SIMULATION ON HYDRAULIC HEATING SYSTEM OF BUILDING UNDER THE CONTROL OF THERMOSTAT RADIATOR VALVES. Xu Baoping, Fu Lin, and Di Hongfa

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1 SIMULAION ON HYDRAULIC HEAING SYSEM OF BUILDING UNDER HE CONROL OF HERMOSA RADIAOR VALVES Xu Baoping Fu Lin and Di Hongfa Deparmen of Building Science and echnology singhua Universiy Beiing China ABSRAC Considering he dynamic conrol process of hermosaic radiaor valves (RVs) and adusemen behavior of consumers as well as hea ransfer hrough neighborhood he main purpose of his paper is o derive a oal model for simulaing and analyzing he dynamic behavior of hydraulic heaing sysem wih he conrol of RVs in muli-family building based on sae space model of room dynamic performance. his is done by reaing building and he heaing sysem as complee eniies. Firs of all he dynamic models for rooms radiaors and RVs are derived. hen he suggesed models are formulaed as a whole sysem. Mulizone model for he simulaion of building hermal performance is complicaed and will be more difficul when considering dynamic process of radiaors and RVs hus he hea ransfer beween neighboring rooms is simplified by using explici difference approximaely. Finally Deailed simulaion of an acual building is given o verify he componen models and heir ineracions. he experimenal measured neighbor rooms emperaure oudoor emperaure and supply emperaure are used as inpu o he model and he calculaed resuls are compared wih he measured air emperaure and reurn waer emperaure. he agreemen beween simulan and measured daa is quie good. KEYWORDS muli-family building simulaion hydraulic heaing sysem hermosa radiaor conrol valves variable flow-rae INRODUCION Lie many European counries China realizes ha hea meering and consumpion-based billing are criical o encourage space-heaing energy conservaion by giving individual households he opporuniy o regulae heir hea energy consumpion. Saring in he mid 1990s he naional and local governmens of China have suppored a range of demonsraion proecs o sudy hea meering echnologies (JP Building Engineers 02). he monioring daa obained from he demonsraion proecs indicaed ha hermosaic radiaor conrol valves (RVs) conribued significanly o reduce hea consumpion and he average reducion was abou 10% (Wang Z C 02). Meanwhile I brings new problems. RVs self-adusing and consumer s regulaion behavior mae he flow-rae variable in he new sysems oher han consan in he radiional ones which requires corresponding changes in design and conrol sraegies of he sysem (Di H F 00). hus a proper simulaion model is needed o serve as a useful ool in analyzing such problems. In order o derive a model for he hea dynamics of a building wo differen approaches may be used. he radiional approach is simply o use he nowledge of physical characerisic and well-esablished models of sub-processes. Mos simulaion models are based on firs principles and are available in a number of sofware pacages including EnergyPlus (Crawley 00) DOE-2 (Lawrence Bereley Laboraory 1982) HVACSIM+ (Clar D R 1985) RNSYS (Klein S A 1976) DES (ZHU Y X 03) ec. Jiang Y (1981) developed sae-space mehod for he simulaion of hermal behavior wihin an air-condiioned room. Hong Z (1997) preed a new mulizone model which is an improvemen on he sae space model. Deailed physical models are ime consuming and always need suiable simplificaion and assumpions. herefore a simplified physical model for esimaing he average air emperaure in muli-zone heaing sysem for use in an inferenial boiler conrol scheme was developed by Liao (04). An alernaive approach is o use building performance daa and saisical mehods. Lehernman (1982) uilized experimenal daa based on pseudrandom binary sequences of he inpu o deermin he hea dynamics. ARMAX models were discussed by Crawford (1985) who considerd a single-family residence wih elecric heaing. A saisical approach he grey box modeling mehod was applied by Mad (1995) in order o drive a oal model for he hea dynamics of a building wih a single es room. Ander (00) uilized colleced building performance daa and saisical mehods o obain a sysem of sochasic difference equaions for he hea dynamics in a residenial building. Braun and Chaurvedi (02) developed an inverse gray box hermal newor model for ransien building load predicion. Wang S W (06) preed he building inernal mass wih a hermal newor srucure of lumped hermal mass and esimaed he lumped parameers using operaion daa. he main drawbacs of saisical models are

2 ha hey require a significan amoun of raining daa and may no always reflec he physical behaviors. Defferen models concenrae on differen aspecs according o heir inenion. A special problem of mos exied models is ha hey focus much on buildings characerisic bu lile on deailed hydraulic heaing sysem e.g. he RVs dynamic conrol process and consumers adusmen behavior is always no ae accoun in which may be especially imporan in analyzing conrol sraegies. Furhermore he models always based on a singlefamily residence or occupied office building hea ransfer hrough neighborhood consumers such as occurred in Chinese muli-family buildings can no be considered. In view of wha menioned above and based on sae space model of room dynamic performance he main purpose of his paper is o derive a oal model for analysis compuaion and simulaion on he dynamic behavior of hydraulic heaing sysem wih he conrol of RVs in muli-room building which is done by reaing buildings and he sysems as complee eniies. Dynamic models for room radiaor and RVs are derived. hen he suggesed models are formulaed as a whole sysem. Mulizone model for he simulaion of building hermal performance is complicaed and will be more difficul when considering dynamic process of radiaor and RVs hus he hea ransfer beween neighboring rooms is simplified. Finally i is demonsraed ha he whole model gives a reasonable descripion of dynamical behavior of he experimenal building. HE MODELING APPROACH he mulizone model is improved from he sae space mehod (Yi Jiang 1981). Insead of reaing all of a building s node ogeher as a sae space i reas a building as separae zones and each zone consrucs a sub sae space wih all is nodes ogeher. Room model he main hea disurbances ha influence he room air emperaure are solar radiaion indoor casual gains ou door emperaure hea inpu from radiaors air emperaure of adacen zones infilraion or venilaion hrough openings. Firs hree of he hea disurbances values menioned above are nown or can be direcly calculaed. he long wave radiaion exchange beween an exernal surface of a zone wih he inernal surfaces of he adacen zone is simplified ino he convecive hea ransfer beween he exernal surface of his zone and he air of he adacen zones. According o he sub sae space model of each zone and he feaure of each hea disurbance he room emperaure can be calculaed as: = + ψ + ψ Q a bz1 0 a 1 + ψ Q + ψ c ρv ()[ ()] rad 0 v p ou ou a + ψ c ρv ()[ ()] (1) v p a a repres he air emperaure of room bz1 wihou considering he influence of hea ransfer beween hermal zones he hea inpu from radiaor and infilraion a ime ; ψ ψ 0 1 ψ rad 0 ψ v separaely repres he influence coefficien of he adacen zones air emperaure a hea emi from adacen zones Q and calculaion zone Q naural venilaionv ou and adacen venilaion V o he room emperaure a ime. Yi Jiang (1981) Gives deailed calculaion mehod of hese influence coefficiens. he only difference is ha Jiang discussed a residenial space-condiioning sysem for which air condiioning influence he room emperaure only hrough convecion while his paper focuses on hydraulic heaing sysem for which hea ransfer from he radiaors no only o he air hrough convecion bu also o he inernal surfaces of envelope hrough radiaion. Considering he conrol process of RVs he sampling ime is cho based on a priori esimae of he smalles ime consan e.g. when ime consan of RVs is 10min 5min is aen as he sampling ime. Room emperaure will be changed lile during wo calculaion sep herefore he previous calculaion resul of neighbour room emperaure and radiaor emi are used o approximae he influence of neighbour disurbance. Equaion (1) can be approximaed as = + ψ ( 1) + ψ Q ( 1) a bz1 0 a 1 + ψrad0 Q + ψv cpρvou ()[ ou a ()] + ψv c ρv ()[ ( 1) a ()] (2) p a his approximaion is esial o simplify he coupling beween one zone and is adacen zones hus he sae space for he building can be decomposed ino sub sae spaces for each zone. Equaion (2) can also be wrien as Q Where () = () +ψ () () (3) a bz 01 bz + [ ψ ( 1) + ψ Q ( 1)] bz1 0 a 1 = 1 + ψ c ρ[ V ( ) + V ( )] v p ou ψ cρ[ V ( ) ( ) + V ( ) ( 1)] v p ou ou a ψ c ρ[ V ( ) + V ( )] v p ou

3 ψ 01 ψ rad0 = + ψ ρ v p ou + 1 c [ V ( ) V ( )] Radiaor model he power from he radiaor is no nown compleely and has o be modeled as well. he radiaor emis hea o he ambien hrough boh convecion and radiaion. For a given ype of radiaor he proporion of convecion and radiaion can be reaed as consan (Zhang X 1996). I has been considered in he calculaion of influence coefficien. Inroducing effecive coefficienε dynamic equaion of radiaor can be wrien as drad Crad = Cwqm ε ()[ s a ()] K ( ) A [ ( ) ( )] (4) rad rad rad a Q ( ) = K ( ) A [ ( ) ( )]. (5) rad rad rad a s re () rad ( ) = + a ( ) (6) s a () ln re a K ( ) = α ( ) β (7) ε rad rad a K A s re rad rad ( ) = = 1exp[ ]. (8) C q s a w m α β are characerisic coefficiens of radiaor gained from sandard experimen. Subscrip rad repres radiaor w repres waer s repres supply waer re repres reurn waer. RVs model Sense emperaure In he process of room emperaure flucuaion he emperaure of RVs se can no be he same as he room emperaure a once because of is hermal capaciy. I can be expressed as d C = K A [ ( ) ( ) ]. (9) a a Define following variable = C K A Equaion 4 will become d + ( ) = a ( ). (10) C is hea capaciy is emperaure is ime K is hea ransfer coefficien A is surface area is ime consan; subscrip repres se a repres air. ae Δ as calculaion sep he relaion beween and a a ( Δ ) may approximaely be described as zero-ran. ( ) = ( η) = ( Δ) η Δ (11) a a a hen he discree soluion of Eq (10) will be Δ Δ () e ( ) (1 e ) ( ) a = Δ + Δ. (12) Flow conrol he radiaor hermosa will always respond o changes in room emperaure by conrolling he flowrae of radiaor. he calibraed pressure in he bellows corresponds o he emperaure of he sor. his pressure is balanced by he force of a regular spring. On a rise in ambien emperaure he pressure rises in he bellows moving he valve cone owards he closed posiion unil equilibrium exiss beween he bellows and he spring. Conrol equaions of RVs can be se up based on he characerisic curves gained from he es according o CEN EN215 sandard (04) wih a pressure drop across he valve a 0.1 bar. Assuming ha he pressure drop across he valve mainains Δ p under operaing siuaion he flow conrol characerisic can be discribed using Eq (13). Coefficiens A B and C in Eq (13) can be gained from he curves by using leas - square fiing. q m 2 2 Δp / 0.1 A ( )+ B ( )+ C ( ) 0; Δ Δ Δ > = (13) 0 Δ ( ) 0. Δ ( ) = ( ) ( ). (14) cls q m is qualiy flow-rae cls is closing emperaure deermined by se value of emperaure selecor. Formulaion of a oal model he models of room radiaor and RVs are no independen. he variables in one model always inerac wih hose in oher models. Some approximae measures are aen as decoupling e.g. dealing wih he influence of neighbour disurbance as menioned above. he variables such as radiaor power and room emperaure are sill coupling which should be simulaneously resolved by equaions. From Eq(3) and Eq(5) Eq(15) will become + ψ K A bz 01 rad rad rad a ( ) =. (15) 1 + ψ 01 ( K ) rad ( A ) rad Pu Eq(15) ino Eq(4) Eq(4) can be ransformed o drad = B2 + B1 rad ( ). (16)

4 ψ K A [ K A C q () ε ] K A B = 1 [1 + ψ K A ] C C 01 rad rad rad rad C q () ε [ K A - C q () ε ] w m s rad rad w m bz B = + 2. C [1 + ψ K A ] C 01 rad rad rad rad w m rad rad rad 01 rad rad rad Resolve differenial equaion (16) he main emperaure of radiaor can be calculaed as B ( ) = e ( Δ) (1 e ). (17) rad B1 Δ 2 B1 Δ rad B1 he model aes weaher parameer supply waer indoor casual hea gains seing poin of RVs and characerisic value of each componen as inpu. For he oal model every room s air emperaure and radiaor power are boh unnown however in every calculaion sep for he calculaing room emperaure and radiaor power of neighbor rooms are ransformed o nown values hrough proper approximaion. Supposing ha he ime varian venilaion scheme is nown and flow rae can be calculaed using room emperaure a ime -1 according o flow conrol model he unnown value lef are air emperaure and radiaor power of room which can be obained from Eq (17) Eq (15) and Eq (5). he reurn emperaure of radiaor can also be go from Eq(8). So a ime all of he rooms radiaor flow rae waer reurn emperaure power and air emperaure can be calculaed one by one. Finally ime series respond of oal waer flow and reurn emperaure in he building can be gained based on he qualiy and hea quaniy conservaion. q = q (18) o m m reo q m = re q model validaion m o bedroom bedroom ichen siingroom Fig.1 heaing sysem in he room (19) θ a/ θ re/ /d observed simulaed Fig.2 measured and calculaed room emperaure For esing he model some disric hea-meering sysem in Beiing was invesigaed during he flow in each radiaor is conrolled by a hermosaic valve (Fig1). Regulae he valve according o schedule during Pu he seing poin of he valves o anifreezing posiion during am 8: pm 17:00 and o maximal value a oher ime. aing norh bedroom as main sudy obec emperaure self-record meers which can record he value per 5min were insalled in he room all of is neighbor rooms ouside he room and a he oule/inle of he radiaors. Solar radiaion and indoor casual hea gains can be ignored in he norhern empy esed room. he experimenal measured neighbor room emperaure oudoor emperaure and supply emperaure are used as inpu o he model hen he measured air emperaure and reurn waer emperaure are compared wih he calculaed values. In figure 2 and figure 3 he agreemen beween simulaed and measured values is quie good. he resul shows ha he maximal simulaion deviaion of reurn emperaure and room emperaure are boh less han 1. Some of he differences mus be aribued o hree facors. One is experimenal error;second he accurae values of hea ransfer coefficien of he envelope is hard o obained; hird /d observed simulaed Fig.3 measured and calculaed reurn waer emperaure 0 θ ou/

5 he influence of he wind speed is no aing ino consideraion. CONCLUSIONS A oal model is formulaed which can serve as a reasonable approximaion of he hea and hydraulic dynamics of muli-family building under he RVs conrol. Brief descripions of models for several componens such as room radiaor and RVs are given. he sub-models are no reaed independenly bu formulaed as a whole model hrough simulaneously resolving he equaions. An approximae mehod is used o simplify he coupling beween one zone and is adacen zones in he building. Comparisons beween simulan and experimenal daa indicae ha he model is suiable for deailed simulaion. REFERENCES JP Building Engineers (Espoo/Finland) Cener for Energy Efficiency in Buildings (Beiing/China). Hea Meering and Billing:echnical Opions Policies and Regulaions.Chinese Demonsraion Proecs and Inernaional Experiences 02 Wang Z C Di H F.he sae-of-ar and problems in hea meering and billing. disric heaing 02 3: 1-5. Di H F Jiang Y Qin X Z.Operaion and managemen of he cenral heaing sysem wih hea meaering and charging. heaing venilaing and air condiioning 00 30(5): Crawley Drury B. Energyplus: energy simulaion program. ASHRAE J 0042(4): Lawrence Bereley Laboraory. DOE-2 engineering manual version 2.1C. Bereley CA Lawrence Bereley Laboraory Clar D R. Dynamic models for HVAC Sysem Componens. ASHRAE ransacions : Klein S A. RNSYS A ransien simulaion program. ASHRAE ransacions : Zhu Y X Jiang Y. DeS A Simulaion ool in HVAC Commissioning. IEA ANNEX 40 Worshop Kyoo Japan April 03. Jiang Y. Sae-space mehod for he calculaion of air-condiioning loads and he simulaion of hermal behavior of he room. ASHRAE ransacions : HONG JIANG Y. A new mulizone model for he simulaion of building hermal performance. Building and Environmen (2): Liao Z Dexer A L. A simplified model for esimaing he average air emperaure in mulizone heaing sysems. Building and Environmen 04 39: Leherman K M Pailing C J Par P M. he measuremen of dynamic hermal response in rooms using psedo-radom binary sequences. Building and Environmen (1). Crawford R R Woods J E. A mehod for deriving a dynamic sysem model from acual building performance daa ASHRAE ransacions (2). Mad H Hols J. Esimaion of coninuous-ime models for he hea dynamics of a building. Energy and Buildings : Ander K K Mad H Han L H. Modeling he hea dynamics of a building using sochasic differenial equaions. Energy and Buildings 00 31: Braun J Chaurvedi N. An inverse gray-box model for ransien building load predicion. HVAC & R Res. 02 8(1): Wang S W Xu X H. Parameer esimaion of inernal hermal mass of building dynamic models using geneic algorihm. Energy Conversion and Managemen : Zhang X Zhang W L Yu W J. Experimenal sudy on he raio beween radiaion and convecion of normal radiaors. heaing venilaing and air condiioning 19946: he European Sandard EN215: hermosaic Radiaor Valves Requiremens and es Mehods