Simulation of a solar domestic water heating system

Transcription

1 Avalable onlne at Energy Proceda 6 (11) MEDGREEN 11-LB Smulaton of a solar domestc water heatng system I.ZEGHIB a*, A.CHAKER Laboratore Physque Energétque, Unversté Mentour Constantne 25000, Algera Abstract Ths paper shows the modellng of a domestc solar water heatng nstallaton. The results of smulatons performed on daly bass for a solar system (collector wth surface of 2 m² and a storage tank of 0 ltres), operated n Constantne (Algera), whch provdes hot water for heatng. The nstallaton conssts n a solar flat collector, a water storage tank, a source of auxlary energy and radators. We analyse more accurately the nfluence of the thermosphon-flow rate and consequently the stratfcaton degree of the tank on the water heatng system performances. The nterest of ths study resdes n the approach used to model the tank and n the analyss of the number of the nodes used on the ganed energy. 11 Publshed by Elsever Ltd. Open access under CC BY-NC-ND lcense. Keywords: Solar collector; Stratfed tank; Flow rate; Modelng; thermosphon 1. Introducton Solar water heatng systems have reached techncal maturty and are used n many countres. After the frst ol crss n 1973, the strateges used by ndustralsed and developng countres to reduce ther ol dependence have been numerous. A dversfcaton of energy mport, a structural change of the large domestc product (ndustral development of actvtes usng a low energy expendture) or an ncrease of the natonal supply have been the essental measures taken by the countres wth varous degree of mportance[1]. One of the most classcal ways to use the solar energy s makng domestc hot water. Solar systems for DHW producton should be optmally desgned and operated. Ths way, the energy effectveness of these systems are often nvestgated, by usng experments or through modellng and smulatons. Ths paper * Correspondng author. Tel.: ; fax: E-mal address:mta75@yahoo.fr Publshed by Elsever Ltd. do:.16/j.egypro Open access under CC BY-NC-ND lcense.

2 I.ZEGHIB and A.CHAKER / Energy Proceda 6 (11) shows the results of the computer smulatons carred out n order to nvestgate the effectveness of a partcular type of the solar system. Such a system should consst of two man elements as solar collector and a storage tank. The mathematcal model takes nto account daly varatons of ambent temperature and solar radaton. Ths mathematcal model s used to develop specfc smulaton software, gve the storage temperature and collector temperature we analyse the nfluence of the thermosphon flow and consequently the stratfcaton of the tank. Nomenclature Ac area of solar collector (m²) C p specfc heat of water ( J/kg K ) d dameter of ppe (m) f 2, f 1 outlet and nlet of the collector, respectvely L ct length connectng tubes (m) K thermal conductvty of materal (W/m K) g acceleraton of gravty (m/s²) It solar rradaton upon horzontal surface, (W/m 2 ) water mass flow rate of the tank nlet (kg/s) m h m l N t T N c mass flow rate of hot water load from the tank (kg/s) number of stratfed layer tme (s) temperature (K) number of tubes n the collector Q u heat transfer coeffcent between ar and collector surface(w/m² K) Greek symbols ρ densty of the flud, (kg/ m ) 3 ν η c knematc vscosty (m²/s) collector effcency θ nclnaton angle of collector ( ) Subscrpts th segment of water n tank,solar collector c crculatng water s tank

3 294 I.ZEGHIB and A.CHAKER / Energy Proceda 6 (11) a ambent 2. Descrpton of the System A schematc dagram of the solar system modeled s shown n Fg. 1. It conssts of a flat plate solar collector, a water-storage tank, a source of auxlary energy [2]. The crculatng water from the collector t gves ts heat to the storage tank water and then returns to the solar collector where t s heated agan by solar energy. An electrc resstance heater s used for auxlary heatng when the temperature of the water n the storage tank s lower than 55ºC, before dstrbutng t n the buldng (space to be heated) usng a radators heatng. Tank Electrc heater Radator Solar collector Buldng Fg. 1. Schematc dagram of solar heatng system- type thermosphon 3. Theoretcal analyss: Equatons and resoluton The mathematcal smulaton of a solar heatng system operaton s complex and not easy to explot drectly. Indeed, the analytcal equatons that characterze the heat and mass transfers n the collector that we use and that one fnds n the works of referenced authors [1,2], are dffcult to solve wthout sgnfcant smplfed assumptons. We present a model of fnte dfferences whch ncludes the essental thermal transfers. Ths model s composed of a seral assemblng of many elementary models. Each model s based on a nodal dscretsaton of a collector secton and of the storage crcut Solar collector The smulaton s done by dvdng the transversal secton collector nto sx sothermal regons: the glass cover, the ar layer, the top half of the absorber, the water layer, the bottom half of the absorber and the nsulaton, therefore, we propose to dvdng the length collector nto ten sectons n order to take nto account the temperature dstrbuton of the workng flud nsde the collector.

4 I.ZEGHIB and A.CHAKER / Energy Proceda 6 (11) Global equatons [3] ( T T ) + φ m cp ( dt / dt) = U, j j (1) j The thermal performance of the solar collector was nvestgated, and the effcency of the collector. Note that the effcency of the η c s defned as [4]: η (2) c = Q U / It Ac 3.2. Storage tank The heat storage water tank could be consdered as a stratfed water tank and could be modeled by dvdng the tank nto N nodes (sectons), wth energy balances wrtten for each secton of the tank. The energy equaton took nto account the energy gan from the solar collectors, energy lost to surroundngs and energy consumed by the heatng system. The result was a set of N dfferental equatons that could be solved for the temperatures of the N nodes as a functon of tme. The smulaton model of the heat storage water tank s shown n fg 2[5]. Fg. 2. nodes stratfed lqud storage tank

5 296 I.ZEGHIB and A.CHAKER / Energy Proceda 6 (11) B c s a collector control functon, whch can be defned to dentfy whch node receves water from the collectors. [5, 6]: 1 f Ts, 1 Tc Ts, Bc = 0 other (3) B l s a load return control functon, whch can be denoted to dentfy whch node receves water returnng from the floor heatng system. [7] 1 f Ts, TL Ts, + 1 B l = 0 other (4) The net flow between nodes can be ether up or down dependng upon the magntudes of the collector and load. Flow rates and the values of the two control functons at any partcular nstant. It s convenent to defne a mxed flow rate that represents the net flow nto node from node 1, excludng the effects of flow, f any, drectly nto the node from load. 1 N γ = j mh Bc ml B l j= 1 j= + 1 (5) an energy balance on node can be expressed as [7,8]: m cp, ( dts, / dt) = U A ( Ta Ts, ) + Bc mh cp ( Tc Ts, ) + B l ml cp ( TL Ts, ) (6) γ cp ( Ts, Ts, + 1) + γ cp ( Ts, 1 Ts, ) f γ 0 f γ The thermosphon loop The governng equaton for the momentum balance equaton of the natural crculaton loop s [9, ]: ( 8k mc / ρ π d ) + (1 + ϕ).(128ν Lctmc / π Ncd ) g ρ β sn( θ ).( Lct / 2).( T f 2 T f 1) = 0 (7)

6 I.ZEGHIB and A.CHAKER / Energy Proceda 6 (11) Ths quadratc equaton n n the thermosphon loop. mc allows calculaton of the nstantaneous theoretcal flud mass flow rate 4. Results and dscusson A detaled smulaton of the whole system was carred out n order to study the operaton and the behavour of water heatng System and to smulate the durnal temperature varatons of the storage flud and energy fluxes exchanged of each part n the solar heatng system: collectng, storage and dstrbuton. In the present study the smulaton s carred out for the calculaton, the month of February was chosen, whch s consdered as the coldest month accordng to the weather data of Constantne. The performance of the systems was modeled by a smulaton program wrtten n Fortran programmng language developed at the Unversty of Constantne. The program calculates the solar gan for the specfed system, based on the radaton, the ambent temperature, the lattude, the parameters specfyng the solar collector system, the volume of storage tank, the total energy demand of heat water and ther daly load profles. The tme step for the calculaton s set to two seconds Table1: Input parameters of the smulaton model Desgn parameters Data Collectors surface 2m² Glass 1. Thckness m 2. Mass densty 2700 Kg m Specfc heat 840 J.k -1 m -1 Plates 1. Thckness m 2. Mass densty 8900 Kg m Thermal conductvty 300 W.k -1 m -1 Insulaton 1. Thckness 0.02 m 2.Mass densty 24 Kg m -3 3.Specfc heat 919 J.k -1 m -1 Storage tank Materal galvanzed ron 1. Heght 1m 2. Dameter 0.5m 3. Capacty 0l Load 1. mass flow rate m l kg/s 2. nlet temperature T au 55 C 3. outlet temperature T L 45 C

7 298 I.ZEGHIB and A.CHAKER / Energy Proceda 6 (11) Fg. 3 show the nfluence of the number of nodes on tank temperature calculated on one day of data. We modeled the tank usng respectvely 5, 15, 18, and 22 nodes correspondng to the orfces number of the manfold dffuser. Accordng to the number of nodes, the calculated performances are dfferent, n order to take nto account ths stratfcaton, We note that the modelng wth and 22 nodes conduces to the same results: so t seems to be not necessary to use more than nodes and so, no more than orfces, to study the behavour of ths solar domestc hot water. In the followng of ths artcle all the presented results wll be computed wth a twenty nodes model for the tank and so wth a manfold dffuser wth orfces Temperature ( C) 30 stratfed Tank- 5 nodes stratfed Tank- nodes stratfed Tank- 15 nodes stratfed Tank- nodes stratfed Tank- 22 nodes Tme (hours) 0 Fg. 3. Temperature n tank nodes Temperature( C) secton 1 secton 2 secton 3 secton 4 secton 5 secton 6 secton 7 secton 8 secton 9 secton Tme(hours) 5 Fg. 4. Temperature profle n the collector

8 I.ZEGHIB and A.CHAKER / Energy Proceda 6 (11) In what follows, all the results presented wll be calculated wth a model of twenty nodes for the tank. We see n Fg. 4 the temperature profle n the collector computed from smulatons. We note n Fg. 5 the temperature profles n the tank for a wnter day, the fnal average temperatures n the storage tank 45 C,degree of stratfcaton max (Ts,1 Ts,) = 25 C, the water temperatures of the sectons dstrbuted n a way ncreasng of bottom to the top of the tank. Heght(m) ,00 0,95 0,90 0,85 0,80 0,75 0,70 0,65 0,60 0,55 0,50 0,45 0,40 0,35 0,30 0,25 0, 0,15 0, Temperature( C) node Fg. 5. Temperature profle n the tank The storage flud temperature and solar radaton for two days s shown n Fg 6, t s observed that the maxmum temperature of the average tank s 48 C, startng from an ntal temperature of 17 C for fresh water n the tank at 7.00 a.m. Three phases of heatng-up perods can be observed. From 7.00 to 9.00 a.m., the water n the tank hardly warms up, as redstrbuton of temperature wthn the tank s takng Temperature( C) nodes 2 nodes 4 nodes 6 nodes 8 nodes nodes 12 nodes 14 nodes 16 nodes 18 nodes radaton radaton (W/m²) Tme (hours) FIg.6. Evoluton of the storage flud temperature and solar radaton

9 300 I.ZEGHIB and A.CHAKER / Energy Proceda 6 (11) place. After ths perod, there s a very rapd ncrease n the rate of heat collecton, the water n the storage tank heats up very fast and ncreases n temperatures untl, about 4 p.m. After ths tme there s a redstrbuton of temperature, whereas the maxmum value of solar flux durng the day s about 800 W/m². Effcency(%) 1,0 0,012 0,9 0,8 Effcency flow rate 0,0 0,008 0,7 0,006 0,004 0,6 0,002 0,5 0,000 0,4-0,002-0,004 0,3-0,006 0,2-0,008 0,1-0,0 0,0-0,012-0, Tme(hours) Flow rate(kg/s) Fg.7. Evoluton of the effcency and flow rate The varaton of the flow thermosphon and effcency of the collector for two days s llustrated by fg 7, at about 8:30 a.m., T c T s there s no flow n the collector, T c ncreases rapdly untl the dfference ( Tc Ts ) reaches the preset actvaton level the controller. The collector loop flow s controlled by a controller, Flow s turned on when collector temperature s hgher than the temperature of the tank the system s movng (natural crculaton), n the contrary case, the system stops and the flow and effcency s equal to 0. Concluson The present model can be vewed as a new smulaton model, whch can be used for parametrc analyss of domestc water heatng systems. The theoretcal model presented can be an effcent tool to predct and desgn solar systems operatng under thermosphon prncple flow condtons. The stratfed storage tank has an advantage of obtanng hgher heat energy output when compared to a conventonal fully mxed hot water storage tank. In ths study, a ult-node model wth varable nlets was chosen to analyse the temperature dstrbuton n storage tanks. Consequently there s better stratfcaton n the tank whch mproves the effcency of both the auxlary heater and the solar collectors. Nevertheless, the presented results are theoretcal and explanatory, we must n future work develop ths system and verfy all these smulaton results.

10 I.ZEGHIB and A.CHAKER / Energy Proceda 6 (11) References [1] C.crstofar,G.Notto,,P,Pogg Modellng and Performance of a copolymer Solar Water Heatng Collector Solar Energy,Vol 72, N 2, 02, pp [2] Runsheng Tang,Yanbn Cheng Maogang Wu Expermental and modelng studes on thermosphon domestc solar water heaters wth flat-plate collectors at clear nghts Energy Converson and Management,Vol 42, 03, pp [3] Alreza Hobb,Kamran Sddqu Optmal desgn of a forced crculaton solar water heatng system for a resdental unt n col clmate usng TRNSYS, Solar Energy,Vol 82, 09, pp [4] A.Zerrouk,A.Bouméden, K.Bouhadef The natural crculaton solar water heater model wth lnear temperature dstrbuton Renewable Energy,Vol 26, 02, pp [5] P.M.E.koff,H.Y.Andoh, P.Gbaha Theoretcal and expermental study of solar water heater wth nternal exchanger usng thermosphon system Energy Converson and Mangement, Vol 25,, pp [6] X.Q.Zha,J.R.Yang,R.Z. Wang, Desgn and performance of the solar- powered floor heatng system n a green buldng Renewable Energy,Vol 34, 09, pp [7] C.Crstofar,G.Notton Influence of the flow rate and the tank stratfcaton degree on the performances of a solar flat-plate collector Internatonal Journal of Thermal Scences,Vol 42, 03, pp [8] J P.Chyng,C.p.Lee Performance analyss of a solar asssted heat pump water heater Solar Energy,Vol 74,03, pp [9] H.M.S Hussen Transent nvestgaton of a tow phase closed thermosyphon flat plate solar water heater Energy Converson and Management,Vol 43, 02, pp [] B.J.Huang.J.H. Wang J.H A fast response heat pump water heater usng thermostat made from shape memory Appled Thermal Engneerng,Vol 29, 09, pp