V & M & NOMENCLATURE. c p

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1 NOMENCLATURE c p specfc heat capacty, J/gK C heat capacty, J/K d dameter, m f save fractonal energy savngs g gravty constant, m/s h storage heght, m M & mass flow rate, kg/s P power (of burner and el. pump) /W prob probablty Q energy (heat) / kwh T temperature, K UA heat transfer coeffcent*area, W/K V & volume flow rate, m³/s Greek α transfer coeffcent, 1/K ρ densty, kg/m 3 ϕ angle of the valve, ν τ ς η Indces aux b conv DHW dom Hx1 l m n out SH REFERENCES velocty, m/s tme constant of the expansble materal, s pressure drop coeffcent effcency auxlary energy of the solar system begn of the regulator temperature nterval of the valve conventonal sytem domestc hot water (system) domestc water heat exchanger, prmary cycle nr. of node, descrbng temperature layer heat losses max. nr. of nodes n the vertcal tube max. nr. of nodes n the heat exchanger outlet (temperature) storage water n the heat exchanger nodes space heatng water (system) Andersen E., Furbo, S. (1999). Thermal Destratfcaton n Small Standard Solar Tanks due to Mxng durng Tappng. In Proceedngs of ISES Solar Word Congress, Israel In Press. Dahm, J., Bales, Ch., Lorenz, K. (1998). Evaluaton of Storage Confguratons wth Internal Heat Exchangers, Solar Energy, Vol. 6, No. 6, pp Dchter E. (1999). Dusch- und Badeverhalten. Bercht zu ener Repräsentatvumfrage, Edgenösssche Drucksachen- und Materalzentrale, Bern. Dttrch A., Lnneberger B., Wegener W. (197). Theoren zur Bedarfsermttlung und Verfahren zur Lestungskennzechnung von Brauchwasser-Erwärmern. HLH 3, Nr.. Drück H. (1994) Weterentwcklung und Valderung des Modells für solare Warmwasserspecher 4Port für das Smulatonsprogr. TRNSYS, Dploma-Thess, ITW, Stuttgart. Drück, H., Hahne, E. (1998) Test and Comparson of Hot Water Stores for Solar Combsystems. In Proceedngs of EuroSun ISES Europe Solar Congress, Sept. 98, Portoroz, Slovena, Vol., III.3.3. Hampel M., Uecker M., Krause M., Vajen K., Ackermann H. (1999). Enfluß des Verbrauchsprofls auf den solaren Ertrag ausgewählter größerer Solaranlagen. In Proceedngs of 9. Symposum Thermsche Solarenerge, pp Jordan U., Vajen K., Knopf B., Speler A., Hlmer F. (1999). Modellng of a thermosyphonally drven dscharge unt of a storage tank. In Proceedngs of ISES Solar Word Congress, Israel In Press. Klen S. A. et al., TRNSYS 14. User s Manual. Unversty of Wsconsn, Solar Energy Laboratory (1998). Lavan Z., Thompson J. (1977). Expermental Study of Thermally Stratfed Hot Water Storage Tanks. Solar Energy 19, pp Loose P. (1991). Der Tagesgang des Trnk-Warmwasser- Bedarfes, HLH 4, Nr.. Mack M., Schwenk C., Köhler, S. (1998). Kollektoranlagen m Geschoßwohnungsbau ene Zwschenblanz. In Proceedngs of 11. Internatonales Sonnenforum, Köln 1998, pp Morrson, G. L., Braun J. E. (1985). System Modelng and Operaton Characterstcs of Thermosyphon Solar Water Heaters. Solar Energy 34, pp Npkow J. (1999). Warmwasser-Zapfungsverhalten. Schlussbercht. Industrelle Betrebe der Stadt Zürch, Zürch. Phllps, W. F., Dave, R. N. (198). Effects of Stratfcaton on the Performance of Lqud-Based Solar Heatng Systems. Solar Energ 9, pp Real M., Npkow J., Tanner L., Stadelmann B., Dnkel F.(1999). Smulaton Warmwassersysteme. Schlussbercht Forschungsprogramm Wasser, Edgenösssche Drucksachenund Materalzentrale, Bern. pren European Standard. (1997). Thermal solar systems and components: Custom bult systems. Test methods. Sharp, M. K., Loehrke, R. I. (1979). Stratfed Thermal Storage n Resdental Solar Energy Applcatons. J. Energy 3, pp Shyu Ruey-Jong, Ln J. Y., Fang L. J. (1989). Thermal Analyss of Stratfed Storage Tanks. Transactons of the ASME 111, pp

2 All of the dstrbutons had a negatve mpact on the fractonal energy savngs. If none of them were appled, the fractonal energy savngs ncreased by.9%-ponts (smulaton e) compared to the profle descrbed n secton. Accordng to the results shown n fg. 14, takng nto account the holday season had the hghest nfluence (.4%-ponts), followed by the yearly sne-dstrbuton (.%-ponts), and the daly dstrbuton (.%-ponts), respectvely. Almost no dfference was found neglectng the dstrbuton for dfferent weekdays. The load profle was further smplfed, defnng only one category of draw-offs wth flow rates dstrbuted around a mean value by a gaussan-functon (fg. b). In fg. a the values of f save are shown for dfferent flow rates and draw-off duratons. They turn out to be n the same range as the ones for the conventonal load patterns. The values do depend on the DHW-flow rates and on the draw-off duratons as well, however not unformly. If the flow regulaton devce s appled, f save vares by more than 1.3 %-ponts. 6. CONCLUSIONS A realstc DHW-load profle wth a one mnute tme step was generated wth statstcal means. Although the dfferences between the values of f save for the realstc and the conventonal DHW-profle are rather small for the nvestgated system, some severe nfluences were found dependng on the DHW-flow rate and on the draw-off tme of the day f the desgn of the dscharge unt s changed. 1.) A comparson between a conventonally used and a more realstc load profle showed that the dfferences n the fractonal energy savngs for the nvestgated system were less than.8%-pt. Durng the summer less solar energy s delvered applyng the realstc DHW-profle..) If the dscharge unt s not desgned properly, f save vares by. %-ponts, dependng on the DHW-flow rate, applyng three daly draw-offs smlar to the DHW-load pattern proposal by pren For a system wth a proper flow regulaton devce, no marked dependence on the flow rate was found. 4.) Varng the draw-off tme of the day for smplfed DHWload patterns wth one or three draw-offs per day, the hghest values of f save were found for draw-offs n the early afternoon. The dfferences of f save for mornng and noon profles dffer between.5%-ponts and 1.1%-ponts. For mornng draw-offs more heat losses occur durng the nght, more solar gans are delvered nto the due to lower temperatures n the durng the daytme than for the evenng draw-off. 5.) Varatons of the realstc DHW-profle concernng dstrbutons of the DHW-consumpton showed, that the hghest nfluence was obtaned by takng nto account a holday perod durng the summer, followed by a yearly dstrbuton of the DHW-consumpton descrbed by a sne-functon, and by the daly dstrbuton. The nfluence of takng nto account the dfferent probabltes at dfferent weekdays could be neglected. If the flow regulaton devce and only one category s appled, f save vared by more than 1.3 %-ponts, dependng on the mean DHW-flow rate and on the draw-off duraton a) b) wthout wthout wthout wthout weekday day year holday none Fg. 14: Fractonal energy savngs calculated wth realstc DHW-load profles. In smulatons a d only one dstrbuton was neglected (weekday, day,..), n e none of the dstrbutons was taken nto account. nr of draw offs dur1 mn dur 1 mn dur 5 mn dur 1 mn c) mean DHW-flow rate / (l/mn) d) wth flow regulaton wthout flow regulaton DHW-flow rate / (l/mn) Fg. a: Fractonal energy savng calculated for dfferent load profles, wth one category of draw-offs wth a gven duraton (1, 5, or 1 mn). Fg. b: The flow rates were dstrbuted around a mean value ( l/mn) wth a gaussan functon; σ = (see eq. 1). It can be concluded that the nfluence of the DHW-load profle may not be dsregarded, for a comparson as well as for optmzaton of combs. Ths s especally true f the duratons and flow rates of the DHW draw-offs have a severe nfluence on the temperature stratfcaton n the storage tank.therefore, t can be expected that the presented profle also has an mpact on SDHW-systems. An optmzaton for only one flow rate and a small number of draw-offs may lead to non optmal solutons for realstc reference condtons. e)

3 temperature / C wth flow regulaton 14 a mornng draw off (at 7 a.m.) tme / h temperature / C wthout flow regulaton b mornng draw off (at 7 a.m.) tme / h temperature / C wth flow regulaton 14 c evenng draw off (at 7 p.m.) tme / h temperature / C wthout flow regulaton 14 d evenng draw off (at 7 p.m.) tme / h Fg. 14a d: Two-days smulatons wth mornng or evenng draw-offs. Ten temperatures n the storage tank are shown at the normalzed heghts:.5,., Intal storage temperature: C. Durng the frst hour, the three top layers are heated by auxlary. Fg. 14a and 14c: smulatons wth flow regulaton, fg. 14b and 14d: wthout flow regulaton. 5.3 Stratfcaton n the Storage Tank: Two-day Smulatons The followng consderatons wll not gve fnal explanatons for the results shown n secton 5., but llustrate some tendences that are nduced by dfferent draw-off patterns and by the mplementaton of a flow regulaton devce. For ths knd of nvestgatons, reference condtons play an mportant role. As an example, extreme reference condtons, a cold storage tank and farly hgh nsolaton, were chosen. In fgures 14 a-d the temperature stratfcaton n the storage tank s shown for two-day smulatons for a warm weather perod n the sprng. The ntal temperatures n the were C. The auxlary heater delveres a set temperature of 6 C when the temperature at a sensor, placed at a normalzed heght of.8, snks below 57 C. Ten temperatures n the n an equal vertcal dstance are shown. The calculatons were done wth 1 temperature nodes, wth the one dmensonal multport storage TRNSYS-type 14. The s heated up n the frst day untl about 4 p.m. to a temperature of 6 C. Therefore, at the frst day much more auxlary energy s needed n the smulatons shown n fg. 14a and 14 c (mornng), and some more solar energy gets nto the than for the evenng draw-offs. At the end of the day, the s hot n the cases of the mornng draw-offs. For the evenng draw-offs, the lowest temperature n the s about 5 C wth flow regulaton, and t drops to about 4 C wthout flow regulaton. Durng the nght, the s for cases c and d are much cooler. The temperature at the bottom of the s below 3 C durng the nght wth flow regulaton compared to above 4 C, wthout. Therefore, the losses are reduced consderably. At the second day agan the s heated to 6 C at 4 p.m. Untl then, there s much more solar energy gan for the mornng profles. For mornng draw-offs more solar energy s delvered nto the, however the overall heat losses are much hgher than for evenng patterns. Therefore the solar system gan (Q hx- Q,l) turns out to be almost exactly the same for the mornng as for the evenng draw-offs n ths example as well. 5.4 Varatons of the Realstc Load Profle The nfluence of assumptons made for the dstrbutons of the DHW-consumpton for the realstc load profle, descrbed n secton was nvestgated. In fgure 14 one year smulaton results are shown for realstc load profles wthout takng nto account the dstrbutons for the DHW-consumpton a) durng the weekday (see fg. 3) b) durng the day (see fg. 4) c) durng the year (sne functon wth mnmum n the summer tme) d) durng the holday season e) of any of the dstrbutons a - d. For smulaton b and e t was assumed, that there were DHWconsumpton between 11 p.m. and 5 a.m. Other than that, the probablty for DHW-consumpton durng the day was equally dstrbuted.

4 One-year-smulaton results are shown n fgures 1 and 13. In fg. 1 the curves at the top show results wth the storage water flow regulaton n operaton, the bottom curves show smulaton results for a system wthout flow regulaton. The fgure ndcates: The maxmum dfference between the values of f save s about 3.5%-ponts for the system wthout usng a flow regulaton devce. ) Flow Rate and Duraton: The fractonal energy savngs, f save, are almost ndependent of the DHW-flow rate wth operaton of the flow regulaton devce. However, f the regulaton s not n operaton, f save depends on the flow rate consderably: Applyng three daly draw-offs as descrbed n table 3, the maxmum dfference between the values of f save s.%-ponts. Related to the value of f save wth a flow rate of 1 l/mn (as proposed n the pren) f save vares by about 1% for the mornng profle and by about 9% for the other profles. These farly hgh dfferences of f save for smulatons wthout a flow regulaton devce can be explaned wth the relaton of the storage- to the domestc-water flow rate r = V & / V & DHW. The value of r turns out to be hgher for low than for hgh domestc-water flow rates durng a draw-off for equal reference condtons. Ths s due to the fact that the pressure drop of the storage water flow depends strongly on the storage water flow rate, as shown n eq. 3. For ths reason, a hgh storage water flow s slowed down to a hgher extend than a small one. The hgher the value of r, the hgher the storage water outlet temperature T,out of the heat exchanger and the more heat s delvered from the top to the bottom of the tank. For example, short term smulatons wth one mornng draw-off and duratons as lsted n table 3, showed: wth flow regulaton: r 1 for V & DHW = 4 l/mn and V & DHW = l/mn and wthout flow regulaton: r 3.6 for V & DHW = 4 l/mn and r 1.5 for V & DHW = l/mn. These values are not generally true, but depend strongly on the temperatures n the storage tank. Nevertheless they ndcate the tendency that the value of the DHW-flow rate does not play an mportant role for the temperature stratfcaton, f the system s desgned wth the flow regulaton devce. Wthout flow regulaton, the desgn of the dscharge unt s more sutable for hgh DHW-flow rates, whereas the pressure drop should be enhanced for small DHW-flow rates. ) Draw-off tme of the day: f save depends on the tme of the draw-off for both constructons. The values resultng from the noon profle are dstnctly above the other values. Wth flow regulaton, the values of f save for the mornng and evenng load are about the same. Futhermore, f the DHW-load s taken at noon, the values of f save are about.7%-ponts hgher than the values for the loads taken n the mornng or n the evenng. Wthout flow regulaton, the mean value of f save resultng from the noon profles dffer from the one from the mornng profles by about 1.%-pt. In fg. 13 smulaton results wth one daly draw-off at dfferent tmes of the day are shown. For all of the profles shown, there s a maxmum value of f save around the early afternoon. ) Comparson to the Realstc DHW-Profle: The mean DHW-flow rate of the realstc profle s 6.9 l/mn. As shown n fg. 1, compared to the smplfed profles wth mornng draw-offs and a DHW-flow rate of about 6.9 l/mn, the value of f save for the realstc profle are slghtly lower. Ths s true, although an even dstrbuton of draw-offs durng the day has a postve mpact on the fractonal energy savngs. The reason for the low values of f save for the realstc profle s that the mean number of draw-offs per day s about 4 compared to one or three draw-offs/day for the smplfed profles. Snce after a draw-off the thermosyphonally drven storage water flow does not stop nstantaneously, warm water flows from the top to the bottom of the tank after every draw-off. Ths s also true wth use of the flow regulaton devce due to the heat capacty of the expansble materal wthout flow regulaton. noon 3 x daly DHW-flow rate / (l/mn) wth flow regulaton mornng Fg. 1: Fractonal energy savngs. One year smulatons wth one or three draw-off durng the day. The DHW flow rate was vared n the range between 4 and l/mn. Crcles: Values resultng from realstc load profle wthout valve, 1 l/mn.3 wth valve, 1 l/mn wthout valve, l/mn tme of the day / h Fg. 13: Fractonal energy savngs. One year smulatons wth one draw-off durng the day. The draw-off tme was vared between 7 a.m. and 7 p.m.

5 For the smulatons shown n the followng and wth the cold water temperature as descrbed n table, the energy demand s reduced by about 13.5 kwh (<.5% of the overall DHWdemand), when applyng the realstc compared to applyng the conventonal load profle. Therefore, the smulaton results of the fractonal energy savngs are expected to be reduced slghtly for the realstc compared to the conventonal profle due to the smaller overall energy consumpton. In fgure 1 one year smulaton results of a solar system wth the realstc and the conventonal load profle, wth and wthout a control valve for the storage water flow, are shown. The dfferences between the smulaton results wth dentcal system constructon turn out to be rather small: Wth use of the flow regulaton devce, the fractonal energy savngs are reduced by.5 %-ponts for the realstc profle compared to the conventonal one. Wthout flow control, the reducton ncreases to.8 %-ponts. The dfferences between the results wth and wthout flow control are 3 %-ponts for the realstc and.7 %-ponts for the conventonal profle. Regardng absolute values, the dfference of the collector energy gan and the losses s ncreased by about 36 kwh/a (16 %) compared wth the value wthout use of the flow regulaton devce, when the realstc DHW-load profle s appled. In Fg. 11 the yearly dstrbuton of the solar system gans are compared. Monthly mean values of the solar system gan are shown, as the dfference between the heat transfered n the heat exchanger of the the collector crcut and the storage losses. The two curves at the top of fg. 11 show the values obtaned wth flow regulaton devce. To ndcate the nfluence of the flow regulaton devce, the two curves at the bottom of fg. 11 show the dfferences between the values of the solar system gan wth and wthout the flow regulaton devce for the two profles. The followng results are ndcated: ) Dstrbuton of the Solar Energy Gan Durng the Year The hghest solar gans are not obtaned durng the summer, but durng sprng and fall. Ths s manly due to the dstrbuton of the space heatng demand durng the year. The varatons of the solar energy gans are qute small compared to the ones for typcal SDHW-systems. For the realstc profle the maxmum value, obtaned n Aprl, s about.4 tmes the December value. Durng the months Nov. to Jan. even 78 % of the solar gan are obtaned, compared to the values between Jun. and Aug. ) Improvements due to the Flow Regulaton Devce n the Course of the Year Durng the whole year there s a postve mpact of the flow control. The dfference between the solar gans wth and wthout flow control s hghest durng the wnter (4 kwh/month) and decreases to about one forth n August. The hgher the temperatures of the, the smaller the nfluence of the flow control. One reason for that s that due to an ncrease of effcency only lttle more energy can be delvered nto the, f the temperatures n the are hgh. A second reason s that the drvng pressures of the storage water flow are hgher for a cold than for a hot. Therefore, there s a hgher mpact of the flow regulaton devce n a cold, to reduce the storage water flow rate. (Qhx-Qls) / (kwh / month) realst. conv. conv. realst. wth flow control dfference wth & wthout flow control month of the year Fg. 11: Dfference between the heat transfered n the heat exchanger of the the collector crcut and the storage losses for the conventonal and realstc profle, wth and wthout flow regulaton. Monthly mean values are shown. ) Dfferences of the Solar Energy Gan due to the DHW- Profles The Values of the solar energy gan for the realstc profle are much lower durng the summer and hgher durng the wnter than the values applyng the conventonal profle. Ths s manly due to the reduced consumpton durng the summer (sne-dstrbuton of the probablty functon) and the holday season that s taken nto account wth the realstc profle. 5. Influence of the Flow Rate and Draw-Off Tme of the Day In order to study the nfluence of the flow rate on the fractonal energy savngs, three types of DHW-load profles smlar to the conventonal one were created: 1.) wth a total load of l/d, the load-dvson nto three parts of /5, 1/5, /5 was kept,.) the total load was set startng at 7 a.m., and 3.) startng at 1 a.m. The flow rate and duraton of draw-offs were vared as shown n table 3. For example, the lowest flow rate was 4 l/mn, wth the duratons mn at 7 a.m., 1 mn at 1 a.m, and mn at 7 p.m. Table 3: Flow rates and duratons of DHW draw-offs flow rate/ (l/mn) duraton/ mn dstrbuton mornng-noon-evenng/ mn

6 h n m tube hhx g ( ( ρ, ρ, tube ) + ( ρ, ρ, hx1) = n m ρ, out ρ ς, out v, out ς v (3) wth v, out >> v, ς = ς ( ϕ, V&, d,...), and ρ,ν, and ς : densty, velocty, and pressure drop coeffcent, respectvely. The ndex ndcates the temperature nodes n the, the heat exchanger (Hx) and n the vertcal tube below the heat exchanger. Due to the fact that the velocty of the storage water n the vertcal ppe s much hgher than the upwards velocty of the storage water n the tank, the second term on the rght hand sde n eq. (3) may be neglected. The transent behavour of the valve s descrbed by τ ϕ& + ϕ = α ( T, Tb ) (4) dom out The value for τ was determned expermentally by the response of the angle of the valve to step changes of T dom,out. The heat exchanger s modeled wth the energy equaton (eq. 5a and 5b). A plug flow heat exchanger model was mplemented nto type 14. (5) Tdom 1 C dom = UA ( Tdom T ) M& dom c p ( Tdom Tdom ) t C stor T t = UA ( T dom T ) + M& c p ( T T + 1 the heat capacty rate (UA) was descrbed as a functon of the domestc water flow rate. b) Expermental Valdaton Temperatures on a vertcal ledge at postons n the storage tank, as well as nlet and outlet temperatures of the heat exchanger and the domestc water flow rate were measured. The storage temperatures at the ledge were nput data to the smulaton. In fg. 9 the measured and calculated outlet temperatures of the heat exchanger, the measured domestc water flow rate, and the calculated storage water flow rate are shown. The domestc water flow rate was vared durng the measurement. The reacton of storage water to the domestc water flow changes occurs much smoother and wth a tme delay. The measured and calculated values of the storage water outlet temperature dffer consderably for low storage water flow rates. These effects, however, do not nfluence the energy balance severely. As shown n fg. 9, the domestc water outlet temperature s descbed qute well wth the model. 5. ONE YEAR SIMULATION RESULTS 5.1 Comparson of Results wth the Realstc and Conventonal Profle. In pren 1977 reference condtons necessary for smulaton studes are proposed. Accordng to ths norm, the DHW-profle s supposed to be composed of three draw-offs durng the day, at 7 a.m., 1 a.m., and at 5 p.m. The total load should be devded up n the proporton /5, 1/5, /5, respectvely. ) temperature / C flow rate / (l/mn) calculated storage temp. at top layer (measured values) DHW-temp. measured temp. at bottom of tube measured calculated tme / mn storage water flow rate DHW-flowrate tme / mn Valdaton of the heat exchanger model (wthout ). Fg. 9a: Comparson between measured and calculated outlet temperatures of the heat exchanger. Fg. 9b: Measured value of DHW-flow rate and calculated storage water flow rate real. conv. real. conv. wth flow regulaton wthout flow regulaton Fg. 1: Fractonal energy savngs: Comparson of one-year smulaton results wth realstc and conventonal DHW-load profle (wth 3 draw-offs durng the day), and wth and wthout storage water flow regulaton. Ths profle, wth the tme of the evenng draw-off changed to 7 p.m., wll be consdered as the 'conventonal' profle n the followng. None of the dstrbutons descrbed n secton two of ths paper are taken nto account for the conventonal profle. The only tme dependant varable used, s the cold domestc water temperature. It s descrbed by a sne-functon, dependng on the clmate of the specfc locaton. Snce the same total DHW-volume s assumed for both, the realstc and the conventonal profle, the energy demand for the two profles dffer slghtly.

7 Dependng on the storage temperatures and on the flow rate, the storage water flow needs to be slowed down, n order to cool t down n the heat exchanger suffcently. Ths s done wth a valve n the vertcal tube, placed below the heat exchanger (fg. 8b). The valve s connected wth a thn cylnder contanng an expansble materal that s placed at the domestc water outlet. For statonary condtons, the angle of the valve s a (lnear) functon of the domestc water outlet temperature. Therefore, the pressure drop at the valve ncreases, f the DHW-temperature rses. Ths leads to a decrease of the storage water flow rate and storage water outlet temperature of the heat exchanger. In ths way, t can be avoded that hot water flows from the top to the bottom part of the. Some of the reference condtons assumed, are lsted n table. b) Defnton of the Target Functon Accordng to pren 1977, the energy savngs shall be calculated by comparng the gross auxlary energy demand of the auxlary heater of the solar heatng system to the gross auxlary energy demand of a conventonal heatng system. Addtonal to the defnton gven n the norm, the electrc energy demand for pumps was taken nto account: () ηburner Qburner, aux + Q pump η pump = 1 ηburner QSH + QDHW + Ql, conv + Q pump, conv η h wth ηburner 85% l, = 644 kwh and = =. η 4 % Q conv P pump = 3W, P burner = 1kW pump. pump The value of Q l,conv was calculated wth values of UA, a storage sze, and set temperatures accordng to pren To calculate the runnng tme of the pumps to load the of the conventonal system, the total energy demand of the conventonal system (ncludng storage losses) was dvded by the assumed power of the burner. Runnng tmes of the solar system pumps result from smulatons. Thermosyphon Heat Exchanger Contanment (Vrtual) Water Columns Weather Data 9 16 Solar Radaton Processor ON/OFF 5 Collector Ppe Hx 31 Ppe 5 Qaux 14 Store 14 ON/OFF 9 DHW-Data 11 Flow Dverter TRL < T SH-Data Fg. 7: Scheme of the TRNSYS-deck, wth a new developed user contrbuted component Type 14 for the dscharge unt (plug flow heat exchanger model combned wth thermosyphon drvng pressures). The numbers ndcate the TRNSYS type numbers used. Table : Reference Condtons weather data Zurch (Meteonorm), t = 1h 4. MODELLING collector area 14 m², 4 l/m²h collector orentaton south, tlt angle: 45 volume 817 l space heatng demand 84 kwh/a (14 m², 6 kwh/m²a) flow rate auxlary heatng 43 kg/h auxlary set Temp. 57 C + 5K daly DHW-load volume l DHW-set temperature 45 C (-1K) desgn temp. SH-dstr. syst. 4 C / 35 C domestc cold water temp. (9.7 ± 6.3) C, snefunc., mn. at May 1 st a) Relatons of the Thermosyphon Loop The model of the dscharge unt s descrbed n Jordan et al., In the followng, a short formulaton of the equatons that are mplemented nto type 14 s gven. A common approach to model a densty drven crculaton loop s the one dmensonal steady state momentum equaton for ncompressble flow, as the balance of the pressure and frctonal forces. The drvng forces for the storage water flow n the dscharge unt are expressed by densty dfferences. Frctonal forces are descrbed by the knetc pressure drop of the storage water. The pressure drop coeffcent s a functon of the geometry of the dscharge unt, the angle of the valve, as well as the flow rate of the storage water. 9 Fg. 8a: Comb wth thermosyphonally drven dscharge unt: Durng a DHW draw-off storage water s drven by densty dfferences nsde the tank. Fg. 8b: (a) Regulaton devce, composed of a valve placed n a vertcal tube below the heat exchanger and a thn cylnder contanng an expansble materal. (b) angle of the valve ϕ. (c) A mxer for the domestc water. Fg. 8b a ϕ Mxer b c

8 prob(day): The assumptons for the daly dstrbuton used, are shown n fg. 4. For a short and medum load the probablty s dstrbuted equally between 5: and 3: h. For the shower bath, a clear peak n the mornng and for the bath tub fllng (whch manly occurs on weekends), a peak n the evenng were appled. prob(holday): For every 1 l/d of consumpton the probablty was set to zero durng a perod of two weeks durng the summer. Therefore, for a one famly house wth a total daly mean consumpton of l/d, two perods n whch the consumpton s reduced by one half are taken nto account. The start day of every holday perod s generated by a random generator. The generator s set n a way that for a consumpton of l/d the two perods of reduced consumpton do not concde, but start on Jul. 14 th and Aug. 8 th, respectvely. The functon prob(holday)s defned as follows: mean volumeof daly load reduced volume prob( holday) =, mean volumeof daly load hence wth a consumpton of l/d: prob(holday) = ½ Jul. 14 th..8 th, Aug. 8 th.. nd prob(holday) = 1 else b) Method The cumulated frequency method was used to dstrbute the draw-off ncdences among the year accordng to the probablty functon. As shown n fg. 6, the probablty functon prob was ntegrated over the year and normalzed. Afterwards the number of draw-offs durng the year was calculated. The same number of random values between zero and one were generated and assgned to a flow rate n the order of occurence. Wth fg. 6, every random value (value on the y- axs) was then assgned to a mnute of the year (value on the x- axs). In ths way load profles were generated for dfferent demands as well. The basc load s 1 ltres/day. Profles were generated n dual order (1,, 4, 8 ltres..), wth dfferent ntal random values. Therefore, t s possble to get any load profle wth consumptons n steps of 1 l/day for a mult-famly house by superposton of the generated fles. For dfferent consumptons the number of ncdences, shown n table 1, wll be adjusted to the mean draw-off volumes. 3. INVESTIGATED SOLAR SYSTEM a) TRNSYS Deck and Reference Condtons A solar combsystem for a one famly house n Zurch s regarded, wth fractonal energy savngs of about 5%. A scheme of the TRNSYS deck used s shown n fg. 7. The weather data as well as a set of space heatng data were mplemented as data fles. The space heatng data from IEA- Task 6 (Internatonal Energy Agency, Solar Combsystems) were used wth nput and output temperatures and the flow rate for the space heatng cycle. The DHW-load was ether read n from a data fle, n case of usng a statstcally generated profle. Alternatvely, conventonal load patterns were mplemented wth the type 14 tme dependent forcng functon. prob(day) volume per day n (l/d) shower bath small and medum bath tub tme / h Fg. 4. Dstbuton of prob(day) durng the day day of the year Fg. 5: Realstc load profle: Daly DHW-load volume n the course of the year. Mean value: l/d. prob day of the year Fg. 6: Accumulated frequency method: Integral of the probablty functon prob. For the thermosyphonally drven dscharge unt of the combtank, a user contrbuted plug-flow heat exchanger model was developed (type 14). Other than that, standard components, ncludng the type 14 multport storage type (Drück, 1994), were used. The solar system conssts of a 14 m² flat plat collector, an external solar heat exchanger, and an 817 l comb wth an nternal thermosyphonally drven DHW-heat exchanger. A scheme of the combtank s shown n fg. 8a. When domestc water s heated, the water nsde a contanment surroundng the heat exchanger s cooled, and flows through an adjacent tube to the bottom of the.

9 a) Basc Assumptons Four categores of loads were defned. Each category-profle was generated separately and superponed afterwards. For each category a mean flow rate was defned. The actual values of the flow rates are spread around the mean value wth a gaussandstrbuton (fgure ): 1 ( V& V& ) prob( V& ) = exp mean (1) πσ σ The values chosen forσ, for the duraton of every load, and for the medum number of ncdences durng the day are shown n table 1. Wth ths approach, t s assumed that there s no correlaton between the weather data and the DHW-load profle. cat A: cat B: cat C: cat D: short l. med. l. bath shower flow rate n l/mn duraton n mn nc/day * sgma vol/load n l vol/day n l porton *once a week Table 1: Reference condtons for the load profle: Four categores are defned wth a mean flow rate and a constant duraton of every DHW-draw-off. The volumes of the loads were chosen wth the assumpton of a load temperature of 45 C. The number of ncdences are refered to a sngle famly house wth a mean consumpton of l/d. 1 The followng assumptons are made: the mean load s l/day four categores to descrbe the dfferent types of loads are defned: cat A: short load (washng hands, etc.) cat B: medum load (dsh-washer, etc.) cat C: bath cat D: shower flow rate / (l/hour) tme / hour A probablty functon, descrbng varatons of the load profle durng the year (also takng nto account the (European) daylght savng tme), the weekday, and the day was defned for every category. The course of probabltes durng the year s descrbed by the product of probablty dstrbutons durng the year, durng the day, at weekdays and durng the holday season: prob = prob(year)* prob(weekday)* prob(day) *prob(holday) prob(year): The course of probabltes durng the year s descrbed by a sne-functon wth an ampltude of 1% of the daly dscharge volume. Mack et al., 1998, found varatons of the energy consumptons accordng to a sne functon wth an ampltude of 5% and a maxmum durng wnter and a mnmum durng summer tme. Ths varaton s due to varatons of the cold water temperature, varable consumpton durng the year, and due to holdays, takng place manly n the summer. Snce holdays are taken nto account separately (see below) and the cold water temperature s not defned by ths load profle, the ampltude gven by Mack et al. was reduced. prob(weekday): At dfferent days of the week the probablty for takng a bath and the mean dstrbuton for the total volume per day are shown n fgure 3. For the categores A, B, and D the probablty for every day of the week s assumed to be the same. The average of DHWconsumpton for the four categores s accordng to the results found by Dchter, Fg. 1. Realstc load profle, Jan 1 st to Jan. 3 rd, generated wth statstcal means. Mean draw-off volume of the year: l/d. nr. of taps / year small load medum load shower bath bath tub 5 1 DHW-flow rate Fg.. Realstc load profle: Nr. of draw-offs durng one year as a functon of the DHW-flow rate. These are dstrbuted wth a gaussan functon (eq. 1) around the mean values, also gven n table 1. prob(weekday) all categores bath tub Mon Tue Wed Thu Fr Sat Sun Fg. 3. Dstbuton of probablty for category C: Bath tub fllng (grey columns). In categores A, B, and D no day of the week was prvleged compared to another.

10 INFLUENCE OF THE DHW-LOAD PROFILE ON THE FRACTIONAL ENERGY SAVINGS: A CASE STUDY OF A SOLAR COMBI-SYSTEM WITH TRNSYS SIMULATIONS Ulrke Jordan, Klaus Vajen Unverstät Marburg, FB Physk, D-353 Marburg, Germany Phone: ++49 / 641 / , Fax: -6535, solar@physk.un-marburg.de Abstract In ths paper the nfluence of domestc hot water (DHW)-load profles wth a constant total heat demand s studed for a solar comb system. Whereas so far smulaton studes are usually done wth a smplfed DHW-load profle (e. g. accordng to pren 1977), a more realstc profle was generated on a 1-mn tme scale wth statstcal means. Assumptons about the dstrbuton of the DHW-consumpton durng the year, dependng on the weekday, and the tme of the day were made. To study the nfluence of the draw-off duraton and flow rate as well as the daytme of DHW-consumpton, TRNSYS smulatons were carred out wth a varety of common and farly realstc load profles. In ths case study the nvestgated solar system conssts of a storage tank wth an nternal thermosyphonally drven dscharge unt. Despte a rather mnor nfluence of the flow rate on the fractonal energy savngs for the gven system, a farly wde range of about. percentage ponts of the fractonal energy savngs were found for the system wth some constructve changes. Furthermore, due to changes of the daytme of the draw-offs, the fractonal energy savngs changed by up to 1.1 percentage ponts for the nvestgated system. It can be concluded that the nfluence of the DHWload profle may not be dsregarded, when combs are compared. Ths s true especally for combs, for whch the duraton and flow rate of a DHW draw-off have a severe nfluence on the temperature stratfcaton n the storage tank. 1. INTRODUCTION The fact that the temperature stratfcaton has a great mpact on the solar energy gan of a solar system has been shown n many publcatons n the past. For example, Sharp and Loehrke already showed n 1979 that mprovements n the system performance of 5-% may be realzed when temperature stratfcaton n the s acheved. Therefore, much effort has been made to mprove the thermal stratfcaton n storage tanks. A lot of studes n the lterature (e. g. Lavan and Thomson, 1977; Phllps and Dave (198); Morrson and Braun, 1985; Shyu et al, 1989) have analyzed the factors that nfluence the stratfcaton, lke flow rates, temperature dfferences, and the geometry of nlets, stratfers, heat exchangers and of the tank desgn. Andersen and Furbo (1999), for example found a decrease of the thermal performance caused by mxng durng draw-offs of up to 3% for small solar domestc hot water (SDHW) systems. Consequently, the solar energy gan depends on the DHWload profle as soon as the stratfcaton of the storage tank depends on the DHW-flow rate, the duraton of a draw-off, or the tme of DHW-consumpton. The mpact of these quanttes agan depends on the constructon of the. In the recent years new types of combs, for combned DHW and space heatng (SH), have been developed. Some of these s are equpped wth an addtonal nternal heat exchanger, thermally connectng the storage water, used for SH, and the DHW-cycle. Tests of these s were carred out, for example by ITW (Stuttgart, Germany) and SERC (Borlänge, Sweden). It has been shown that the temperature stratfcaton n the storage tanks of ths knd may depend strongly on constructve detals (Dahm et. al., 1998, Drück and Hahne, 1998). Hampel et al., 1999, found n a smulaton study an ncrease of the collector output of almost 5% for a SDHW system of a mult-famly house when the DHW-load s taken n the evenng nstead of takng t n the mornng. In contrast to that, so far TRNSYS smulaton studes are usually carred out wth a domestc hot water profle consstng of three draw-offs durng the day wth a constant flow rate of 1 l/mn (pren 1977). In ths case study, a combsystem wth an nternal thermosyphonally drven DHW-heat exchanger s nvestgated and the dependence of the fractonal energy savngs on the flow rate, the daytme, and on the draw-off duraton due to flow patterns durng and after a draw-off s shown. For that purpose a farly realstc DHW-load profle was developed. It s descrbed n the followng secton. Assumptons made are based on varous studes about DHW consumpton n Swtzlerland and Germany (Dttrch et al., 197; Loose, 1991; Mack et al., 1998; Dchter, 1999; Npkow, 1999; Real et al., 1999). In the thrd secton, the model of the solar system, the reference condtons, and the appled TRNSYS deck are descrbed brefly. The mathematcal model for the DHWdscharge unt s shown n secton four. In secton fve, oneyear-smulaton results of the realstc load profle are compared wth results of the commonly used one, n terms of dstrbutons of solar gans durng the year. Non realstc profles were used to analyze the nfluence of the DHW-flow rate, duraton, and the daytme on fractonal energy savngs. Temperature dstrbutons, resultng from two day smulatons are shown. Also, smplfcatons are appled concernng the assumptons made to the statstcally generated profle.. REALISTIC DHW-LOAD PROFILE A load profle for the domestc hot water demand for a perod of one year was generated. In order to take nto account farly realstc condtons, a tme step of one mnute was chosen. The values of the flow rate and the tmes of the draw-offs were selected by statstcal means. The frst three days of the the profle wth a daly mean draw-off volume of l are shown n fgure 1.