The experimental characterization of a lithium bromide–water absorption chiller and the development of a calibrated model

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ScienceDirect Solar Energy 122 (2015) 368–381 www.elsevier.com/locate/solener

The experimental characterization of a lithium bromide–water absorption chiller and the development of a calibrated model Ian Beausoleil-Morrison ⇑, Geoffrey Johnson, Briana Paige Kemery Sustainable Building Energy Systems, Faculty of Engineering and Design, Carleton University, Ottawa, Canada Received 24 March 2015; received in revised form 29 July 2015; accepted 11 September 2015

Communicated by: Associate Editor Ruzhu Wang

Abstract Small-scale solar air conditioning systems based upon thermally activated chillers offer great potential for cooling houses with minimal demands upon the central electrical system. Building performance simulation can be used to assess the potential of the technology and to explore the impact of system design (e.g. type and area of solar collectors, volume of hot and cold thermal stores, operating strategies), but only if appropriate models calibrated with accurate and reliable data are available. Experiments were conducted on a commercially available lithium bromide–water absorption chiller under a controlled set of operating conditions. Instrumentation was selected, calibrated, and installed in order to derive quantities of interest at acceptable levels of measurement uncertainty. Over this range of experiments, the cooling capacity varied from 6.9 kW to 40.5 kW, and the thermal coefficient of performance ranged from 0.56 to 0.83. A quasi-steady-state model suitable for use in building performance simulations that expressed the chiller’s performance was developed. Based upon statistical significance testing, it was found that the rates of heat transfer to both the generator and the evaporator could be expressed as linear functions of the generator inlet temperature, absorber/condenser inlet temperature, and flow rate of water to the generator. The validity of the calibrated model was then tested using measurements from a disjunct experiment whose data were not used to calibrate the model. Ó 2015 Elsevier Ltd. All rights reserved.

Keywords: Absorption chiller; Solar cooling; Calibrated model

1. Introduction In many cases, the availability of solar energy is in-phase with residential-building cooling loads (Henning, 2007). By employing this available solar energy to drive a cooling cycle on-site where cooling loads occur, the reliance on the central electrical supply system and the transmission and distribution networks to drive a conventional vapourcompression air-conditioning system can be reduced. ⇑ Corresponding author.

E-mail address: [email protected] (I. BeausoleilMorrison). http://dx.doi.org/10.1016/j.solener.2015.09.009 0038-092X/Ó 2015 Elsevier Ltd. All rights reserved.

For these reasons, small-scale solar air-conditioning systems (with cooling capacities less than 50 kW) based on thermally activated chillers have been gaining attention by researchers in recent years. Currently, solar air-conditioning systems that employ an absorption chiller as the active cooling component are the most widespread (Sparber et al., 2009). Siddiqui and Said (2015) provide an in-depth review of recent research activities related to solar air-conditioning systems based on absorption chillers. Among the research reviewed by Siddiqui and Said (2015), there are many studies with a significant building performance simulation (BPS) component where the

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369

Nomenclature T g;i T g;o DT g T e;i T e;o DT e T c;i V TP V_ g

temperature of water at inlet of generator’s heat exchanger (°C) temperature of water at outlet of generator’s heat exchanger (°C) T g;i  T g;o (°C) temperature of water at inlet of evaporator’s heat exchanger (°C) temperature of water at outlet of evaporator’s heat exchanger (°C) T e;i  T e;o (°C) temperature of water at inlet of cooling heat exchanger (°C) voltage signal generated by thermopile (mV) flow rate of water through generator circuit (L/s)

performance of solar air-conditioning systems are simulated using models of absorption chillers to assess the potential benefits of these systems. 1.1. Absorption chiller modelling approaches used in building performance simulation A detailed description of all the major components of the absorption cycle and its principles of operation are discussed by Siddiqui and Said (2015). A common type of absorption chiller model employed in BPS follows a ‘‘grey-box” approach wherein the physical principles of the absorption cycle are simplified in favour of functions describing input–output relationships that can be calibrated with experimental data. One possible grey-box absorption chiller model is illustrated in Fig. 1. This figure illustrates three fluid streams connected to the absorption chiller at its generator, evaporator, and absorber/condenser. With grey-box models it is common to represent the heat transfer rates between the absorption chiller and these fluid streams (qgen ; qevap , and qcond Þ as functions of fluid inlet temperatures (T g;i ; T e;i , and T c;i ) and flow rates (m_ g;i ; m_ e;i , and m_ c;i ). Such an approach has been shown to be effective by Monne´ et al. (2011), for example. Other studies (e.g. Borg and Kelly, 2012; Cascales et al., 2011) have shown that more complex models may not necessarily result in more accurate predictions.

V_ e q cP qevap qgen COP th B S t ðU Þ95% X

flow rate of water through evaporator circuit (L/s) density of water (kg/L) heat capacity of water (kJ/kgK) rate of heat transfer at evaporator (kW) rate of heat transfer at generator (kW) thermal coefficient of performance (–) bias error precision index standard statistical Student’s t-value uncertainty at 95% confidence level time-averaged value of quantity X over duration of experiment ae . . . fe qevap calibration coefficients ag . . . fg qgen calibration coefficients a1 . . . c2 COP th calibration coefficients

resorted to calibrating or validating absorption chiller models with data of unreported uncertainty and/or have introduced simplifying assumptions due to a lack of reliable performance data (e.g. Eicker et al., 2014; Lo´pezVillada et al., 2014; Gomri, 2013; Eicker and Pietruschka, 2009; Mateus and Oliveira, 2009; Lecuona et al., 2009; Balghouthi et al., 2008; Mazloumi et al., 2008; Assilzadeh et al., 2005). Clearly more reliable data are required on the performance of absorption chillers to advance the domain. Numerous researchers have provided measured data on the performance of absorption chillers. However, in many cases the methods used to measure performance have not been adequately described and instrumentation and measurement uncertainties have not been provided (e.g. Prasartkaew, 2014; Borg and Kelly, 2012; Eicker et al., 2012; Yin et al., 2012; Monne´ et al., 2011; Helm et al., 2009;

T c,i

m

T c,o

Absorption Chiller

c,i

Absorber/Condenser

q

(T ,T ,T ,m

cond g,i c,i

Generator q

gen

e,i

g,i

,m

c,i

,m

)

e,i

Evaporator

(T ,T ,T ,m g,i c,i

e,i

g,i

,m

,m

c,i

)

e,i

q

(T ,T ,T ,m

evap g,i c,i

e,i

g,i

,m ,m ) c,i

e,i

1.2. Literature review Effective exploitation of solar-cooling requires accurate BPS models that can be used to configure hydronic systems and to determine appropriate control strategies. However, in many existing simulation studies researchers have

T g,i

m

g,i

T g,o

T e,i

m

e,i

T e,o

Fig. 1. A typical grey box model representation of an absorption chiller used in building performance simulations.

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Melograno et al., 2009; Adao et al., 2008; Ali et al., 2008; Hidalgo et al., 2008; Pongtornkulpanich et al., 2008; Aphornratana and Sriveerakul, 2007; Izquierdo et al., 2005; Florides et al., 2002; Li and Sumathy, 2001). Some researchers have reported experimental uncertainty, but unfortunately have not provided data over a suitable range of operating conditions for the purposes of model calibration (e.g. Izquierdo et al., 2014; Evola et al., 2013; Marc et al., 2012; Martı´nez et al., 2012; Praene et al., 2011; Venegas et al., 2011; Agyenim et al., 2010; Vega et al., 2006; Asdrubali and Grignaffini, 2005). To this date, Le Lostec et al. (2012) have published the most comprehensive absorption chiller performance data set where the uncertainty of their measurements were reported. They provided data from 18 sets of operating conditions of an ammonia/water absorption chiller with a nominal cooling capacity of 10 kW and later used these data to validate a model (Le Lostec et al., 2013). As few measured data are available that accurately characterize the performance of small-scale absorption chillers there is a need for accurate measured data under controlled conditions for the purposes of model calibration. This is especially true for the case of a lithium bromide–water absorption chiller, as there is currently no study available where data are published from a wide enough range of operating conditions and with reported uncertainty at acceptable levels. 1.3. Objectives and outline To address the scarcity of high-quality lithium bromide– water absorption chiller performance data available to researchers, the objectives of the research reported here were to: 1. Accurately measure the performance of a commercially available lithium bromide–water absorption chiller with a nominal cooling capacity of 35 kW under a wide range of controlled boundary conditions. 2. Analyze the experimental data to derive a calibration data set. 3. Determine an appropriate functional form to suitably represent the heat-transfer rates required for a greybox model similar to the one shown in Fig. 1. 4. Calibrate the grey-box model. 5. Validate the model and its calibration using both steadystate and transient data gathered from disjunct experiments. The following sections describe the experimental methods used to gather data capable of characterizing an absorption chiller’s performance over a wide range of operating conditions. The measured data are then presented and analysed. A simple grey-box model is then proposed and calibrated with these data. Finally, this calibrated model is validated with a disjunct set of experiments, and then conclusions are drawn.

2. Experiments 2.1. Test bench A test bench was designed and commissioned to expose the absorption chiller to a broad range of controlled boundary conditions. This facility, illustrated in Fig. 2, was composed of three fluid circuits. The circuit shown on the right of the figure (named the generator circuit) recirculates a stream of water between three in-line electric resistance heaters and the heat exchanger of the absorption chiller’s generator. The electric heaters had a combined capacity of 65 kW and were controlled to achieve a target inlet temperature to the generator’s heat exchanger. A fixed-speed pump was used to circulate water through this loop. The desired flow rate was achieved by manually adjusting a balance valve (not shown in the figure). With this arrangement, the test bench could mimic the thermal input that could be provided by solar thermal collectors (or another source such as a micro-cogeneration device) in a controlled fashion to achieve either steady or timevarying boundary conditions for the absorption chiller’s generator. The temperature of the water supplied to the inlet of the generator’s heat exchanger could be varied from 70 °C to 93 °C. This spanned the full practical operating range of the chiller. (The chiller’s internal controller would initiate a shutdown sequence if the supply temperature rose above a nominal value of 95 °C.) The water flow rate through this circuit could be varied from 0.9 L/s to 1.3 L/s. The lower end of the this range was close to the manufacturer’s minimum recommended flow rate. The circuit shown on the bottom of Fig. 2 (named the evaporator circuit) was designed in a similar manner to provide controlled boundary conditions to the heat exchanger of the absorption chiller’s evaporator. The flat-plate heat exchanger shown in the figure and an in-line electric heater (19 kW capacity) were used to mimic the cooling load imposed by a building. The flat-plate heat exchanger was used to transfer thermal energy from the circuit shown on the left of the figure (described below) and essentially replaced the functionality that could have been provided by a second in-line heater. The amount of flow being diverted to this heat exchanger could be manually controlled with a bypass valve in each circuit. The temperature of the water supplied to the inlet of the evaporator’s heat exchanger was varied from 15 °C to 19 °C. The test bench was capable of supplying colder water; however, this was avoided because it could cause the absorption chiller’s internal controller to modulate its output to prevent the temperature exiting the heat exchanger from dropping below 7 °C. A limited range of water flow rates could be achieved: 1.2 L/s to 1.3 L/s. The third circuit, shown on the left of Fig. 2 (named the absorber/condenser circuit), provided controlled boundary conditions to the heat exchanger of the absorption chiller’s cooling circuit, to which energy was rejected by the absorber and by the condenser. A portion of this energy was

Bypass Valve Proportioning Valve

g

Flow Meter V g,i

Absorption Chiller

Generator Circuit

Pump

Thermopile T −Tg,o

Heat Exchanger

Chilled Glycol

Thermocouple T c,i

Absorber/Condenser Circuit

371

Thermocouple T g,o

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In−Line Heaters

Pump

Thermopile T e,i −Te,o

Thermocouple T e,o

In−Line Heater Flow Meter V Heat Exchanger

e

Pump Evaporator Circuit Bypass Valve Fig. 2. Schematic of test bench.

transferred to the evaporator circuit through the heat exchanger previously described. A second flat-plate heat exchanger was used to transfer the remainder of the absorption chiller’s rejected thermal energy to a loop circulating chilled glycol. This glycol was cooled to 7 °C by a dry-cooling tower or a vapour-compression chiller (depending upon the time of year) located on the roof of the building. Water circulated at a high flow rate (approximately 5 L/s) through this circuit. A proportioning valve was modulated to bypass a portion of the water flow around the heat exchanger in order to precisely control the temperature of the water at the inlet to the absorption chiller’s cooling circuit heat exchanger. This temperature was not allowed to rise above 33 °C during the experiments, as higher temperatures would cause the absorption chiller’s internal controller to initiate a shutdown procedure to protect the chiller. This temperature was also controlled to remain above 27 °C during the experiments, this to avoid the risk of crystallizing salt in the absorption chiller’s cycle, as cautioned by the manufacturer. Configured in this manner, the water and glycol circuit mimicked a cooling tower, ground heat exchanger, or other heat rejection device that would normally be used for heat rejection from the absorption chiller.

2.2. Instrumentation Accurate measurements of various state points in the three water circuits described above were required for control purposes, as well as for deriving the absorption chiller’s performance characteristics. Positive displacement flow meters of the oval-gear type were used to measure the flow rate of water through the generator (V_ g ) and evaporator (V_ e ) circuits. These devices produced a pulse signal whose frequency was proportional to the water’s volumetric flow rate. Each was calibrated by the manufacturer and certified to have a bias error ±1% of the reading. There was no additional bias error associated with the data acquisition (DAQ) system that recorded the meter’s pulse signal. However, the DAQ did introduce a precision error as it could only count an integer number of pulses per time interval (treated later). In order to derive the rate of heat transfer from the generator circuit’s water to the absorption chiller (qg ), it was necessary to accurately measure the water’s temperature difference between the inlet and outlet of generator’s heat exchanger (DT g ). The accuracy of the results would have been greatly impaired had DT g been derived from separate measurements of the inlet (T g;i ) and outlet (T g;o )

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temperatures. Consequently, a 4-junction thermopile was fabricated from copper-constantan (Type T) thermocouple wire and the beads were immersed in the water stream. This was accomplished by passing the wires through holes that were drilled in a pipe fitting. The holes were sealed with epoxy to prevent water leakage, and care was taken to ensure that there was no electrical contact between the individual thermopile junctions. With this arrangement the thermopile produced a voltage signal that was proportional to the temperature difference between the water at the inlet and the water at the outlet of the generator’s heat exchanger. Single-bead copper-constantan thermocouples were also immersed in the water stream at the outlet of the generator’s heat exchanger to measure T g;o . This measured temperature was used for control purposes, as well as providing necessary input to the calibration used to convert the thermopile voltage signal to DT g (see below). The generator circuit’s thermopile and thermocouple were calibrated using two precision-controlled water baths and two Pt100 platinum resistance thermometers (certified bias error less than ±0.02 °C). The cold junctions of the thermopile were immersed in one bath along with one of the Pt100 thermometers, while the hot junctions and the other Pt100 thermometer were immersed in the other bath. The bath temperatures were then controlled to span the ranges of T g;i ; T g;o , and DT g examined in the experiments. The thermopile’s voltage signal was then calibrated to the Pt100 temperature measurements from this calibration data set using a regression equation of the following form, DT g ¼ n1  V TP þ n2  T g;o þ n3

ð1Þ

where V TP is the voltage signal (mV) produced by the thermopile, T g;o is the temperature of the water at the outlet to the generator’s heat exchanger (°C), and ni are calibration coefficients. All possible sources of bias errors were accounted for during this calibration procedure. This included the DAQ’s resolution at reading the V TP voltage (±0.008 mV), the bias error of the Pt100 thermometers, and imperfections in the calibration regression (Eq. (1)). Additionally, the possible sources of bias errors in deriving DT g during the experiments were considered, which included (again) the DAQ’s resolution at reading the V TP voltage, as well as the bias associated with the T g;o thermocouple reading (since T g;o appears in Eq. (1)). When all of these individual sources of bias error were combined using the root-sum-square method recommended by Moffat (1988), it was found that DT g could be determined with a total bias error of ±0.13 °C. An in-situ test was performed to verify the correct functioning of the thermopile measuring DT g . The Pt100 thermometers were temporarily placed in thermowells mounted in the water stream close to the inlet and outlet of the generator’s heat exchanger. The T g;i and T g;o

readings from the Pt100 thermometers were in close agreement with the DT g measured with the thermopile. Similar thermal instrumentation was employed on the evaporator circuit. A copper-constantan thermocouple was immersed in the water flow to measure the evaporator heat exchanger’s outlet temperature (T e;o ). A 5-junction copper-constantan thermopile was used to measure the difference between the inlet (T e;i ) and outlet temperatures (DT e ). The calibration procedure described above employing the precision-controlled water baths and Pt100 thermometers was repeated to generate a correlation of the form of Eq. (1) for the evaporator’s thermopile. When all possible sources of bias error were combined as before, it was found that DT e could be determined with a total bias error of ±0.08 °C. A copper-constantan thermocouple was also immersed in the water flow at the inlet of the absorption chiller’s cooling heat exchanger on the absorber/condenser circuit to measure T c;i . The three thermocouples used to measure T g;o , T e;o , and T c;i were calibrated using one of the precision-controlled water baths and one of the Pt100 thermometers. All possible sources of bias error contributing to the prediction of these temperatures were accounted for and combined as before. These sources included the DAQ’s resolution at reading thermocouple voltages (during the calibration and during the experiments), the bias error of the Pt100 thermometer, imperfections in the calibration curve, and temperature fluctuations in the laboratory during the calibration process. The DAQ’s resolution at reading thermocouple voltages was more significant in relative terms in reading the thermocouples than in reading the thermopiles, since the thermopiles produce a higher voltage due to their multi-junction arrangement. The significant bias errors associated with cold-junction compensation when reading thermocouples were also accounted for. Specifically, the thermistor used to measure the temperature of the cold junction at the DAQ had a bias error of ±0.25 °C. Furthermore, the DAQ’s manufacturer suggests an additional bias error of ±0.2 °C to account for the distance between the mounting location of this thermistor and the location of the thermocouple cold junction. When all these individual sources of bias error were combined using the root-sum-square method recommended by Moffat (1988), it was found that the thermocouples could determine T g;o and T e;o with a total bias error of ±0.5 °C, and T c;i with a total bias error of ±0.4 °C. 2.3. Derived quantities The primary measurements described in the previous subsection were used to derive the absorption chiller’s performance parameters of interest. The rate of heat transfer from the generator circuit to the absorption chiller’s generator heat exchanger was derived from an energy balance. By treating the water as

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an incompressible fluid with constant heat capacity between T g;i and T g;o , it could be determined from,

ð3Þ

where qevap is the rate of heat transfer (kW) and V_ e is the flow rate of water through the evaporator’s heat exchanger (L/s). q is evaluated at T e;o and cP is evaluated at T e , the average of T e;i and T e;o . The thermal coefficient of performance of the absorption chiller is then derived from these two derived heat transfer rates, COP th ¼

qevap V_ e  qjT e;o  cP jT e  DT e ¼ qgen V_ g  qjT g;o  cP jT g  DT g

ð4Þ

The bias errors of the individual primary measurements were propagated into these derived quantities using the root-sum-square method recommended by Moffat (1988) to determine the total bias errors associated with the derived quantities. In this way, the bias errors associated with the water flow meters, thermocouples, and thermopiles discussed in the previous subsection were propagated to estimate the total bias error according to the magnitude of the primary measurements. These calculations were repeated for each measurement point. The propagated bias error for qgen was found to range from 1.5% to 6.2%, that for qevap from 1.5% to 7.2%, and that for COP th from 2.1% to 9.4%. 2.4. Steady-state experiments A series of experiments was conducted with various combinations of boundary conditions in the generator, evaporator, and absorber/condenser circuits. The goal was to maintain these boundary conditions as steady as possible for a sufficiently long period to enable the logging of data under steady-state conditions. In each case, conditions were allowed to stabilize until target flow rates and temperatures were achieved in each of the three circuits. Once steady conditions had been achieved, data were logged each 5 s to record the primary measurements described in Section 2.2. Some of the primary measurements recorded during one of these steady-state experiments are illustrated in Fig. 3. As can be seen, T g;o was

. Vg . Ve

120

ð2Þ

1.4

110 1.2

100 90

Tg,o 70

Tc,i

0.8

Te,o

60

0.6

50

Flow rate (L/s)

1.0 80

o

where qgen is the rate of heat transfer (kW). V_ g is the flow rate of water through the generator’s heat exchanger (L/s). q is the density of water (kg/L), which is evaluated at T g;o , the temperature measurement point closest to the flow meter. cP is the heat capacity (kJ/kgK) of water evaluated at T g , the average of T g;i and T g;o . The rate of heat transfer from the absorption chiller’s evaporator heat exchanger to the evaporator circuit (the absorption chiller’s cooling capacity) was derived in a similar manner, qevap ¼ V_ e  qjT e;o  cP jT e  DT e

130

Temperature ( C)

qgen ¼ V_ g  qjT g;o  cP jT g  DT g

373

40 0.4 30 20

0.2

10 0

0

2

4

6

8

10

12

0.0 14

Time from start of experiment (min)

Fig. 3. Boundary conditions maintained during one of the steady-state experiments.

held steady at approximately 82 °C throughout the 14-min duration of this experiment; the standard deviation of this temperature was less than 0.1 °C. A similar degree of stability was achieved on T e;o , which was maintained at approximately 9 °C with a standard deviation of less than 0.1 °C. Although it was more difficult to precisely control T c;i , this temperature was maintained at approximately 29 °C with a standard deviation of 0.5 °C. The water flow rates through the generator and evaporator circuits during this experiment are also illustrated in Fig. 3. It may appear from the figure that V_ g was fluctuating. However, this was an artefact caused by the length of the data logging interval (5 s) and the resolution of the flow meter. As explained in Section 2.2, the flow meters produced an integer number of pulses per time interval. In fact, at each of the 166 5-s logging intervals over this experiment, the flow meter generated either 87 or 88 pulses. Further evidence of the steadiness of the boundary conditions can be seen in Fig. 4, which plots T g;i and T g;o throughout this same experiment. The values of T g;i in this figure were derived from the thermocouple measuring T g;o and the thermopile measuring DT g . The error bars represent the bias errors associated with these data, while the solid horizontal lines represent the values of these temperatures averaged over the duration of the experiment. As can be seen, the experiment-averaged T g;i and T g;o lie within the ranges of the bias errors of each measurement point. (Although data are logged at 5-s intervals, for the sake of clarity Fig. 4 plots only the measurements taken every 30 s.) The heat transfer rates and the thermal coefficient of performance were derived from the primary measurements at each 5-s logging interval of this experiment using Eqs. (2)–(4). The results can be seen in Fig. 5. The bias errors

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measurements by the square root of the number of measurements taken (166) over the nearly 14-min experiment, as detailed by Moffat (1988). Therefore, the precision index of qgen is only 0.06 kW. Finally, the uncertainty in qgen at the 95% confidence level can be determined by combining the bias errors and the precision index (Moffat, 1988), qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2
2ffi ð5Þ Bqgen þ tS qgen U qgen 95% ¼

96

94

92

o

Temperature ( C)

90

Tg,i Tg,o

88

where t is the standard statistical
Student’s t-value. For this experiment, U qgen 95% was found to be 0.85 kW, which is only 1.6% of qgen . The mean values of the three derived quantities of interest over this experiment along with their uncertainty at the 95% confidence interval are summarized as follows,

86

84

82

80

qgen ¼ 54:16  0:85 kW ¼ 54:16 kW  1:6% 78

qevap ¼ 40:46  0:62 kW ¼ 40:46 kW  1:5% 0

2

4

6

8

10

12

14

Time from start of experiment (min)

Fig. 4. Water temperatures at inlet and outlet of generator heat exchanger during one of the steady-state experiments.

associated with the primary measurements were propagated into these derived quantities (as discussed in Section 2.2) and are illustrated as error bars in Fig. 5. Once again, for the sake of clarity the graph plots only the data logged each 30 s. Over this experiment, the average bias error of qgen was found to be 0.84 kW while that of qevap was 0.61 kW. The average bias error of COP th was 0.016. qgen had an average value of 54.16 kW over the experiment (qgen , plotted as a horizontal bar in Fig. 5) and a standard deviation of 0.77 kW. The precision index of qgen is determined by dividing the standard deviation of the 100

1.0

90

0.9

80

0.8

70

0.7

60

0.6

50

0.5

40

0.4

qgen qevap

30

0.2

10

0.1

0

2

3. Analysis of results The methods detailed in Section 2 were repeated to conduct a total of 36 steady-state experiments. Each of these 36 experiments examined a different combination of T g;i ; T e;i ; T c;i ; V_ g , and V_ e . Once steady conditions had been achieved for a given set of boundary conditions, data were logged at 5-s intervals for a period of 6 to 22 min. The range of these variables examined in the 36 experiments is summarized in Table 1. Fig. 6 examines the impact of T g;i on the absorption chiller’s cooling capacity (blue symbols) over these 36 experiments. The experiment-averaged quantities of qevap and T g;i were derived for each of the 36 experiments. The error bars in Fig. 6 represent the experimental uncertainty of these averaged quantities at the 95% confidence level. The clear influence of T g;i upon qevap is evident from the figure. For example, there is more than a fivefold increase in the cooling capacity over the range of T g;i examined (6.9 kW to 40.5 kW). The chiller’s manufacturer provides performance data at nominal operating conditions (T g;i ¼ 88  C; T c;i ¼ 31  C; T e;i ¼ 12:5  C, V_ g ¼ 2:4 L/s, and V_ e ¼ 1:52 L/s) as well as curves for approximating performance at off-design conditions. The manufacturer’s data at these nominal operating conditions, once adjusted for V_ g , are plotted in Fig. 6 using

0.3

20

0

COPth

Heat transfer rate (kW)

COPth

COP th ¼ 0:747  0:016 ¼ 0:747  2:2%

4

6

8

10

12

14

0.0

Time from start of experiment (min)

Fig. 5. Derived quantities during one of the steady-state experiments.

Table 1 Range of boundary conditions examined during the 36 steady-state experiments. 71:3  C 6 T g;i 6 93:2  C 14:8  C 6 T e;i 6 18:8  C 27:2  C 6 T c;i 6 32:7  C 0:9 L=s 6 V_ g 6 1:2 L=s 1:2 L=s 6 V_ e 6 1:3 L=s

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375

26

1.0 80

COPth 70

0.9

0.8 24 0.7

0.6

50

0.5 40 0.4

qevap (kW)

manufacturer’s data

COPth

Heat transfer rate (kW)

60

22

30 manufacturer’s data

0.3

20

20 0.2

qgen 10

qevap

0.1 18

0 65

70

75

80

o

85

90

95

0.0 100

Tg,i ( C)

qevap 29

30

31

32

o

Fig. 6. Impact of generator inlet temperature on chiller performance during 36 steady-state experiments.

solid diamond symbols. As can be seen, the manufacturer’s data for the nominal operating conditions fall within the range of the measured data. It is important to note that the instrumentation used by the manufacturer and their associated uncertainty are not declared. Notwithstanding, there is reasonable agreement when the manufacturer’s data are compared to the measured data from the experiment most closely corresponding to the rated conditions: qevap agrees within 4% and qgen agrees within 12%. Fig. 6 also clearly illustrates the dependence of qgen upon T g;i (red symbols). The relationship between T g;i and COP th is less clearly seen in the figure (green symbols), although it can be observed that the lowest COP th values occurred when T g;i was less than 75 °C, while the greatest values occurred when T g;i was between 80 °C and 90 °C. COP th values greater than 0.8 were achieved in a number of the experiments. The dotted lines in Fig. 6 were established by performing linear regressions of qevap and qgen to T g;i . Although these show a clear correlation, there is considerable spread around these lines. The root-mean of the square of the deviations between the measured and fitted data in relative terms was in the order of 10%. If T g;i were the only determinant upon the absorption chiller’s performance, then the data would have revealed much less deviation from these linear fits. This leads to the observation that the absorption chiller’s performance depends as well on T e;i ; T c;i ; V_ g , and/or V_ e . The data from the 36 experiments were examined graphically to reveal the nature of these functional dependencies. However, the correlation between chiller performance and these variables was less manifest. A glimpse of one of the

Tc,i ( C)

Fig. 7. Impact of absorber/condenser inlet temperature on cooling capacity during the 11 steady-state experiments for which 79  C < T g;i < 82  C.

relationships can be seen in Fig. 7, which plots qevap versus T c;i for a subset of 11 of the 36 experiments. This subset was chosen to span a narrow range of T g;i (79 °C to 82 °C) in an attempt to isolate the impact of T c;i . The scale of the vertical axis is exaggerated and a line fitting a linear regression to the data are used to illustrate a functional dependency. As a consequence, it can be seen that qevap tends to decrease as T c;i increases. The electric power consumption of the absorption chiller was also measured during normal operation for one experiment. This experiment was separate from the 36 previously described experiments used to characterize this absorption chiller’s thermal performance. The chiller required a balanced, three-phase 208/120 Vac power supply at a frequency of 60 Hz. The major electric power consumers within the chiller were the solution pump along with its data acquisition and control system. During this one experiment, the average single-phase power consumption was measured as 46.7 ± 2.1 W corresponding to a balanced three-phase average consumption of 140.1 ± 6.3 W. Measurements of the electric power consumption were taken using an energy transducer that determined consumption over a given period of time based upon signals produced by a 30 A magnetic coil current transducer and a voltage monitor. This energy transducer also accounted for the phase shift between the current and voltage. For this size of current transducer, a pulse was produced for every 0.75 J of energy consumed. This translated into a measured average single-phase power consumption resolution of ±45 W within the 1-min sample interval that was used. To compensate for this poor resolution relative to

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the measured power consumption of a single phase, data were logged during steady-state operation for approximately 80 min to achieve the previously described uncertainty margins on the single and three-phase average power consumption measurements. The next section treats the calibration of the absorption chiller’s performance to the five independent variables controlled in the 36 steady-state experiments. 4. Model calibration The previous section described how the experimentaveraged derived quantities of qevap ; qgen , and COP th were determined for the 36 combinations of T g;i ; T e;i ; T c;i , V_ g , and V_ e examined in the experiments. It also discussed some of the functional dependencies these data revealed. This section determines appropriate calibrations for expressing these functional dependencies. After examining several possible functional forms to relate qevap to the five independent variables, the following equation was used to regress the measured data: qevap ¼ ae þ be  ðT g;i  71Þ þ ce  ðT e;i  14Þ þ de  ðT c;i  27Þ þ e  ðV_ g  0:9Þ þ fe  ðV_ e  1:2Þ ð6Þ where ae . . . fe are calibration coefficients. Eq. (6) provided a good fit to the experimental data. The Pearson correlation coefficient (r-value) was 0.994. The average error between the measured and correlated qevap values was 2.9% while the root-mean-square (rms) error was 3.6%. The maximum deviation for a single experiment was 9.3%. A statistical significance test (Kutner et al., 2004) was then performed in which the p-values of each coefficient in Eq. (6) were determined. This analysis revealed that the null hypothesis could be safely rejected (p-value  0.01) for the T g;i and T c;i terms of Eq. (6), and that there was a strong presumption against the null hypothesis (0.01 < p-value < 0.05) for the T e;i and V_ g terms. However, it indicated that the null hypothesis could not be rejected (p-value > 0.1) for the V_ e term. As a result of this statistical significance test, the fe coefficient was set to zero. The regression and statistical significance test were then repeated to produce a second set of calibration coefficients for the qevap equation. The removal of the fe term had a negligible impact on the Pearson correlation coefficient (it was still 0.994) while the average error and rms errors slightly increased (to 3.3% and 3.8%, respectively). The maximum deviation for a single experiment was found to decrease to 8.0%. The p-value for T e;i term did, however, increase after the removal of the V_ e term into a region (0.1 > p-value > 0.05) where there was no longer a strong presumption against the null hypothesis. The p-values for the other terms did not change significantly. Consequently, the T e;i term was removed by setting the corresponding coefficient to zero.

After the removal of the T e;i term, the regression was repeated along with the statistical significance test. The removal of the T e;i term had a negligible impact on the Pearson correlation coefficient (it decreased slightly to 0.993) while the average error and rms errors slightly increased (to 3.4% and 4.0%, respectively). The maximum deviation for a single experiment was found to increase to 9.4%. The p-values for the remaining terms did not change significantly. These findings suggest that while it is possible T e;i may have a small impact on qevap , it is difficult to justify retaining the T e;i term in Eq. (6) because removing it does not significantly reduce the quality of the regression equation fit to the data. As will be shown later in this section, it is also justifiable to remove the T e;i term from the qgen calibration equation for similar reasons. By removing the T e;i term from both the qevap and qgen equations the overall absorption chiller model is greatly simplified with little loss of accuracy. Without the T e;i term, this absorption chiller model can be coupled to cold storage tank models that do not account for thermal stratification within the storage tank and still produce accurate simulation results. The coefficients derived from the previously described calibration process for Eq. (6) are provided in Table 2. The goodness of fit of Eq. (6) using the coefficients in Table 2 to the measured data is illustrated in Fig. 8. This plots the values of qevap derived from the measurements along the x-axis and the values determined from Eq. (6) along the y-axis. The error bars represent the experimental uncertainty at the 95% confidence level. The diagonal dashed line in the figure represents the line of perfect agreement. The same functional form was found to be appropriate for regressing qgen . Once again the statistical significance test revealed that the null hypothesis could not be rejected (p-value > 0.1) for the T e;i and V_ e terms. Consequently, the cg and fg coefficients were set to zero: qgen ¼ ag þ bg  ðT g;i  71Þ þ

ðT e;i  14Þ

þ dg  ðT c;i  27Þ þ g  ðV_ g  0:9Þ þ

ðV_ e  1:2Þ ð7Þ

The coefficients resulting from the regression of Eq. (7) are provided in Table 2. The Pearson correlation coefficient (r-value) was 0.995. The average error between the measured and correlated qevap values was 2.6% while the Table 2 Calibration coefficients for Eqs. (6) and (7).

ai bi ci di i fi

qevap

qgen

10.9334 1.40233 0 1.67718 7.06095 0

16.1421 1.69588 0 1.99578 6.93785 0

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Fig. 8. Goodness of fit of Eq. (6) and Table 2 coefficients at representing experimentally derived cooling capacity from 36 steady-state experiments.

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It is interesting to contrast the sensitivities of the qevap and qgen calibrations to the curves provided by the chiller’s manufacturer for approximating performance at off-design conditions. It must be noted that the manufacturer cautions that their performance curves must only be used for broad reference purposes. Eqs. (6) and (7) and the calibration coefficients given in Table 2 indicate that qevap and qgen increase with T g;i . This trend is in agreement with the manufacturer’s performance curves, although the calibrated model is seen to have greater sensitivity to T g;i . Both the calibrated model and the manufacturer’s curves predict that qevap and qgen decrease as T c;i increases, although the calibrated model is less sensitive to T c;i . The calibrated model and the manufacturer’s curves are in close agreement in terms of the increase in qevap and qgen with V_ g . A number of functional forms were examined to find a suitable correlation of COP th to the measured data from the 36 experiments. One option examined was to substitute the correlations of Eqs. (6) and (7) into Eq. (4): COP th ¼ ¼

60 55

qevap qgen ae þ be  ðT g;i  71Þ þ de  ðT c;i  27Þ þ e  ðV_ g  0:9Þ ag þ bg  ðT g;i  71Þ þ dg  ðT c;i  27Þ þ g  ðV_ g  0:9Þ ð8Þ

50

Due to the propagation of imperfections in each of the Eq. (6) and Eq. (7) correlations, the quality of the fit produced by Eq. (8) was found to be less than satisfactory. The Pearson correlation coefficient (r-value) was 0.704. The average error between the measured and correlated COP th values was 4.5% while the root-mean-square error was 5.7%. The maximum deviation for a single experiment was 15.2%. Consequently, an alternate functional form was sought. By preserving the rational form of Eq. (8), but by deriving calibration coefficients directly from COP th data, an improved fit was obtained. This form is shown below in Eq. (9).

qgen from correlation (kW)

45 40 35 30 25 20 15 10 5 0

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qgen derived from measurements (kW)

Fig. 9. Goodness of fit of Eq. (7) and Table 2 coefficients at representing experimentally derived rate of heat input from 36 steady-state experiments.

root-mean-square error was 3.5%. The maximum deviation for a single experiment was 11.1%. The goodness of fit of Eq. (7) using the coefficients in Table 2 to the measured data is illustrated in Fig. 9. This plots the values of qgen derived from the measurements along the x-axis and the values determined from Eq. (6) along the y-axis. The error bars represent the experimental uncertainty at the 95% confidence level. The diagonal dashed line in the figure represents the line of perfect agreement.

COP th ¼

a1  ðT g;i  71Þ þ b1  ðT c;i  27Þ þ c1  ðV_ g  0:9Þ a2  ðT g;i  71Þ þ b2  ðT c;i  27Þ þ c2  ðV_ g  0:9Þ ð9Þ

The coefficients derived from an iterative, non-linearcurve-fit procedure for Eq. (9) are provided in Table 3. Note that the ci coefficients derived from this procedure went to zero during this iterative curve-fit procedure, suggesting that generator flow rate does not play a strong role Table 3 Calibration coefficients for Eq. (9). a1 b1 c1

0.735376 0.251982 0

a2 b2 c2

0.924023 0.477536 0

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90

80

70

Tg,i o

in determining COP th . The Pearson correlation coefficient (r-value) was 0.778. The average error between the measured and correlated COP th values was 3.9% while the root-mean-square error was 4.8%. The maximum deviation for a single experiment was 11.9%. The goodness of fit of Eq. (9) using the coefficients in Table 3 to the measured data is illustrated in Fig. 10. This plots the values of COP th derived from the measurements along the x-axis and the values determined from Eq. (9) along the y-axis. The error bars represent the experimental uncertainty at the 95% confidence level. The diagonal dashed line in the figure represents the line of perfect agreement.

Temperature ( C)

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Te,o 50

40

30

5. Validation

20

The previous section discussed how data from 36 steadystate experiments were used to establish the functional form of the qevap ; qgen , and COP th calibrations and to regress their calibration coefficients. The validity of these functional forms and the calibration coefficients are examined in this section by contrasting their predictions to measurements from a disjunct experiment whose data were not used to calibrate the model. T g;i was made to vary over this validation experiment, as illustrated in Fig. 11. This figure illustrates the measured data at 1-min intervals, each data point representing the average of the measurements taken during the preceding 12 5-s logging intervals. As can be seen, T g;i was rapidly increased from 80 °C to almost 88 °C between minute 2 and minute 6 (most of the increase having occurred by minute 4). It was then suddenly raised to almost 91 °C between minute 17 and minute 20. T e;i was also suddenly increased

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Fig. 11. Boundary experiment.

conditions

maintained

during

the

validation

by about 1 °C between minute 17 and minute 19. There were more minor variations in T c;i over the validation experiment while V_ g and V_ e were held constant at 1.2 L/s. The qevap calibration was then compared to the measurements from this validation experiment. Values of qevap were derived from the measurements using Eq. (3). The 1-min averaged values of T g;i ; T c;i , and V_ g were determined over the 31 min of the validation experiment. Eq. (6) and the

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COPth from correlation (-)

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Fig. 10. Goodness of fit of Eq. (9) and Table 3 coefficients at representing experimentally derived coefficient of performance from 36 steady-state experiments.

Fig. 12. Comparison of calibration and measured heat transfer rates during the validation experiment.

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integrated quantity of qgen over the experiment’s 31 min duration was found to be 3.6% (2.9%) less with the calibration than with the measured data. Therefore, apart from the 3-min period following a sudden increase in T g;i , the qgen calibration performs equally well during the validation experiment as it did at representing the data from the 36 steady-state experiments. As can be seen from the Fig. 12 (at minute 3), there is no time lag between the change in the T g;i boundary condition and measured response in qgen . In contrast, qevap responds gradually over a few minutes to this change in T g;i (compare the measured qevap of minute 3 to that of minute 2). The thermal mass of the generator’s heat exchanger and/ or the thermal mass of other components in the absorption cycle are the most likely explanations for these observations. The COP th calibration was also compared to the measurements from the validation experiment by evaluating Eq. (9) using the Table 3 coefficients. The results can be seen in Fig. 13, which indicates that the calibration overpredicts COP th throughout the validation experiment. The Pearson correlation coefficient was 0.379 for the full experiment (and 0.488 without the data from minutes 3, 4, and 5). The average error between the measured and correlated qgen values was 7.4% (4.1%) while the rms error was 13.9% (4.3%). The maximum deviation for a single minutes was 52% (8.4%). Therefore, apart from the 3-min period following a sudden increase in T g;i , the COP th calibration’s average, rms, and maximum errors are commensurate with the values seen with the calibration data set. However, the Pearson correlation coefficient is much worse.

1.0 0.9 0.8 0.7 0.6

COPth (-)

Table 2 coefficients were then evaluated using these quantities for each of the 31 min of the experiment. Fig. 12 contrasts the calibration predictions to the measured data. This figure indicates close agreement between the measured and calibrated qevap values during much of the experiment, in particular the periods of steady conditions (1–2 min, 6–17 min, 22–31 min). However, the qevap calibration predictions are seen to deviate significantly from the measurements when T g;i is suddenly increased between minute 2 and minute 4 (see Fig. 11). The calibration predicts a sudden increase in qevap between minute 2 and minute 3. However, the measurements clearly indicate a lag in the absorption chiller’s response: the measured qevap at minute 3 is approximately the same as at minute 2. In fact, it is not until minute 7 that the qevap derived from the measurements stabilizes to a new steady-state, at which time the measurements and calibration come into closer agreement once again. A similar but less significant deviation between calibration and measurements is also seen when T g;i is increased between minute 17 and 20. Again, the calibration is found to exceed the measured value for a period of approximately 4 min. The Pearson correlation coefficient between the calibrated and measured qevap during the validation experiment’s 31 min duration was 0.937. The average error between the measured and correlated qevap values was 4.0% while the rms error was 8.7%. The maximum deviation for a single minute was 37%. The integrated quantity of qevap over the experiment’s 31 min duration was found to be 3.3% greater with the calibration than with the measured data. The greatest deviation between calibrated and measured qevap values occurs at minutes 3, 4, and 5, the period during and immediately following the rapid rise in T g;i . Removing the data from these 3 min significantly affects the goodness-of-fit metrics: the Pearson correlation coefficient rises to 0.992; the average relative error drops to 1.9%; the rms error drops to 2.2%; and the maximum deviation for a single minute is reduced to 5.6%. This suggests that apart from the 3-min period following a sudden increase in T g;i , the calibration performs equally well during the validation experiment as it did at representing the data from the 36 steady-state experiments. Fig. 12 also compares the calibrated and measured values of qgen . In this case the calibrated quantities are seen to be in close agreement with the measurements during steady periods of operation, with poor agreement between minutes 3 and 6 and between minutes 18 to 21, when T g;i was undergoing rapid changes. As before, the goodnessof-fit metrics were calculated for the full validation experiment and then recalculated after removing the data for minutes 3, 4, and 5. The Pearson correlation coefficient was 0.965 for the full experiment (and 0.993 without the data from minutes 3, 4, and 5). The average error between the measured and correlated qgen values was 3.6% (2.9%) while the rms error was 4.7% (3.0%). The maximum deviation for a single minutes was 17% (7.2%) while the

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measurements calibration

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Fig. 13. Comparison of calibration and measured COP th during the validation experiment.

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6. Conclusions A series of experiments was conducted on a commercially available lithium bromide–water absorption chiller with a nominal cooling capacity of 35 kW in order to develop a calibrated ‘‘grey-box” model. A test bench was designed and commissioned to expose the absorption chiller to a broad range of controlled boundary conditions. The temperature of the water supplied to the inlet of the heat exchanger at the chiller’s generator was varied from 71 °C to 93 °C while the temperature of the water supplied to the inlet of the evaporator’s heat exchanger was varied from 15 °C to 19 °C. A range from 27 °C to 33 °C was examined at the inlet of the absorber/condenser’s heat exchanger. Instrumentation was calibrated and installed to accurately measure temperatures, temperature differences, and flow rates through the chiller’s generator and evaporator heat exchangers, and the temperature at the inlet of the absorber/condenser. A total of 36 steady-state experiments were conducted with various combinations of boundary conditions at the generator, evaporator, and absorber/condenser. The rates of heat transfer to the chiller’s generator and evaporator and the chiller’s thermal coefficient of performance were derived from the measurements for each of these 36 steady-state experiments. The rate of heat transfer to the evaporator (i.e. the chiller’s cooling capacity) was observed to increase with the temperature supplied to the generator and to decrease with the temperature supplied to the absorber/condenser. The cooling capacity was found to vary from 6.9 kW to 40.5 kW over the range of the experiments, and the thermal coefficient of performance from 0.56 to 0.83. A model suitable for use in quasi-steady-state simulations and that expressed the chiller’s performance as a function of the controlled boundary conditions was developed. Based upon statistical significance testing, it was found that the rates of heat transfer to both the generator and the evaporator could be expressed as linear functions of the generator inlet temperature, absorber/condenser inlet temperature, and flow rate of water to the generator. Regressions of these functions to the data from the 36 experiments produced Pearson correlation coefficients (r-value) of greater than 0.99. In a similar manner, a model was developed to express the thermal coefficient of performance as a function of the generator inlet temperature and the absorber/condenser inlet temperature; however, the Pearson correlation coefficient of this regression to the data was only 0.78. The validity of the calibrated model was then tested using measurements from a disjunct experiment whose data were not used to calibrate the model. Close agreement between the model predictions of the heat transfer rates to the generator and evaporator were found throughout this validation experiment, except during times of rapid changes in boundary conditions. Specifically, when the temperature of the water supplied to the generator was

suddenly increased by 8 °C, the model predictions were found to significantly differ from the measurements for approximately 4 min. Clearly, this quasi-steady-state model cannot represent the chiller’s transient response that occurs following a sudden change in boundary conditions. However, such a rapid change in boundary conditions is not likely to occur in practice and the chiller’s response time is of the same order of magnitude as the time-step that would be used in building performance simulations. Moreover, when the results were integrated over the 31-min validation experiment that included two sudden changes in boundary conditions, the model was able to predict the energy transfer to the generator and evaporator to within 3–4% of the measurements. The calibrated quasi-steady-state grey-box model of the chiller proposed here is suitable for application in building performance simulation studies. Specifically, it can be used to assess how a solar air-conditioning system employing this chiller can perform with various combinations of solar collector type and array size, thermal storage configurations, control strategies, building type, occupant behaviour, and geographic location. Acknowledgement The authors gratefully acknowledge the financial support provided through the NSERC-funded Smart NetZero Energy Buildings Strategic Research Network and the Canadian Foundation for Innovation. References Adao, P., Pereira, M., Costa, A., 2008. Pre-commercial development of a cost-effective solar-driven absorption chiller. In: Proc. Eurosun. Lisbon, Portugal. Agyenim, F., Knight, I., Rhodes, M., 2010. Design and experimental testing of the performance of an outdoor H2O/LiBr solar thermal absorption cooling system with a cold store. Sol. Energy 84 (5), 735–744. Ali, H., Noeres, P., Pollerberg, C., 2008. Performance assessment of an integrated free cooling and solar powered single-effect lithium bromide–water absorption chiller. Sol. Energy 82, 1021–1031. Aphornratana, S., Sriveerakul, T., 2007. Experimental studies of a singleeffect absorption refrigerator using aqueous lithium-bromide: effect of operating condition to system performance. Exp. Therm. Fluid Sci. 32, 658–669. Asdrubali, F., Grignaffini, S., 2005. Evaluation of the performances of a H2O–LiBr absorption refrigerator under different service conditions. J. Refrig. 28, 489–497. Assilzadeh, F., Kalogirou, S., Ali, Y., Sopian, K., 2005. Simulation and optimization of a LiBr solar absorption cooling system with evacuated tube collectors. Renew. Energy 30, 1143–1159. Balghouthi, M., Chahbani, M., Guizani, A., 2008. Feasibility of solar absorption air conditioning in Tunisia. Build. Environ. 43, 1459–1470. Borg, S.P., Kelly, N.J., 2012. The development and calibration of a generic dynamic absorption chiller model. Energy Buildings 55, 533–544. Cascales, J., Garcı´a, F., Izquierdo, J., Marı´n, J., Sa´nchez, R., 2011. Modelling an absorption system assisted by solar energy. Appl. Therm. Eng. 31, 112–118. Eicker, U., Colmenar-Santos, A., Teran, L., Cotrado, M., Borge-Diez, D., 2014. Economic evaluation of solar thermal and photovoltaic cooling systems through simulation in different climatic conditions: an analysis in three different cities in Europe. Energy Buildings 70, 207–223.

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