Numerical Analysis of Comfort and Energy Performance of Radiant Heat Emission Systems

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1 Numercal Analyss of Comfort and Energy Performance of Radant Heat Emsson Systems Ochs *, Magn, Segele and Janett Unversty of Innsbruck, Unversty of Bologna *Correspondng author: Technkerstr. 3, 600 Innsbruck, Austra, Abstract: Radant heatng generally addresses all heat emsson systems that have a share of radant heat emsson greater than 50 %, compared to a convector or fan col where the heat s transferred manly by means of convecton. Recently, so-called nfrared-heatng systems are ncreasngly dscussed as a costeffectve heatng system. Relatve small areas of typcally 0.6 m x. m wth hgh surface temperatures up to 0 C are used. In order to nvestgate n detal radant heatng systems, buldng models able to reproduce accurately the occurrng physcs phenomena are requred. Physcs-detaled steady state and transent room models have been developed n Matlab. The requred vew factors for the radatve exchange between all surfaces and between each surface and a sphere representng a person are calculated usng COMSOL Multphyscs. Moreover, the thermal comfort n dfferent postons of the room has been evaluated. Keywords: Radant Heatng, Vew Factor, Buldng Smulaton, NZEB, Passve House. Introducton The mplementaton of the concept of NZEB [] wll lead to a further reducton of the heatng demand of new buldngs. Also the heatng demand of the buldng stock wll decrease by applyng deep renovaton. The technology to acheve very low energy demands s avalable snce about 5 years, when the frst Passve House was bult n Darmstadt, Germany []. Technology and products have been further mproved snce then and cost-effectveness has been sgnfcantly mproved. However, n order to mprove the economc feasblty of these very effcent buldngs, cost-effectve heatng systems are requred. In parallel the share of renewable energes (such as PV or wnd) n the electrc grd wll further ncrease. Both these developments make electrc heatng nterestng agan n spte of the fact that, because of thermodynamc prncples, electrcty should not be used for heatng.. Motvaton and Objectve Recently so-called nfrared-heatng systems are ncreasngly dscussed as a cost-effectve heatng system. Relatve small areas of typcally 0.6 m x. m wth hgh surface temperatures of up to 0 C are used. The followng questons have to be answered: What s the approprate dmensonng of the radant system dependng on the load of the buldng? What are the comfort condtons wth radant heatng systems and how should they be determned and evaluated? What s the energy performance compared to reference systems such as hydronc heat emsson systems e.g. wth ar-sourced heat pump? Is there a beneft n ntermttent operaton due to the relatve fast response of these heatng systems? 3. Radatve Heatng - Defnton Wth a convectve heat emsson system, such as e.g. a convector or a fan col, thermal energy s emtted manly convectvely (ether through free and/or forced convecton) drectly nto the ar. Contrarwse, wth a so-called radatve heat emsson system,.e. a heated area where mn. 50 % of the heat emsson occurs as long-wave radaton, the major share of the heat s dstrbuted to the surroundng surfaces. Radaton heat emsson systems are n prncple ndependent of the type of heat supply (.e. electrcal or hydronc), however, often electrcally heated systems are addressed (nfrared heatng system). Remark: The so-called supply ar heatng n a Passve House s wth regard to the supply ar rooms also a radant heatng system. The warm supply ar flows close to the celng due to the Coanda effect [3]. In turn the celng s heated up n an area close to Excerpt from the Proceedngs of the 06 COMSOL Conference n Munch

2 the ar outlet and, consequently, t emts heat as long-wave radaton to the other surfaces. In case of a radant heat emsson system, the temperature of the surroundng surfaces ncreases compared to a predomnantly convectve heatng system, assumng the same heatng power. As a consequence, a lower convectve (.e. ar) temperature s requred for the same operatve temperature, whch conssts of about 0 % to 50 % of the convectve temperature and 50 % to 60 % of the surface temperature of the surroundng areas. Ths means for the energy balance of a room, that wth a radant heatng system compared to a convectve heatng system the same thermal comfort can be obtaned wth slghtly reduced ventlaton losses, but also slghtly ncreased transmsson losses (especally when the radant heater s mounted on an external wall or when external walls form the radaton partner of the radant heater). In buldngs wth very hgh qualty of the thermal envelope, the ncrease of the transmsson losses s almost neglgble (unless the drect radaton partner s a wndow). In case of very effcent buldngs, as demanded by the EU energy performance of buldngs drectve (EPBD []), the ventlaton losses are also low (due to the heat recovery requred for achevng hgh thermal comfort and low heatng demands), hence, also the reducton of ventlaton losses s of mnor mportance. Decreased and ncreased losses are more or less balanced. The dfference of the heatng demand between a radant and a convectve heatng system ncreases wth better qualty of the buldng envelope and hgher energetcally effectve ar exchange rate (the equvalent ar change that s not covered by the heat recovery). In case of poor qualty of the envelope the energy consumpton for heatng can even ncrease compared to a convectve heatng system.. Thermal Comfort The radant temperature asymmetry (halfspace and small hot surfaces) has to be consdered when dmensonng a radant heat emsson system. The ISO 7730 [5] (as well as the ASHRAE 55 [6]) specfes a maxmum radant temperature asymmetry of 5 K for heated celngs and 3 K for a heated wall. More recent studes, such as e.g. [7] ndcate slghtly hgher values wth about 8 K for heated celngs. Here, t s mportant to note that slghtly dfferent results mght be obtaned for the heatng demand dependng on whether optmal thermal comfort at the most unfavorable locaton n the room or n average wth respect to the occuped area s demanded. For a meanngful comparson, equal room ar qualty and equal thermal comfort are prerequste. In addton to the potental energy savngs due to reduced ventlaton losses, there s a further reducton potental due to the possblty to provde thermal comfort only locally. Ths can refer to a specfc place n the room (e.g. the workng place) or on separate heatng of the occuped areas (n contrast to heatng the entre nhabted space). A correct szng and a temporally and spatally correct functonng control of the radant heatng system s a prerequste to acheve thermal comfort. 5. Modellng and Buldng Smulaton A buldng model wth a detaled calculaton of the radaton exchange (between each of the surroundng surfaces, as well as between all surroundng surfaces and a sphere (or ellpse or cube), smulatng a person n the room and used for calculatng the operatng temperature) s requred to represent these effects wth suffcent accuracy. Wth such a model, the effects can be determned wth hgher accuracy compared to a two-star e.g., Dynbl [8], Energy+ [9]) or star node e.g. EN ISO 3790 [0], TRNSYS [] model that are usually used for buldng smulatons [, 3]. R rad J C J R R conv Two star model J c J S R comb Star-node model Fgure. star-node model (rght) and two-star model (left) wth four surfaces: Jr radatve node, Jc convectve node, Js star node (mxture of surface and ar temperature), Rrad radatve resstance, Rconv convectve resstance, Rcom combned radatve and convectve resstance and Rsc the resstance between the star node and the convectve node Excerpt from the Proceedngs of the 06 COMSOL Conference n Munch

3 Wth such a detaled physcal model of a room a possble nfluence on the heatng demand wth a radant heatng system compared to a convectve heatng system can be calculated dependng on the buldng standard (.e. the qualty of the buldng envelope and the energetcally effectve ar exchange rate). Here, a low lnear temperature stratfcaton n the room (.e. an deal mxng) s assumed, see Fg.. Ths assumpton s acceptable n rooms wth very good nsulaton level and ventlaton wth heat recovery. However, t wll not hold n case of radant celngs and/or cold ar supply. For a more accurate analyss, n addton, a computatonal flow smulaton (CFD) for determnng the temperature stratfcaton would be needed. The convectve heat transfer coeffcents are calculated wth well-known power law correlatons, see []: n h C J (eq. ) conv Fgure 3. Model for long-wave radaton exchange wth 6 surfaces 6.. Vew Factor Calculaton The vew factor F j represents the fracton of the radaton whch leaves the surface A and strkes the surface A, as shown n Fg.. fully mxed celng convectve J floor Fgure. Calculaton of Vew Factor [5] 6.. Analytc Calculaton of Vew Factors Fgure. Temperature stratfcaton for dfferent heatng stuatons, celng and floor heatng, convectve heatng and fully mxed 6. Physcal Room Model Detaled steady state and transent physcal room models have been developed n Matlab based on the radosty approach [3,, 5], see Fg. 3. The requred vew factors for the radaton exchange between all surfaces and between each surface and a sphere representng a person or a thermal comfort n dfferent postons of the room are calculated usng COMSOL Multphyscs software, see secton 6..3 for detals. H s the radosty. The resstances R j can be calculated wth the vew factor F j the area A and r s the emssvty resstance. Rj (eq. ) A F j If the radaton ntensty s constant over the surface the vew factor can be calculated analytcally by solvng eq. 3. the vew factor does not depend only on the geometrcal confguraton. cos cos F da da A (eq. 3) r A A For many smple geometres vew factors are avalable n the lterature, e.g. n [5, 6]. For complex geometres numercal methods have to be used. If the surfaces radate dffusely, have constant temperature and radaton propertes over the entre area numercal ntegraton can be appled. 6.. Numercal Integraton In Matlab CDIF (contour double ntegral formula) can be used to calculate vew factors between planar surfaces (.e. polygons) for any shape and orentaton e.g. wth [7]. Excerpt from the Proceedngs of the 06 COMSOL Conference n Munch

4 6..3 Vew Factor Calculaton wth COMSOL Multphyscs In COMSOL Multphyscs surface to surface radaton problems can be solved usng the radosty approach wth the rradaton G (here G s the mutual rradaton comng from the other boundares), the radosty H and the emssvty : ( ) G H T (eq. ) The emssvty can be a functon of wavelength ( ) and surface temperature (T). Complex geometres also wth obstructons can be consdered. But the hypothess of dffuse grey surface has to hold.e. every surface has the absorpton coeffcent equal to the emssvty coeffcent and emssvty and absorptvty are ndependent of the angle of emsson or absorpton, respectvely. Here, two dfferent methods are studed and compared: ) Surface to surface radaton physcs, where t s necessary to run one smulaton for every vew factor whch has to be calculated. The COMSOL operators radopd(h up, H down) and radopu(h up, H down) are used. ) Heat Transfer wth Surface-to-Surface Radaton physcs where surfaces are presented as sold objects. ( ) H Q T (eq. 5) A 6. Valdaton For a room wth 6 surfaces, the vew factors are calculated wth the three numercal methods (numercal ntegraton wth Matlab and the two methods usng COMSOL ) and are compared aganst the analytcal soluton. For sx surfaces, there are 36 unknown vew factors. Consderng that the surfaces are plane and there are symmetres and applyng recprocal condtons the unknowns are reduced to four. Wth one smulaton wth COMSOL method, for sx surface temperatures sx heat fluxes are determned. The remanng lnear system of equatons can be solved, e.g. wth Matlab. The vew factors of the analytcal soluton are reported n the Table. Maxmum devatons for each case are summarzed n Table. Table : Vew factors for the sx surface problem () () (3) () (5) (6) () () (3) () (5) (6) Table : Max and mean devatons wth respect to the analytcal soluton COMSOL COMSOL Method Method Numercal ntegraton (Matlab ) Max 6.089E E-06 Mean.78E E-06 Numercal ntegraton wth Matlab and COMSOL Method delver suffcently accurate results wth respect to the analytcal soluton. The reason for the devatons n case of the method has to be further nvestgated. The man advantage of usng COMSOL for the determnaton of the vew factors s that the problem can be coupled to further physc problems such as CFD smulatons. 7. Case Study 7. Descrpton For a smple room model wth the dmensons 8 m x 6 m x.7 m (WxDxH) the theoretcal change of the heatng power and the (annual) heatng demand were calculated exemplarly. The room has one external façade wth a share of wndow surface of 30 % (or 60 % as a varant) and an external celng (nsulated flat roof, or adabatc as a varant) each n Passve House qualty. Dfferent szes and postons of the radant heater have been nvestgated, (see Table 3) and compared aganst the reference case wth convectve heatng. Table 3: Investgated cases poston and sze of radant heater centrc (c) and acentrc (ac), see Fg. 5 Large Medum Small c. Small ac. Sde wall x X x x Rear wall x X x x Floor x x Celng x x x x Excerpt from the Proceedngs of the 06 COMSOL Conference n Munch

5 J rad / [ C] x / [m] J rad / [ C] x / [m] Fgure 5 shows a scheme of the case wth small radant heater centered and acentrc and Fgure 6 shows the correspondng spatal dstrbuton of the radatve temperature n.5 m heght as a result of a steady state calculaton for an operatve temperature of 0 C. L= B=6 H=.7 Fgure 5. Scheme of small radant heater centered (left) and acentrc (rght). y / [m] Fgure 6. Spatal dstrbuton of the radaton temperature n.5 m heght for the small radant heater centered (left) and acentrc (rght) 7. Results The calculated reducton of the heatng demand depends on the energetcally effectve ar exchange rate see Fg. 7. HD / [kwh/(m² a)] C R C R W energetcally effectve ar exchange rate / [m³/h] Fgure 7. Heatng demand (HD) for the small radatve heater on the celng (R C) and wall (R W) and reducton wth respect to convectve heatng (C) dependng on the energetcally effectve ar exchange rate It s n case of a specfc heatng demand (HD) of about 0 kwh/(m² a) correspondng to an ar change rate of 60 m³/h wth heat recovery wth an effectveness of 85% (wth correspondngly very low energetcally effectve ar exchange rate of only 9 m³/h) n the range of y / [m].9 L= B=6 reducton / [-] H=.7 0 % for a small celng mounted radant heater and 6 % for a small wall mounted radant heater (each wth m²), see Table. The reducton results from the fact that good thermal comfort n ths constellaton s gven only locally. For the same temporal and spatal comfort, no sgnfcant dfferences between a predomnantly convectve heat emsson system and one whch emts predomnantly long-wave radaton can be determned wthn the model accuracy. Dfferences n the heatng demand, whch are based on dfferences n local comfort cannot be valued as energy savngs. The radant temperature asymmetry s n case of the small celng mounted radant heater at the lmt of the thermal comfort range. The maxmum radant temperature asymmetry permtted accordng to ISO 7730 s 5 K an can be exceeded wth a small radant heater wth correspondngly hgh surface temperature. Consderng that, n case of a comfort ventlaton, the ar s further heated n the exhaust ar rooms (especally n the bathroom, where accordng to the standards a temperature of C should be mantaned), the dfference between predomnantly convectve heat emsson and radatve heat emsson s lkely to be further reduced n realty,.e. the calculated dfference wll be lower when related to the entre buldng. Table : Heatng Demand (HD) for dfferent szes and postons of the radant heater compared to pure convectve heatng, clmate of Innsbruck Case HD / [kwh/(m² a) Convectve 0. Floor Heatng (large) 0.7 Celng Heatng (large) Celng Heatng (small) 9. Wall Heatng (small) 9.6 Wth large radatve surfaces the possblty of provdng local comfort s lmted and the reducton of the ventlaton losses s (over-) compensated by ncreased transmsson losses. For an ncreased effectve ar exchange (.e. n the case of wndow ventlaton or an exhaust ar system) the dfference of the heatng demand would be theoretcally larger, however the heatng demand would then have an order of magntude such that an electrc heater as a sole heatng system cannot be recommended. It must be further noted that wthout heat recovery, due to cold ar drop and due to the hgh radant Excerpt from the Proceedngs of the 06 COMSOL Conference n Munch

6 temperature asymmetry, thermal comfort cannot be provded. A radant heatng system as a sole heatng system s generally not recommend wthout heat recovery. Wthout heat recovery, a convectve heatng part s requred to preheat the occasonally very cold fresh ar n order to avod cold ar drop and cold ar stratfcaton. 8. Dscusson The savngs potental s relatvely low wth respect to the heatng demand. However, not only the heatng demand, but the entre producton, transport and storage chan must be consdered n a comprehensve comparson,.e. eventually, the prmary energy consumpton of the whole buldng must be compared. It has to be taken nto account that heat storage and dstrbuton losses can occur wth conventonal heatng systems, f they are placed outsde the thermal envelope. Compared e.g. to an ar heat pump heatng system, whch generally has a relatvely low seasonal performance factor (SPF) of around to 3 for heatng due to low ar temperatures n wnter, the electrcty and prmary energy demand s hgher for an electrc radant heatng system even takng nto account all thermal losses. Assumng a specfc heatng demand of 5 kwh/(m² a), 0 % reducton of the heatng demand n the case of radant heatng system and 0 % dstrbuton and storage losses for the conventonal heatng system, an electrcty consumpton of 3.5 kwh/(m² a) results for the radant heatng system and 8.5 kwh/(m² a) for the heat pump heatng system wth a SPF of. Electrc radant heaters are wth regard to the nvestment a low-cost alternatve to conventonal heatng systems. Based on the lfe cycle cost, the prce of electrcty can have an mportant nfluence, especally t s subject to seasonal fluctuatons, whch mght be expected wth ncreasng share of renewables n the electrcty mx. The soluton for the hot water preparaton should be consdered n addton for a fnal comparson. 9. Summary and Conclusons For a meanngful comparson of the heatng demand of dfferent heat emsson systems, for the nvestgated varants the ndoor ar qualty and the thermal comfort (evaluated accordng to ISO 7730 wth the operatng temperature n the lvng area (generally n the center of the room) and the maxmum acceptable radaton temperature asymmetry as well as takng the draught rsk nto account) must be dentcal. In order to compute the dfferences of a heat emsson system, whch s predomnantly convectve or predomnantly radatve wth suffcent accuracy, a buldng model wth a detaled calculaton of the radaton exchange (between each of the surroundng areas, as well as between the surroundng surfaces and a sphere that s used for calculatng the operatve temperature) s requred. Wth such a model, these effects can be fgured out more precsely than wth a two-star or star node model, as usually used for buldng smulatons. The assumpton of an deal mxng of ar s acceptable n rooms wth very good nsulaton level and mechancal ventlaton wth heat recovery, however, t does not apply n case of radatve celng and/or ventlaton wthout heat recovery. A computatonal flow smulaton (CFD) for determnng the temperature stratfcaton would be requred addtonally for a more accurate analyss. For the same temporal and spatal thermal comfort, wthn the model accuracy no sgnfcant dfferences n the heatng demand can be obtaned between a heat emsson whch s predomnantly convectve and one whch s predomnately radatve. A numercally or expermentally determned reducton of the heatng demand, whch results from ether a reducton of ndoor ar qualty or of the thermal comfort, cannot be called a reducton n the strct sense (.e. n the sense of a better effcency of the heat emsson system n the same way as a reducton of the heatng demand by reducng the ar exchange cannot be accounted for energy savngs, but represents a deteroraton of ndoor ar qualty or energy savngs through temporary heatng or local heatng s not energy savng but a temporal or spatal reducton of the thermal comfort). If comfort s only defned for the occuped space,.e. traffc area (n the same way as n case of ventlaton on demand ndoor ar qualty s defned only durng presence.e. there s no loss of comfort wth regard to the temporal and local presence of the user), a low energy savng can be acheved wthout loss of comfort (.e. wth local Excerpt from the Proceedngs of the 06 COMSOL Conference n Munch

7 comfort). It must be noted that the potental to create thermal comfort only locally s greater for small (and consequently hot) areas whle however, the radant temperature asymmetry n ths case can even exceed the lmt defned n ISO Careful plannng and proper szng of the radatve heater s essental. A precse temporal and spatal control of the radant heater s also crucal to acheve good thermal comfort. A radant heater as a sole heatng system s generally not recommend wthout heat recovery. A convectve heatng part s requred to preheat the occasonally very cold ar n order to avod cold ar drop and cold ar stratfcaton. Not only the heatng demand, but the entre producton, transport and storage chan must be consdered n a comprehensve assessment. In contrast to a central heatng system there are no storage and dstrbuton losses n case of an electrc radant heatng system. Eventually, the prmary energy consumpton of the whole buldng needs to be compared. The techncal soluton for domestc hot water preparaton has to be consdered for that, too. 9. Outlook Especally for deep energy renovaton of buldngs (e.g. accordng to the EnerPHt standard [8, 9]) the radant heatng can represent an nterestng soluton n combnaton wth ar heatng (e.g. exhaust ar HP or splt unt) for room-wse control (nstead of an electrcal reheatng of the ar), n partcular f there s no (unform) heat dstrbuton and emsson nfrastructure. 9 Acknowledgements IFI Insttut für Infrarotwärme GmbH ntated ths work. The authors thank IFI Insttut für Infrarotwärme GmbH for ths ntatve and for ther support. For part of ths work fnancal support was provded by the Austran research fundng assocaton (FFG) under the scope of Innovatonscheck Plus. 0. References [] J. Kurntsk (Ed.), Cost Optmal and Nearly Zero-Energy Buldngs (nzeb) Defntons, Calculaton Prncples and Case Studes, Sprnger (03) [] W. Fest, Passvhaus - de langlebge Lösung, Prof. Dr. Wolfgang Fest, PHI, 0th Internatonal Passve House Conference, Darmstadt (06) [3] Felder Anton, Untersuchungen zum Coanda- Effekt-möglche Anwendung m Baungeneurwesen. Dss., TU München 993. [] EPBD: /energy-effcency/buldngs (0) [5] ISO 7730:005, Ergonomcs of the thermal envronment - Analytcal determnaton and nterpretaton of thermal comfort usng calculaton of the PMV and PPD ndces and local thermal comfort crtera, 005 [6] ASHRAE 55: Standard Thermal Envronmental Condtons for Human Occupancy [7] Glück Bernd (99). Zulässge Strahlungstemperatur-Asymmetre, Gesundhetsngeneur.5. Jg., H , 99 [8] t/0_kompetenzbereche/0_smulaton/0_ gebaeudesmulaton/0_gebaeudesmulaton.htm [9] [0] EN ISO 3790: Energy Performance of Buldngs: Calculaton of energy Use for Space Heatng and Coolng, (008) [] [] Crawley, Drury B., Jon W. Hand, Mchael Kummert, and Brent T. Grffth, Contrastng the Capabltes of Buldng Energy Performance Smulaton Programs, IBPSA 005 [3] M. G. Daves, Buldng Heat Transfer, Wley (00) [] Awb, HB and Hatton, A (999): Natural convecton from heated room surfaces, Energy and Buldngs, 30,33-. [5] Baehr Hans Deter, Stephan Karl, Wärmeund Stoffübertragung, 7. Auflage, Sprnger, DOI 0.007/ , p. 683 ff. (00) [6] VDI Heat Atlas, Sprnger ISBN (00) [7] exchange/566-vew-factors [8] Passve House: [9] EnerPHt: /03_certfcaton/ 0_certfcaton_buldngs/ 0_enerpht/0_enerpht.htm Excerpt from the Proceedngs of the 06 COMSOL Conference n Munch