EXPERIMENTAL AND NUMERICAL ANALYSIS OF HEAT TRANSFER IN THE CAVITIES OF HOLLOW BLOCKS

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1 EXPERIMENTAL AND NUMERICAL ANALYSIS OF HEAT TRANSFER IN THE CAVITIES OF HOLLOW BLOCKS Pietro Stefanizzi, Antonio Lippolis, Stefania Liuzzi Politecnico i Bari, Via Orabona 4, 715 Bari SUMMARY Given te importance of te assessment of te insulation performance of te builing envelope in te context of energy certification of builings, a etaile analysis of te reliability of te metos of evaluation of eat transfer in te air cavities of ollow blocks as been carrie out. An experimental stuy was conucte in te laboratory. Heat transfer measurements on specimens wit parallelepipe cavities were one, toug a guare ot plate evice accoring to UNI EN A numerical analysis of te eat transfer in te specimens toug te software ANSYS FLUENT was carrie out. Te analysis of te numerical an experimental results wen compare wit te preictions obtaine from simplifie moels of tecnical stanars, ave calle attention to te orer of magnitue of te calculation accuracy obtainable wit suc proceures. For some geometric configurations an bounary conitions, te application of te stanars can lea to large errors of evaluation of te termal resistance of te cavity. 1. INTRODUCTION In builing constructions, air cavities in a soli matrix are use to increase te termal resistance wit a simultaneous ecrease of apparent ensity of te structure. A large number of stuies were conucte, eiter experimentally or toug numerical simulations, on te eat transfer in air cavities of ifferent sapes. Bounary conitions as impose flux or known temperature were consiere. A comparison between te experimental results an a numerical simulation moel as been reporte in [1], for a configuration of te cavity surroune by conuctive soli walls. Te presence of te termal conuction in te bounary walls influence te convective motion insie te cavity, lowering te velocity of te internal flui. Te irect raiation between te inner surfaces of te cavity elps to reuce te movement of air toug a more uniform istribution of te surface temperatures. A numerical stuy on natural convection in a suare cavity surroune by tin vertical porous walls is reporte in []. Te main effect of te porous layers is te reuction of vertical upwar flow an a conseuent reuction of te convective eat excange. A numerical stuy on te transmission of eat in two imensions in structures wit cavities use in builing construction as been reporte in [3]. Te eat transfer in te builing walls of ollow blocks wit various number of air cavities in te eat flux irection as been stuie. Te effects of conuction in te bounary walls an of te raiation between te inner surfaces in te conition of natural convection in two-imensional cavities of rectangular sape are reporte in [4]. Te convection in te cavity is attenuate by termal conuction in te bounary walls an by te raiative eat excange among te inner surfaces. Natural convection is very sensitive to te configuration of te cavity an to te bounary conitions [5]; terefore it is esirable tat te numerical results are valiate by experimental measurements. A simplifie analytical meto for te assessment of te eat transfer in ollow blocks wit vertical perforations as been propose in [6]. Te autor claims to be in goo agreement wit previous experimental measurements. Stanar metos reporte in various national an European tecnical stanars are often use for tecnical calculations of sufficient accuracy. UNI EN ISO 6946 [7] reports a proceure for te calculation of eat transfer in ventilate an non-ventilate air cavities. UNI 1355 [8] reports a proceure for te numerical calculation of te termal resistance of walls an roofs, an in particular for te estimation of te termal resistance of air cavities. Te eat transfer in te cavity, ue to convection an raiation, is moele as an euivalent termal conuction tat gives rise to te same eat flux transfer as in te real cavity. Te results of a numerical Finite Differences Moel (D) for solving te system of ifferential euations tat escribe te combine transport by conuction, convection an raiation in air cavities boune by conuctive walls are reporte in [9]. Te termal beavior of te walls of ollow blocks as been stuie in [1, 11] also from te point of view of te interaction between temperature an umiity in te presence of air cavities. A stuy to optimize te termal performance of ollow blocks wit low-emissivity coatings on te inner surfaces of te cavity is reporte in [1].. EXPERIMENTAL MEASUREMENTS Te ollow blocks can be installe in two ways: in eiter wit vertical perforations or wit orizontal perforations. Depening upon te position of te blocks te air cavities ave ifferent eigt-to-tickness an wit-to-tickness ratios. Tese ratios affect te convective eat transfer but also te raiation toug te cavities. At te Laboratory of Tecnical Pysics of te University of Politecnico i Bari, measurements of termal resistance of 149

2 specimens wit air cavities of parallelepipe sape ave been carrie out. Te measurements were one on a guare ot plate euipment accoring to UNI EN 1664 [13]. Te evice as an excange section 5x5 cm wit a central metering area 5x5 cm. Measurements were one wit central ot plate in vertical arrangement. A specimen was put on te rigt an one to te left an finally te col plate containment tigtene to close te package wit te minimum pressure reuire by te tecnical stanar. Measurements were carrie out in stationary termal conitions wit uniform istribution of surface temperatures. Te eat flux, generate in te central zone, crosses te two specimens an is iscarge in te eat sink mae up by two en plates cille by circulating col water at constant temperature. Te measurement of eat flux () is carrie out toug te measurement of voltage an current (irect current) supplie to te electrical resistance in te central area of measurement. In orer to eepen te termal beavior of te air cavity boune by soli material, it was consiere necessary to use specimens constructe in te laboratory by seets of PVC foam tat allow partitions of reuce tickness an plain an parallel walls. Te seets of PVC foam a a tickness of mm an te specimens were manufacture by inserting between two suare plates (5x5 cm ) transverse partitions eually space so as to acieve cavities wit rectangular transverse section (Fig. 1). PVC-air cavities, te termal resistance of te air cavities was estimate. Measurements of te termal resistance was carrie out wit termal conitions corresponing to an average temperature of 88 K an a temperature ifference between te two faces of te specimen (ot an col sies) eual to 4, 6 an 1 K respectively. Results are sown in Fig.. Fig. Experimental results. Termal resistance of te air cavities. 3. CALCULATION MODELS eat flow metering area (5x5 cm ) guar area Fig. 1 Scematic of te specimen of PVC foam (5x5 cm ) Pairs of specimens wit a tickness of 1, 3 an 5 cm were built up. Te oter imensions of te air cavity were 4. cm in eigt an 3.8 cm in wit. Te value of te eigt is limite by te size of te metering area of te apparatus, but in any case it is close to te one wic is te normal size of cutting brick blocks. Te wit as assume a value in orer to ave a wole number of cavities insie te metering zone of te apparatus. Te termal conuctivity of PVC was measure wit te same apparatus an was foun to be.77 W/(m K), wile te emisperical emissivity was assume eual to.9 accoring to [14]. From te measurement of eat flux transmitte () an temperature ifference on te ot an col sies of te specimen, te termal resistance of te specimen was foun: R = (1) From a series-parallel resistances moel of te structure CFD A numerical analysis of te eat transfer in te specimens toug te software ANSYS FLUENT [15] as been carrie out. Te simulation was one in a D section of te specimen at te centerline of a cavity, wit te bounary conitions reporte in Fig. 3. A eat transport by natural convection wit flui motion activate by te variation of ensity wit temperature, uner te action of gravity, as been moele in te cavity. Te air flow is laminar (Ra«1 8 ). A stationary, ouble precision an pressure-base solver wit a SIMPLE sceme was use in orer to segregate te pressure-velocity coupling. Te eat transfer by raiation into a cavity of N grayiffusive surfaces, wit emissivity ε k, area A k, temperature T k (k=1,..,n), is computable from te following system of euations [16, 17]: 1 Q = B C () { } { } [ ] { } Were, { Q} is te column-matrix of te raiation fluxes, C is a column-matrix wit ( ) 4 N C = δ F σt an k kj kj j j = 1 [ B ] is te matrix of coefficients wit δ F kj Bkj = ε elta. kj ( ε j ) 1 1, were δ kj is te Kronecker's ε A j j j

3 aiabatic u=v= g T u=v= u=v= T c L l y u=v= x aiabatic D Fig. 3 Coorinate system an bounary conitions. Fig. 5 Deviation (%) of te termal resistance of te cavity evaluate wit FLUENT D versus te experimental value. A raiative eat transfer coefficient on te ot surface of te cavity is calculate, as: 1 L, ra y mean ra L r = = (3) an a convection eat transfer coefficient as: 1 L 1 L,, tot ra mean tot y y mean ra L L a = = (4) Te total termal resistance of te cavity was calculate as: R 1 = (5) a + r Te percentage eviation of te termal resistance value of te cavity evaluate wit FLUENT D versus te measure value is reporte in Fig. 5. Te result is witin te range of te estimate error for te experimental measurement (7%). 3. UNI EN ISO 6946 Fig. 4 Temperature (left) an velocity (rigt) for 5 cm tick cavity, =1 K, T m =88 K. Fig 4 sows te solution obtaine for te cavity of 5 cm tickness wit =1 K. Tis approac reuires te calculation of te black boy view factors (F kj, k = 1,... N, j = 1,... N) between all pairs of surfaces tat face into te cavity. Tis meto correspons to wat in FLUENT is calle SS meto (surface-to-surface). If te computational omain as more tan one cavity, te meto SS is not usable. So te meto DTRM (Discrete Transfer Raiation Moel) was selecte, wic uses a raytracing tecniue to assess te excange of raiation in te cavity [15]. For vertical air cavities (orizontal eat flux) te stanar UNI EN ISO 6946 proposes two calculation metos epening on te type of cavity: 1) Air layer of wit b (Fig 6) larger tan 1 times te tickness ; ) Air voi wit b<1. In bot cases, te termal resistance of te air cavity is calculate toug te relation (5). For unventilate cavities te convection coefficient ( a ), in bot cases, is given by:.5 a = max 1.5; per 5K (6) 13.5 a = max.73 ( ) ; per Δ T > 5K Instea, te raiation coefficient is given by: = se b ε ε 1 (7) (8) 151

4 wit r = se b< ε + 1 ε + r 4 3 m b b (9) = σt, ε 1 an ε emisperical emissivity of te 8 W ot an col surfaces of te cavity, σ = mk T = T + T mean Stefan-Boltzmann s coefficient, ( ) temperature (K). m 1 intermeiate value of te tickness (3 cm) an temperature ifferences of 6 an 1 K. Fig. 6 Dimensions of te air cavity (UNI EN ISO 6946). 3.3 UNI 1355 Te Italian stanar UNI 1355 [8] proposes a meto for te calculation of te termal resistance of te cavity uner te combine effect of convection ( a ) an raiation ( r ) wit air transparent to te raiation. Te excange by raiation is evaluate consiering te cavity as a space between two flat plates, parallel an inefinite at a istance eual to te tickness of te cavity, i.e. te imension in te irection of eat flux. If is te tickness of te cavity in te irection parallel to te prevailing irection of te eat transfer, it follows tat: R 1 = (1) a + r were, = 1ε1 + 1ε 1 ; Nu λ a = ; λ =.5 W/(m K) is te termal conuctivity of te still air; L Nu = Ra is te Nusselt number for vertical cavity (orizontal eat flux); L is te cavity eigt; 3 ρβg c p Ra = is te Rayleig number; μλ is te temperature ifference between te two surfaces, te ot an te col one, facing into te cavity. 4. RESULTS FOR PVC SPECIMENS Te percentage eviations of te termal resistance values calculate by te two stanars compare to te value measure experimentally are reporte in Fig. 7 for Δ T = 4 K. Te first moel (UNI 1355) makes a conservative estimate (-1%) of te resistance to te smaller tickness (1 cm) at a temperature ifference of 4 K. Te secon moel (UNI EN ISO 6946) sows te maximum error (+8%) for te 15 Fig. 7 Deviation (%) te termal resistance compare to te experimental measurement, =4 K. Te tren of te percentage eviations leas to tink of a fault tat coul be in te moels of te tecnical stanars. Unfortunately it is not easy to etermine weter te problem is in te moel for calculating te contribution of te convective or raiative or bot. 5. AIR CAVITIES IN HOLLOW BRICK BLOCKS Accoring to te results obtaine it was ecie to eepen te analysis by stuying ifferent geometries of air cavities separate by webs. Typical geometry of te blocks installe wit orizontal perforations an wit vertical perforations ave been stuie, consiering some values of mean temperature an of temperature ifference on te faces normal to te eat flux irection. Te case stuies ere analyze are sown in Table 1. Te bounary walls of te cavity were suppose to be of brick wit 5 mm tickness, termal conuctivity.41 W/(m K) an emissivity.9. b [cm] [cm] L [cm] T m [K] [K] Vertical perforations Horizontal perforations Tab. 1 Geometry an bounary conitions. Te reference solution was obtaine wit FLUENT D, moeling te raiation in te cavity wit te DTRM meto an te convection as in laminar regime. Te bounary conitions are tose summarize in Fig INSTALLATION WITH VERTICAL PERFORATIONS Te percentage eviations of te values of total resistance of te cavity (R) are reporte in Figures 8. Actually, bot from te point of view of te convection an from tat of te raiation, te most influential imension soul be te eigt L of te cavity. In orer to test tis, we rei te calculation accoring to te stanars by using te ratio L/ in place of b/. Results, in terms of eviation from te D calculation, are sown in Figures 9.

5 Fig. 8 Deviation (%) of te value of total termal resistance calculate by te stanars, versus te ratio b/. Fig. 1 Deviation (%) of te value of total termal resistance calculate by te stanars, versus te ratio b/. Two faults are evient in te stanars: 1) te moel of raiation excange of UNI EN ISO 6946 is lacking for low values of b/ (i.e. lesser wit an greater tickness), a eviation of 3% was etecte for b/=.4; ) te moel of convection excange of UNI 1355 oes not give an acceptable estimate of te excange for all values of b/ (for very narrow cavity overestimates te convection, +9.7% for b/=.4, an for te oter unerestimates it, -39% for b/=1.). Fig. 11 Deviation (%) of te value of total termal resistance calculate by te stanars, versus te ratio L/. Fig. 9 Deviation (%) of te value of total termal resistance calculate by te stanars, versus te ratio L/. It is confirme tat in te calculation of te raiation accoring to te UNI EN ISO 6946, te imension tat must be correlate to te tickness of te cavity is te greatest imension of te isotermal faces normal to te eat flux irection. Furtermore, an imprecision of te convection calculation wit UNI 1355 is evient for L/=5 (+4%). 5. INSTALLATION WITH HORIZONTAL PERFORATIONS In tis moe of installation te largest imension of te cavity is orizontal an coincient wit te cutting lengt of te block. In Fig. 1 te percentage eviations of te total resistance R are sown. Even in tis case, faults are evient in te stanars: 1) te moel of raiation excange of UNI 1355 is lacking for low values of b/, +9% for b/=.5; ) te moel of convection of UNI EN ISO 6946 it overestimates te excange for lower b/, +3% for b/=.5, an unerestimates it for iger values, -43% for b/=. Te uestion arises, even in tis case, weter te ratio L/ coul not be te most suitable in te moels of te stanars. Te percentage eviations of calculation moels versus te ratio L/ are reporte in Figures 11. It is evient a still large iscrepancy between te actual convection an raiation excange an te estimate of stanars. Looking at te istribution of temperature an air velocity in te cavity wit b = cm an = 4 cm (Fig. 1) it is evient an asymmetry of temperature istribution on te orizontal walls tat coul ave a major influence on te real eat excange by raiation. Te stanars, in suc a configuration, fail to moel te real eat excange. Consiering a wall of ollow blocks tat are installe wit orizontal perforations an te cavity of te type above escribe (results in Table ), we can see ow an approximate evaluation, accoring to te tecnical stanars consiere, leas to unerestimate te termal resistance of te wall wit very important conseuences. Starting from a wall wit termal transmittance eual to te max value amitte by national law (Decree 311-6) of.4 W/m K, typical of te climatic Zone C, te calculation accoring to UNI 1355 woul lea to a termal transmittance of orer.6 W/m K. Tat is, it woul be an obvious problem for te proper evaluation of energy class of te builing. Tis estimation was one in a first approximation by assuming a wall of ollow blocks wit 9 cavities of te type sown in Table put in series in te eat flux irection. 153

6 REFERENCES Fig. 1 Temperature (top) an velocity (bottom) in te cavity wit b= cm an =4 cm. (T m =95 K, =7,5 K. FLUENT D UNI EN ISO 6946 UNI 1355 R(b/) R(L/) a (b/) a (L/) r (b/) r (L/) Tab. Results for cavity wit b=cm, =4 cm, L=4.5 cm, Tm=95 K, =7,5 K. CONCLUSIONS Te termal resistance of te cavity is routinely calculate in accorance wit UNI EN ISO 6946 or UNI Te experimental an numerical investigation carrie out as pointe out tat te use of te stanars for estimating te termal resistance of te air cavities can lea to large errors in some geometric configurations an bounary conitions. For example, for cavity into ollow brick blocks installe wit orizontal perforations, te termal resistance coul be unerestimate in te orer of 4%. Te error in estimating te termal resistance of te single cavity affects significantly te assessment of te overall termal performance of te wall of ollow blocks. Tat is an extremely serious matter if one tinks of te importance of "certifing" te termal transmittance values compare wit te legal limits on te certification of energy performance, as well as te importance tat te energy class of te builing as from te point of view of its economic value, an from te point of view of te energy consumption estimate to acieve goo inoor climate control. 1. D.M. Kim an R.Viskanta, Effect of wall eat conuction on natural convection eat transfer in a suare enclosure, J. of Heat Transfer, vol. 17 (), pp , P. Le Breton, J. P. Caltagirone an E. Aruis, Natural convection in a suare cavity wit porous layers on its vertical walls, Transactions of te ASME, J.of Heat Transfer, vol. 113, pp , A. Abelbaki an Z. Zrikem, Simulation numériue es transferts termiues couplés à travers les parois alvéolaires es bâtiments, Int. J. Term. Sci., vol. 38, pp , D.M. Kim an R.Viskanta, Heat transfer by conuction, natural convection an raiation across a rectangular cellular structure, Int. J. Heat & Flui Flow, vol. 5 (4), pp. 5-13, S. Ostrac, Natural convection in enclosures, Transactions of te ASME, J. of Heat Transfer, vol. 11, pp , S. Lorente, M. Petit an R. Javelas, Simplifie analytical moel for termal transfer in vertical ollow brick, Energy an Builings, vol. 4, pp , UNI EN ISO 6946, Builing components an builing elements Termal resistance an termal transmittance Calculation meto, UNI 1355, Walls an floors Termal resistance values an calculation meto, A. Lippolis an P. Stefanizzi, Trasmissione el calore in strutture con cavità aria, Proc. XIII UIT National Heat Transfer Conference, pp , P. Boni an P. Stefanizzi, Resistenza termica i murature e solai, Costruire in Laterizio, vol., pp , P. Boni an P. Stefanizzi, Hygro-termal performance of ollow bricks an current stanars, Energy an Builings, vol. 33, pp P. Principi, R. Fioretti, Termal analysis of te application of pcm an low emissivity coating in ollow bricks, Energy an Builings, pp , UNI EN 1664, Termal performance of builing materials an proucts - Determination of termal resistance by means of guare ot plate an eat flow meter metos - Dry an moist proucts of meium an low termal resistance,. 14. Y. S. Touloukyan an D. P. DeWitt, Termopysical properties of matter, vol. 7, IFI/Plenum, New York, ANSYS-FLUENT, Teory Guie, Release 14., ANSYS Inc., Canonsburg, P. Stefanizzi, A. Wilson an A. Pinney, Internal longwave raiation excange in builings: Comparison of calculation metos: I Review of algoritms, Builing Services Engineering Researc an Tecnology, vol. 11, pp , R. Siegel an J.R. Howell, Termal raiation eat transfer (3t En), Hemispere, Wasington D.C.,