© Strojni{ki vestnik 46(2000)6,342-346 © Journal of Mechanical Engineering 46(2000)6,342-346 ISSN 0039-2480 ISSN 0039-2480 UDK 697.97:628.85 UDC 697.97:628.85 Izvirni znanstveni ~lanek (1.01) Original scientific paper (1.01) Dinami~ni model nadzora temperature prostora s stropnim hlajenjem A Dynamic Model for the Control of a Room’s Temperature by Means of Ceiling Cooling Tonko ]urko - Ivan Galaso V prispevku je predstavljen model dinamičnega simuliranja toplotnih razmer v prostoru v poletnem času. Analizirali smo dva različna sistema nadzora temperature prostora: stropno hlajenje in dovod hladnega zraka. Predstavljene so primerjave obeh sistemov: primerjava parametrov vpliva in vpliv na spremembo temperature prostora. © 2000 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: modeli dinamični, temperature sobne, regulacija temperature, hlajenje stropov) This paper presents a dynamic-simulation model of a room s thermal behavior during summer conditions. Two different systems for the room s temperature control, i.e. ceiling cooling and cold air supply, were analyzed. A comparison of the influencing parameters and the influence on the operating room temperature variation applying both systems are reported. © 2000 Journal of Mechanical Engineering. All rights reserved. (Keywords: dynamic models, room temperature control, ceiling cooling) 0 UVOD Hladilno obremenitev lahko definiramo kot količino energije, ki jo vnašamo v prostor in hkrati odvzemamo klimatizacijski napravi, da ohranjamo stalno temperaturo v prostoru. To količino energije lahko odvzamemo z vpihovanjem ohlajenega zraka v prostor ali z ohlajanjem katere izmed površin v prostoru, npr. stropno hlajenje. V tem primeru se izmenjava energije večinoma izvaja s prenosom toplote s sevanjem med notranjimi površinami v prostoru. Različna načina ohranjanja sobne temperature v teh dveh primerih predstavljata prav tako različne parametre toplotnega ugodja. Hladilna obremenitev prostora je toplota, ki jo je treba prenesti iz prostora (s hlajenjem), da ohranimo stalno temperaturo zraka - povprečno sobno temperaturo. Hlajenje izvajamo z zrakom, ki ga hladimo z različnimi sistemi (OPKH -ogrevanje, prezračevanje, klimatizacija, hlajenje -HVAC). Eden izmed načinov nadzora temperature prostora je stropno hlajenje. Pri tem postopku se večina toplote znotraj prostora prenaša s sevanjem med hladnejšim stropom in preostalimi, toplejšimi površinami v prostoru. Različni sistemi za OPKH, ki jih uporabljamo za nadzor temperature v prostoru, 0 INTRODUCTION The cooling load may be defined as the amount of energy that is transferred to the room air and simultaneously removed by conditioning equip-ment, to keep a constant temperature in the room. This amount of energy can be removed either by blowing cooled air in to the room or by cooling one of the interior surfaces of the room, for example, ceil-ing cooling. In this case, the exchange of energy takes place mostly as heat transfer due to radiation between interior surfaces of the room. The different charac-ters of room temperature maintenance in these two cases also mean different thermal comfort parameters. The room-cooling load is the heat to be transferred out of the room (by cooling) in order to keep a constant air temperature – the mean room temperature. Cooling is carried out by the air, which is cooled in various HVAC (Heating, Ventilation, Airconditioning, Cooling) systems. One of the meth-ods for room temperature control is ceiling cooling. In this procedure, the majority of the heat transferred within the room is a result of radiation between the colder room ceiling and other room surfaces, which are warmer. A different HVAC system used for con-trol of the room’s temperature causes a different varia- VBgfFMK stran 342 T. ]urko - I. Galaso: Dinami~ni model nadzora - A Dynamic Model for the Control povzročajo različne oblike parametrov, ki določajo posameznikovo ugodje v prostoru. Da bi lahko raziskali medsebojni vpliv parametrov, smo razvili modeliranje in simuliranje toplotnih sprememb določenega prostora. V analiziranem modelu je bila zahtevana temperatura zraka v prostoru J = 24°C za obdobje 24 ur. Določili smo hladilno obremenitev prostora in temperature vseh površin za oba obravnavana primera. 1 RAČUNSKA METODA Izračun stropne hladilne obremenitve je mogoč, ko določimo enačbe toplotnega ravnotežja za vse stične površine prostora [1]. Enačbe, ki določajo stopnjo prenosa toplote na katerikoli notranji površini j v določenem času t, so: tion of the parameters, which determine personal comfort. In order to examine this interaction, modeling and simulation of the thermal behavior specific of the room has been carried out. In the analyzed model, the required air temperature of the room during the 24 hour period was J = 24 °C. The cooling load of the room and the temperatures of all the surfaces were determined in both the treated models. 1 CALCULATION METHOD Calculation of the room-cooling load is possible when the equations for thermal equilibrium for all bordering surfaces of the room and for the room air are established [1]. The equations determining the heat trans-fer rate at any interior surface j at a specific time t are: B qj ,t = aj,t (Jp - J j ,t) + X Gj,k (Jk ,t - J j ,t) + RAj ,t k=1 kjer je Gj,k: where Gj, k is: 4 e ek s T3 Fj, (1) (2) Toplotni tok na notranjo površino, ki se izvaja s konvekcijo in sevanjem, je enak toplotnemu toku prenesenemu na površino s prevodom. The heat flux on the inner surface, which is realized through convection and radiation, equals the heat flux transferred to the surface by conduction. Nj Nj qj,t = lL Xj,iJ j,t-i-lL Yj,iJ j,t-i+Rjqj,t-i (3) Vstopni parametri, ki določajo toplotno obremenitev, so spremembe temperature na zunanji površini zidu j, ki hkrati vplivajo na spremembe temperature na notranji površini zidu j in nasprotno. Zato je treba določiti enačbe toplotnega ravnotežja na znanji površini j. Zunanje površine mejijo na okolico ali na sosednje prostore. Ko določimo vse enačbe toplotnega ravnotežja, oz. toplotne tokove za vse zidove na notranjih in zunanjih površinah, dobimo sistem n enačb z n neznanimi temperaturami notranjih površin zidov. Izračun hladilne obremenitve prostora je sedaj mogoč s povprečenjem enačbe za toplotno ravnotežje zraka v prostoru. Input parameters, which determine the heat load, are the temperature changes on the exterior wall surface j, which at the same time influence temperature changes on the interior wall surface j, and vice versa. It is necessary therefore, to establish the equations of thermal equilibrium on the exterior surface j. The exterior sur-faces are adjacent either to the environment or to the neigh-boring rooms. When all the thermal-balance equations, i.e. the heat fluxes for all the walls on the interior and exterior surfaces are established, a system of n equations with n unknown temperatures for the interior wall sur-face is obtained. Calculation of the room-cooling load is now possible by means of the equation for thermal equi-librium of the interior air. B Fp,t = rcpVKl ,t ( Jp - JKl,t ) = Z Aja j,t ( J j,t - Jp ) + rcpVIn,t ( Jv,t -Jp) + RKp,t Sistem enačb, ki določajo temperature notranjih površin in hladilno obremenitev, je v primeru stropnega hlajenja enak. V prvem koraku izračuna določimo temperaturo površine stropa in nato v časovnih korakih vsako uro, ko je hladilna obremenitev enaka nič. Tako lahko nadziramo notranjo temperaturo prostora z nadzorom stropne temperature. Na temelju opisanega modela, smo razvili lasten računalniški program. Program omogoča simuliranje toplotnega obnašanja določenega prostora. (4) The system of the equations which determine the interior-surface temperatures and the cooling load is identical to the case of ceiling cooling. The temperature of the ceiling surface is set for the first step of the calculation, and is subsequently determined in hour-by-hour steps for the ceiling temperature at which the cooling load equals zero. In this way, control of the interior temperature is pos-sible by controlling the ceiling temperature. Based on the described model, an authorized computer program was developed. The program enables simulation of the thermal behavior of one specific room. gfin^OtJJlMlSCSD 00-6 stran 343 |^BSSITIMIGC T. ]urko - I. Galaso: Dinami~ni model nadzora - A Dynamic Model for the Control 2 OPIS MODELA IN REZULTATI Izmere izbranega prostora so 4 x 5 x 3 m z eno zunanjo steno (1) in enim oknom (7), velikosti 3,2 x 1,25 m. Vmesni zidovi (2,3,4), tla (5) in strop (6) mejijo na prostore z enakimi toplotnimi razmerami, kakršne ima analiziran prostor. Prostor je usmerjen na jug in postavljen v zagrebški regiji, z vsemi potrebnimi podatki za značilen poletni dan, 21. julij. Notranji viri toplote so tri osebe in naprave z močjo 100 W. Temperatura v prostoru je S = 24°C. Analize rezultatov so prikazane v diagramih, Sl. 1-4. »C 19 -—i—i—F—f—TT—i—j—r—i—t—i—i—t—i—[—i—i—i T-" r ¦ I o 4 . ,as2 ,. ,oh M time Sl.1. Potek zunanje temperature in notranjih temperatur površin v prostoru Fig. 1. Variation of enviroment temperature and room surface interior temperature Sl.3. Pretok stropne hladilne obremenitve Fig. 3. Ceiling cooling load flow 2 MODEL DESCRIPTION AND RESULTS The dimensions of the chosen room are 4 x 5 x 3 m with one external wall (1) having one win-dow (7) of size 3.2 x 1.25 m. Partitioning walls (2,3,4), floor (5) and ceiling (6) are adjacent to the rooms having thermal conditions identical to the conditions in the analyzed room. The room orientation is south, the location is the Zagreb region, with all relevant data characteristic for a summer’s day i.e. July 21. The internal heat sources are three persons and equipment of 100 W power. The room temperature is S = 24 °C. Analysis of the results are shown in diagrams, Fig.1 - 4. 0.8 - i,3,i 0-0 ~f—I—I—I—I—I—I—I—I—1—I—I—I—1—I—I—I—I—I—I—I—I—[—I—I 12 čas '6 M h 2* time Sl.2. Razlika med temperaturami površin v prostoru z upoštevanjem in brez upoštevanja hladilne obremenitve Fig. 2. Difference between room-surface temperatures with and without applied ceiling cooling load °C 25 24 23 22 21 20 19 18 17 J o,a 04 12 16 20 24 čas h time Sl.4. Sprememba temperature stropa in občutene temperature z upoštevanjem hladilne obremenitve na sliki 3 Fig. 4. Variation of ceiling temperature and operating temperature with applied cooling load in figure 3 maimskixmmm ^BsfUWHIK | stran 344 T. ]urko - I. Galaso: Dinami~ni model nadzora - A Dynamic Model for the Control Sprememba zunanje temperature J in ustreznih temperatur vseh notranjih površin prostora so prikazane na sliki 1. Ustrezna hladilna obremenitev F je prikazana na sliki 3. Na temelju največje hladilne obremenitve smo izračunali pretok zraka, ki je potreben za pokritje potreb hladilne obremenitve, V„ = 600 m3/h. Izračunali smo tudi ustrezno temperaturo zraka J, ki je prikazana na sliki 4. Diagram na sliki 2 prikazuje razliko med temperaturami na površinah v prostoru v skladu s sliko 1 in temperaturami istih površin ob upoštevanju stropnega hlajenja. Sprememba hladilne obremenitve za ta primer je prikazana na sliki 3, ustrezna temperatura stropa, J , pa na sliki 4. Ustrezni občuteni temperaturi prostora J0 in J0 sta prav tako prikazani na sliki 4. Na temelju izračuna temperatur notranjih površin smo za oba analizirana modela določili srednjo sevalno temperaturo in občuteno temperaturo [4]. V primeru, ko vzdržujemo temperaturo prostora s “pokrivanjem” hladilne obremenitve s cirkulacijo hladnega zraka, se srednja temperatura sevanja spreminja od 24,3°C (ob 5h) do 25,9°C (ob 17h) in občutena temperatura prostora od 24,3°C do 25°C. Sprememba teh parametrov ustreza spremembi hladilne obremenitve prostora. Kadar uporabljamo stropno hlajenje, sta srednja temperatura sevanja in občutena temperatura prostora stabilni in sta enaki 23,8°C oziroma 23,9°C. 3 SKLEP Krmiljenje temperature prostora z uporabo zračnega sistema je v primerjavi s stropnim hlajenjem pokazal zmanjšanje časovne zakasnitve in povečanje amplitude največje hladilne obremenitve. Z upoštevanjem kriterija posameznikovega ugodja v določenem prostoru, to je z upoštevanjem srednje sevalne temperature in dejanske temperature v prostoru, stropno hlajenje zagotovi izjemno stabilnost teh temperatur. Hkrati pa je njihova vrednost zelo blizu temperaturi zraka v prostoru kar ustreza sobni temperaturi. The variation of the environment temperature, J , and the corresponding temperatures of all the room’s" interior surfaces are shown in Fig. 1. The adequate cooling load, F , is shown in Fig. 3. Based on the maximal cooling load, the air volume needed to cover the cooling load is calculated, it is Vk = 600 m3/h The corresponding air temperature, J, is also calculated and is shown in Fig. 4. The diagram in Fig. 2 shows the difference between the room-surface temperatures according to Fig. 1 and the temperatures of the same surfaces when ceiling cooling is applied. The cooling-load variation in this case is shown in Fig.3 and the corresponding ceiling temperature, J ; , is shown in Fig. 4. The corresponding operating'room temperatures J0 and J0 are also shown in Fig. 4. Based on the calculation of interior-surface temperatures in the room, in both analyzed models the mean temperature of radiation and the operating room temperature are determined [4]. In the case when the room temperature is maintained by covering of the cooling load by means of cold air circulation, the mean temperature of radiation varies from 24.5 °C (5 A.M.) to 25.9 °C (5 P.M.), and the operating room temperature varies from 24.3 °C to 25 °C. The variation in these parameters corresponds with the variation in the room-cooling load. When ceiling cooling is used, the mean temperature of radiation and operating room temperature are stable, i.e. 23.8 °C and 23.9 °C, respectively. 3 CONCLUSION Control of the temperature of the room by means of the air system shows a decrease in the time delay and an increase of the amplitude of the maximum cooling load, in comparison with ceiling cooling. When considering the criteria for personal comfort in a specific room, i.e. the mean radiation temperature and the actual room temperature, ceiling cooling provides remarkable stability of these temperatures. At the same time, their value is very close to the temperature of the room air, which corresponds to the room temperature. 4 OZNAČBE 4 NOMENCLATURE količina toplote prenesena z notranje površine j včasu t, W/m2 koeficient prestopa toplote notranje površine j včasu t, W/m2K temperatura notranjega zraka, °C povprečna temperatura notranje površine j v času t, °C število površin ( j = 1, 2,.... B, k = 1,2,.... B) emisijski faktor površin j in k Boltzmannova sevalna konstanta, 5,67-108 W/ (m2 K4) J J t B ej , e k s rate of heat conducted out of interior surface j at time t, W/m2 convective heat transfer coefficient at the interior surface j at time t, W/m2K inside-air temperature, °C uniform temperature of interior surface j at time t, °C number of surfaces ( j = 1, 2,.... B, k = 1,2,.... B) emission factor of the j and k surface Boltzmann radiation constant, 5.67108 W/ (m2 K4) gfin^OtJJIMISCSD 00-6 stran 345 |^BSSITIMIGC T. ]urko - I. Galaso: Dinami~ni model nadzora - A Dynamic Model for the Control faktor oblike sevanja med notranjima površinama j in k povprečna temperatura notranje površine k v času t, °C količina sončnega sevanja in sevalne toplote opreme, razsvetljave in ljudi v prostoru, ki jo absorbira notranja površina j v času t, W/m2 funkciji prevoda, [2], [3] število členov funkcije prevoda (i = 0,1,.....Nj) povprečna temperatura notranje površine j v času t-1, t-2,........, t-Nj (ure) pred časom t, °C hladilna obremenitev prostora v času t, W gostota zraka, kg/m3 specifična toplota zraka, J/kgK masni pretok ventilacijskega zraka v času t, kg/s temperatura ventilacijskega zraka v času t, °C masni pretok zunanjega zraka, ki prehaja v prostor v času t, kg/s temperatura zunanjega zraka v času t, °C količina toplote,ki jo oddajajo oprema, ljudje v prostoru in zrak, ki prehaja v prostor v času t, W občutena temperatura v prostoru, ko je hlajenje zraka upoštevano, °C občutena temperatura v prostoru, ko je stropno hlajenje upoštevano, °C RA j, t X ,Y j, i j, i Nj Jj j, t- i r p, t Kl, t J Kl, t In, t RK p, t 0,a 0,c radiation shape factor between interior sur-faces j and k uniform temperature of interior surface k at time t, °C rate of solar heat and rate of heat radiated from equipment, lights and occupants absorbed by interior surface j at time t, W/m2 ,(R) conduction transfer functions, [2], [3] j number of conduction transfer function terms (i = 0,1,.....Nj) uniform temperature of interior surface j at time t-1, t-2, ........, t-Nj (hours) before time t, °C room-cooling load at time t, W air density, kg/m3 air specific heat capacity, J/kgK mass flow rate of conditioning air at time t, kg/s conditioning air temperature at time t, °C mass flow rate of outdoor air infiltrating into room at time t, kg/s outdoor air temperature at time t, °C rate of heat obtained from equipment, occupants and convected into room air at time t, W operating room temperature when air cooling is applied, °C operating room temperature when ceiling cooling is applied, °C 5 LITERATURA 5 REFERENCES [1] Procedure for determining heating and cooling loads for computerizing energy calculations, Algorithms for building heat transfer subroutines (1976) ASHRAE, Atlanta. [2] Stephenson, D.G., G.P. Mitalas (1967) Cooling load calculation by thermal response factor method; Room thermal response factors. ASHRAE Transactions, Vol. 73/1, III.11-III.1.7, III.2.1-III.2.10. [3] Kusuda, T. (1969) Thermal response factors for multi-layer structures of various heat conduction systems. ASHRAE Transactions, Vol. 75/1, 246-271. [4] ASHRAE Handbook, (1999) HVAC Applications, Comfort Applications, ASHRAE, Atlanta,GA. Naslov avtorjev: prof. dr. Tonko Čurko prof. dr. Ivan Galaso Univerza v Zagrebu Fakulteta za strojništvo in pomorstvo Ivana Lučiča 5 10 000 Zagreb, Hrvaška Authors’ Address: ProfDr. Tonko Čurko Prof.Dr. Ivan Galaso University of Zagreb Faculty of Mechanical Engineer ing and Naval Architecture Ivana Lučiča 5 10 000 Zagreb, Croatia Prejeto: Received: 23.12.1999 Sprejeto: Accepted: 2.6.2000 VH^tTPsDDIK stran 346