© Strojni{ki vestnik 47(2001)7,325-335 © Journal of Mechanical Engineering 47(2001)7,325-335 ISSN 0039-2480 ISSN 0039-2480 UDK 699.86:006.06:536.21 UDC 699.86:006.06:536.21 Strokovni ~lanek (1.04) Speciality paper (1.04) Toplotne izgube v tla pri stavbah glede na standard SIST EN ISO 13370 -poenostavljena metoda izra~una Heat Losses to the Ground According to the SIST EN ISO 13370 Standard - a Simplified Calculation Method Bo{tjan ^erne - Sa{o Medved Toplotne izgube v tla imajo, se posebej pri velikih stavbah, velik vpliv na rabo energije za ogrevanje. V uporabi so različne metode za določitev teh izgub, vključno z metodo, ki jo predpisuje standard SIST EN ISO 13370. Ta metoda je razmeroma zahtevna. Zato smo oblikovali poenostavljeno metodo z utežnimi faktorji, ki jo predstavljamo v prispevku. Utežni faktorji so določeni za nepodkletene in podkletene stavbe z različnimi toplotnimi prehodnostmi konstrukcij, ki so v stiku s tlemi. Zmanjšano je bilo tudi število vplivnih parametrov, ki so uporabljeni v SIST EN ISO 13370. Uporaba poenostavljene metode je posebej primerna pri postopku načrtovanja toplotne zaščite stavb in določevanja specifičnih toplotnih izgub le-teh. © 2001 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: zaščita toplotna, zaščita zgradb, prenos toplote, metode izračunavanja) Heat losses from buildings through contact with the ground, especially in the case of large buildings, have a strong influence on energy demand. Various methods for calculating these heat losses are available, including one method that is defined by the SIST EN ISO 13370 standard. Due of the complexity of this method we have developed a method that is presented in this paper. Using our method we have calculated weighting factors for buildings with and without basements with a variety of thermal transmittances of structures in the contact between the building and the ground. Also the number of influential parameters used in SIST EN ISO 13370 is reduced. Our simplified method is particularly appropriate for use in the process of designing the thermal insulation of buildings and determining the specific heat losses from buildings. © 2001 Journal of Mechanical Engineering. All rights reserved. (Keywords: thermal insulation, building insulation, heat transfer, calculation methods) 0 UVOD Izkušnje kažejo, da toplotno zaščito in njeno pravilno vgradnjo načrtujejo arhitekti v začetni fazi snovanja stavbe. Zato je odločitev arhitektov povezana z dolgoročnimi posledicami. Metode za določitev toplotnih lastnosti gradbenih konstrukcij, ki potrebujejo veliko vhodnih podatkov, so zahtevne in lahko vodijo k nepravilnostim. Kot zahtevno lahko ocenimo tudi metodo za izračun toplotnih tokov v tla, ki jo določa SIST EN ISO 13370. V tem prispevku je opisan razvoj poenostavljene metode, s katero določimo toplotni tok skozi gradbeno konstrukcijo, ki je v stiku s tlemi. Toplotni tok lahko normaliziramo glede na ogrevano prostornino ali površino ovoja stavbe in se tako prilagodimo različnim predpisom o toplotni zaščiti stavb. Ker je razvita metoda namenjena načrtovanju toplotne izolacije, smo uporabili izraze, ki določajo največji mesečni toplotni tok. 0 INTRODUCTION Experience shows us that heat insulation and its appropriate installation is the responsibility of the architect in the early stages of a building’s design. The decisions made by architect are, therefore, bound to long-term consequences. Methods for determining the thermal and technical properties of building struc-tures, with their large amount of input data, are compli-cated, which leads to calculation inconsistencies. SIST EN ISO 13370 is one such method for determining heat losses through floors and walls. In this paper we de-velop a simple method for calculating heat losses to the ground, which can later be normalised to the volume or the surface of the building according to the different regulations of building’s thermal insulation. As the simplified method is designed to be used for rating a building’s thermal insulation, the expression for maximum monthly heat flow rate will be used. gfin^OtJJIMISCSD 01-7 stran 325 |^BSSITIMIGC B. ^erne - S. Medved: Toplotne izgube v tla - Heat Losses to the Ground 1 DOLOČITEV TOPLOTNIH IZGUB V TLA -OPIS METOD Raba energije za ogrevanje v sodobnih stavbah se zmanjšuje zaradi vse večjega spoznanja o omejenih zalogah fosilnih goriv, spoznanj o njihovih negativnih vplivih na okolje in tudi vse strožjih predpisov o toplotni zaščiti stavb. Toplotna zaščita stavb je lahko predpisana z dovoljenimi toplotnimi prehodnostmi gradbenih konstrukcij, specifičnimi toplotnimi izgubami poslopja ([2], [15] in [16]), ali letno rabo energije za ogrevanje ([3] do [5]). Zaradi manjših toplotnih prehodnosti zunanjih zidov, strehe in še posebej oken se je povečal relativni delež toplotnih izgub v tla. To je še posebej pomembno pri poslopjih z veliko tlorisno površino, kakršno imajo trgovski centri in industrijski objekti. Toplotni tok v tla lahko določimo na različne načine: analitično z reševanjem diferencialnih enačb neustaljenega prevoda toplote ([6] in [7]); s primernimi numeričnimi metodami in programskimi paketi ([8] in [9]); semiempiričnimi enačbami v obliki linijskih toplotnih prehodnosti ([10], [11] in [13]) ali z utežnimi faktorji ([2], [12] in [14]). 1 DETERMINATION OF THE HEAT FLUX TO THE GROUND – A DESCRIPTION OF COMMON METHODS The energy used for heating in new buildings is being reduced as a result of better understanding of the limited quantities of fosil fuels, their negative influ-ence on the environment and also because of the tighter regulations that apply to the heated building’s. The thermal insulation thickness can be determined by the permitted thermal trasmittance, the specific building heat losses ([2], [15] and [16]) or the annual heat use ([3] to [5]). As a consequences of the lower thermal transmit-tances of external walls, roofs and especially windows, the relative amount of heat lost to the ground has in-creased. This point is particularly important for large-area buildings, such as modern shopping centres and industrial premises. Heat flux to the ground can be determined using various methods: analiticaly by solving differential equations of non-stationary heat conduction ([6] and [7]); with appropriate numerical methods and program codes ([8] and [9]); semi-empirical equations in the form of linear thermal transmittance ([10], [11] and [13]); or weighting factors ([2], [12] and [14]). Sl. 1. Časovno ustaljene temperature tal pod ogrevano nepodkleteno stavbo, določene numerično z metodo nadzornih površin; zgoraj stavba s tlorisno površino 100x50 m, specifični toplotni tok skozi pod je 2,1 W/m2; spodaj stavba s tlorisno površino 10x10 m, specifični toplotni tok skozi pod je 7,3 W/m2 [9] Fig. 1. Steady state temperatures below the buildings on the ground - above for building with foor area 100 x 50 m, below for the building with floor area 10 x 10 m, specific heat flux to the ground is 2.1 W/m2 in case of the larger and 7.3 W/m2 in case of the smaller building [9] V standardu SIST EN ISO 13370 je toplotni tok v tla določen s semiempiričnimi enačbami, ki vsebujejo različne parametre, kot so velikost in oblika poda, toplotne prehodnosti gradbenih konstrukcij, toplotne prevodnosti tal, povprečne mesečne temperature znotraj in zunaj stavbe itn., torej razmeroma veliko število različnih vhodnih podatkov. Z uporabo metode utežnih faktorjev lahko število vplivnih parametrov zmanjšamo. Toplotni tok v tla je tako določen z enačbo: In SIST EN ISO 13370 the heat flux is deter-mined with semi-empirical equations that are depen-dent on many different factors, such as the size and shape of the building’s floor, the thermal transmittances of the building’s structures, the ground’s thermal con-ductivity, the average monthly temperatures inside and outside building, etc., a relatively large number of differ-ent input data. With the introduction of weight factors, the amount of input data required is reduced. The heat flux to the ground is then determined by: FG=FG-UG-AG-(di-0ep) (1). Utežni faktorji (F), ki so v uporabi, so ali The weight factors (FG) in use recently are nespremenljivi (npr. 0,5 [2]) oziroma nespremenljivi v either constant (for instance 0.5 [2]) or expresed as con- VügTPsDI malce I grin^SfcflMISDSD stran 326 B. ^erne - S. Medved: Toplotne izgube v tla - Heat Losses to the Ground določenem območju parametrov [12]. Glede na standard SIST EN ISO 13370 utežne faktorje lahko določimo iz enačbe za največji mesečni toplotni tok: stants for different variable ranges [12]. According to EN ISO 13370 the weight factor can be determined from the expression for the maximum monthly heat flux: F max (ei-ee) ) FG-UG-AG ¦(3-m/3- Sl. 3. Analizirane oblike podov stavb Fig. 3. Analysed shapes of building floors Ta karakteristična izmera je uporabljena tudi v [1] in [12]. Obseg P je opredeljen v [1]. Slika 3 prikazuje analizirane oblike podov stavb z enotnim mrežnim korakom m. Utežni faktorji (F*), določeni glede na SIST EN ISO 13370 z upoštevanjem izraza (2) za različne pode stavb, so prikazani na sliki 4. Izračuni so bili narejeni za m med 2 in 50 oziroma površino poda od 10 do 10000 m2. Vrednosti utežnih faktorjev F* so neodvisne od oblike in velikosti stavbe pri enaki karakteristični izmeri, zato pri oblikovanju poenostavljene metode ta parametra v celoti nadomestimo s karakteristično izmero stavbe B’. This characteristic dimension is also used in [1] and [12]. The perimeter P is defined in [1]. Figure 3 shows the analysed shapes of building floors with a unified raster m. Weight factor (FG*) determined ac-cording to EN ISO 13370 by using equation (2) for differently shaped building floors are shown in Figure 4. In the calculations the raster m from 2 to 50 and floor areas from 10 to 10000 m2 were taken into account. We can see that the characteristic dimension B’ is appro-priate to value the building’s shape influence since the values of FG* are independent of the building shape with the same characteristic dimension B’. 1,2-1 0,6- 0,4- 0,2-0 x oblika "H" / shape "H" oblika "L" / shape "L" ¦ pravokotnik / rectangle ¦kvadrat / square 0 10 20 30 40 50 B' Sl. 4. Utežni faktorji F* so določeni za k = 1,5 W/mK, U = 0,4 W/m2K, za nepodkleteno stavbo, zgrajeno v klimatskem območju z SD = 2985 Kdan in 6 = -18°C, črtkani črti pomenita mejo ±20% Fig. 4. Values F* are determined for k =1.5 W/mK, UF = 0.4 W/m2K, building without basement built in city (area) with DD = 2985 Kday and 6 = -18oC, dotted lines represent border ±20% Največji toplotni tok v tla je v SIST EN ISO 13370 določen s povprečno letno zunanjo temperaturo in letno periodično spremembo povprečnih mesečnih temperatur. V naši metodi smo želeli te temperature nadomestili z zunanjo projektno temperaturo. Podatki o zunanjih projektnih temperaturah so namreč na voljo za veliko število krajev. Za analizo primernosti take zamenjave je bilo izbranih pet tipičnih krajev v različnih klimatskih območjih. Njihovi osnovni The maximum heat flux through a building floor according to SIST EN ISO 13370 is defined with the average annual external temperature and the an-nual variation in the average monthly temperatures. In the simplified method the average annual tempera-tures and the variation in temperatures are replaced by an external project temperature. External project temperature data are available for a larger number of cities. Also, the determination of the specific heat losses of the building is easier. For the analysis, five VH^tTPsDI wm&\ grin^sfcflMISDSD stran 328 B. ^erne - S. Medved: Toplotne izgube v tla - Heat Losses to the Ground Preglednica 1. Meteorološki podatki izbranih krajev (območij) Table1. Meteorological data of selected cities (areas) klimatsko področje climatic area mediteransko mediteranean celinsko continental alpsko alpine SD/DD (Kdan/Kday) 1874 q e,p (oC) -6 13,8 9,0 qe (oC) 2700 -12 10,8 9,5 2985 -18 9,7 10,5 3208 -21 9,2 11,0 3505 -24 8,2 11,0 ) qe (oC) meteorološki podatki so prikazani v preglednici 1. Za vsak izbran kraj smo izračunali utežne faktorje FG* za široko območje karakteristične izmere B’. Rezultati s prikazom funkcijske odvisnosti so prikazani na sliki 5. Razvidno je, da so vrednosti FG * za dani primer znotraj območja -8% do +12%. Pri vseh preostalih analiziranih primerih pa je pričakovana nenatančnost med metodo po SIST EN ISO 13370 in razvito poenostavljeno metodo znotraj območja, ki ga predpisuje standard [13] za metode, ki temeljijo na “izračunu z uporabo kataloga”. Iz tega izhaja, da je povprečne letne zunanje temperature in letne periodične spremembe povprečnih mesečnih temperatur mogoče nadomestiti z zunanjo projektno temperaturo določenega kraja. 1,4 typical cities in different climatic areas were chosen. Their basic meteorological data are shown in Table 1. The values of weight factors (FG*) for each selected city and a wide range of characteristic dimension’s B’ were calculated. The results, together with a function curve, are shown in Figure 5. It is evident that all FG* values are within –8% and +12% limits. It was also observed that for all analysed combinations of the influencing parameters, the differences between the Fmax calculated using EN ISO 13370 and our simpli-fied method are smaller than expected uncertainly for manual calculations and “catalogue” methods accord-ing to reference [13]. Therefore, the average annual temperature and the variation in the average monthly tem-peratures can be replaced by project temperatures that are characteristic of a wide range of climatic conditions. 1,2 1 0,8 0,6 0,4 0,2 9e,p x - 6 ¦ - 12 o - 18 ¦ - 21 * - 24 0 10 20 30 40 50 B' Sl. 5. Utežni faktorji F* so določeni za k =1,5 W/mK, U=0,4 W/m2K, za nepodkleteno stavbo, 6=20 "C, črtkani črti pomenita mejo ±20 odstotkov Fig. 5. Values F* are determined for k =1.5 W/mK, U=0.4 W/m2K, building without basement, 6 = 20oC, dotted lines represent border ±20% Vrednosti (F*) pa so odvisne tudi od drugih toplotnih in konstrukcijskih parametrov. Pri razvoju poenostavljene metode smo upoštevali, da so tla bodisi glinena (k=1,5 W/mK), peščena (k=2 W/mK) ali skalnata (k=3,5 W/mK). Predpostavili smo, da so stavbe enakomerno ogrevane na 6=20 °C in da je debelina zunanjega zidu na stiku s i podom 0,35 m. Te vrednosti so bile izbrane kot najbolj The values of the weight factors (FG*) also depend on other thermal and design parameters. When designing the simplified method we took into consideration that the ground can be clay (kG = 1.5 W/m2K), sand (kG = 2.0 W/m2K) or homogeneous rock (kG = 3.5 W/m2K). The buildings are assumed to be uniformly heated to a constant temperature qi=20oC and have constructions in contact with the ground | IgfinHŽslbJlIMlIgiCšD I stran 329 glTMDDC 0 B. ^erne - S. Medved: Toplotne izgube v tla - Heat Losses to the Ground pogoste, v praksi pričakovana odstopanja pa ne vplivajo bistveno na rezultat analize. Toplotne prehodnosti gradbenih konstrukcij v stiku s tlemi, ki smo jih analizirali, so bile 0,3; 0,4; 0,5 in 0,6 W/ m2K. Te vrednosti so bile izbrane glede na predpis o toplotni zaščiti stavb in trdnostne lastnosti gradbene konstrukcije. Glede na lastnosti konstrukcije in globino podkletitve so stavbe razdeljene na tri kategorije, kakor je prikazano na sliki 6: - nepodkletene stavbe, - podkletene stavbe z različnima toplotnima prehodnostima poda in vkopanega zidu, - podkletene stavbe z enakima toplotnima prehodnostima poda in vkopanega zidu. that are 0.35 m wide. These values were chosen as the most representative, but in any case their influence on the results is negligible. The analysed thermal trans-mittances of the building structures were 0.3, 0.4, 0.5 and 0.6 W/m2K. When choosing these values, civil engineering technologies and common building ther-mal protection regulations were taken into consider-ation. According to the building’s structural proper-ties and the depth of the basement, buildings are di-vided into three categories, as shown in Figure 6: - buildings without basement - buildings with basement with different thermal trans-mittances of the basement floor and basement walls; - buildings with basement with the same thermal trans-mittances of the basement floor and basement walls; Sl. 6. Shematski prikaz analiziranih stavb. Na levi nepodkletena stavba, na sredini podkletena stavba z različnima toplotnima prehodnostima poda in vkopanega zidu, na desni podkletena stavba z enakima toplotnima prehodnostima poda in vkopanega zidu Fig. 6. Schematic survey of the buildings analysed in this work; on the left is building without a basement; in the middle is a building with a basement with different thermal transmittances of the basement floor and basement wall; and on the right, a building with a basement with equal thermal transmittances of the basement floor and the basement wall 3 OBLIKOVANJE ENAČBE UTEŽNIH FAKTORJEV (FG*) Enačbe utežnih faktorjev smo določili s statistično analizo 18720 analiziranih primerov. Enačbe za toplotni tok skozi tla (0 ) in utežne faktorje (F*) za različne tipe stavb so prikazane v nadaljevanju: - za nepodkletene stavbe je največji toplotni tok v tla določen z izrazom : kjer FG,F* določimo z izrazom: Utežni faktorji v odvisnosti od karakteristične izmere stavbe B’ za izbrano nepodkleteno stavbo so prikazani na sliki 7. Vrednosti konstant aF za analizirano polje spremenljivk so podane v preglednici 2. - za podkletene stavbe z različnima toplotnima prehodnostima poda in vkopanega zidu je največji 3 DESIGNING OF WEIGHT FACTOR (FG*) EQUATIONS Weight factor equations were determined with a statistical analysis of 18720 analysed combi-nations. The equations for the heat flux to the ground (Fmax) and the weight factors (FG*) for different types of buildings are shown below: - for buildings without a basement the maximum heat flux to the ground is determined by: (4), max =F* G,F ¦UF ¦AF(3-X-.-^-..-^.-.-^.-.-^l_-.- --.-7- : -¦--.-^r ¦¦-¦¦-¦¦-¦¦-¦¦- : -I 0 10 20 30 40 50 B' Sl. 8. Vrednosti utežnih faktorjev FG, * in FG, * za podkleteno stavbo z = 3 m, k =1,5 W/mK, 0 =20 °C, 2