ECONOMIC VIABILITY OF UNDER FLOOR HEATING SYSTEM: A CASE STUDY IN BEIRUT CLIMATE

Transcription

1 ECONOMIC VIABILITY OF UNDER FLOOR HEATING SYSTEM: A CASE STUDY IN BEIRUT CLIMATE K. Ghal Department o Mechancal Engneerng, Berut Arab Unversty, Berut, Lebanon ABSTRACT: Ths paper explores the economc easblty o the underloor heatng system or the clmatc condtons o Berut. A case study o a typcal resdental room (5 m 2 ) s selected to compare ts heatng energy requrement when usng ether the conventonal convectve heatng system or the underloor heatng system at smlar comort and ndoor ar qualty condtons. Two mathematcal models are developed, a steady space thermal model to establsh the energy consumpton at the peak load and a transent smulaton model to nd the energy consumpton durng the wnter heatng season. In addton, the economc easblty o the underloor heatng system s assesd when ntegrated wth solar energy. Based on the steady space model, the calculated peak heatng load s reduced by 2% when the test space s heated by the underloor heatng system and a thermal comort level o PPD 8.3% s acheved or a loor temperature o 27. ºC. The smulaton results o the transent space model ndcates that the seasonal heatng energy consumpton s reduced by 8% and that the yearly energy savngs s $ or an on-o control strategy that mantans a PMV comort level greater than -.5. The pay back perod o the underloor heatng system s years or an ntal ncremental cost o $85. When ntegrated wth solar collector unts, the yearly energy savngs o the ntegrated system s ncreased to $35 and the pay back perod s years. Keywords: Underloor, Thermal comort, solar energy. INTRODUCTION Heatng or thermal comort can be acheved by: ) convectve heatng where the heatng load s ndrectly sastsed by heatng the space ar; 2) by radant heaters whch drectly satsy the radant heatng loads by the proper szng and nstallaton o the radant heaters and 3) by under loorheatng where the surace o the heated concrete transers the heat to the space by convecton and radaton. The desgn o radant and under loor heatng systems s not as drect as the case o the conventonal heatng system. The desgn gudelnes or szng and calculatng the energy consumpton o a orced ar heatng system s well establshed by Ashrae []. However, the desgn o radant and under loor heatng system have several added complextes that are not present n a conventonal system. These dcultes, whch nclude the thermal storage o the concrete slab and the combned radatve and convectve heat transer rom the slab surace, makes underloor heatng system dcult to model and not as popular as the orced heatng system. In recent years, consderable attenton has been gven to radant and underloor heatng systems as a method o heatng warehouses, schools, and resdental houses. Buckley [2] reported that radant heatng can reduce energy costs by 3% or more wth equal comort compared to convecton heatng. Strand et.al [3] developed a transent heat conducton model through the buldng walls to determne the radant system ecency and to compare the underloor heatng system to the conventonal convectve system and ound that the radant system s more energy ecent. Van Gerpen and Shapro [] ocused on the thermal storage o the slabs and analyzed the use o bured heatng elements at derent depth to sht some electrc power demand to o-peak hours. Whle Athents and Chen [5] developed control strateges to reduce operatonal cost o the radant heatng system and nvestgated the perormance o an electrc loor radant heatng system wth thermal storage. Also, Athents [6] presented a non-lnear nte derence numercal model to study the perormance o a loor heatng system wth hgh solar gan. In addton o havng the potental to be an energyecent alternatve to the orced heatng system, the underloor heatng s characterzed by mnmal ndoor ar crculaton compared to the convectve heatng. The underloor heatng system reles on natutal ar movement whereas the convectve heatng uses orced ar crculaton. The lower ar velocty ncreases the human comort and also reduces the conducton transmsson through exposed parttons and external walls. Also the underloor heatng s characterzed by havng a unorm temperature proles n heated spaces and homogenous temperature dstrbuton. The radant loor heatng has been ound to cause mnmal loor-tocelng temperature gradents [7]. In underloor heatng the warmth starts at the eet where t s mostly desred nstead o blowng hot ar rom ar outlets located at the celng level whch causes excess warmth at the head heght whch wll result n dscomort. The temperaure o the ar that satses thermal comort n underloor heatng s generally lower than the ar temperature o the conventonal convectve heatng system. The thermal comort at the lower ar temperature s acheved because o the hgher mean radant temperature as was ound by RE&PQJ, Vol., No.5, March 27

2 Ghal et.al. [8]. The ablty to mantan low ndoor ar temperature reduces heat loss by transmsson and by nltraton and could result n a better ndoor ar qualty at low energy cost. The underloor heatng system have ganed popularty n Europe because o the potental they can provde n creatng thermally comortable envronment and a better nternal ar qualty at lower energy consumpton. However such a heatng system s unpopular n Lebanon. Ths makes t very temptng to study the economc vablty o such a system n Berut especally when knowng that one thrd o the energy (electrcty) produced n Lebanon s spent on space heatng o resdences and commercal buldngs. Lebanon, n the absence o rch natural resources has to depend on mported ol or ts energy use. The contnung rse n energy demand, costs and the assocated envronmental polluton problems are causng ncreased emphass on the nvestgaton o potental energy ecent heatng systems. The man objectve o ths research s to explore the economc easblty o the under loorheatng system or the clmatc condtons o Lebanon. A case study o a typcal space n Berut s consdered. A comparson wll be presented o the annual energy consumpton and cost o the underloor heatng system as compared to that o the conventonal heatng system at smlar comort and ndoor ar qualty condtons. In addton, the econmc perormance o the underloor heatng system wll be assesd when ntegrated wth solar energy. 2. Feasblty o the Under-Floor Heatng System to a Test Case n Berut The test case consdered or the study s (m x 5m x 3m) space. The north wall has a sngle glazng wndow o area equal 7.5 m 2 wth an overall heat transer coecent, U g, o 5.8 W/m 2 k. The celng and loor are consdered nternal parttons. The overall heat transer coecent o the nsulated loor s.5 W/m 2 K whle that o the celng s 2.5 W/m 2 K. The vertcal walls are external suraces that are adjacent to the outsde ar wth an assumed overall heat transer coecent o U w o 3 W/m 2 K whch s typcal or Lebanese buldngs constructon materal. The conventonal orced convectve heatng system was smulated usng TRNSYS thermal sotware [9] or.75 ACH and ndoor desgn condton o 23 C and 5% relatve humdty. The smulaton was run rom the month o (November-March) to determne the heatng peak load Fg. and also to determne the monthly energy requrement or heatng Fg. 2. Heatng energy peak demand [watts] November December January February March Fg.: The monthly peak demand o the test case durng the heatng season or the conventonal system Heatng Energy Demand [GJ] November December January February March Fg.2: The monthly space energy demand durng the heatng season or the conventonal system The peak heat load s 25 W. It occurred on the 26 th o February. The calculated mean nternal space surace temperature s 7. C when the nternal ar temperature was controlled at 23 C. The resulted human thermal satsacton wth the thermal envronment at the peak was also calculated by TRNSYS. The predcted mean vote (PMV) s -.79 and the percentage o dssatsed people (PPD) s 8.3 %. To study the economc easblty o the under loor heatng system or the clmatc condtons o Berut, t s mportant to determne the energy requrement o ths heatng system at the peak wnter season condtons or equal PPD comort values obtaned rom the conventonal heatng system. Ths step s very mportant because t wll determne the economc vablty o such a system snce the captal cost and nstallaton o the underloor heatng system s more than that o the conventonal orced ar heatng system. In the ollowng, two mathematcal models wll be presented, a steady space thermal model to establsh the energy consumpton at the peak load and a transent smulaton model to nd the energy consumpton durng the wnter heatng season. A. Steady Space Thermal Model: The energy requrement or heatng the space at a specc thermal comort level s acheved as ollows: For a partcular surace temperature o the loor the nternal space surace temperatures and ar temperature are computed by the steady space thermal model whch wll be explaned n the next paragraph. The nternal surace temperature values are then used to determne the mean radant temperature, mrt. The resultant value o the mrt along wth the nternal ar temperature are used n Fanger model [] to determne the comort level o a sedentary human subject. I the obtaned PPD comort level s not equal to the specc requred value o comort, then the loor temperature s changed. Ths process s contnued untl convergence occurs and the comort level o PPD s equal to the requred value. Once the comort level s acheved the heat energy requrement can be calculated by the determnaton o the total heat loss rom the space. The ormulaton o the steady space thermal model s adapted rom Howell et.al [] model that was developed or szng radant heater panels. Each space surace ( walls, celng and wndow) s n radant exchange wth all other suraces and s n convectve exchange wth the ar n the room. The sum o these two heat lows q r and q cv, wll under steady RE&PQJ, Vol., No.5, March 27

3 state condtons equal to the conductve heat low through the surace: q r + q cv + q cd = () q r net radaton heat transer rom surace, W/m 2 q cv convectve heat transer, W/m 2 q cd conducton through the surace, W/m 2 The radant exchange rate (q r ) or each surace can be expressed as: q = εσ T ε σt F (2) r, j= A Aj q r, net radant heat transerred rom surace A,W/m 2 T absolute temperature o surace A, C σ Stean-Boltzman constant, 5.67 x -8 W/m 2 k F A-Aj angle actor rom surace to surace j ε emssvty o the surace A,.9 The angle actors are calculated rom algorthms avalable n Incropera and Dewtt [2] and the convectve heat transer s evaluated rom the ollowng equaton: q = h ( T T ) (3) cv, c, a q cv, convectve heat transer rom surace, W/m 2 A h c, convectve heat transer coecent, W/m 2 K T a nternal space ar temperature, C T surace A temperature, C The convectve heat transer coecents, h c,, s calculated rom correlaton rom the book o Incropera and Dewtt [2] and the conductve heat transer, q cd, per unt area, A, s gven by: q = C ( T T ) () cd, o C overall wall conductance rom nsde surace to the outsde ambent ar dependng on the wall constructon materal, W/m 2 K T o ambent ar temperature, C The above analyss results n sx coupled non-lnear equatons because o the radaton term wth seven unknown varables( sx unknown surace temperatures and one temperature or the space ar). Thereore, an addtonal energy balance equaton on the ar wthn the space wll be needed to solve or the unknown temperatures. The results o the steady state space s used to determne the peak heat load o the system by summng up the heat losses rom each surace and the nltraton load. B.Transent Space thermal Model: The evaluaton o the under loor heatng requres a detaled transent smulaton analyss o the system. The transent smulaton gves an estmaton o the energy consumpton o the desgned unerloor heatng system over a perod o tme to compare ts perormance wth the conventonal heatng system. In the transent analyss, the ambent condtons are not constant and are obtaned rom measured weather data les or a typcal day o each month or whch heatng s needed (November to March), Ghaddar et.al. [3]. The thermal storage o the wall cannot be gnored and the loor temperature cannot be consdered constant durng the smulaton perod. Thereore, the equatons o the steady space model have to be moded to nclude these eects. The space wall s assumed to be composed o one concrete 25 cm layer thckness and the heat transer across wall s one dmensonal and t s represented as ollows: ( k x Tw ( ρct ) = x t w ) K conductvty o each layer o wall, W/m C C s the thermal capactance o each layer, kj/ kg C ρ s the densty o each layer, Kg/m 3 The outer boundary o each wall exchanges heat wth outsde envronment by convecton and the nner surace exchanges heat wth the nsde space by convecton and radaton. Snce the loor s consdered a partton (.e t s adjacent to an ar condtoned space), a lumped temperature or the loor s assumed. The heat equlbrum or the loor can be wrtten as: dt U wt Awt ( Twa T ) qr qcv = m c dt (6) U wt overall heat transer coecent between lowng water and concrete, W/m 2 K A wt surace area o the embedded ppng system n contact wth the concrete, m 2 T wa average crculatng water temperature, C T average loor temperature, C m mass o the loor, Kg c heat capactance o the loor, kj/ kg C The smulaton or the transent model s perormed or an on-o control strategy whch s used to mantan a level o thermal comort greater than a PMV o -.5. Whenever, the estmated PMV s lower than -.5, the crculatng water s turned on to transer heat to the concrete loor. The mplct Cranck-Ncolson method s used n the wall temperature equatons and the senstvty o the results to the tme step and the grd sze o the wall was examned. A spatal grd sze o.5 mm or the external walls and a tme step o s are used. For each month o the heatng season, the (5) 2 RE&PQJ, Vol., No.5, March 27

4 smulatons are done over a perod o days to reach a convergent steady perodc soluton or a perod o 2 hours. The perodc soluton s obtaned or a typcal day o every month o the heatng season. The average heatng energy requrement o each month s estmated rom the typcal day energy consumpton. 3. Results and Dscussons A. Steady space thermal model results: Based on the steady space model, the temperature o the loor that acheves thermal comort level PPD o 8.3%, whch s equal to the value obtaned by the ar orced conventonal system, s equal to 27. C. The calculated peak heatng load s 337 Watts whch s a reducton o 2% o the peak load obtaned by the conventonal system or the same level o comort. The mean radant temperature o the underloor heatng system at the peak load s 22.5 C and the ar temperature s 2 C. The thermal comort level o PPD 8.3% s attaned at a lower temperature compared to that o the orced convectve system because o the hgher mean radant temperature. The reducton o the heatng load orgnates rom the reducton o the nltraton ar load. However, the cost eectveness cannot be assessed on the bass o the peak load but on the energy consumpton o the system or the entre heatng season. B. Transent space thermal model results: The underloor heatng ppng system that s used n the smulaton o the transent model has a dameter o 2 mm wth a thckness o 2 mm and a ppe thermal conductvty o.38 W/ m 2 K. It s located 5 mm below the surace loor concrete layer at a spacng dstance o 3 mm. The smulaton o the transent model requres the knowledge o the average temperature o the heatng water, T wa, and the overall heat transer coecent between the lowng water and concrete, U wt. The average temperature o the heatng water can be calculated rom the peak load usng the steady state model. U wt s related to the nternal resstance o the lowng water and the conductve resstance o the ppng system. The crculatng water low rate n the underloor heatng system, m wt, requred n determnng the nternal resstance o lowng water s calculated rom the steady space thermal model or a heatng water temperature derence o 5 C by the ollowng equaton: Qh m wt = (7) cwt (5) Q h peak heat load, W c wt specc heat o water, kj/ kg C The smulaton results o the transent space model ndcates the monthly heatng energy load o the underloor heatng system or the test case as shown n Fg. 3. Heatng energy Demand GJ. Fg.3: The monthly energy demand o the test case usng the under loor heatng system The maxmum heatng energy demand occurs n the month o February. A reducton n total energy demand o 8 % energy s attaned when underloor heatng replaces the conventonal heatng system whle satsyng comparable comort levels. The reducton n energy consumpton s only ndcatve snce t s lmted to the test case and to the chosen control strategy. A derent control strategy could have been used n the smulaton whch mght result n a better energy reducton. It s mportant to perorm an economc easblty analyss on the test case because the underloor heatng system has a hgher ntal cost. Ths s due to the cost and nstallment o the water ppng system. The ncremental ntal cost o the underloor heatng system s consdered or a value o $ 85 over the ntal cost o the conventonal system. The cost o other equpment s assumed to be the same or both systems such as the boler. On the other hand, the yearly heatng energy consumpton s reduced rom rom 3 GJ to 27.8 GJ or the underloor heatng system compared to the conventonal heatng system. The ol energy bll s assumed to be.5638 $/kg. The savng n the yearly energy bll s about $. Assumng a dscount rate o.8 and an nlaton rate o.5. Fgure shows the pay back perod o the underloor heatng system s about years. Le Cycle energy savngs $ November Decemeber January February March Years Fg. Le cycle savngs o the underloor heatng system C. Undeloor heatng ntegrated wth solar energy easblty results: Underloor heatng has the potental to be an energy ecent alternatve to the conventonal system when ted wth solar energy Snce moderate water temperatures s used n ts heatng system. The economc easblty o ntegratng the under loor wth solar energy s nvestgated or the Berut test case. The solar system s composed o sngle glazng lat-plate 3 RE&PQJ, Vol., No.5, March 27

5 collectors that stores solar energy n a water storage tank. Each unt has an eectve area o m 2. The transent perormance o the collector-tank system s smulated numercally usng the theory o Hottel and Whller presented by Due and Beckman [] durng the wnter heatng season. I the water temperature n the storage tank collector system s hgher than the water temperature leavng the underloor heatng, then the crculatng heatng water s assumed to pass through the storage tank, not; water s bypassed drectly nto the auxlary heater as shown n Fg. 5. The water pump o the solar collector turns whenever the temperature derence between the tank and the absorber plate exceeds C and shuts o when ths derence drops below.5 C. The smulaton o the solar collector tank system s perormed by usng the rst order Euler- Forward ntegraton scheme. A quas-steady-state system s assumed;.e. the varables, whle varyng rom hour to hour, are consdered constant durng every hour o the analyss. The ambent condtons are obtaned rom the measured weather les, Ghaddar [3]. Fg. 5 Integrated solar underloor heatng system The smulaton s perormed or a typcal day o every month o the heatng season to obtan energy contrbuton o the solar collector tank system. The ntegrated solar underloor heatng system energy requrement or the heatng season s reduced to 5.5 GJ and the yearly energy savngs s ncreased to $35. An economc assessment s perormed or a collector-tank ntal cost o $/m 2. The pay back perod or the ntegrated system s years.. Conclusons A transent and steady thermal space models are developed to nvestgate the economc easblty o underloor heatng system to a test case n Berut n comparson wth the conventonal heatng system. The comparson between the two systems s perormed under equal comort levels and ndoor ar qualty. The underloor heatng system reduces the seasonal heatng energy consumpton by 8% and results n yearly savngs o $. The pay back perod o the underloor heatng system s years. The ntegrated solar under loor heatng system ncreases the energy savngs to 35$ and the pay back perod o the ntegrated system s years or a collector-tank ntal cost o $/m 2 Reerences - Ashrae Handbook, 993. Fundamentals, Publshed by the Amercan Socety o Heatng, Rergeratng and Ar-Condtonng Engneers, Inc. 2- N.A. Buckley, Applcaton o radant heatng saves energy, Ashrae Transactons 96(2), R.K.Strand and C.O. Pedersen, Analytcal vercaton o heat source transer unctons, Frst Jont Conerence o Internatonal Smulaton Socetes, Zurch, Swtzerland, 99 - J.H Van Gerpen, 98, The desgn and analyss o slab heatng systems. M.Sc. Thess, Iowa State Unversty, Ames, Iowa. 5- A. K. Athents T.Y. Chen, Expermental and theoretcal nvestgaton o loor heatng wth thermal storage, Ashrae Transactons 99(), A. K. Athents, Numercal model o loor heatng system, Ashrae Transactons 99(), E. R. Ambrose, Progress report on o-peak electrc heatng, Ar condtonng Heatng and Ventlatng, Vol (58), July, pp. 5-56, K. Ghal, S. Chehade, and K. El-Khoury, Radant loor heatng: an opportunty or energy savngs, Internatonal conerence on thermal Engneerng: theory and applcatons, Berut, Lebanon, 2 9- TRNSYS, A transent smulaton program, verson 5, Solar Energy Laboratory, Unversty o Wsconsn-Madson, USA, 2. - Fanger, P.O Thermal comort. Robert E. Publshng Co., Malabar, Fl, USA. - R. Howell and S. Suryanarayana, Szng o radant heatng systems: part -celng Panels, Ashrae Transactons, vol. 96, part. pp , F.P. Incropera and D.P. Dewtt, 985. Fundamentals o heat and mass transer, second edton. John Wley and Sons. New York. 3- N. Ghaddar and A. Bsat, Energy conservaton o resdental buldngs n Berut, Internatonal Journal o energy Research. 32 (2) , J. A. Due and W. A. Beckman, 98. Solar Engneerng thermal processes. John Wley and Sons. RE&PQJ, Vol., No.5, March 27