PERFORMANCE PREDICTION ON THE FINNED-TUBE DRY COOLER IN WINTER PERIOD

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1 Eleventh Interntonl IBPSA onference Glsgow, Scotlnd July 27-30, 2009 PERFORMANE PREDITION ON THE FINNED-TUBE DRY OOLER IN WINTER PERIOD Bng Yu,2,3, Xchun Wng, Peter Luscuere 2,3 Royl Hskonng onsultng (Shngh o. Ltd, Shngh, hn 2 Dvson Buldng Servces, Hskonng Nederlnd BV, Njmegen, the Netherlnds 3 Fculty of Envronmentl Scence nd Engneerng, Tnjn Unversty, Tnjn, hn ABSTRAT A mthemtcl model s presented to predct the behvour of condenston nd ost formton on het trnsfer surfces by smultneously consderng the condensng nd ost lyer. The model employs one-dmensonl trnsent formulton bsed upon locl vergng technque, tkng nto ccount the vrton of the ost densty nd thckness. The presented model s vldted by comprng to expermentl dt provded by the dry cooler mnufcturer. It s found tht the model cn predct the het trnsfer performnce of the dry cooler wth n ccurcy of wthn 2.9%. The dry cooler s het trnsfer performnce re predcted t dfferent r nd wter flow rtes opertng wth wter s het trnsfer flud durng the wnter perod. The model nd dscusson re helpful for the operton of such knd of dry cooler wth wter durng the wnter perod. INTRODUTION Frost phenomen re encountered n numerous felds of ndustry delng wth low tempertures, ncludng regertors, r condtons, gs coolers nd cold stores. In r-cooled het pumps, ost phenomenon on het trnsfer surfces of fned-tube het exchngers s common problem. The het resstnce between the het trnsfer surfce nd r flow s ncresed nd the r flow rte through the het exchnger s decresed due to the ost on the het trnsfer surfce, ll of whch unfortuntely degrde the performnce of the het exchnger (Yu et l., 998, Yu et l., 998 nd Yu nd Feng, Furthermore: due to the ost on the surfce of the het exchnger, the sze of the regerton unt used for ndustry s 50% lrger n sze nd 25% hgher n energy consumpton, compred wth the unt wthout ost (O Nel nd Tree, 985. For dry coolng operton wth wter s het trnsfer flud durng the wnter perod, eezng s problem. The vscosty of wter lso ncreses sgnfcntly wth decresng temperture, whch results n hgher energy consumpton of the pump system. In ddton, the phenomenon of ppe brekng occurs wth ce formton n the ppe. For these resons, t s obvously necessry to use numercl model to predct ccurtely het trnsfer chrcterstcs of the fnned-tube het exchnger under ost nd ozen condtons. Accordng to the prevous studes bout the ost formton on the surfce of the het exchnger, most reserchers hve developed numercl model bsed on the lump prmeter method ssumng ce formton on the het trnsfer surfce to be unform nd mesured het trnsfer chrcterstcs of the typcl het exchnger durng the ce formton process (O Nel nd Tree, 985, Pdk et l., 989. However, n ccurte model of dynmc ost formton on the het trnsfer surfce hs not been ntegrted nto the het exchnger model n ths pper. In ths pper, mthemtcl model hs been developed to predct the behvour of condenston nd ost formton on the het trnsfer surfce. The model concerns the dynmc formton of ost nd condensng. Therefore, t hs hgh ccurcy n the predcton of both the ost formton on one sde nd eezng phenomen on the wtersde. In ddton, the optml control strtegy hs been developed to run the dry cooler wth wter s het trnsfer flud wthout eezng phenomen n the wnter perod. MATHEMATIAL MODEL The eezng process on the het exchnger surfce nvolves smultneous het nd mss trnsfer. The followng ssumptons hve been mde n the development of the model: The eezng process cn be consdered s qus-stedy-stte process, thus n tme step, the r flow s stble nd the propertes of r nd the ost re constnts; 2 Snce het resstnces of the fns nd tube s much lower thn the het resstnces of the ost lyer nd the r flow, therml conductvty of fns nd tube re neglected; 3 The rdton between the het trnsfer surfce nd r s neglgble. Numercl nlyss s performed to predct the chrcterstcs nd ost lyer growth of the het nd mss trnsfer n the confgurton of Fgure

2 Wter T T2 T s h0 h T T n+ T s h Fgure x0 lculton x element of the het exchnger surfce T sn hn Most r For the dry surfce on the r sde when humdty bsed on the fn surfce temperture s hgher thn the r humdty (x(t s x, the het nd mss equtons cn be expressed s : m ( T T = α A ( T T x p,,,, s,, x, = 0 α A ( T T = α A ( T T, s, w w s, w, ( (2 (3 When humdty, bsed on the fn surfce temperture s lower thn the r humdty (x(t s <x, the het nd mss equtons, for the wet or ost surfce on the sde cn be expressed s: m ( h h = α A ( T T +,, +, s, m ( x x c,, + α m ( x x = A ( x x,, +, s p, α α A ( T T = A ( h h w w s w,, s p, (4 (5 (6 The het trnsfer on the wter sde cn be expressed s: m ( T T = α A ( T T w p, w w, w, w w w, s The enthlpy of humd r cn be express s: h = ( T (2500 +, p,.84( T 273 x,, (7 (8 onsderng the tem of.84t, s much less thn 2500, t s neglected n the model, thus the enthlpy dfference between neghborng elements cn be expressed s: h h = ( T T +,, + p,,, + ( x x,, + (9 s the ltent het nd s 0, 2500 nd 2835 (dry, wet nd ost. By rrngng the bove equtons for three dfferent condtons (dry, wet nd ost nd four locl vrbles, the problem cn be solved. For dry surfce condtons ( x, = const, ( =... n, three sets of equtons (Equtons, 3 nd 7 re suffcent to solve the problem: ( α A m T + m T w w w p, w w, w p, w w, + α A T = 0 w w s, ( α A m T + m T p,, p,, α A T = 0 s, α A T α A T + w w w,, ( α α waw + A Ts, = 0 (0 ( (2 For wet nd ost surfce condtons ( x( Ts x,, four sets of equtons wth four sets of vrbles nd more generl equtons wth c (c=0, 2500, 2835 ~ dry, wet, ost nd c0=2500 for enthlpy clcultons re used. The equtons used for the clculton re rrnged s: ( α A m T + m T p,, p,, + α A T α A + m x + m x α A = x T s,, p, (, + s, p, ( α m T + m T w p, w w p, w w, w p, w w, α = wawt s, 0 ( α A T α A T + α A + α A T, w w w, w w s, α A x α A = x T ( s,, p, p, ( α = α A x ( Ts, A m x + m x p,, p,, + (3 (4 (5 (6 The het trnsfer coeffcent for the r sde of the het exchnger cn be clculted by the correlton equton proposed by Vmpol (966: Nu hd 0.25Re P d b 0.67 t b = = k db Pt d b Pt d b + Pd δ f pd db (7 Where d b =externl dmeter of the tube, P d =dgonl δ f ptch, P t =Trnsverse ptch, =fn thckness The het trnsfer coeffcent for the wter sde of the dry cooler cn be clculted by the followng equtons. For turbulent nd trnston wter flows (Re=2300~5 0 6, het trnsfer coeffcent cn be

3 clculted by the correlton equton proposed by Gnelnsk (976 ( ( hd b f / 8 Re 000 Pr Nu = = k f / 8 Pr f = 2/3 ( (.82 log 2 0 Re.64 where (8 For lmnr wter flow (Re 2300 unform het flux nd het trnsfer coeffcent cn be clculted by (Frnk nd Dvd, 996 hd Nu = b = 4.36 k (9 There re mny fctors, such s r velocty, surfce temperture, r temperture nd humdty, whch nfluence the densty of the ost on the het trnsfer surfce of the het exchnger. In ths pper, the correlton equton proposed by Bng (996 s used to clculte the densty vrtons of the ost on the het trnsfer surfce; t s expressed s the functon of the het exchnger surfce temperture: ( t ρ = 650 exp s (20 Therml conductvty of the ost cn be expressed s functon of the densty s follows: k = ρ (2 In the dynmc process of eezng, the het exchnger surfce temperture s functon of the tme, therefore, the densty of the ost chnges t dfferent perods. The thckness of the ost lyer for ech tme ntervl on the het exchnger surfce cn be clculted s follows: w τ δ = ρ A e MODEL VALIDATION (22 In order to exm the vldty of the clculton model descrbed n the secton of the mthemtc model, numercl smultons were mplemented wth the propertes nd condtons of the dry cooler provded by the AIA nd the smulton results re then compred to the expermentl results. The ont nd sde vews of the dry cooler used for the smulton re shown s follows. Fgure 2 Front nd sde vews of the dry cooler The dry cooler s ctully knd of fnned-tube het exchnger wth wter flowng nsde the tubes nd r flowng round the outsde of the tubes nd fns. The tubes nd fns re mde om copper nd lumnum, respectvely. The detled confgurton of the fns nd tubes re shown s follows: Fgure 3 Detled confgurton of fns nd tubes of the dry cooler The dmenson of the r cooler used for smulton s showed n Tble s follows

4 Tble Dmenson of r cooler DRY OOLER DIMENSION DIMENSION Fn type Fn mterl Fn Thckness Fn wdth Fn length Totl loop 92 Epoxy@2.5 mm 0.3 mm 9600 mm 920 mm Het trnsfer re t wter sde m 3 Externl dmeter of the tube Thckness of the tube Totl het trnsfer re t wter sde 2.6 mm 0.35 mm m 3 For the mesurements mplemented by the mnufctures, wter-glycol soluton s used s het trnsfer flud n the tubes. The het trnsfer flud propertes nd the expermentl results of the r cooler re shown n Tble 2. Tble 2 Propertes nd boundry condtons of wter-glycol nd r AIR PROPERTIES & BOUNDARY Ar flow rte 47.4 m 3 /s Ar velocty Desgn r nlet temperture Desgn r outlet temperture 2.57 m/s 35 o 46 o Ar densty,46 kg/ m 3 Reltve humdty 60% GLYOL-WATER MIXTURE Flow rte Flow velocty l/s.27 m/s Densty kg/ m 3 Specfc het Therml conductvty Desgn nlet temperture Desgn outlet temperture Totl cpcty J/kg.K W/m.K 50 o 44 o kw Bsed on the smulton model, the outlet tempertures of both r nd glycol-wter soluton cn be clculted. The smulted results nd the mesured dt re compred n Tble 3. Tble 3 Outlet temperture of r nd glycol-wter t desgn condton OUTLET TEMP ( O MEASURED SIMULATED DEV T glycol_wter ( o o T r ( o o Totl pcty (kw % As cn be seen om Tble 3, mesured nd smulted outlet tempertures of the dry cooler re mtched very well. On the other hnd, the devton between the mesured nd smulted het trnsfer cpcty of the het exchnger s 2.9%, ths s mnly due to the neglected het trnsfer resstnce of the tubes nd fns of the dry cooler. ASE STUDIES A new KPN dtcenter s gong to be constructed n Arhnem, the Netherlnds. Dry coolers, s shown n Fgure 2, re used to produce coolng wter to remove the het generted by the computers of the dtcenter durng the wnter perod. It s plnned to use wter s het trnsfer flud n the dry cooler due to the lower vscosty compred wth wter-glycol soluton or glycol soluton. However, there wll be rsk of eezng of wter durng the wnter perod, so the het trnsfer chrcterstcs should be predcted before mplementton of the project. Accordng to the desgn schedule, the coolng demnd wll be mplemented n three constructon phses: Phse : 0 ~ 00kW of coolng demnd, wth 6 het exchngers; Phse 2: 0 ~ 2200kW of coolng demnd, wth 8 het exchngers; Phse 3:: 220 ~ 3300kW of coolng demnd, wth 0 het exchngers. In the st stge, lmost 00kW of coolng demnd s requred. Dvded by 6 het exchngers, ths ccounts for 83.33kW per unt. Bsed on the dfferent extreme operton condtons, the followng cses wll be checked:. Wter supply & return temperture of 8/0 o nd mbent r temperture -5 o nd 50% RH 2. Wter supply & return temperture of 6/0 o nd mbent r temperture -5 o nd 50% RH 3. Wter supply & return temperture of 24/0 o nd mbent r temperture -5 o nd 50% RH 4. Wter supply & return temperture of 6/0 o nd mbent r temperture -20 o nd 50% RH 5. Wter supply & return temperture of 6/0 o nd mbent r temperture -5 o nd 90% RH

5 The crtcl stuton s the perod when Phse 2 strts but coolng demnd s stll 0kW,.e. 37.5kW per unt, snce there s hgh possblty of eezng of wter durng the wnter perod. The het trnsfer behvour of wter n the dry cooler should be exmned t such crtcl stutons. Requred wter flow condton for fve dfferent cses When Phse 2 strts but coolng demnd s 0kW, the coolng cpcty for ech exchnger s 37.5kW. Bsed on coolng cpcty of 37.5kW for ech exchnger nd the dfferent extreme opertons of the dry coolers, the wter flow rtes nd flow condtons for fve dfferent cses cn be obtned s follows: Tble 4 Flow condtons of the fve cses ASES T w,n ( O T w,out ( O T, n ( O RH s,out (% M wter (l/s Re wter se se se se se As cn be seen om Tble 4, when coolng demnd for ech het exchnger s set to 37.5kW, the wter flow n se shll sty lmnr wheres the wter flow n ses 2, 3, 4 nd 5 wll be n trnston om lmnr to fully turbulent. Keepng the wter flow t requred vlues s shown n Tble 4 for fve cses nd tunng the r flow rtes to meet the requred coolng cpcty of 37.5kW of ech het exchnger, the requred r flow rtes nd outlet tempertures of r for fve cses cn then be obtned s follows: Tble 5 Ar flow rtes nd outlet tempertures for fve cses ASES Q r (m 3 /s T r,out ( o se se se se se As cn be seen om Tble 5, the coolng cpcty of the het exchnger cn lso be controlled for fve cses by keepng the wter flow rte t constnt vlues s shown n Tble 4 nd tunng the r flow rtes. The r outlet tempertures for ll fve cses re hgher thn the dew pont temperture. Therefore, there re no eezng phenomen on the surfce of the het exchngers. However, the mnmum controllble fn r flow rte s 9.48m 3 /s (V r =0.54m/s, whch s hgher thn the requred r flow rte s shown n Tble 5. From system control pont of vew, t s not fesble to relze such control strtegy. Rsk nlyss As dscussed n the bove secton, t s not possble to keep the vrble speed fn t the controllble rnge whth the control strtegy of keepng constnt wter flow rte whlst tunng the r temperture. In order to vod the rsk of eezng of the wter n the ppes nd keep the r t the controllble flow rnge, t s necessry to fnd the lowest outsde envronmentl temperture llowed for the proper operton of the dry coolers. The clculton routne to fnd the lowest outsde temperture llowed s descrbed s follows:. Keep the r flow velocty t the mnml vld vlue (Vr=0.54m/s. 2. lculte the requred wter flow rte, bsed on: n outlet wter temperture of 3 o to vod eezng, requred nlet wter tempertures nd coolng cpcty of 37.5kW. 3. Fnd the lowest outsde envronmentl temperture llowed for, usng the smulton progrm. The lowest outsde tempertures llowed for the operton of the fn t the controllble rnge for fve cses re obtned s follows: Tble 6 The lowest outsde tempertures llowed for runnng the fn ASES T r, lowest llowed ( o Q wter (l/s T wter,out ( o se se se se se Bsed on the lowest outsde temperture for ech cse, t s possble to defne the control scheme for proper operton of the dry cooler. Tkng cse for exmple, when the outsde temperture s lower thn -4 o, the control system shll gve wrnng or shut down the fn n order to vod eezng of wter n the ppes. However, we stll hve the rsk of eezng of wter n the ppes when the fn of the dry cooler s swtched off. In ths cse, the r flow n the dry cooler tkes the form of nturl ventlton. The clculton results for outlet tempertures for fve cses when the fn s swtched off re shown s follows:

6 Tble 7 Predcted results for n nopertve fn ASES T wter,out (PREDITED WATER TEMPERATURE Q wter (l/s (MINIMAL WATER FLOW RATE se se se se se $ It s found tht the predcted outlet tempertures of wter om the dry cooler for ll fve cses whth wter t mnml flow rtes (see Tble 4 re hgher thn 3 o. Therefore, there s no rsk of eezng of wter n the ppes n cse of n nopertve fn. At the sme tme, t s lso found tht there s no ostng or condenston of the r on the surfce of the dry cooler for ll fve cses. Sutble control strtegy From the bove dscusson, t s possble to develop fesble control strtegy for the proper operton of the dry cooler durng the wnter perod. The wter outlet temperture of the dry cooler s tken s the settng vlue to control the r flow rte nd wter flow rte. On the other hnd, the trnston of the wter flow om turbulent to lmnr sgnfcntly degrdes the het trnsfer coeffcent, whch cn be used to reduce the coolng cpcty s to vod eezng of the wter n the dry cooler when the requred coolng cpcty s reduced. An exmple of control strtegy of the dry cooler s showed s follows (Fgure 4: Intlly, ssumng the wter flow rte t mnmum of 4. l/s nd fns swtched off. When the wter outlet temperture of the dry cooler s hgher thn 0 o, the fn s swtched on nd s set to the mnmum flow rte of 9.48m 3 /s (0.54m/s, f the wter outlet temperture s stll hgher thn 0º, the fn speed s contnuously ncresed untl fulfllment of the set pont temperture of 0 o. When the fn s t full speed (Q r =47.4m 3 /s nd the set pont temperture of 0º cnnot be fulflled, the pump speed s ncresed to fulfll the set pont of 0 o. When coolng demnd of the dry cooler s decresed, the outlet temperture wll lso decrese. Tkng the wter outlet temperture of 5 o s the set pont temperture n ths cse, the fn s swtched off nd wter flow rte s decresed shrply to mnmum vlue of 4. l/s when the wter outlet temperture s below 5 o.! "# Fgure 4. A sutble control strtegy ONLUSIONS A mthemtcl model, whch cn predct the behvour of condenston nd ost formton on the het trnsfer surfces hs been developed by smultneously consderng condenston nd ost lyer,. The model for the predcton of the performnce of the het exchnger cn be used to ccurtely predct the het trnsfer behvour of the dry cooler operted n cold wnter perod. The control strtegy of keepng wter t requred vlues bsed on the coolng cpcty nd nlet nd outlet wter temperture dfference nd tunng the r flow rte hs been proved to be not fesble due to the lmtton of the mnmum controllble flow rte of the vrble speed fn. The control strtegy of keepng the r flow rte t mnmum controllble vlue of the fn whlst tunng the wter flow rte to obtn requred coolng cpcty hs been proved to be lmted by the outsde r temperture. In ddton, there s no condenston or ostng phenomen found on the het trnsfer surfce of the dry coolers for ll fve cses, snce the r temperture flowng through the dry cooler s lwys keepng temperture bove the dew pont temperture of the

7 r. It s fesble to use wter s het trnsfer medum n the dry cooler durng extremely cold wnter perods f the proper control strtegy s ppled. REFERENES Frnk P.I., Dvd P.D., Introducton to het trnsfer, John Wlley & Sons, Inc. New York, 996, pp Gnelnsk V., New Equtons for het nd mss trnsfer n turbulent ppe nd chnnel flow, Interntonl hemcl Engneerng, 6, , 976. O Nel D.L., Tree D.R., A revew of ost formton n smple geometres, ASHRAE Trnsctons, 985, 9(, Pdk M.M., Sherf S.A., Nelson R.M., A smple method for modelng the ost formton phenomenon n dfferent geometres, ASHRAE Trnsctons, 989, Vmpol, J. (966, Het trnsfer nd pressure drop n flow of gses cross fnned tube bnks, Strojrenstv, Yu B., Reserches on chrcterstc of smll-scle regerton nstllton wth r forced convecton coolng, Ph.D dssertton of Shngh JoTong Unversty, 996, pp. 3. Yu B., Que X.., hen Z.J., Quntttve experment nlyss on testng ost thckness of fnned-tube evportor by mge processng, hnese Journl of Engneerng Thermophyscs, 998. Yu B. et l., Theoretcl nlyss nd mprovement on fn effcency functon of het exchnger surfce under forstng, hnese Journl of Engneerng Thermophyscs, 999. Yu B. nd Y. Feng, Theoretcl nlyss of fn effcency wth ost deposton on het exchnger surfce, Proceedngs of 7 th REHVA World ongress, LIMA 2000, Npol, 200, Itly