd on a suprmarkt rfrigration systm must b highly rliabl, as it will oprat 24 hours a day for up to 10 yars. Closd-cll lastomric matrials hav bn usd in this application for many yars bcaus thy ar xtrmly rliabl and cost-ffctiv. It is a primary product usd for suprmarkt rfrigration applications bcaus of its low WV, allowabl us tmpratur rang, and as of installation. Using a coating or flxibl jackting can improv th apparanc, durability, wathr rsistanc, and longvity of th insulation on a unit. Flxibl, closd-cll lastomric insulation is th prdominat product usd in this application. A 2.0 cm thicknss is commonly usd. Food procssing, frzing, storag, and distribution applications oftn us ammonia rfrigration bcaus of its lowr oprating costs. As ammonia systms ar dsignd for smallr applications at an conomical up-front cost, thy ar gtting mor considration than mor xpnsiv oprating systms. Whil most aras do not xcd high tmpraturs abov 70 C, som sctions may cycl from 40 C to 120 C. Lowr tmpraturs (down to 20 C) man gratr insulation thicknss (5 8 cm) is usually rquird to prvnt condnsation. ypically, 8 cm of insulation is usd to prvnt condnsation, as many of ths applications ar in highhumidity aras. h majority of th insulation is installd outdoors, so jackting slction is critical. As a rsult of th cost and thicknss rquird, polystyrn and polyisocyurant with a stainlss stl jackt ar th most common matrials usd. Of ky concrn is corrosion of iron pip. Propr insulation installation (with no opn or through sams) is a major concrn, and us of scondary vapor-rtardr systms is th norm. h rfrigration markt covrs a broad spctrum of applications, ach with uniqu rquirmnts but all with a common goal: prvntion of moistur intrusion and condnsation to maintain long-trm systm rliability. Installation tchniqus ar just as critical as matrial slction. h consquncs of systm failur can includ dgradd thrmal prformanc of th insulation, highr systm oprating cost, inadquat cooling capacity, mold and mildw, ic formation, ruind cilings, slippry floors, quipmnt downtim, and corrodd pips. In blow-ambint systms lik rfrigration applications (including chilld watr and cryognic systms) closd-cll insulation products ar prfrrd bcaus of thir low WV and inhrnt moistur rsistanc. It s important to slct th right insulation product for th application. Customr xpctations must b matchd to product prformanc and cost. Rfrigration applications ar dmanding and rquir carful considration in matrial slction and installation to obtain optimum prformanc for th nd usr. III. OPIMIZAION MODEL h optimation mthod minims th analytical xprssion of various simpl or compound optimation critria. h computational modl involvs som known data as: gnral data, nrgy-conomic paramtrs, rfrring data to

3 Issu 5, Volum 7, rooms or piping and to construction lmnts or rfrigrant utild in rfrigration systm. In Figurs 1 and 2 ar prsntd calculation schma of rfrigration insulation for a flat and rspctivly cylindrical surfac. Fig. 1 Diagram of rfrigration insulation to a flat surfac Fig. 2 Diagram of rfrigration insulation to a cylindrical surfac h thrmal conductivity λ of insulation is xprssd as an analytical dpndnc: = b 0 + bt m λ (1) in which b 0, b ar constants dpnding on insulation matrial [11]; t m man tmpratur of insulator layr. otal rsistanc to hat transfr R is calculatd with quations: for flat surfacs of coold rooms: NS δ 1 δ j 1 R = λ α i λ j= j α 1 for cylindrical surfacs of cold pips: d R = + + ( ln πα d πα d 2π λ d whr: i i p 1 d 1 d p + ln + ) (3) λ d λ d p c i + (2) d = d + δ ; d = d + 2δ ; d p = d + 2δ p (4) i 2 c in which: δ is insulation thicknss; δ j, λ j thicknss and thrmal conductivity of layr j of componnt matrial of a flat surfac; δ c wall thicknss of a pip; δ p protctiv layr thicknss of pip insulation; d i, d insid and outsid diamtr of th pip; α i, α intrnal and xtrnal hat transfr cofficints of componnt lmnt of coold nvironmnt; NS matrial layrs numbr of a lmnt. Analytic optimation critria ar minimd and is fulfilld th condition of air condnsation prvnt on insulation surfac: flat surfacs: t ti = α i ( t p ti ) (5) R cylindrical surfacs: d d 2λ t ti ln 1 (6) d d α d t t pr in which: t i is coold nvironmnt tmpratur (indoor air or rfrigrant from pip); t outdoor air tmpratur; t p intrnal surfac tmpratur of a flat wall; t pr air dw-point tmpratur. It is assumd that th rfrigration systm is on with vapour mchanical comprssion and lctric driv. h optimal insulation thicknss can b dtrmind by considring as optimation critria: th insulation achivmnt cost, th oprating costs, th nrgy mbddd in insulation or th nrgy consumd to maintain low tmpratur [14]. A. Economic Critrion Economic critrion adoptd for optiming rfrigration insulation thicknss is th minimum updatd total cost (capital cost and nrgy cost). aking into account th spcific invstmnt cost for insulation I, th annual cost for maintnanc and rpair of insulation C ir, th annual cost of nrgy losss by insulatd surfac C f and th xprssion of updatd rat r for annual costs during normal rcovry tim: 1 ( 1+ r0 ) 1 r = =, (7) t 1+ r r r ( ) ( ) t = this critrion implis th miniming of following objctiv function: Cir + C f FC = I + (8) t= ( + ) t 1 1 r0 in which r 0 =1/ is dprciation rat for rcovry priod (10 15 yars). h optimal insulation thicknss is obtaind by solving th quation: F C / δ =0. For flat surfacs that finally lad to th rlation: ( ) NS rστ c f t ti λ = 1 δ j 1 δ + + λ rp + c (9) 1000( 1) αi j= 1 λ j α For cylindrical surfacs is applid th mthod of succssiv approximations aftr xplicating th objctiv function (8):

4 Issu 5, Volum 7, F C ( t t ) rσ τc f i = ( rp + 1) cδ ( d + δ ) + (10) 1000 R in which: c is th spcific invstmnt cost of a m 3 of insulation; p th dprciation, rpairs and maintnanc rat for an insulation ( ); σ additional cold loss cofficint through pip fittings or du to non-stady stat ( ); τ th numbr of hours ndd to provid cool during a yar ( hours/yar); c f cooling nrgy cost pric B. Enrgy Critrion h nrgy optimal insulation thicknss is dtrmind miniming th sum of nrgy mbddd in insulation E and oprating nrgy E rquird to maintain low tmpratur in coold nvironmnt. Enrgy critrion is xprssd analytically by th function: F E = E + E (11) For cylindrical surfacs this function rcivs particular form: F E ( t t ) σ τ i = δ ( d + δ ) + (12) 1000 R and could b minimd applying succssiv approximations mthod. Explicating th quation (11) for flat surfacs and introducing minimum condition ( F E / δ =0), aftr a sris of algbraic transformations, is obtaind th trm nrgy optimum insulation thicknss for coold rooms: δ ( )( ) NS t ( ) c t0 t ti στ λ 1 δ j 1 λ η + η f t0 273 α i λ j= 1 j α = (13) in which: is spcific nrgy mbddd in on m 3 of insulation; t c, t 0 th condnsation and vaporation tmpraturs of th rfrigrant; η avrag fficincy of obtaining lctricity from primary nrgy ( ); η f fficincy of ral rfrigration cycl vrsus rfrntial rvrsd Carnot cycl ( ). C. Enrgy-Economical Critrion Enrgy-conomical optimation critrion considrs th two abov critria combind. hus rflcts in a mor objctiv way th wight of tchnical and nrgy aspcts during lif-cycl of th insulatd construction or pip. So, if ar illustratd curvs F C =f(δ ) and F E =f(δ ) in two prpndicular plans (Fig. 3), thr is absolutly optimal point M (F C,min and F E,min ). his point rprsntd in a third plan formd by axs F C and F E is a fictional point, bcaus, in gnral, is not in th xistnc fild of functional rlationship F E =f(f C ). It is lookd for anothr point N so that MN distanc is minimd. It is dfind a complx critrion that includs th two abov mntiond in th form of miniming th Euclidan distanc in th plan (F C, F E ): F Fig. 3 3D-Rprsntation of bicritrial optimation function CE 2 ( F F ) + (1 ψ ( F F ) 2 = ψ (14) C C, min ) E E,min whr ψ is a critrial wight cofficint by which can b giv prfrnc to on or anothr of th componnt critria in diffrnt prics circumstancs, rspctivly in nrgy pnury. For flat surfacs, is obtaind th gnral xprssion of optimum insulation thicknss: δ = ψrc f (1 ψ) + η η ψ( rp + 1) c f ( tc t ) ( t + 273) 0 ( t t ) i στ (1 ψ) 0 λ NS λ 1 δ j α i j= 1 λ j α (15) By ψ = 1 and ψ = 0 in (14) or (15) ar found particular cass of optimation on conomic and nrgy critrion, xprssd by rlations (9) and (13) for flat surfacs and th rlations (10) and (12) for cylindrical surfacs. Basd on th prviously dvlopd optimation modl, two computr programs DEFRIZOP for coold rooms and COFRIZOP for cold pips hav laboratd in FORRAN programming languag, for PC microsystms. hs programs oprat squntially and hav flow charts in Figurs 4 and 5. IV. NUMERICAL APPLICAIONS It is xmplifid th application of th proposd computational modl for optimal sing of insulation on a plastrd xtrnal wall of a coold room to t i = 10 C tmpratur, which oprat all yar round and on a stl prssur pip carrying liquid ammonia at tmpratur t i = 10 C.

5 Issu 5, Volum 7, Fig. 4 Flow chart of DEFRIZOP program

6 Issu 5, Volum 7, Fig. 5 Flow chart of COFRIZOP program

7 Issu 5, Volum 7, h xtrnal wall is north orintd, has dimnsions 6 4 m, and ar known gnral data: δ 1 = 0.02 m; λ 1 = 0.93 W/(m K), δ 2 = 0.30 m, λ 2 = 0.80 W/(m K), t = 30 o C, w = 4 m/s, w i = 0 m/s, p = 0.05, = 10 yars, β o = 0.1, σ = 1.1, η = 0.3, η f = 0.6. h cold pip has diamtrs d /d i = 219/203 mm, lngth L = 15 m, flow rat G = m 3 /s and ar known gnral data: t = 30 o C, w = 0 m/s, δ p = 0.02 m, λ p = 0.29 W/(m K), p = 0.05, = 10 yars, σ = 1.1. abl 1. Insulation thicknss for xtrnal wall Using computr programs DEFRIZOP and COFRIZOP is prformd a rating comparativ study of ths insulations both with optimation modl and classical mthod. Considr svral cofficints ψ and as insulation xpandd polystyrn (EP) and minral wool (MW). Ar also allowd mor valus c f to highlight thir variation on insulation thicknss. h numrical rsults obtaind ar summard in abls 1 and 2. δ [mm] Optimation modl c f Classical Enrgy crit. Enrgy-conomical critrion c Econ. crit. [ /kwh] mthod ψ = 0 ψ = 0.25 ψ = 0.50 ψ = 0.75 ψ = 1.00 EP MW EP MW EP MW EP MW EP MW EP MW abl 2. Insulation thicknss for rfrigrant pip δ [mm] Optimation modl c f Classical Enrgy crit. Enrgy-conomical critrion c Econ. crit. [ /kwh] mthod ψ = 0 ψ = 0.25 ψ = 0.50 ψ = 0.75 ψ = 1.00 EP MW EP MW EP MW EP MW EP MW EP MW V. CONCLUSIONS From th prformd study rsults th following: h insulation thicknss dtrmind basd on conomic critrion, and also spcially nrgy critrion, is gratr than th thicknss usually practicd. Vry high insulation thicknss valus obtaind using xclusivly nrgy optimation critrion, is du to th larg wight of nrgy ndd to maintain th low tmpratur in pip compard with nrgy mbddd. hr is a slow variation of th optimal insulation thicknss with th cooling nrgy cost. Applying complx optimation critrion for a highr wight of nrgy critrion and for qual wights of both componnt critria, insulation thicknss valus ar high; this situation is normald admitting a dcrasd wight for nrgy critrion compard to th conomic critrion. h proposd optimation modl is complx and mor fficint. Dvlopd computr programs ar applicabl to any significant changs in conomic and nrgy policy. hy can hlp achiv savings in capital and nrgy, particularly important in th currnt conomic junctur. REFERENCES [1] ASHRAE, Fundamntals Handbook, Amrican Socity of Hating, Rfrigrating and Air-Conditioning Enginrs, Atlanta, [2] ASHRAE, Rfrigration Handbook, Amrican Socity of Hating, Rfrigrating and Air-Conditioning Enginrs, Atlanta, [3] J.P. Curtis, Optimation of multipl thin thrmal insulation layrs, Procdings of th 3 th IASME/ WSEAS Int. Confrnc on Hat ransfr, hrmal Enginring and Environmnt, Corfu, Grc, August 20-22, 2005, pp [4] N. Gorgscu, Mthodology to stablish th total mbddd nrgy in building matrials, Civil Enginring Journal, Bucharst, no. 9, [5] C.P. Hdlin, Moistur gains by foam plastic roof insulations undr controlld tmpratur gradints, Journal of Cllular Plastics, no 3, 1977, pp [6] V. Korsgaard, Innovativ concpt to prvnt moistur formation and icing of cold pip insulation, ASHRAE ransactions, vol. 99, no. 1, 1993, pp [7] M.K. Kumaran, Vapour transport charactristics of minral fibbr insulation from hat flow mtr masurmnts, In: ASM SP 1039, Watr vapour transmission through building matrials and systms: Mchanisms and masurmnt, Amrican Socity for sting and Matrials, 1989, pp [8] R.S. Lnox, P.A. Hough, Miniming corrosion of coopr tubing usd in rfrigration systms, ASHRAE Journal, vol. 37, 1995, pp. 11. [9] J.F. Malloy, hrmal insulation, Van Nostrand Rinhold, Nw York, 1969.

8 Issu 5, Volum 7, [10] I. Sarbu, I. Numrical modlling and optimations in building srvics, Polytchnic Publishing Hous, imisoara, 2010 (in Romanian). [11] I. Sarbu, Rfrigration systms, Mirton Publishing Hous, imisoara, 1998 (in Romanian). [12] I. Sarbu, C. Sbarchivici, hrmal rhabilitation of buildings, NAUN Intrnational Journal of Enrgy, vol.5, no.2, 2011, pp [13] I. Sarbu, I. C. Sbarchivici, Effcts analysis of additional thrmal protction for rtrofittd buildings, Journal of Enginring and Applid Scincs, vol. 6, no. 6, 2011, pp [14] I. Sarbu, E. Vala, G. Ostaf, Insulation rating optimation for rfrigrating systms, In: Rcnt Advancs in Environmntal Scinc, Procdings of th 9 th WSEAS Int. Confrnc on Enrgy, Environmnt, Ecosystms and Sustainabl Dvlopmnt, Lmsos, Cyprus, March 21-23, 2013, pp [15] M. Storkmann, Insulating against th low tmpraturs by flxibl insulation matrials, chnical Building Equipmnts, vol. 22, no. 5, g. Murs, Romania, 2004, pp [16] W.C. urnr, J.F. Malloy, hrmal insulation handbook, McGraw Hill Book Company, Nw York, 1981.