Numerical model of a solar DHW including PCM media in the solar collector

Transcription

1 Numercal model of a solar DHW ncludng PCM meda n the solar collector Dder Hallot [1],[2], Franços Nepveu [1], Vncent Goetz [1], Xaver Py [1], Mohamed Benabdelkarm [2] 1. PROMES CNRS UPR8521 : PROcess, Materals and Solar Energy Laboratory, Unversté de Perpgnan Va Domta, Rambla de la Thermodynamque Tecnosud Perpgnan, France Contact: dder.hallot@unv-perp.fr 2. Sauner Duval Eau Chaude Chauffage Industre, 17 rue de la Pette Baratte, BP Nantes Cedex 03, France ABSTRACT In ths work we propose to mplement a tradtonal domestc hot water (DHW) sytems wth an ntegrated collector storage (ICS) type collector ncludng phase change materals (PCM). Such knds of collectors were recently developed, buld, and tested n our laboratory. Expermental results were successfully compared to numercal values estmated wth a dynamc smulaton model [Hallot, 2008]. Then a DHW system model has been establshed and annual smulatons were carred out wth measured envronmental condtons (Solar radaton, ambent temperature) and compared to an nstrumented commercal DHW runnng snce one year n our laboratory. Results are compared and allow us to valdate our model. Fnally the model s mplemented wth the ICS-PCM solar collector model. Results wth and wthout ths element are compared leadng to an estmaton of the potental mprovement of a DHW energetc performance thanks to the ICS-PCM. Keywords: ntegrated solar collector, thermal modelng, phase change materals, domestc hot water system. 1. INTRODUCTION Solar energy s an mportant alternatve energy source for present and future. In the constructon ndustry, DHW systems wth flat plate collectors are the most common systems, due to thers low costs and smplctes. However these systems need a bg tank that many tmes s not easy to locate. PCM placed at the top of the hot water tank has been already proposed several tmes [Cabeza 2005, Mazman 2009] as a hgh energy densty storage meda to reduce tank volume. An evaluaton of the actual contrbuton of such system has been recently proposed [Talmastsky 2008] concludng that the addton of PCM nsde a storage tank does not ncrease the overall system effcency. The new approach developed n ths communcaton s to use the PCM drectly nsde the solar collector. These solar collectors have already been studed and modelng [Tarhan 2005, Alva 2006] but never coupled wth a tradtonal DHW system. An ICS solar collector wth a composte materal based on PCM and compressed expanded natural graphte (CENG) as storage meda has been recently buld and tested n our laboratory. A numercal model has been developed and successfully valdated by a comparson between expermental data and numercal smulatons. In ths communcaton we present a DHW system model developed wth a nodal method and valdated wth expermental data. Then we propose to mplement

2 ths DHW model wth the ICS-PCM solar collector model. Such system could present several advantages as the reducton n needed storage volume and the enhancement of the avalable effcency. Smulaton has been performed n dfferent confguratons. A frst estmaton of the potental mprovement of the whole system s then possble. 2. SIMULATION MODEL 2.1. Domestc Hot Water system A numercal model of a complete DHW has been developed under MATLAB envronment. The smulated DHW s composed of 2 solar collectors, a storage tank wth electrc resstance auxlary heater and a forced crculaton loop heat transfer flud wth a pump. A nodal method had been used to descrbe thermal behavour n the system. The DHW system s dvded n 20 nodes (8 for the forced crculaton loop: 5 n the tank and 3 for the heat transfer flud tube, 10 for the storage tank and 2 for the water nlet and outlet) as presented n fgure 1. Thermal loses ST10 Wout Data (t): TW n (t), W user (t), T ext (t), GHI(t) Temperature ntalzaton at t=0, j=0 Thermal exchange t=t+dt Data (t+dt) Flow rate Pump/auxlary start T t+dt =T t Abs HTF2 HTF3 Ex5 ST5 Ex3 HTF1 Ex1 ST1 Wn Fgure 1: Node defnton n the DHW model Exchange coeffcent (t+dt) A and B Matrx A -1 Calculaton [T ] t+dt =[A ] -1.[B ] Stratfcaton algorthm Solar collector algorthm No T t+dt -T t <0.001? No t=t fnal? Yes Yes Savng Fgure 2: Developed algorthm The energy balances n mono dmensonal form s: δq + Cp ( (T m& n n ) (Toutm& out )) = ( ρ Cp ) V. For each of the 20 nodes the flow rate, heat transfers and nlet, outlet temperatures are determned and a system of 20 equatons s accomplshed. A fully mplct method s used to solve the frst order dfferental equaton. Contrary to explct method, the fully mplct method avods dvergence when usng mportant tme step smulaton. In a numercal form, the varaton of the temperature wth the tme (Eq.2) could be wrtten as: T j+ 1 j+ 1 t+ dt = dt T j And the system of 20 equatons developed from equaton 2 n a matrx form s wrtten: j 1 [ A ][.T] = [ B] dt dt Eq.1 Eq.2 + Eq.3 Consequently the temperature at tme j+1 s drectly calculated from the nverse matrx [A ] -1. j+ 1 1 [ T ] [ A].[ B ] = Eq.4

3 Once, temperatures calculate a reverson-elmnaton mxng algorthm s used to smulate the stratfcaton n the storage tank. Ths algorthm conssts n a thermal mx of some storage tank nodes to obtan a temperature correcton n order to have at each tme step a postve gradent from the bottom to the top of the tank. The solar collector algorthm s a 4 nodes teratve loop contanng factors n conducton, convecton and radaton takng place n the solar panel. Ths model s not explaned n ths communcaton as t has been prevously developed and valdated [Hallot, 2008]. The pump and auxlary heater start up s calculated from temperature at tme step j. The auxlary electrcal heatng s actvated when the temperature n node ST8 falls below 60 C and stops when t exceeds 65 C. The pump s actvated when the dfference between the absorber and the ST1 node temperature exceeds the crtera don wth: don= 0.16( TST 1 20 ) + 9 Eq.5 A scheme of the system resoluton s presented n fgure Model Valdaton The model valdaton has been performed by comparng numercal smulatons wth the expermental data of a commercal DHW system tested for one year n the laboratory and provded by Vallant Group. The DHW system s composed of two 2.02 m 2 aperture flat plate solar collector (η 0 =0.79, a 1 =3.78 W.m -2.K -1, a 2 =0.015 W.m -2.K -2 ), a 256 lters stratfed storage tank and a 2000 kw power electrc resstance auxlary heater. A user load profle was used to smulate a famly utlzaton of the DHW and presented fgure 3 as profle 1. An electro-valve placed at the water outlet allows drvng user consumpton. Others major system parameters are presented n table 1. Daly water consumpton profle (l) Tme (h) Fgure 3: End-user daly load profle 1 (grey) and 2 (hatched) Symbol Value α Abs 0.95 ε Abs 0.05 λ Ins W.m -1.K -1 eins 0.04 m DSt 0.5 m LSt m KSt 3.23 W.K -1 Table 1: Majors system desgned parameters A network of thermocouples s placed at the collector nlet, outlet and absorber surface, n the solar tank and at the water nlet and outlet. Several probes record the auxlary electrcal heatng and the pump start-up and also the heat transfer flud flow rates. Global ncdent radatons are followed by a pyranometer system placed n a plan parallel to the solar collector. Data acquston wth a lab Vew nterface allows us to treat and record data and drvng the electro-valve.

4 Boundary condtons for the smulatons are: the exteror temperature, the water nlet temperature, the water user consumpton and the global ncdent radaton. Smulatons have been performed wth boundary condtons from year 2008 except for months July and August (year 2007). The solar fracton and the solar effcency are defned as the amount of energy provded by the solar collector respectvely dvded by the total energy requred and the solar energy receved n the solar collector aperture. Comparson between the expermental and numercal value of solar coverage, solar effcency and collector effcency for these months are presented n fgure a) b) Solar Fracton (%) Solar Effcency (%) Jan Mar May Jul Sep Nov Month 0 Jan Mar May Jul Sep Nov Month Fgure 4: Expermental(hatched) and numercal(black) data comparson: solar fracton (a) and solar effcency (b) Consderng the solar fracton, a good correlaton between expermental and numercal results s observed as the average relatve error s 0.35 % for all the year. The maxmum errors are due to the wnter month. The same observaton can be done regardng the solar effcency and the average relatve error s hgher (15.15%) but stll acceptable DHW coupled wth an Integrated Collector Storage (ICS) As explan n paragraph 2.1. an algorthm for a solar collector has been prevously valdated n a prevous communcaton. In the same manner, an algorthm for the ICS has been prevously developed. The ICS s composed of CENG plate flled wth paraffn composte and placed under a conventonal solar absorber (fgure 5.a). The storage meda s fxed wth a copolymer envelope confnng the molten PCM. Composte materal s dvded n fve volumes correspondng to fve nodes (fgure 5.b). The frst node T c1 represents the composte layer just placed behnd the absorber and the last node T c5 the composte layer on the back. The dfferental equaton for the frst node s gven by: dtc1 λc.s C mc1cpc1 = hc / AbsSC (TAbs TC1 ) + (TC 2 TC 1 ) dt e C1 Eq.6

5 For the central node: dtc( ) λc.s C λc.s C m C( ) CpC( ) =.(TC( + 1 ) TC( ) ) +.(TC( 1 ) TC( ) ) dt e e C( ) And for the fnal node n contact wth the polymerc envelope: dtc5 λc.s C mc 5CpC5 = (TC( 1 ) TC5 ) + hc / PolySC(TPoly TC 5 ) dt e C5 C( ) Eq.7 Eq.8 a) G b) Absorber Transparent glass cover (T g ) Ar layer Absorber (T abs ) GNE/PCM Composte T f/ Heat transfer flud (T f ) Composte materal (T c ) T f/o T c1 T c2 T c3 20 Polymer 1080 Polymer envelope (T poly ) Insulaton T c4 T c5 590 Fgure 5: Schematc presentaton of the ICS/PCM system Exteror (T amb ) The effectve heat capacty Cp c of the PCM takes nto account ts latent heat (soldfcaton/fuson) through the ntegraton of an effectve functon (Cp=f(T)) defned by a prelmnary calormetrc analyss of the materal. The PCM uses n the smulaton s a paraffn/gne composte type wth a meltng pont of 70 C, a 910 kg.m -3 denstes a mass enthalpy of 170 kj.kg -1 and a conductvty of 4 W.m -1.K RESULTS AND DISCUSSIONS Smulatons of the DHW system coupled wth the ICS had been performed wth varous combnatons of system parameters and boundary condtons ncludng: - Meteorologcal boundares: a wnter and a summer month (January 2008 and August 2007) - Water user consumpton: once wth a large amount of water dps nto the storage tank on the mornng (fgure 3, profle1), the other on the evenng (fgure 3, profle 2). - Amount of PCM composte n the ICS: 36, 73 and 109 kg (correspondng to 1, 2 and 3 cm wdth under the absorber). - Storage tank volume: 250, 200, 150 and 100L For each set of parameters the numercal solar fracton s calculated and presented n the fgure below for the summer month.

6 76 a) 80 b) Solar fracton (%) Solar fracton (%) PCM wdth (cm) PCM wdth (cm) Fgure 5: Solar fracton of the DHW system coupled wth a ICS flled wth varous amount of PCM durng a summer month for dfferent storage tank volume : 250 ( ), 200( ) 150 ( ) and 100L ( ) (a): user consumpton profle 1, (b): profle 2 Fgure 4 shows that the gan n solar fracton to the end user due to the addton of PCM n the solar collector s negatve for a storage tank wth a volume superor to 150L. Decreasng the storage tank volume leads to a sgnfcant ncrease of the solar fracton for summer month. Ths observaton s partcularly true regardng a 100L storage tank and a water user consumpton focused on the evenng. In ths case, the 100L DHW system coupled wth an ICS flled wth 2cm wdth PCM has the same solar fracton as the 150L DHW system wthout PCM. The reducton of the storage tank volume and the transfer of the storage volume from the storage tank to the collector, researched n ths work, are here realzed. Same smulatons have been done for a wnter month and are presented fgure a) 52 b) Solar fracton (%) 44 Solar fracton (%) PCM wdth (cm) PCM wdth (cm) Fgure 6: Solar fracton of the DHW system coupled wth a ICS flled wth varous amount of PCM durng a wnter month for dfferent storage tank volume : 250 ( ), 200( ) 150 ( ) and 100L ( ) (a): user consumpton profle 1, (b): profle 2

7 In ths case whatever the storage tank volume the solar fracton decrease wth the nserton of PCM n the solar collector. Another observaton could be done concernng the storage tank volume. Ths study underlne the oversze ndustral solar tank overszed (250L). Indeed durng wnter month, the numercal results from the DHW contanng a 250L and the 200L storage tank have the same solar fracton. 4. CONCLUSION AND PROSPECTS The thermal modelng of a DWH system was carred out and valdated wth expermental data. Ths DHW model had been coupled wth a PCM based solar ICS and numercal smulatons of the whole system had been done. Mans observatons are: - Solar fracton decreases by PCM addton n the solar collector durng the smulated wnter month - Solar fracton ncreases durng summer month f PCM s added to the collector of a DWH system n the case of a solar tank volume nferor to 150L Results from a prmarly work on a PCM based solar ICS combned wth a tradtonal solar tank had been ntroduced. The model developed s a precous tool n order to optmze the whole system. Next work wll focus on the smulaton of a PCM based ICS wth dfferent: knd of phase change materal, solar collector geometry and system desgn.

8 NOMENCLATURE Cp Specfc heat [kj/kg K] ε Emssvty don Regulaton crtera λ Thermal conductvty [W/m K] D Dameter ρ Densty [kg/m -3 ] h Heat transfert coeffcent [W/m 2 K] K Tank heat loss coeffcent [Wh/l K days] Subscrpt L Length Abs Absorber m Mass flow [kg/s] C Composte Q Thermal power [W] Node number t Tme [s] n Inlet T Temperature [K] Ins Insulaton V Volume [m 3 ] out Outlet Poly Polymerc envelope Greek symbols j Tme step number α Absorbance St Storage tank ACKNOWLEDGMENTS The authors wsh to express ther apprecaton to the Sauner Duval ndustry part of Vallant Group and the French Government (through the ANRT) for fnancal fundng. REFERENCES Alva S., Gonzales J., Dukhan N., (2006). Intal analyss of PCM ntegrated solar collecors, Journal of Solar Energy Engneerng, Vol. 128, pp Cabeza L., Ibanez M., Solé C., Roca J., Nogués M. (2006). Expermentaton wth a water tank ncludng a PCM module, Solar Energy Materals and Solar Cells, Vol.90, pp Hallot D., Py X, Goetz V., Benabdelkarm M. (2008). Numercal model of a solar DHW ncludng PCM meda, Proceedng of Eurosun08. Mazman M., Cabeza L., Mehlng H., Nogues M., Evlga H, Paksoy H., (2009). Utlzaton of phase change materals n solar domestc hot water systems, Renewable energy Vol. 34, pp Reddy K.S., (2007). Thermal modelng of PCM-based solar ntegrated collector storage water heatng system,, Journal of Solar Energy Engneerng, Vol. 129, pp Talmatsky E., Krbus A.(2008). PCM storage for solar DHW: An unfulflled promse?, Solar Energy. Vol 82. pp Tarhan S., Sar A., Yardm M., (2006). Temperature dstrbutons n trapezodal bult n storage solar water heater wth/wthout phase change materal, Energy converson and management, Vol. 47, pp