instance, most of building simulation programs use 1- h time step since weather files normally give hourly values.

Transcription

1 Seventh Internatonal IBPSA Conference Ro de Janero, Brazl August 13-15, 21 DYNAMIC ANALYSIS OF BUILDING HYGROTHERMAL BEHAIOR Nathan Mendes and Gerson H. dos Santos Pontfcal Catholc Unversty of Paraná PUC/CCET Curtba PR Brazl ABSTRACT e descrbe a mathematcal model appled to analyss of hygrothermal behavor of buldngs. A lumped approach to model the room temperature and humdty s used and a mult-layer model n fnte dfferences for the buldng envelope s employed. The capactance model allows studyng the transent humdty and temperature of a room when t s submtted to the weather of the cty of Curtba-PR, Brazl. To evaluate the buldng performance wth thermal parameters, we have wrtten a code whch ncludes ltraton, conducton loads, ernal gans of people, lghts and equpment and short and long wave radaton. In the results secton, we show the luences of smulaton tme step on ernal temperature and humdty and temperature profles wthn the buldng envelope. INTRODUCTION The world-wde crss of energy n the 7 s and long perods of poltcal nstablty and economy recesson made wth that the erest n energy consumpton reducton were made n wde scale all over the world. For example, only n the U.S.A, many energy smulaton programs such as BLAST (1977), DOE-1 (1978), NBSLD (1974) and TRNSYS (1975) had been developed to smulate the buldng energy performance and to adopt ratonal poltcs of energy conservaton. However, exstng programs of smulaton can present nconsstent scenes of what really occurs n buldngs, especally n the heat and mass transfer area. The mathematcal descrpton for predcton of buldng hygrothermal dynamcs s complex, due to the non-lneartes and erdependence among several varables. The parametrc uncertaes n the modelng, smulaton tme steps, external clmate, buldng schedules, ground temperature and mosture content also contrbute to ncrease ths complexty. Several nvestgators have developed models for buldng energy analyss by usng dfferent approaches such as response factor method, fnte dfferences, fnte volumes or even smple RC crcut analogy. However, ndependently on the method accuracy, many smplfcatons n nput data have to be faced such as schedules and weather data. For nstance, most of buldng smulaton programs use 1- h tme step snce weather fles normally gve hourly values. Hence, n ths work, we present a mathematcal model n order to test the hygrothermal performance of buldngs and tme step effects. Heat dffuson through buldng envelope s calculated by Fourer s law by consderng only the pure transport of heat treated by the fnte dfference method. The room s submtted to loads of solar radaton, er-surface long wave radaton, convecton, ltraton and ernal gans from lght, equpment and people. To calculate the room temperature and relatve humdty, we have used a lumped formulaton for energy and water vapor balances. e also analyze the senstvty of hygrothermal buldng performance and wall temperature profles to the smulaton tme step. METHODOLOGY The present work uses a dynamc model for analyss of the hygrothermal behavor of a room wthout HAC system. Thus, a lumped formulaton for temperature as well as for water vapor s adopted. Eq. 1 descrbes the energy balance, where the room s submtted to loads of conducton, convecton, shortwave solar radaton, er-surface long-wave radaton and ltraton. E dt dt & t + E& g = ρc (1) E & t energy flow that crosses the room control surface () E & g ernal energy generaton rate () ρ densty (kg/m 3 ) c specfc heat of (J/kg-K) room volume (m 3 ) T room temperature ( o C) The term E & t, on the energy conservaton equaton, ncludes loads for buldng envelope (conducton), fenestraton (conducton and solar radaton) and openngs (ventlaton and ltraton). The

2 conducton heat flux - Q & (t) - that crosses the room control surface s calculated by the Newton s law for coolng, [ ( t) T ( )] & (2) Q( t) = ha Tn t where h represents the convecton heat transfer coeffcent, A, the heat transfer area, and T n (t) the envelope ernal surface temperature. Ths temperature s calculated by the energy balance, n an elemental volume, usng the Fourer s law as t s presented below: 2 T T ρ c = λ (3) 2 t x Thus, the temperature T shown n Eq. 3, s the temperature for a control volume wthn the buldng envelope, calculated as a functon of the followng thermophyscal constants: densty (ρ), specfc heat (c) and thermal conductvy (λ). On the external sde of the room, the walls, celng, doors and wndows are exposed to solar radaton and to convecton heat transfer. Ths way, the external boundary condton (x=) of Eq. 3 can be mathematcally expressed as: T λ + ( Text Tx ) αqr = hext = x x= On the ernal sde(x=l), we have ncluded the ersurface longwave radaton as: (4) T 4 4 λ = h ( T T ) + = f εθ(t T = ) x L f sur x L x x = L (5) where: f shape factor. ε f emssvty. θ Stefan-Boltzmann constant ( x1 /(m K ) ) T sur temperature of ernal surfaces of surroundng walls (K). were consdered (Rlw) so that Eq. 4 has assumed the followng form: T λ = hext = x x= where the term emssvty. ( Text Tx ) + αq r ( ε ) cel Rlw (6) ( ε ) cel represents the celng The ltraton loads formulaton was taken from ASHRAE (1993). The solar radaton (drect and reflected) came from models presented by Szokolay (1993) and ASHRAE (1993). In terms of water-vapor balance, t was consdered ventlaton, ltraton and ernal generaton from equpment and people breath so that the lumped formulaton becomes: (& & )( ) m + m + + vent ext where: mass flow by ltraton (kg/s) vent b mass flow by ventlaton (kg/s) = ρ d dt ext external humdty rato (kg water/kg dry ) ernal humdty rato (kg water/kg dry ) m b water vapor flow from the breath of occupants (kg/s) ρ ernal water-vapor generaton rate (kg/s) densty (kg dry /s) room volume (m 3 ) The water-vapor mass flow from the people breath s calculated as t s shown n ASHRAE (1993) whch takes o account the room temperature, humdty rato and physcal actvty as well. The equatons of balance of energy and water-vapor can be descrbed n the form: (7) T = The temperature x L of Eq. 5 s equvalent to a temperature of the n-th node of the wall; the temperature needed to calculate Q & (t). For the floor, we have adopted the mposedtemperature boundary condton, makng T x= equal to the ground temperature at a depth of 2m. On the other hand, for the celng, long-wave radaton losses T& = & n = 1 h A β ρc m b 1 ρ 1 β 2 ρc ρ& m ρ b 2 T

3 + where: T & & T n = 1 h A T ρ& ( x= L), + Q ext ρc + m ρ + β b 3 Tme dervatve ernal temperature Tme dervatve ernal humdty Room temperature Internal humdty rato 3 + ω + R = 1, n Number of surfaces of the room rad 2 m of area and 2.5 m heght, havng 2 wndows and 1 door, dstrbuted as t s shown n Fg. 1. The concrete celng was consdered flat. For the conducton load calculaton usng the fnte dfference method, we have consdered,19 m thck walls composed by 3 layers: mortar, brck and mortar. The wndows were consdered as a smple glass layer, whle the floor, was composed by wood, concrete and sol. h A Convecton heat transfer coeffcent Heat transfer area β 1,2,3 T ( x= L) Q R rad ρ c mb 1,2,3 & ω ext Heat transfer by ltraton Internal temperature of surface Heat gan by peolple, equpments and lghtng Heat gan by solar radaton Ar densty Room volume Specfc heat of ater vapor flow from the breath of occupants Infltraton flow ater vapor generated External humdty rato SIMULATION The analyss of hygrothermal buldng performance s made by the development of computatonal code, wrtten n language C, usng the equatons of the model presented n secton 2. These equatons were treated by the fnte dfference method wth a unform grd n a fully mplct scheme. For the smulaton, a sngle-zone buldng located n the cty of Curtba-PR, Brazl was consdered, wth 25 N Fgure 1: Dmensons of the sngle-zone buldng studed. For the external condtons, we have adopted the Umdus program (Mendes et al., 1999) weather fle for the cty of Curtba whch provdes dry bulb temperature, relatve humdty, drect and dffuse solar radaton and wnd velocty and drecton. T (ºC) External Temperature External Relatve Humdty Fgure 2: External temperature and relatve humdty for Curtba n the perod from 1 st to 3 rd of January. In Fgure 2, we observe how the temperature and relatve humdty vary along the three frst days n January n Curtba-PR (whch s south of the equator at lattude ), Brazl Relatve Humdty

4 As t was expected n Fg. 1, contrarly to the temperature behavor, the external relatve humdty presents the hghest values at nght tme. Fg. 3 llustrates values of total solar radaton (dffuse plus drect), for ths same perod. e observe n Fg. 3, that solar radaton mght reach values as hgh as 9 /m 2 at noon. In order to reduce the ntal condton luences, the program was submtted to three pre-smulatons (warm-up) for these same 3 frst days of January. Total Radaton (/m^2) Total Radaton Solar (/m2) Fgure 5: Snusodal total solar radaton for Curtba. The snusodal representaton for total (drect + dffuse) solar radaton can be seen n Fg. 5. The functon provdes the snusodal behavor between 6 am and 6 pm, elsewhere the total solar radaton was consdered. A peak value of 8 /m 2 at the noon was set to ths functon Fgure 3: Total solar radaton for Curtba n the perod from1 st to 3 rd of January. e also have used snusodal weather functons to represent n a very well-behaved way a typcal Brazlan weather clmate for ths summer perod. In Fg. 4, we observe the snusodal varaton for temperature and relatve humdty. T (ºC) External Temperature External Relatve Humdty Fgure 4: Snusodal weather functon for external temperature and relatve humdty Relatve Humdty RESULTS The lnearzaton of temperature tme dervatve, Eqs. 3-6 (transent conducton heat transfer), n the fnte dfference method, causes errors n buldng thermal smulaton snce t s normally used 1-h tme step and most of the buldng smulaton programs use a such hgh tme step. Therefore, we do a senstvty analyss of buldng thermal performance to the smulaton tme step. In Fgures 6 to 11, we have neglected the effect of er-surface long-wave radaton. Fgs. 6 and 7 shows the room temperature and relatve humdty for 3 dfferent tme steps (dt). In terms of temperature, we have notced a varaton of up to 4 ºC for peaks. On the other hand, for relatve humdty, t was observed a varaton of up to 1%. Fg. 7 shows the room relatve humdty. e notce that there s not much dfference between external and ernal relatve humdtes whch s manly due to the hgh ltraton load of 3l/s, accordng to the Brazlan standards (ABNT, NBR 641). Hgh temperatures are attaned when t s nserted wthn the room, an energy generaton rate. Such temperatures are verfed n Fg. 8, where an ernal generaton of 62 /m 2 was adopted and t s typcally fnd n offces

5 Internal Temperature (ºC) dt= 36 s dt= 18 s dt= 1 s External Temperature Another mportant factor that explans why hgh temperatures are presented n Fg.8, s the radaton energy flux that crosses the wndows, therefore t s beng consdered as an nstantaneous ernal gan. Fg. 9 presents the west facng wall temperature profle, at 3 pm on January 3 rd. Fgure 6: Room temperature for Curtba n the perod of 1 st to 3 rd of January for tme steps of 1s, 18s and 36 s T(ºC) dt= 36 s dt= 18 s dt= 1s Internal Relatve Humdty dt= 36 s dt= 1 s dt= 18 s External Relatve Humdty Fgure 7: Room relatve humdty for Curtba n the perod of 1 st to 3 rd of January. Internal Temperature (ºC) dt= 36 s Fgure 8: Internal temperature for Curtba n the perod of 1 st to 3 rd of January for 1-h tme step and ernal gan of 62 /m x (mm) Fgure 9: est facng wall temperature profle at 3 pm. It s notced, n Fg. 9, a consderable dscrepancy between temperature profles obtaned wth tme steps of 1 s, 18 s and 36 s, wthn a sunny wall (facng west at 3 pm). Ths dscrepancy s largely responsble to the temperature dfferences found n the fgures above. It was notced wth ths study the bg s the the energy ncdence on buldng envelope the greater wll be the error due to 1-h tme step adopton. Fgures 1 and 11 show room temperature and relatve humdty by usng external snusodal functons. In ths case, a maxmum of 1.5 ºC for temperature peaks and 2% for relatve humdty are verfed. Internal Temperature (ºC) dt= 1 s dt= 18 s dt= 36 s External Temperature Fgure 1: Room temperature for Curtba by usng the snusodal weather fle

6 In Fg. 12, a temperature dfference close to.8 ºC (peak value) was observed, by comparng smulatons wth and wthout e-surface long wave radaton. In ths case, an emssvty of.5 for all surfaces was used. It s mportant to remember that the adopton of tme steps dfferent of 1h, mples n lnear erpolatons (except for the snusodal weather), addng errors to the estmaton of temperature profles. However, ths s unavodable snce weather data fles normally do not provde ormaton at ervals smaller than 1h. Fgure 11: Room relatve humdty for Curtba by usng the snusodal weather fle. Temperature (ºC) Internal Relatve Humdty dt= 1 s dt= 18 s dt= 36 s External Relatve Humdty Internal Temperature wthout Radaton Internal Temperature wth Radaton Fgure 12: Comparson of room temperature for Curtba by consderng or not the er-surface long wave radaton for an 1-h tme step. CONCLUSIONS A mathematcal model to evaluate buldng hygrothermal performance was descrbed the buldng hygrothermal behavor. It was used a global approach for the room and fnte dfferences for the buldng envelope, celng and floor. It was shown the tme step luence on smulaton results, such as ernal temperature and temperature and relatve humdty profles wthn the buldng envelope. Relevant dfferences between values obtaned by dfferent smulaton tme steps were observed, showng the relevance of ths analyss. For further work, we end to nclude routnes to calculate the heat transfer n attcs and to smulate HAC systems. In concluson, ths work has shown the mportance of tme step choce for buldng smulaton programs and that more work needs to be done to mprove frst order approaches for tme dervatves appled to thermal buldng performance smulaton models. REFERENCES ASHRAE Amercan Socety of Heatng Refraton and Ar-Condtonng Engneerng - Handbook-Fundamentals, 1993, Atlanta: ASHRAE. Athents A.K., Stylanou M. and Shou J., 199, A Methodology for Buldng Thermal Dynamcs Studes and Control Applcatons, ASHRAE Transactons - SL Don J.M., Dugard L., Franco A., Nguyen Mnh Tr and Rey D., 1991, MIMO Adaptve Constranes Predctve Control Case Study: An Envronment Test Chamber, Automatca, ol. 27, N o 4, pp , Great Brtan. Hudson G. and Underwood C.P., 1999, A Smple buldng modellng procedure for MATLAB/ SIMULINK, Proceedngs of the 6 th Internatonal Conference on Buldng Performance Smulaton (IBPSA 99), September, Kyoto-Japan, pp Mendes N., Araújo H.X. e Olvera G.H.C., 2, O Problema do Controle de Temperatura em Aquecmento de Edfcações, III Encontro Naconal de Tecnologa do Ambente Construdo (ENTAC 2), Abrl 23-28, Salvador-Brasl. Mendes N., Rdley I., Lamberts R., Phlpp P.C. and Budag K., 1999, UMIDUS: A PC Program for the Predcton of Heat and Mosture Transfer n Porous Buldng Elements, Buldng Smulaton Conference IBPSA 99, p ,Kyoto, Japan. Santos G.H. e Mendes, N., 2, Modelos para Avalação Térmca de Ambentes, Relatóro erno do Laboratóro de Sstemas Térmcos da PUCPR, Curtba-PR. Stoecker. F. e Jones J.., 1985, Refração e Ar Condconado, McGraw Hll do Brasl. Szokolay S., 1993, Solar Geometry, PLEA Passve and Low Energy Archtecture Conference - NOTES,

7 Department of Archtecture at Unversty of Queensland, Brsbane, Australa. NOMENCLATURE E & energy flow that crosses the room control surface t E & g ernal energy generaton rate ρ densty c specfc heat of room volume T room temperature Q & (t) conducton heat flux that crosses the room control surface h convecton heat transfer coeffcent A heat transfer area T n (t) envelope ernal surface temperature ρ densty c specfc heat λ thermal conductvy f shape factor. f ε θ emssvty. Stefan-Boltzmann constant T sur temperature of ernal surfaces of surroundng walls Rlw long-wave radaton losses for the celng ε cel celng emssvty. vent mass flow by ltraton mass flow by ventlaton ext external humdty rato ernal humdty rato b water vapor flow from the breath of occupants ernal water-vapor generaton rate room volume

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