1、2011 ASHRAE 683ABSTRACTIn this study, the applicability of a linear input/outputmodel to gas-fired, tankless water heaters has been evaluated.This simple model assumes that the relationship between inputand output, averaged over both active draw and idle periods,is linear. This approach is being app
2、lied to boilers in otherstudies and offers the potential to make a small number ofsimple measurements to obtain the model parameters. Theseparameters can then be used to predict performance undercomplex load patterns. Both condensing and non-condensingwater heaters have been tested under a very wide
3、 range of loadconditions. It is shown that this approach can be used to repro-duce performance metrics, such as the energy factor, and canbe used to evaluate the impacts of alternative draw patternsand conditions. INTRODUCTIONIn the US, energy factor (EF) is currently used as themetric for the energ
4、y efficiency of residential water heaters(ASHRAE 2006; DOE 2001). This test was developed andevolved as a compromise between testing complexity and thegoal of being representative of typical field conditions. The EFis a direct input/output testit is essentially the ratio of theenergy output, in hot
5、water, to the fuel and/or electrical energyinput integrated over a 24-hour period. During this time, hotwater is produced in six draws over a 6-hour period. Thebalance of the 24-hour period is the idle time and energy usedduring this time is taken as part of the daily input. Each of thesix draws is
6、10.7 gal. (40.6 L) for a total daily draw of 64.3 gal(243.7 L). The target temperature of the produced hot water is135F (57.2C).Increasingly, the effectiveness of the EF test in evaluatingenergy use to meet domestic hot-water demand and providinga basis for comparison of different technologies is be
7、ing ques-tioned. One of the specific concerns is the draw pattern. Fieldstudies have shown that hot water is actually drawn in manyshort draws. While this impacts the performance of tank-typestorage water heaters, it may be more important for newertankless (also sometimes termed instantaneous or dem
8、and)water heaters that have “near zero” volumes and higher inputrates (Hoeschele and Springer 2006). These units are designedto meet domestic hot-water loads based on continuous, modu-lating input with very low standby or idle losses.Thomas et al. (2006) did a study of domestic hot-wateruse patterns
9、 in Toronto and found an average daily draw ofabout 43.8 gal (166 L). In addition, they showed that the actualdraw patterns involve many very short draws and that thedifference between actual draw patterns and the draw patternsthat are used in the EF test can significantly affect efficiency.Based on
10、 this, they developed alternative draw patterns thatcould be used in a modified test method. In the present study, we have explored the use of a linearinput/output model to represent the performance of a range ofwater heater types over a wide load range. We then show howsuch a model could be used to
11、 calculate the impact that drawpatterns and total daily consumption have on water heater effi-ciency. Relative to the current test method, the key advantageof the input/output approach is the ability to use one set ofmeasurements to evaluate performance of a specific unit overa range of draw pattern
12、s. The concept of the linear input/output method is straight-forwardfor a given appliance there is a linear (or nearlylinear) relationship between energy output and energy input atApplication of a Linear Input/Output Model to Tankless Water HeatersThomas A. Butcher, PhD Ben SchoenbauerMember ASHRAE
13、Associate Member ASHRAEThomas A. Butcher is deputy chair of the Sustainable Energy Technologies Department at Brookhaven National Laboratory, Upton, NY.Ben Schoenbauer is a research engineer at the Center for Energy and Environment, Minneapolis, MN.LV-11-0032011. American Society of Heating, Refrige
14、rating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions, Volume 117, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAES prior written permission.684 ASHRAE Trans
15、actionsleast over the range that is relevant for the application. For timeperiods over which the load is intermittent, output and inputare averaged over the entire period. The line is unique to theinlet and outlet water temperatures. Decicco (1990) used a linear boiler model to evaluatefield perform
16、ance data for commercial boilers and showedhow results could be used to evaluate annual performance andthe potential of energy saving upgrades. Rosa and Tostato(1990) showed the linear model could be applied to condens-ing boilers if the impact of seasonal water temperaturechanges imposed by the con
17、trol system is included. Currently, ASHRAE Special Project Committee 155(SPC 155) is developing a method of test for commercial boil-ers that implements the linear model (Hewett 2005). With arelatively simple set of measurements, the characteristicperformance characteristics can then be combined wit
18、hsystem configuration and control characteristics and buildingload profiles to produce an application seasonal efficiency(ASE).OBJECTIVESThe objectives of this study are to evaluate the applica-bility of the linear input/output model to tankless water heatersand to use the results of characterizatio
19、n tests to evaluateimpacts of draw patterns and total daily draw volume on effi-ciency. EXPERIMENTALAll water heaters tested were setup for direct input/outputmeasurements using the arrangement shown in Figure 1.Energy input was measured using a dry test meter for gas flowwith a pulse output sensor.
20、 The resolution of this system is1000 pulses/ft3, and total pulses each second are recordedusing a local pulse logger. Natural gas fuel composition andrelevant properties are measured periodically using an “on-line” gas chromatograph. Energy output is measured usinginlet and outlet thermocouples and
21、 a weigh scale that commu-nicates with the labs measurement and control system. Thescale is located on the second floor balcony of the lab anddrains down during the periods between hot-water drawsunder control of the labs central system. Draining of this tankis stopped 15 seconds before each draw an
22、d for a 15-secondperiod after the end of the draw to allow readings to stabilize.Temperatures and scale mass are recorded at 5-second inter-vals. For some very short draw tests, a 1-second temperaturemeasurement interval was used. A 40 gal (151 L) precondi-tioning tank was used to heat or cool the i
23、nlet water. Inlet andoutlet thermocouples were located 4 in. from the appliance. For each appliance tested, a basic protocol was estab-lished which included steady state tests covering inlet watertemperatures from 40F to 70F (4.4C to 21.1C) and outlettemperatures from 105F to 133F (40.6C to 56.1C).
24、Theprotocol also includes a wide range of cycling conditionsintended to replicate cold, warm, and hot conditions at the startof the draw. Table 1 shows the test matrix followed for eachunit. All tests were done with the lab at a nominal temperatureof 70F. Cyclic testing was done under computer contr
25、ol. A seriesof cyclic test conditions were defined in an input file and thistypically contained combinations of draw patterns with thetotal test period as long as 20 hours. For each specific drawpattern, multiple draw/idle cycles were imposed and thisranged from 3 to 20. Short draws required more cy
26、cles forFigure 1 Illustration of test setup.2011 ASHRAE 685Table 1. Planned Test Conditions for Each Water HeaterCyclic TestsTest No. Volume, gal Volume, L T cold in, F T cold in, C T out, F T out, C Idle time, minCyclic Tests at 7.6 L/min (2.0 gal/min) 1 1 3.8 60 15.6 133 56.1 22 1 3.8 60 15.6 133
27、56.1 43 1 3.8 60 15.6 133 56.1 454 2 7.6 60 15.6 133 56.1 25 2 7.6 60 15.6 133 56.1 46 2 7.6 60 15.6 133 56.1 457 3 11.4 60 15.6 133 56.1 28 3 11.4 60 15.6 133 56.1 49 3 11.4 60 15.6 133 56.1 4510 4 15.1 60 15.6 133 56.1 211 4 15.1 60 15.6 133 56.1 412 4 15.1 60 15.6 133 56.1 4513 5 18.9 60 15.6 133
28、 56.1 214 5 18.9 60 15.6 133 56.1 415 5 18.9 60 15.6 133 56.1 4516 10 37.9 60 15.6 133 56.1 217 10 37.9 60 15.6 133 56.1 418 10 37.9 60 15.6 133 56.1 45Cyclic Tests at less than 3.8 L/min (2 hours, use the actual measuredstandby energy use to estimate input required. This 2-hourtime period is assume
29、d for example and should be further eval-uated).In evaluating the 24-hour performance, the procedureused here has been to apply the standby energy consumptionto the entire idle period. During the active draw period, theoutput rate is evaluated for each draw individually combiningthe draw period and
30、preceding idle period. For the first draw,it has been assumed that it follows a 1-hour idle period. To better illustrate the use of this approach during theactive draw period, the following example is provided. In theEF tests the amount of energy output during the hourly draw is(3)The corresponding
31、input during this period, for Unit A fromEquation 1, is(4)This procedure is applied to all draws during the simu-lated use test, combined with the power use during theextended idle period, and all inputs and outputs are summedover the 24-hour period.Using this approach, for Unit A, an EF of 0.90 isp
32、redicted. This can be compared with an actual measured EFof 0.9. For this same unit, with the modified draw pattern 1above, the efficiency over a 24-hour period is 0.88. The actualmeasured efficiency over this draw pattern is 0.87. The perfor-mance calculated over modified draw pattern 2 is similar.
33、 Thekey advantage of the second draw pattern is the lower flow rateand, in turn, longer draw periods, which greatly improvesaccuracy during testing. For Unit B, using the regression results in Equation 2, thepredicted EF is 0.80. The listed EF is 0.82. The predictedperformance of this unit over modi
34、fied draw pattern 1 is 0.79. This approach can be used to illustrate the impact thattotal daily water use has on performance as measured with anydraw pattern. Figure 7 shows the results, for example, of theEF draw pattern (i.e., six equal draws, one hour apart, followedby an 18-hour idle period) wit
35、h varied daily water use usingUnit B. To obtain the results shown in Figure 7, the pattern ofthe EF or modified draw pattern 1 was held the same, but thetotal volume during the day was varied by changing thevolume in each draw, e.g., to reduce the total daily volume to80% of the standard value, the
36、volume of each draw would bemultiplied by 0.8. For each draw, energy output divided bytime of the draw and preceding idle period was used to calcu-late average output rate, Btu/h (kW). The linear relation for thespecific water heater considered is then used to calculate theenergy input for that draw
37、 and these are summed for the entiredraw period. The results shown in Figure 7 could be considered relativeto the results of Hoeschele and Springer (2006), in which itwas shown that the performance of tankless water heaters islower under conditions of frequent short draws relative to thelong draws o
38、f the EF test. The input/output relationshipmethod discussed here also yields a strongly reduced effi-ciency under conditions where the cycling pattern produces alow average input and output rate, i.e., on the left side of theline in Figure 3. How this translates to a daily average effi-ciency depen
39、ds strongly upon the details of the assumed drawpattern. For this reason it is very important that draw patternsused for comparing actual in-field efficiency be realistic. As another illustration of the potential use of thisapproach, Figure 8 shows the impact of electrical power drawduring the long
40、standby period on the EF and EF from themodified draw pattern 1. In the case of the modified drawpattern, the impact of the standby electrical power use isgreater because the 24-hour total load is lower and the idleperiod is larger.The data used to develop the input output relationshipspresented her
41、e are based on actual cyclic draw patterns and, inthis sense, capture the effects of cycling that are built into drawpatterns. The results, however, may not be accurate for drawEnergy out 10.7galh- 8.329Btugal F- 135 58()F 6862Btuh-=Energy in 1.073 6862 Btu/h 211.95+ 7575 Btu/h=Figure 8 Illustration
42、 of the use of the input/output method topredict impact of standby electrical power drawon EF or EF under modified draw pattern 1.Figure 7 Illustration of the use of the input/output method topredict impact of total daily water use on EF or EFunder modified draw pattern 1.2011 ASHRAE 689patterns tha
43、t differ significantly from the range of patternsevaluated in this study. CONCLUSIONResults of laboratory tests have shown that with cyclicdraw patterns over a very wide range of load, a linear input/output model reasonably represents performance. For predicting energy use during extended standby pe
44、ri-ods with these units, the extrapolation of the linear input/output relationship should not be used; instead, use of resultsof direct measurement of standby power is recommended.This approach can be used to evaluate the performance ofspecific tankless water heaters over a wide range of use condi-t
45、ions. ACKNOWLEDGMENTSThis work has been sponsored by the Minnesota Depart-ment of Commerce, Office of Energy Security, and New YorkState Energy Research and Development Authority throughthe U.S. Department of Energy State Technology Advance-ment Collaboration (STAC) program.REFERENCESASHRAE. 2006. A
46、NSI/ASHRAE Standard 118.2-2006,Method of Testing for Rating Residential Water Heaters.Atlanta: American Society of Heating, Refrigeratingand Air-Conditioning Engineers, Inc.DeCicco, J.M. 1990. Applying a linear model to diagnoseboiler fuel consumption. ASHRAE Transactions96(1):296 304.DOE. 2001. Fin
47、al rule regarding test procedures and energyconservation standards for water heaters. 10CFR430,Federal Register 55(201), U.S. Department of Energy. Hewett, M. 2005. Inside ASHRAE Standard 155: A newmeasure of commercial boiler system performance.Boiler Systems Engineering.Hoeschele, M., and D. Sprin
48、ger. 2006. Field and laboratorytesting of gas tankless water heater performance.ASHRAE Transactions 114(2). Rosa, L., and R. Tosato.1990. Experimental evaluation of theseasonal efficiency of condensing boilers, Energy andBuildings 14:237 41.Thomas, M., S. Hayden, K. Wittich, D. MacKenzie, and H.Lomax. 2009. Hot water use in Canada and the implica-tions for performance test standards. Presentation atACEEE Water Heater Forum, Asilomar, California,June 2009. American Council for an Energy EfficientEconomy.
