Applying the energy conservation equation for each element, the following mathematical formulation is obtained.

Transcription

1 Seventh Internatonal IBPS Conferene Ro de Janero, Brazl ugust 3-5, 200 BUILDING THERML PERFORMNCE NLYSIS BY USING MTLB/SIMULINK Nathan Mendes, Gustavo H.C. Olvera and Huberto X. de raúo Pontfal Cathol Unversty of Paraná PUCPR/CCET Theral Systes Laboratory (LST) and utoaton and Systes Laboratory (LS) Rua Iaulada Coneção, 55 Curtba PR, Brazl et.pupr.br; et.pupr.br BSTRCT Ths paper s foused on a atheatal odel appled to both buldng theral analyss and ontrol systes desgn. luped approah s used to odel the roo ar teperature and a ult-layer odel for the buldng envelope. The apatane odel allows to study the transent analyss of roo ar teperature when t s subtted to snusodal varaton of external ar teperature, representng a ase study for a old day n the south Brazl. To evaluate the buldng perforane wth theral paraeters, we use MTLB/SIMULINK. In the results seton, we show the nfluenes of theral paraeters on the buldng ar teperature, heatng syste perforane, energy onsupton and the advantages of usng MTLB/SIMULINK n buldng theral and energy analyss. INTRODUCTION The atheatal desrpton of buldng systes s oplex due to several non-lneartes and unertantes suh as onveton oeffents, ateral propertes, external weather, radaton effets, HVC systes odelng and buldng shedules n ters of people, lght and equpent. In the lterature, soe researhers used MTLB/Sulnk to sulate therodyna odels and analyze ther haratersts n ters of effeny and teperature ontrol. Hudson and Underwood (999) presented a atheatal odel for buldng sulaton that an be represented by an RC eletr rut. The odel s onsdered adequate for hgh ass buldngs sne they are predonantly apatve. thents et al. (990) and Don et al. (99) presented soe approahes for the study of buldng theral sulaton and HVC systes so that they ould analyze advaned ontrol strateges. Mendes et l. (2000a) elaborated a splfed odel for ontrol strategy analyss of heatng systes for low ass onstrutons, whh akes a worse onon to be et by the heatng syste than that found n a real stuaton. Mendes et al. (2000b) proved ther odel by onsderng a apatve ult-layer buldng envelope so that hgh ass onstrutons ould be analyzed as well. The solar radaton was ndretly nluded by usng the onept of equvalent teperature (ar-sun). It was onsdered a dyna luped odel so that t ould be nluded the transsson loads and nternal gans (lghtng, equpent and people). The onveton oeffents were onsdered onstant and they adopted external teperature values varyng as a sne funton to sulate a old day n south Brazl wth a theral apltude of 4ºC. In ths paper, the apatve ult-layer odel presented by Mendes et al. (2000b) s proved by addng the nter-surfae long-wave radaton n the theral odel whh eans that we have nluded the radaton phenoena on all nternal surfaes and on the heater surfae as well. The odel s pleented n the MTLB/Sulnk envronent and oparsons are ade n ters of buldng envelope apatanes, heater perforane, heater onveton and radaton losses and energy onsupton senstve analyss. It s shown an effent way to analyze buldng theral perforane and heatng syste ontrol strateges by usng MTLB/Sulnk n order to reah theral ofort onons and redue energy onsupton. MTHEMTICL MODEL Ths work presents a dyna odel for theral buldng perforane analyss, whh nludes an eletr heater. The roo s onsdered heretally losed wth a unfor dstrbuton of nternal energy. We onsdered theral losses ust by heat transfer through the buldng envelope. pplyng the energy onservaton equaton for eah eleent, the followng atheatal forulaton s obtaned. For the roo enlosed by surfaes, we fnd,

2 ρ + h V dt( = h = nt [ T T ] + D(, [ T T ] n, where ρ,, V, T n, (, h nt, and are respetvely the ar densty, spef heat, roo volue, the n-th layer teperature of wall, the onveton heat transfer oeffent and the surfae area. T ( the roo ar teperature and T ( the heater teperature. The perturbaton D( nludes the heat exhanged wth the external ar through low ass surfaes of the buldng envelope suh as doors and wndows and nternal gans of energy due to equpent, lghts and people. Ths ter an be wrtten as: T D( = = eq T R + q p + q e + q where q p,q e and q I are the nternal gans under the presene of people, equpent and lghtng syste. The theral resstane R of -th surfae s alulated as: L R = + + h λ h ext where s the low-ass surfae- area and h nt, the nternal heat transfer onveton oeffent. For eah layer k wthn the wall, we an obtan the followng energy balane equaton: k, k, k, nt dtk, ρ k, k, Vk, = K k+, [ T K [ T T ], k+, I T k, () (2) (3) ( t (4) where the theral ondutane K, an be estated by a haron ean as: K k, = (L k, / 2) / λ k, + (L k, / 2) / λ where L k, denotes the thkness of layer k and λ k,, ts theral ondutvty. The boundary onon for the external layer an be wrtten as, K, ( T T ) = h ( T T ) 2,, ext, T eq represents the equvalent teperature (r-sun) gven by the followng expresson: T eq = T ext αi + h ext eq k, where α, s the wall external surfae absorptvty, I, the total solar radaton (dret plus dffuse) and h ext, the external oeffent of onvetve heat transfer. For the nternal layer (k=n) of the -th wall, we an wrte the followng boundary onon equaton: K n, σε σε ( Tn, Tn, ) = hnt ( Tn, T ) 4 4 Fs, [ Tn, T ] Fs, [ Tn, Tn, ] = where σ, ε and F s are Stefan-Boltzann onstant, essvty and shape fator. However, for the floor (=5), we onsder for k=, a onstant sol teperature at a depth of 5 and we apply the boundary onon of posed teperature. The eletr heater s globally odeled as: dt ρ V = Q( h σε = F 4 4 [ T T ( t ] s, n, ) + [ T T ] where Q( s the energy rate generated wthn the heater by Joule effet, ρ, the heater densty,, the spef heat, V, the ol volue wthn the heater, h, heat transfer onveton oeffent between roo ar and heater and the heat exhange area. The heatng syste sensor teperature T s ( an be odelled as: dts ρ ssvs = hs s[ T TS ] (6) where ρ s, S, V S, h S and S are respetvely the sensor densty, spef heat, volue, onveton heat transfer between the sensor opper sphere and the ar and the sensor heat exhange area. SIMULTION PROCEDURE The analyss of buldng theral perforane s done by the dyna odel pleentaton n MTLB/Sulnk envronent. MTLB s a software that ontans a wde atheatal lbrary that akes t uh spler for rapd prototypng than other prograng languages suh as C or Fortran. Sulnk s MTLB graph user nterfae, whh was espeally bult for dyna systes sulaton. (5)

3 The odel pleentaton n Sulnk envronent s ade as t s llustrated n the dagra of Fgure, where the buldng odel s nserted n the blok Buldng Model n the forat of state equatons. Therefore, to deterne the state equatons, we have onsdered a buldng envelope oposed by three layers so that the state vetor x( ontans besdes the teperature of eah buldng envelope layer, the teperatures of roo ar, sensor and heater as well. Thus, the odel ontans 2 state varables (6 envelope surfaes tes 3 layers plus 3 state varables). Hene, the odel desrbed by equatons -6, an be suntly wrtten n ters of state equaton as: x& = x( + Bu, y( = Cx( where u( s the vetor related to the odel nputs suh as the heater power, equvalent teperature, nternal gans (people, lghtng and equpen and sol teperature. The output y( vetor orresponds to the roo ar teperature. The non-lnear effets assoated to the radaton heat transfer were pleented by the Sulnk toolbox falty. The odel paraeters desrbed n the odel equatons are gathered fro SHRE (993) and Inropera and De Wtt (998). For the eletr heater, we have onsdered t as an equpent whh has an ol volue of 2 lters. It s analyzed the roo ar teperature for dfferent odel paraeters when the outdoor teperature vares as a snus funton as t s shown n Fg.2. On the other hand, the sol teperature s kept onstant as 5 C and the ntal teperatures for the roo ar and the buldng struture are assued to be equal to 3 C. Ths hypothess s physally onsstent sne the ntal onons effets are not portant n longter sulatons. The ntal onons are very portant when t s requred a dyna buldng response for very short-ter sulatons. Table presents the eleents densons and theral propertes used n the sulatons. RESULTS ND DISCUSSIONS In ths seton, a roo ar teperature senstvty analyss s done n ters of theral apatane and theral ontrbuton of radaton heat transfer fro heatng syste. We also analyze the heater perforane and ts nstantaneous ontrbuton relatve to the roo ar heatng proess. The buldng envelope theral apatane (C=ρV) effets on the roo ar teperature (T ) are shown n Fg. 2. We note that for the low apatane ase (0% of the referene value), the transent duraton s alost pereptble. On the other hand, for the hgh apatane ase (0 x referene), t takes nearly 0 days to elnate the ntal onon effets. For the referene apatane ase, ths te perod s lose to 2 days. Fg. 2 shows learly the delay and the theral apltude redutons regardng the external teperature sgnal of 2.2h and 2.33 C, 5.7h and 5.07 C and.49h and 5.97 C for the respetve ases wth low theral apatane (0% of the referene), theral apatane of referene and hgh theral apatane (0x referene). Ths an be explaned by the fat that the hgher the wall theral apatane the hgher the needed energy to hange ts teperature. The sae thng an be nterpreted by the envelope theral dffusvty ( α= λ ρ ) by hangng the theral ondutvty. The use of Sulnk akes easy to analyze the roo ar teperature behavor ntegrated to a heatng syste. In ths paper, we onsdered an on-off ontrol heatng syste as t an be seen n Fg. 3. The heatng syste s oposed by three 5-kW heaters. In Fg. 4, t s presented how the teperatures of roo ar, nternal buldng envelope surfae and heater vary wth te. We note fro Fg 4 the wall teperature, due to a hgh theral nerta, does not vary sgnfantly. There s a delay of 5.08h wth a peak-topeak theral apltude of.9 C. The ontrolled roo ar teperature goes up and down very often due to the heatng syste ontrol strateges and theral haratersts. If we zoo part of Fg. 4, we an see, n Fg. 5, sall sne-lke flutuatons for the wall nternal surfae teperature due to the heatng syste teperature varaton. These flutuatons would be ertanly hgher for low ass onstrutons. s MTLB an handle hghly non-lnear systes, we have onsdered nter-surfae long-wave radaton so that ts effet on roo ar teperature and heater perforane an be analyzed. Frst, we have defned a heater perforane oeffent (η), whh an be atheatally desrbed as: η = t 2 t t 2 t h σε [ T ( T (] t 2 t = Q( & F s, t 2 t 4 4 [ T ( T (] Q( & + n,, where the frst rght-hand ter s the rato between the te-ntegrated onveton heat transfer losses and the te-ntegrated heater power; the seond

4 rght-hand ter orresponds to the rato between the radaton heat transfer losses and the heater power. Norally, the radaton ter, on the equaton shown above, s negleted and we an nspet how ts effets n the ase studed n ths work. The heater perforane oeffent for a perod of week and an essvty of 0.8 was alulated as beng 99.97%, fro whh 2% was due to the radaton losses. In the ase the essvty s 0 (no radaton), all the energy released by the heater s nstantaneously absorbed by the roo ar, whh gves, for the sae equpent, a perforane oeffent of 99.99%, whh eans the radaton effets on the roo ar heatng proess delay s very sall (about 2% n ters of energy). In Fgures 6 and 7, we an observe, the essvty effets on roo ar teperature (Fg. 6) and heater surfae teperature (Fg. 7). In these ases, the ter wth radaton eans we have used an essvty of 0.8. and wthout radaton an essvty of 0.0. We have noted that when the external teperature goes down to ts lower lt the heater run te goes up fro 058.8s to s. In Fg. 6, we see that the heater surfae essvty does not play an portant role on the roo ar teperature, gvng ust a short delay of about 5 n. Ths delay depends on the wall theral dffusvty. The hgher the theral dffusvty the lower the essvty effets on roo ar teperature, whh eans the ar absorb ore nstantaneously the energy released by the heater. Fg. 7 shows the heater teperature behavor. We reark ths teperature s not very senstve to the essvty, gvng ust a short delay. However, we note the heater theral apatane ay not be adequate sne t s subtted to a hgh teperature varaton n a very short perod of te. Table 2 shows the heater energy onsupton for a 7- day perod, akng oparsons f the buldng envelope theral resstanes would be dereased by a fator of 0 and f the heat released by the heater were ust gven by onveton heat transfer (nstantaneous gan or null essvty). Table 2: Energy onsupton for heatng for a 7-day perod. Ref. 0λ ε = 0 Energy Consupton (kwh) s t was expeted, an nrease on theral ondutvty represents an nrease on energy onsupton sne the heat flux s dretly nreased. However, f we dsregard the radaton heat transfer effets or the heater surfae essvty s onsdered to be very low, the energy onsupton should be slghtly dereased. CONCLUSIONS In ths work, we have used MTLB/Sulnk for buldng theral perforane analyss, whh shows how pratal and fast-to-pleent t s. We have elaborated a dyna ultnodal apatve luped non-lnear odel to desrbe a buldng, onsderng onduton heat fluxes, envelope theral apaty, lghtng and people loads, nfltraton, fenestraton and theral nerta of heatng systes, whh allowed the verfaton of theral paraeters effets on roo ar teperature. The theral apatane was analyzed and sulaton results deonstrated that hgh theral ass buldngs an sgnfantly redue the roo ar teperature varaton. We have shown that hghly non-lnear phenoena, suh as radaton heat exhanged between walls and a heater, an be easly pleented n MTLB/Sulnk. In onluson, we have shown an effent way for the oupled analyss of buldng theral perforane and heatng systes effeny by usng MTLB/Sulnk donally, t s portant to reeber that buldng heatng systes onsttuted by eletr resstanes, n general, have ust on-off teperature ontrol deves. However, the auray of ths ontrol strategy depends strongly on the onstruton theral nerta and there s also, n any ases, a large teperature dfferene between the on-off set ponts akng the teperature ontrol even worse for fne tune on teperature settng. Thus, for further work, as MTLB has shown a very hgh potental to analyze ontrol strateges, we ntend to evaluate other strateges than the on-off one whh, usually brngs hgher energy deands. Besdes, we ntend also to analyze huy effets when 2 varables have to be ontrolled. REFERENCES SHRE Handbook-Fundaentals, 993, tlanta: SHRE. thents.k., Stylanou M. and Shou J., 990, Methodology for Buldng Theral Dynas Studes and Control pplatons, SHRE Transatons - SL Clarke, J.., 985, Energy Sulaton n Buldng Desgn, da Hlger Ltd., US. Don J.M., Dugard L., Frano., Nguyen Mnh Tr and Rey D., 99, MIMO daptve Constranes Preve Control Case Study: n Envronent Test

5 Chaber, utoata, Vol. 27, No. 4, pp , Great Brtan. Hudson G. and Underwood C.P., 999, Sple buldng odellng proedure for MTLB/SIMULINK, Proeedngs of the 6th Internatonal Conferene on Buldng Perforane Sulaton (IBPS 99), Septeber, Kyoto-Japan, pp Inropera F.P. e De Wtt D.P., 998, Fundaentos de Transferêna de Calor e de Massa, LTC - Lvros Ténos e Centífos Eora, 4ª Edção, Ro de Janero. Mendes N., raúo H.X. e Olvera G.H.C., 2000a, O Problea do Controle de Teperatura e queento de Edfações, VIII Enontro Naonal de Tenologa do bente Construdo (ENTC 2000), brl 23-28, Salvador-Brasl. Mendes N., Olvera G.H.C. e raúo H.X., 2000b, O Uso do MTLB/Sulnk para valação do oportaento téro de abentes, ENCIT th Brazlan Conferene on Theral Engneerng and Senes, nas e CD ROM,Porto legre, Brasl. User s Gude Dyna Syste Sulaton Software, 999, MTLB 5.0, The MathWorks, In.. LIST OF TBLES Table : Densons and theral propertes. ρ (kg/ 3 ) (J/kg-K) λ (W/-K) h (W/ 2 -K) ( 2 ) L () V (3) Heater () 884, , ,002 Roo (), ,0 25* ,5 Sensor (s) ,0,26e-5 0, 4,2e ,92 2,5 2 0,25 Walls and ,985 5,0 2,5 0,25 elng ,92 2,5 2 0, , ,00 Floor ,4 5, , , ,50 * Floor and elng surfae area. LIST OF FIGURES Fgure Modular odel shee by Sulnk

6 Fgure 2: Theral apatane effets on the delay and theral apltude reduton of T (. Fgure 3: Closed loop for a buldng on-off ontrol heatng syste by usng Sulnk

7 Fg. 4: Teperature varaton wth te. Fgure 5: plfaton of nternal surfae teperature flutuatons

8 Fgure 6: Roo ar teperature as a funton of te and heater surfae essvty. Fgure 7: Heater surfae teperature as a funton of te and essvty