NUMERICAL ANALYSIS ON HUMIDITY DISTRIBUTION IN A VENTILATED ROOM

Transcription

1 NMERIAL ANALYSIS ON HMIDIY DISRIBION IN A ENILAED ROOM Asushi Iwme Deprmen of Archiecure, School of Science nd Engineering, KINKI niversi, Osk, Jpn ABSRA e lred hve hd heoreicl model o predic emperure nd humidi vriions in room. Mn works hve esimed he ccurc of he numericl model, bu he migh be influenced b he ir movemen. hus, heoreicll he emperure nd humidi vriions should be solved wih ir movemen in room. In his pper, I clculed he minue emperure nd moisure disribuions in room which hs he moisure buffering effecs b he porous wlls. he room spce is regrded s recngulr bo which hs wo hole, inle nd oule for venilion. A humidifier se on he floor nd i srs o dd moisure poin in ime. Firs I clculed he sed ir veloci disribuion b FD. I ried wo urbulen models, such s sndrd k-e equions nd low-re model. hen, I clculed he he nd vpor rnspor process in wlls nd spce. As resuls, i ws shown h moisure disribuion is no negligible. Mn works depend on insnneous diffusion, bu his hpohesis should be vlided. Also I go he humidi difference which depends on he urbulen model. KEYORDS Moisure, He, FD, Moisure buffering effec, Air movemen INRODION Humidi hs lo of effecs on room spce. Len he for cooling energ is ver significn in mois climes of empere regions. I rises overll energ consumpion in houses, especill highl insuled nd well solr-refleced houses, which hve smll sensible he for cooling. Durbili of iems in room nd he room iself grel depend on humidi. Ecessive moisure cuses condension, which cceleres dmge processes. ood rcs fungi nd ermies, nd mels corrode fser in he presence of liquid wer. Some reserchers s dr ir dmges humn helh, cusing sore hros nd noses, nd skin o dr ou. hus, i is imporn o predic humidi vriion in room. According o mss blnce, humidi in room depends on 4 fcors: 1 moisure flow hrough wll surfces, moisure crried b venilion, 3 moisure genered in he room, nd 4 disribuion in he spce. I is known h we cn clcule he firs flu b ppling simulneous he nd moisure rnspor processes in porous medium. he second is simpl given b venilion volume. he hird cn be solved b reserch nd mesuremen. his work will be presened in noher pper. If ir moves fs, humidi is relivel consn. However, wind veloci in room is no high, so here is some humidi disribuion. I is lso known h ir movemen in room cn be clculed b FD simulion, lhough here re some differences mong soluions depending on he pe of urbulence models for Renolds sress nd remen of numericl clculions. A lierure surve revels some repors focusing on humidi disribuion in room spce. However, he re wlls s impermeble vpor brriers. Generll, wlls re of porous meril, even when he re covered wih merils such s vinl wll pper, nd he bsorb he moisure o some een. In his pper, he humidi disribuion in room spce inside vpor bsorb/desorb wlls is clculed b comprehensive models combining H&M rnspor in wlls nd FD simulion. he

2 subjec room is recngulr bo-shped nd i hs inle nd oule holes for venilion. he resuls re compred wih hose of simplified models nd differen FD urbulence models. ALLAION MODELS 1. Governing equions For porous merils, we use Msumoo s hgroscopic model1, which is bsed on simulneous he nd moisure rnspor processes. he humidi rio is used o represen moisure civi. q r r J ' ' 0 ( ( = = = = κ κ γ φ (1 ( In he ir spce, humidi nd emperure re given b blnce equions s: dd dd q j = = ' (3 (4 Here, erms of j dd nd q dd re moisure nd he generion re per uni volume (g/m 3 s b somehing in room such s humidifier. elociies on 3 recngulr es re given b FD sed se clculion, s given below. he humidi vriion which is bsed on he ssumpion of insnneous diffusion wihou he porous wll s moisure sorpion/desorpion is given b sum of flow re crried b venilion nd humidi source dded b humidifier. S c r J d d = ( 0 (5 B inegrion of his equion wih he iniil condiion = 0 = 0, humidi n poin of ime cn be given s follows. } ep( 1 { J c c S o = (6 Here, c is he venilion rio, given b c / r. In his pper his is clled heoreicl soluion. In he FD clculion, consiuion equions for incompressible fluid re s follows, Mss blnce: = 0 (7 Momenum blnce: ( g P P P = = = β (8 (9 (10 Energ blnce: γ γ Q S / = (11 Moisure mss blnce: S m m J D D = ( (1

3 Here, : kineic viscosi coefficien = µ / (kg/ms µ : viscosi coefficien µ = µ s µ µ s : moleculr viscosi (kg/ms µ : edd viscosi µ = 0.09 k /ε (kg/ms : herml conducivi (J/msK : edd herml conducivi = 1.1 γ µ (J/msK D m : diffusivi coefficien (m /s D m : edd diffusivi coefficien D m = 1.1 µ / (m /s k : urbulence kineic energ 1 k = ( u' u' v' v' w' w' ' ' ε : urbulence dissipion re k ui ui ε = = l j j l : urbulence scle ble-1 shows he clculion model nd is componens which re used in his pper. Simplified model is bsed on he ssumpion of no disribuion in he spce. hus, i is he soluion of Eq.(3 ble-1: Models in his pper In wlls In Air (urbulen model heoreicl model - Humidi (6 - Simplified model - Humidi (5 - omprehensive Humidi nd emperure (3(4 Sndrd k-e model H&M process (1( model eloci nd urbulen diffusiviies (7~(1 ANK low-re model 3. lculed room spce H. Yoshino e l.3 mesured he ime vriion of humidi disribuion in bou m cubic bo. All he clculions in his pper correspond o he mesuremens of Yoshino. Figure-1 shows schemic view of he clculed spce. enilion ws creed b sucking fn se he oule hole nd is re is idenified b mesuremen of wind veloci he oule hole. he mesured re ws imes per hour. In he FD simulion, i is se o 1.0 imes/h. Yoshino e l. mesured humidi nd emperure vriion in he bo for number of cses. he covered some of he gpsum wlls wih vinl shee o suppress gpsum s Moisure Buffering Effecs. his pper shows clculions for wo cses: wih no vinl-covered wlls, nd wih 5 vinl-covered wlls. In Yoshino s mesuremen, he humidifier comprised plsic r wih n elecric heer filled wih wer. In his pper, he r is omied nd he humidifier is regrded s merel ho wer, or more precisel, he surfce of he ho wer. Moisure vpories from he op nd he is rnsferred b convecion. he oher surfces re dibic nd impermeble. In he FD simulions, emperure he wer surfce is regrded s consn 9 degrees elsius. In ddiion, he wll surfce emperure in he FD simulion is consn 0 degrees elsius, s for he inle ir for venilion. ble- shows he hgroherml properies of gpsum bord. In he clculion, 100mm hickness of polsrene is regrded s creing n dibic wll4. hus, we clcule humidi nd emperure vriions onl for he gpsum bord. Behind i, on he surfce of luminum shee, he he flu nd moisure flu re equl o ero. o clcule he moisure vriion in gpsum bord, we need he moisure cpci, which is he RH differenil of equilibrium wer conen. Figure- shows he relion beween RH nd wer conen bsed on he wo poins in ble- ( 80 nd f. he curve is numericll fied b wo equions s follows. Rh < 0.8 = Rh

4 Rh 0.8 = / (Rh ble-3 shows he properies of dr ir in he FD clculion. Polsrene form 100mm Aluminum shee enilion inle Gpsum bord 1.5mm 1,795 Humidifier 1,595 enilion oule 1,607.5 Ouside onsrucion of wlls Inside Figure-1: Schemic view of clculed spce nd wll consrucion hickness [m] Densi [kg/m 3 ] ble-: Hgroherml properies of Gpsum bord Porosi [m 3 /m 3 ] p [J/kgK] dr [/mk] µ dr [-] 80 [kg/m 3 ] f [kg/m 3 ] Densi [kg/m 3 ] Moleculr viscosi [kg/ms] ble-3: Properies of dr ir p herml conducivi [J/kgK] [/mk] olume epnsion re [1/K] e e e- Figure- shows he clculion grid used for he FD simulion. he spce is divided ino 1,78,000 cells ( for ech is. Ech cell comprises bou 15mm cube. he grid defining he inle nd oule holes for venilion re divided more minuel, s shown in he figure. -Z secion Y-Z secion -Y Plne Figure-: Grid for FD simulion ALLAION RESLS 1. Air movemen nd emperure disribuion sed se he veloci in he spce is mimum he inle hole nd is vlue is bou 0.16 m/s, since ir of 1.0 imes/h venilion re flows hrough 0.1m-dimeer hole (4.6m 3 /h / 0.05 π. Generll, i is

5 hough h he urbulence effec is no lrge, especill ner he wll surfce. hus, he low-re model is beer hn he sndrd k-e model o be pplied o his problem. Figures-3, 4 show he clculion resuls of he disribuions of ir veloci nd emperure in he -Y horionl plne he inle hole cener heigh, which is 1,645 mm bove he floor surfce. he Low-Re model resul is comple compred wih he simplici of he sndrd k-e model resul. his follows he bsic heor. In he low-ir-veloci region, urbulence effec is smll nd he difference of veloci becomes relivel lrge. hen edd is smll, he urbulen herml rnsfer is lso smll. hus, emperure difference is lso relivel lrge. Sndrd k-e model Low-Re AKN mode Sndrd k-e model Low-Re AKN model In -Y plne he heigh of he cener of inle hole in -Z cener secion Figure-3: Air veloci m/s Sndrd k-e model Low-Re AKN mode Sndrd k-e model Low-Re AKN model In -Y plne he heigh of he cener of inle hole in -Z cener secion Figure-4: emperure deg... Moisure diffusion process Figure-5 shows he clculed vriion of humidi rio some poins in he spce, depiced in he schemic figure. All he wll surfces re impermeble o vpor. he heoreicl soluion nd simplified soluion re lso showed. he simplified soluion perfecl corresponds wih heoreicl soluion. I is shown h here re some differences mong he humidi rios hese poins. nil now, he humidi rio hs been regrded s unique in he spce since he vpor diffusion speed is ver fs. However, if here is n ir flow, even hough mos spces eperience i, he vpor moves wih he bulk ir flow creing some disribuion in he spce. his figure lso shows h he verge of he disribuion is roughl equl o he heoreicl soluion. Figure-6 shows he resuls for spce enclosed b gpsum bord. Gpsum bord bsorbs he vpor. he difference beween he humidi rios is greer hn he former. Humidi bsorpion b he

6 wlls cuses bigger differences beween he humidi rios in he spce. Humidi rio [g/kg'] ll-l ll-f eiling ll-b ener ll-r ll-b eiling ll-l ener ll-r ll-f Simplified model heoreicl soluion Elpsed ime [hours] Figure-5: lculion resul of humidi rio Humidi rio [g/kg'] ll-b ener ll-f eiling ll-r ll-l Elpsed ime [hours] Figure-6: lculion resul of humidi rio in he spce whose wlls re gpsum bord Figure-7 shows he wo resuls of differen urbulen models. One is he sndrd k-e equion model nd he oher is he Low-Re k-e model. As shown in he flow pern, Low-Re model hs big disribuion of ir veloci in he spce. In his figure, i mkes greer difference of humidi rio. Figure-11 shows he comprison wih wo resuls. I clerl shows issues s follows, 1 he Low-Re model hs wider disribuion of humidi rio in he spce hn he sndrd k-e model. A mos poins, Humidi rion clculed wih he Low-Re model is bigger hn wih he sndrd model. Figure-7 shows he resuls of he wo differen urbulen models: he sndrd k-e equion model nd he Low-Re k-e model. As shown b he flow pern, he Low-Re model hs big disribuion of ir veloci in he spce. he figure shows greer differences mong humidi rios. Figure-8 compres he wo resuls. I clerl shows issues: 1 he Low-Re model shows wider disribuion of humidi rios in he spce hn he sndrd k-e model. A mos poins, he humidi rio clculed from he Low-Re model is bigger hn h from he sndrd model.

7 80% SD eiling ANK eiling 70% Relive Humidi [%] 60% 50% ANK ener SD ener 40% Elpsed ime [hours] Figure-7: Difference wih urbulen model 1.5 eiling ll-b Humidi rio resuls of ANK [g/kg'] ener ll-l ll-f ll-f ll-r ll-l ener ll-r eiling ll-b Humidi rio resuls of SD [g/kg'] Figure-8: omprison wih he wo urbulen model resuls Figure-9 shows he ppernce frequenc of sclr ir veloci ech clculed poin in he spce. A glnce, i cn be seen h he Low-Re model s veloci is smller hn he sndrd k-e model s veloci. In he high-veloci rnge, however, he frequenc of Low-Re is greer. he bigger he veloci disribuion, he bigger disribuion of he humidi rio in spce. Figure 10 shows he urbulence diffusivi ech clculed poin, sored b vlue. I is cler h he sndrd k-e model hs much bigger urbulence diffusion, which crees smller disribuion of humidi rio in he spce.

8 Number of ppernce Low-Re AKN model Sndrd k-e model ind veloci [m/s] Figure-9: Appernce frequenc of sclr of veloci 1E-01 1E-0 1E-03 Sndrd k-e model urbulen diffusivi [m /s] 1E-04 1E-05 1E-06 1E-07 1E-08 Low-Re AKN model 1E-09 1E-10 1E-11 Ech cell sored b vlue Figure-10: urbulen diffusivi (sored b vlue ONLSIONS I hs been considered h humidi rio in spce hs no disribuion since i diffuses so fs. In his sud, however, ir veloci cused b venilion crees some disribuion. omprison of urbulence models hs shown h he sndrd k-e model hs smll disribuion since i hs smller ir veloci nd bigger urbulen diffusivi. I is lso shown h vpor-bsorbing wlls crees wider disribuion of humidi rio. In noher words, he locions of wlls should considered when esiming he moisure buffering effecs of building merils. AKNOLEDGEMENS his pper is bsed on he civi of IEA-EBS/Anne41. I pprecie o Prof. Yoshino nd Dr. Mimur for heir splendid eperimenl sudies. I lso hnk o Prof. Hokoi for mn dvices o his sud. REFERENES Hiroshi Yoshino, eruki Mimur nd Ken-ichi Hsegw: ANNE41 Subsk 1 ommon Eercise Smll chmber es (H es room in he clime chmber, IEA ANNE41 meeing repor, 006 M. Kumr KMARAN, IEA ANNE4 He, Air nd Moisure rnsfer hrough New nd Rerofied Insuled Envelope Prs (Hmie Finl Repor olume 3 ASK 3: MAERIAL PROPERIES