Thermal Performance Analysis of an Absorption Cooling System Based on Parabolic Trough Solar Collectors

Home , Thermal efficiency, Variable air volume

Article Thermal Performance Analysis of an Absorption Cooling System Based on Parabolic Trough Solar Collectors

Jiangjiang Wang * , Rujing Yan, Zhuang Wang, Xutao Zhang and Guohua Shi

School of Energy, Power and Mechanical Engineering, North China Electric Power University, Baoding 071003, Hebei, China; [email protected] (R.Y.); [email protected] (Z.W.); [email protected] (X.Z.); [email protected] (G.S.) * Correspondence: [email protected]; Tel.: +86-312-752-2792

Received: 4 September 2018; Accepted: 7 October 2018; Published: 9 October 2018

Abstract: Solar radiation intensity significantly influences the cooling loads of building, and the two are correlated and accorded to a certain extent. This study proposes a double effect LiBr–H2O absorption cooling system based on the parabolic trough collector (PTC) of solar heat energy. Thermodynamic models including PTC and absorption chiller are constructed, and their accuracy is verified by comparing the simulation results and the experimental data. Subsequently, the impact of variable design parameters on the thermodynamic performance is analyzed and discussed. The analysis of a solar cooling system in a hotel case study is related to its operation in a typical day, the average coefficient of performance of the absorption chiller is approximately 1.195, and the whole solar cooling system achieves 61.98% solar energy utilization efficiency. Furthermore, the performance comparison of a solar cooling system in different types of building indicates that higher matching and a higher correlation coefficient between the transient solar direct normal irradiance and cooling load is helpful in decreasing the heat loss and improving systemic performance. The solar cooling system in the office building exhibits a correlation coefficient of approximately 0.81 and achieves 69.47% systemic thermal efficiency.

Keywords: solar cooling system; absorption chiller; solar energy; parabolic trough solar collector (PTC)

1. Introduction The energy consumption of heating, ventilation, and air conditioning (HVAC) systems in office buildings generally accounts for 30% of the total building energy consumption [1]. Moreover, in developed countries or areas with extreme climates, it increases up to 50% [2]. In order to improve energy efﬁciency and reduce energy consumption, passive technologies such as solar gain wall; photovoltaic (PV) green roofs and passive cooling; and HVAC technologies including radiant heating/cooling systems, variable-air-volume-based air-conditioning systems, and so on, have been proposed and developed from different aspects [3]. A method used in these technologies involves adopting renewable energy, such as biomass [4] and solar energy [5], to replace fossil fuels. Solar energy is an alternative for fossil energy owing to its high reserve, wide distribution, renewal, and non-polluting capabilities. The combination of cooling and solar energy is a suitable method to realize a better balance between solar thermal energy input and cooling output in the future market [6]. Typically, the collection of higher solar energy is involved when a building needs increased cooling demand. Consequently, a solar cooling system is employed to reduce electricity consumption at the peak of summer and relieve electricity shortages. The main alternative routes from solar energy into the cooling system include solar thermal or electric PV, and the corresponding cooling thermodynamic cycles such as absorption

Energies 2018, 11, 2679; doi:10.3390/en11102679 www.mdpi.com/journal/energies Energies 2018, 11, 2679 2 of 17 and vapor compression are different [7]. In this case, the PV electric cooling system nowadays has higher energy efficiency and better economic performance [7]. With the development and promotion of solar heat collectors including concentrating and non-concentrating collectors, the technologies of cooling driven by solar thermal energy, such as solar adsorption cooling system [8], solar assisted liquid desiccant dehumidifier [9], and solar adsorption desalination-cooling system [10], were developed and analyzed from different aspects including energetic efficiency, economic feasibility [11], and environmental assessment [12] by researchers from different countries and regions [13]. Parabolic trough collector (PTC) for solar thermal energy is a relatively mature technology corresponding to a concentrating-type solar collector that ensures heat collecting efficiency at a higher temperature [14]. The temperature of the heat source from PTC is compatible with the heat demand of a double-effect LiBr–H2O absorption chiller that achieves a higher coefficient of performance (COP). The double-effect absorption chiller coupled with PTC can reach almost the same parity as PV-driven electric chillers, only in terms of energy efficiency [7,15]. Currently, several studies examined performance improvement and practical application of solar cooling system using experiments, simulations, and other methods. Tsilingiris [16] proposed the theoretical modelling of a solar cooling system for domestic applications in homes and confirmed the economic performance of the solar cooling system at the cost of fossil fuels. Mazloumi et al. [17] simulated the thermal performances of a solar single effect LiBr–H2O absorption chiller system integrated with a heat storage tank at the end of PTC, and the results indicated that the optimal capacity of the thermal storage tank significantly affects systemic operation performances. Li et al. [18] investigated the performance of a 23 kW solar powered single-effect LiBr–H2O absorption cooling system using a PTC of 56 m2 aperture area, and the experiment results indicated that the daily cooling COP varied from 0.11 to 0.27 in the sunny and clear sky days and the daily solar heat fraction ranged from 0.33 to 0.41. Qu et al. [19] modeled a PTC absorption chiller system in the transient system simulation program and constructed a corresponding 52 m2 experimental platform. The systemic performances in different wind speeds and solar radiations were analyzed and verified with the experimental data, and it was concluded that the solar thermal system could potentially supply 39% of the cooling and 20% of the heating demands for the building space. Tzivanidis and Bellos [20] investigated the influences of design parameters such as mass flow rate and storage tank volume on the performance of a one-stage absorption chiller coupled with a PTC in the climate of Athens, and concluded that using a 54 m2 collecting area and a storage tank of 1.35 m3, it is possible to achieve a maximum cooling load of 12.8 kW. Besides PTC, solar cooling systems coupled with different collectors were developed and analyzed. Aman et al. [21] proposed an ammonia–water absorption cooling system based on a flat plate solar collector for residential application and focused on energy and exergy analyses of an absorption chiller. Furthermore, Bellos et al. [22] presented exergetic, energetic, and economic evaluations of a solar-driven absorption cooling system with four various collectors including flat plate collectors, evacuated tube collectors, compound parabolic collectors, and PTCs. The comparisons illustrated that the system with the higher solar COP is the one with PTC because of their high efficiency, and is also the one with the maximum solar exergetic efficiency. Aiming to achieve greater energy efficiency, Delaˇcet al. [23] designed a solar heating and cooling system configured with condenser and absorber heat recovery, and the presentation of scenario shows recovery of up to 53% of waster condenser and absorber heat. Neyer et al. [24] focused on the integration of a single-/half-effect NH3/H2O absorption chiller into parallel/serial to conventional systems and concluded that its application for solar- and combined heating and power(CHP)-driven systems are reaching non-renewable primary energy savings of 30–70% at almost equal costs compared with conventional systems. Calise et al. [25] proposed a novel high-temperature solar assisted triple-pressure level combined cycle power plant and presented the thermoeconomic analysis of a novel solar cooling system for the combined cycle power plant. The application of solar cooling system integrated with different technologies is the current research focus, and the previous studies focused on the performances of a solar cooling system integrated with different solar collectors by Energies 2018, 11, x FOR PEER REVIEW 3 of 17 Energies 2018, 11, 2679 3 of 17 studies focused on the performances of a solar cooling system integrated with different solar collectors by simulations or experiments. However, the performances in off-design work conditions simulations or experiments. However, the performances in off-design work conditions involved the involved the whole system and the different characteristics of building cooling loads were examined whole system and the different characteristics of building cooling loads were examined in a few studies in a few studies from the literature. from the literature. The specific objectives of this work are to propose a double-effect absorption chiller system The specific objectives of this work are to propose a double-effect absorption chiller system driven driven by solar thermal energy collection through PTC, to analyze the thermodynamic performances by solar thermal energy collection through PTC, to analyze the thermodynamic performances of the of the solar cooling system, and to characterize its applicability in different buildings with different solar cooling system, and to characterize its applicability in different buildings with different cooling cooling loads using the correlation coefficient. Section 2 proposes the integrated solar cooling system loads using the correlation coefficient. Section2 proposes the integrated solar cooling system and and models the equipment and system. Section 3 analyzes the thermal performances including design models the equipment and system. Section3 analyzes the thermal performances including design and and off-design work conditions, and discusses application performances in different kinds of off-design work conditions, and discusses application performances in different kinds of buildings. buildings. Section 4 summarizes the conclusions of the study. Section4 summarizes the conclusions of the study.

2.2. SystemSystem andand ModelModel

2.1.2.1. SystemSystem DescriptionDescription

TheThe flowchart flowchart of of the the proposed proposed double-effect double-effect LiBr–H LiBr–H2O2O absorption absorption chiller chiller system system driven driven by by PTC PTC is shownis shown in Figurein Figure1 The 1 The complete complete system system consists consists of of a solara solar heat heat collecting collecting subsystem, subsystem, a a heat heat storage storage subsystem,subsystem, aa heatheat exchangeexchange subsystem,subsystem, andand aa double-effectdouble-effect LiBr–HLiBr–H22OO absorptionabsorption chillerchiller drivendriven byby steam.steam. Sunlight is is irradiated irradiated on on a aparabolic parabolic reflecto reflectorr and and is reflected is reflected on onthe theabsorber absorber by a by mirror. a mirror. The Theheat heat conducting conducting oil (HCO) oil (HCO) into the into absorption the absorption tube (s tubetate 1) (state is heated 1) is heatedto a high to temperature a high temperature (state 2). (stateSubsequently, 2). Subsequently, the high temperature the high temperature HCO (state HCO 7) en (stateters the 7) heat enters exchanger the heat to exchanger produce steam to produce (state steam14), and (state the 14),low and temperature the low temperature HCO is returned HCO isto returnedthe PTC tothrough the PTC heat through release heat (state release 8). The (state steam 8). Thewith steam high withtemperature high temperature and high andpressure high pressureis used to is drive used tothe drive absorption the absorption chiller to chiller produce to produce chilled chilledwater for water space for cooling space cooling (states (states19 and 19 20). and The 20). steam The steamreleasing releasing heat becomes heat becomes the condensated the condensated water water(state (state15) and 15) then and returns then returns to the to heat the exchanger. heat exchanger.

Figure 1. Double-effect LiBr–H2O absorption chiller system driven by parabolic trough collector Figure 1. Double-effect LiBr–H2O absorption chiller system driven by parabolic trough collector (PTC). HG—high-pressure generator; HX—high temperature exchanger; LG—low-pressure generator; (PTC). HG—high-pressure generator; HX—high temperature exchanger; LG—low-pressure LX—low temperature heat exchanger. generator; LX—low temperature heat exchanger.

The double-effect LiBr–H2O absorption chiller includes a high-pressure generator (HG), a The double-effect LiBr–H2O absorption chiller includes a high-pressure generator (HG), a low- low-pressure generator (LG), a condenser, an evaporator, an absorber, a low temperature heat pressure generator (LG), a condenser, an evaporator, an absorber, a low temperature heat exchanger exchanger (LX), a high temperature exchanger (HX), two solution reducing valves, and two refrigerant (LX), a high temperature exchanger (HX), two solution reducing valves, and two refrigerant expansion valves. The high temperature steam produced by the HCO ﬂows into the HG to generate expansion valves. The high temperature steam produced by the HCO flows into the HG to generate the primary steam (state r1) and a concentrated working solution (state s5). Subsequently, the two the primary steam (state r1) and a concentrated working solution (state s5). Subsequently, the two streams enter into two different circulations: solution circulation and refrigerant circulation. In the streams enter into two different circulations: solution circulation and refrigerant circulation. In the

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solution circulation, the weak solution (state s1) produced in the absorber is pumped through the LX Energies 2018, 11, 2679 4 of 17 and HX to recover the surplus heat of the medium concentration solution from LG (states s8 and s9) and the strong concentration solution from HG (states s5 and s6), respectively. The weak solution solution(state s4) circulation, is then introduced the weak solution into the (state HG, s1) wher producede it is in heated the absorber and concentrated is pumped through into medium the LX andconcentration HX to recover solution the surplus (state s5) heat by ofthe the steam medium resour concentrationce, and thus high solution pressure from refrigerant LG (states steam s8 and (state s9) andr1) theis produced. strong concentration The medium solution concentration from HG solution (states s5(state and s5) s6), then respectively. passes through The weak the solutionHX and (stateenters s4)the is LG then after introduced decreasing into the the pressure HG, where (state it iss7), heated where and the concentratedmedium concentration into medium solution concentration is further solutionconcentrated (state s5)into by a thestrong steam solution resource, (state and s8). thus The high strong pressure solution refrigerant enters the steam absorber (state r1)after is produced.it is cooled Thein the medium LX. In concentrationthe refrigerant solutioncirculation, (state the s5) refrigerant then passes steam through from the the HG HX (state and entersr1) condenses the LG afterin the decreasingLG and low-pressure the pressure refrigerant (state s7), where steam the (state medium r2) is concentrationgenerated. Both solution the high-pressure is further concentrated refrigerant intowater a strong (state r2) solution and low-pressure (state s8). The refrigerant strong solution steam (s enterstate r3) the flow absorber into the after condenser. it is cooled The inrefrigerant the LX. Inwater the refrigerant (state r5) is circulation, throttled and the refrigerantintroduced steaminto the from evaporator the HG (stateto generate r1) condenses chilled water in the (states LG and 19 low-pressureand 20). Finally, refrigerant the refrigerant steam (state steam r2) (state is generated. r7) is absorbed Both the by high-pressure a strong solution refrigerant in the absorber. water (state r2) andIn low-pressure the solar cooling refrigerant system, steam a heat (state storage r3) flow tank into (HST) the is condenser. necessary The to match refrigerant the heat water supply (state from r5) issolar throttled PTC andand introducedthe cooling into demand the evaporator of building, to generateand it adopts chilled molten water (statesphase change 19 and 20).material Finally, (PCM) the refrigerantstorage. The steam PCM (state HST r7) isis absorbedconnected by in a strongparallel solution to the in collector the absorber. field to enable charging and discharging.In the solar There cooling are system,three operation a heat storage switch tank modes (HST) of HST. is necessary Firstly, towhen match the the heat heat collected supply by from the solarPTC PTCexceeds and the the heat cooling demand demand for cooling of building, load, andthe valve it adopts V1 splits molten HCO phase to two change streams material (states (PCM) 3 and storage.5). One Theof streams PCM HST through is connected the valves in parallelV2 and V3 to the is sent collector to heat field exchanger to enable to charging produce andsteam discharging. for chiller, Thereand another are three stream operation being switch the excess modes heat of HST. through Firstly, the when HCO the (states heat 3 collected and 4) is by stored the PTC in the exceeds HST. theThe heatreturn demand HCO forfrom cooling HST load,and heat the valve exchanger V1 splits (states HCO 4 toand two 8) streams through (states the valves 3 and 5).V4 One and of V5 streams is sent throughtogether the to valvesthe PTC V2 again. and V3 Secondly, is sent to when heat exchanger the heat collected to produce by the steam PTC for is chiller, less than and the another heat demand, stream beinga part the of excessHCO (state heat through 10) is sent the to HCO the HST (states to 3absorb and 4) the is stored stored in heat, the HST.and then, The returnwith all HCO HCO from from HST the andPTC heat through exchanger controlling (states the 4 and valve 8) throughV1, it is thesent valves to the V4 heat and exchanger V5 is sent to together produce to steam. the PTC Thus, again. the Secondly,heat from when the HST the heat(states collected 10 and by 11) the is PTCremoved is less to than supplement the heat demand,the shortage. a part Finally, of HCO when (state the 10) heat is sentcollected to the from HST the to absorb PTC is the not stored available heat, in and the then,night withor daytime all HCO with from no thesolar PTC radiation, through the controlling valves V1 theand valve V5 are V1, closed it is sent and to the the cycle heat of exchanger the collected to produce heat of PTC steam. (states Thus, 3 and the heat4) does from not the work. HST The (states heat 10demand and 11) of is cooling removed system to supplement is supplied the by shortage. the HST through Finally, whencontrolling the heat the collected valves V2 from and theV4. PTCDuring is notthe available operation in process, the night the or heat daytime of flows, with including no solar radiation,that of HCO, the steam, valves and V1 andstorage V5are stream, closed is andadjusted the cycleby changing of the collected the flow heat rates. of PTC (states 3 and 4) does not work. The heat demand of cooling system is supplied by the HST through controlling the valves V2 and V4. During the operation process, the heat of2.2. flows, Thermodynamic including that Model of HCO, steam, and storage stream, is adjusted by changing the flow rates.

2.2.2.2.1. Thermodynamic PTC Model

2.2.1. PTCA solar PTC mainly consists of a parabolic mirror, a glass tube, and a metal tube [26], and this is shown in Figure 2 The parabolic mirror uses aluminum or silver to reflect solar radiation to the surfaceA solar of the PTC metal mainly tube consists and is ofcovered a parabolic by a mirror,coating awith glass high tube, absorptivity and a metal and tube low [26 ],emissivity; and this is it shownthen heats in Figure the 2HCO The parabolicin the metal mirror tube. uses The aluminum space be ortween silver the to reﬂectglass tube solar and radiation metal to tube the surfaceis set to ofvacuum the metal to tubereduce and heat is coveredloss. by a coating with high absorptivity and low emissivity; it then heats the HCO in the metal tube. The space between the glass tube and metal tube is set to vacuum to reduce heat loss.

Figure 2. PTC structure diagram. Figure 2. PTC structure diagram.

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TheThe heat heat transfer transfer process process and and the the thermal thermal resistance resistance model model considering considering one-dimensional one-dimensional heat heat transfertransfer is shown is shown in Figure in Figure 3 [27].3[ 27 The]. The solar solar radi radiationation is reflected is reflected onto onto the theglass glass tube tube through through the the parabolicparabolic mirror. mirror. The The reflected reflected sunl sunlightight passes passes through through the theglass glass tube tube to reach to reach the theouter outer surface surface of of thethe metal metal tube. tube. The The metal metal pipe pipe is heated is heated owing owing to th toe thehigher higher density density of sunlig of sunlightht on onthe theouter outer wall wall of of thethe metal metal tube, tube, and and the thethermal thermal energy energy is then is then tran transmittedsmitted to the to theworking working fluid, fluid, HCO, HCO, through through heat heat conductionconduction and and convection, convection, in that in that order. order. Thus, Thus, the the flowing flowing HCO HCO is heated is heated to collect to collect solar solar heat. heat.

Figure 3. Thermal resistance model. Figure 3. Thermal resistance model. The following points are assumed during the heat transfer analysis of PTC. The following points are assumed during the heat transfer analysis of PTC. (1).(1). TheThe space space between between the themetal metal and and glass glass tubes tubes does does not notabsolutely absolutely correspond correspond to the to thevacuum vacuum becausebecause of a ofsmall a small amount amount of residual of residual air, air,thus thus the theconvection convection heat heat transfer transfer exists. exists. (2).(2). TheThe heat heat conduction conduction between between the themetal metal tube tube and and hose hose is ignored. is ignored. (3).(3). TheThe heat heat conduction conduction between between the themetal metal tube tube and and bracket bracket of the of thePTC PTC is ignored. is ignored.

TheThe solar solar radiation radiation energy energy absorbed absorbed by bythe themetal metal tube, tube, Q Qsolsol, is, is expressed expressed as as follows follows [28]: [28]: =⋅⋅⋅⋅⋅−η θε QIAIAMsol opt cos (15 ) (1) Qsol = I · A · ηopt · IAM · cos θ · (1 − ε5) (1) η where I is the solar direct normal irradiance (DNI), A is the collector area, opt is the PTC’s optical where I is the solar direct normal irradiance (DNI), A is the collector area, η is the PTC’s optical θ opt ε efficiency, is the solar incidence angle, IAM is the solar incidence angle modifier, and 5 is the efficiency, θ is the solar incidence angle, IAM is the solar incidence angle modifier, and ε5 is the reflectivityreflectivity of glass of glass outer outer wall. wall. A part A part of the of theabsorbed absorbed heat heat of the of themetal metal tube tube is transmitted is transmitted to the to the workingworking fluid, fluid, HCO, HCO, and and another another pa partrt is istransferred transferred to to the the inner inner wall wall of of glass tube. Consequently, the theheat heat balancebalance isis expressedexpressedas asfollows follows [ 27[27]:]: ++ + QQsol= 23 cond Q 34 rad Q 34 cond Q 34 conv (2) Qsol = Q23cond + Q34rad + Q34cond + Q34conv (2) where Q23cond is the heat conduction between the inner wall and outer wall of the metal tube; Q34rad andwhere Q Q23condare isthe the radiation heat conduction heat and between the convection the inner wallheat and between outer wallmetal of thetube metal and tube; glassQ 34tube,rad and 34conv Q34conv are the radiation heat and the convection heat between metal tube and glass tube, respectively; respectively; and Q34cond is the heat conduction of the air in the space between metal and glass tubes. and Q is the heat conduction of the air in the space between metal and glass tubes. The conductive The conductive34cond heat from the outer wall of metal tube to inner wall is absorbed by the HCO through heat from the outer wall of metal tube to inner wall is absorbed by the HCO through convective heat convective heat transfer, and it is assumed that they are equal at the instantaneous steady state transfer, and it is assumed that they are equal at the instantaneous steady state condition. condition. = QQ12Qconv12conv = 23Q cond23cond (3) (3)

Additionally,Additionally, the the heat heat absorbed absorbed by bythe the HCO, HCO, Q12Qconv12conv, is, calculated is calculated as asfollows follows [29]: [29 ]: =⋅⋅−λ QATT12conv 12 conv 2() 2 1 (4) Q12conv = λ12conv · A2 · (T2 − T1) (4) λ where 12conv is the convective heat transfer coefficient in the single-phase region and can be defined λ where 12conv is the convective heat transfer coefficient0.8 0.4 in the single-phase region and can be defined k1 k = as follows: λ = Nu and1 NuD 0.023Re Pr ,0.8 for 0.4which the validity is in the ranges of as follows:12λconv12conv = D2 NuD and 2NuD = 0.023Re Pr , for which the validity is in the ranges of D 2 D2 2 2 L 0.6 ≤ Pr ≤ 160, Re ≥ 10, 000, and > 10. L is the length of collector; D2 is the diameter inside of L D2 0.6≤≤ Pr 160 , Re≥ 10000 , and >10 . L is the length of collector; D is the diameter inside of the the metal tube; NuD2 is the Nusselt number; Re is the Reynolds number;2 Pr is the Prandtl number; D2 k1 is the thermal conductivity coefficient of the HCO at the temperature of T1; A2 is the inner area of T +T metal tube; NuD is the Nusselt number; Re is the Reynolds number; Pr i is theo Prandtl number; the metal tube;2 T1 and T2 are the average temperatures of the HCO (T1 = 2 ) and the inner wall of metal tube, respectively; and T and T are the inlet and outlet temperatures of HCO, respectively. k is the thermal conductivity coefficii ento of the HCO at the temperature of T ; A is the inner area 1 1 2 TT+ of the metal tube; T and T are the average temperatures of the HCO (T = io) and the inner 1 2 1 2

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The heat absorbed in the inner wall of glass tube through heat conduction, convection, and radiation transfers to its outer wall through conduction and is expressed as follows:

Q45cond = Q34rad + Q34cond + Q34conv (5) where Q45cond is the heat conduction between the inner and outer wall of the glass tube, and is emitted to the atmosphere through heat convection and radiation. Thus, the following expression holds:

Q45cond = Q56conv + Q57rad (6) where Q56conv and Q57rad are the convective heat and radiation heat between the outer wall of glass tube and atmosphere, respectively. Therefore, the thermal efficiency of the collector is defined as the ratio of the solar radiation energy absorbed by the working fluid in the metal tube to the received total energy on the mirror of the PTC, and is expressed as follows [30]: Q η = 12conv (7) PTC I · A where ηPTC is the thermal efficiency of the PTC. In the study, the SEGS (Solar Electric Generating System) LS-2 PTC [31] is employed to heat the HCO for the generation of steam. The design parameters [5,30,31] are listed in Table1.

Table 1. Design parameters of the parabolic trough collector.

Parameter Value Parameter Value Structure Torsion tube Inside diameter of glass tube, m 0.115 Concentration ratio 71:1 Thermal conductivity, W/m·K 54 Length, m 7.8 Optical efﬁciency 0.733 Opening width, m 5 Coating absorptivity 0.915 Outside diameter of metal tube, m 0.075 Metal tube emissivity 0.08 Inside diameter of metal tube, m 0.067 Glass tube emissivity 0.88 Outside diameter of glass tube, m 0.118 Solar incidence angle modiﬁer 1.0

Because of the discontinuity of solar energy, the additional collection area should be considered to satisfy the heat demand for producing chilled water at night. Thus, the collected heat from the PTC covers the heat demand in the daytime and the stored heat for utilization at night. Consequently, the total collection area of the PTC is estimated according to the heat demands of cooling loads, as follows:

X X N N QD−night A · I · η = Q + (8) ∑ i i ∑ Di (1 − a)(1 − b)(1 − c) i=X1 i=X1

X1−1 23 QD−night = ∑ QDi + ∑ QDi (9) i=0 i=XN +1 where QDi is the heat demand to match the hourly cold load when solar energy is available; QD−night is the heat collected by the PTC to satisfy the total demand at night; X1 is the time when the collector begins to work; XN is the last time of the collector’s work; a, b, and c are the heat loss coefficients during heat storing, static storage, and heat releasing of the HST, respectively (herein, all of them are set to 0.1); and Ii and ηi are the DNI in the i-th hour and the corresponding collection efficiency of solar thermal energy, respectively. During the computation process of the collector’s area, the thermal efficiency of PTC is obtained through simulation programs using Engineering Equation Solver (EES) after setting the cooling load of a building in a typical day. Energies 2018, 11, 2679 7 of 17

2.2.2. Absorption Chiller

A double effect LiBr–H2O absorption chiller driven by steam is integrated with the solar thermal collection system in which its COP is relatively high in several types of absorption chillers driven by hot water or exhausted gas. During modeling and calculation of the absorption chiller, the following assumptions are considered [5]: (1). The heat losses in each component and the pressure losses between each connection lines are ignored.

(2). The systemic analysis is based on the steady state, and the LiBr–H2O solution is steady during the cycle. (3). The states are statured and include the outlet refrigerant steam of evaporator, the outlet refrigerant liquid of condenser, the outlet weak solution of absorber, and the outlet solution of HG and LG. (4). The power consumption of solution pump is ignored. (5). Counter ﬂow heat exchanger is employed, and the logarithmic mean temperature difference is adopted in the heat transfer calculation.

During the cycle of LiBr–H2O solution, the balances of each component including mass, energy, and solution phase equilibrium are employed to construct the thermodynamic model and the universal formulations are listed as follows [32]:

∑ mi − ∑ mo = 0 (10)

∑ miwi − ∑ mowo = 0 (11)

∑ mihi − ∑ moho = 0 (12) where m, w, and h represent mass, concentration, and enthalpy, respectively; and the subscripts i and o represent the inlet and outlet of the component, respectively. Thus, given the pump’s power consumption, the energy balance of the absorption chiller is expressed as follows [33]: QHG + QC = QA + QCon (13) where QHG is the heat absorbed by the HG, QC is the heat absorbed by the evaporator, QA is the heat released by the absorber, and QCon is the heat released by the condenser. Its COP is deﬁned as follows:

Q COP = C (14) QHG

2.3. Evaluation Criteria Appropriate evaluation criteria are selected to assess the performances of the absorption system based on the parabolic trough solar collector. The systemic thermal efﬁciency, ηsys, is deﬁned as the ratio of the cooling output to the total solar energy input, and is expressed as follows [30]:

Q η = C × 100% (15) sys I · A

3. Results and Discussions

3.1. Validity of Models The main constructed models, including PTC and absorption chiller, are veriﬁed to show their validities. Firstly, the simulated outlet temperature of HCO in the PTC model is compared with the experimental data at the same parameters [31], and the relative errors of the outlet temperature of HCO at seven sets of work conditions are shown in Table2. The maximum relative error is 1.29%, and the average relative error is 0.89%, which is within the acceptable range. Energies 2018, 11, 2679 8 of 17

Table 2. Relative error of the outlet temperature of heat conducting oil (HCO) in the parabolic trough collector (PTC) model. DNI—direct normal irradiance.

DNI, Inlet Temperature Outlet Temperature of HCO, ◦C Relative Number 2 of HCO, ◦C Error, % W/m Experimental Data Simulation Data 1 933.7 102.2 124 122.4 1.29 2 968.2 151.0 173.3 171.7 0.92 3 982.3 197.5 219.5 217.7 0.82 4 909.5 250.7 269.4 267.3 0.78 5 937.7 297.8 316.9 314.4 0.79 6 880.6 299.0 317.2 314.5 0.85 7 920.9 379.5 398 394.8 0.80

Secondly, the thermodynamic model of the absorption chiller driven by steam is established and simulated by using EES, and in particular, the thermal properties of the LiBr–H2O solution are directly obtained in the EES software. In order to verify the accuracy of the simulated model, the model and results from the literature [34] are referred to for comparison purposes. Because there are 17 internal states in the absorption chiller and 7 interactive states, the average relative errors of each parameter are employed to verify the model of absorption chiller, and the comparison results are shown in Table3. It is observed that the error of temperature is the highest, although it is only 0.056%. Consequently, the simulation error and the accuracy of modeling is acceptable. Given the simulation, the COP of absorption chiller is approximately 1.312, which is the same as the reference value in previous studies.

Table 3. Average relative error of each parameter of the absorption chiller.

Parameters m, kg/s T, ◦C w,% Q, kW kA, kW/K Average relative error 0.056% 0.038% 0 0.01% 0.015%

3.2. Performances of the Solar Collector The solar heat collecting subsystem is the base of the absorption chilling system, and this significantly influences the systemic performances. The impacts of solar DNI and temperature and flow rate of the HCO on the thermal efficiency of a LS-2 PTC in Table1 are analyzed on the base parameters of No. 2 work conditions in Table2. Figure4 displays the variations in the heat collecting efficiency and HCO outlet temperature with the different DNI when the inlet temperature and flow rate of the HCO are 151 ◦C and 47.8 L/min, respectively. It is evident that the thermal efficiency increases with the increasing DNI. The thermal efficiency is approximately 63.2% when the DNI is 200 W/m2. When the outlet temperature is set as constant, the lower DNI requires a lower flow rate of the HCO. However, the HCO easily appears as a coking phenomenon in the heat collecting tube as a result of an excessively high temperature when the flow rate of the HCO is excessively low, and then coke deposits will affect the heat transfer performance, even resulting in tube failures. Consequently, the heat collection system stops working to avoid the phenomenon of coking at an excessively low flow rate, resulting from the low DNI. The higher DNI leads to a higher temperature of the metal tube wall, and this enlarges the temperature difference between the HCO and the metal tube and enforces their heat transfer. The collection thermal efficiency increases to 65.4% when the DNI increases to 900 W/m2. Additionally, the growth rate of the heat collecting efficiency at the lower solar radiation exceeds that at the higher solar radiation. At the initial stage of increasing DNI, the higher temperature difference between the metal tube and HCO promotes heat conduction and then leads to the overall increase in the solar collector efficiency. A further increase in the DNI decreases the temperature difference between the metal tube and HCO and the increasing rate of the collection efficiency also becomes slow. In addition, differently to the changing trend of collection efficiency, the HCO outlet temperature increases with the increasing Energies 2018, 11, x FOR PEER REVIEW 9 of 17

temperature difference between the HCO and the metal tube and enforces their heat transfer. The collection thermal efficiency increases to 65.4% when the DNI increases to 900 W/m2. Additionally, the growth rate of the heat collecting efficiency at the lower solar radiation exceeds that at the higher solar radiation. At the initial stage of increasing DNI, the higher temperature difference between the metal tube and HCO promotes heat conduction and then leads to the overall increase in the solar collector efficiency. A further increase in the DNI decreases the temperature difference between the Energiesmetal 2018tube, 11 and, 2679 HCO and the increasing rate of the collection efficiency also becomes slow.9 of In 17 addition, differently to the changing trend of collection efficiency, the HCO outlet temperature DNIincreases and thewith increasing the increasing speed DNI is keptand the constant. increasing When speed the is DNI kept increases constant. by When 100 W/mthe DNI2, the increases outlet 2 temperatureby 100 W/m of, the the outlet LS-2 temperature collector will of increase the LS-2 by collector approximately will increase 2 ◦C. by approximately 2 °C.

66.0 172 65.5 170 65.0

％ 168 64.5 166 64.0 164 63.5 162 63.0 62.5 160 Thermal efficiency 158

Thermal efficiency, efficiency, Thermal 62.0 Outlet temperature 61.5 156 HCO outlettemperature, ℃ 61.0 154 200 300 400 500 600 700 800 900 Direct normal irradiance, W/m2

Figure 4. Variations in heat collecting efficiency and heat conducting oil (HCO) outlet temperature of theFigure LS-2 4. PTC Variations with the in differentheat collecting direct normalefficiency irradiance and heat (DNI) conducting (the inlet oil temperature(HCO) outlet and temperature flow rate ofof thethe HCOLS-2 PTC are 151with◦C the and different 47.8 L/min, direct respectively). normal irradiance (DNI) (the inlet temperature and flow rate of the HCO are 151 °C and 47.8 L/min, respectively). The variations in heat collecting efficiency with the DNI and HCO temperature (from 100 ◦C to 300 ◦C)The are variations shown in in Figure heat 5collecting, when the efficiency flow rate wi ofth HCO the isDNI 47.8 and L/min. HCO It temperature is observed that (from the 100 thermal °C to efficiency300 °C) are decreases shown in with Figure the 5, increasing when the inletflow temperaturerate of HCO ofis HCO.47.8 L/min. The lower It is observed inlet temperature that the thermal results inefficiency a higher decreases temperature with difference the increasing between inlet the metal temperature tube and of the HCO. HCO andThe enhanceslower inlet the heattemperature transfer ofresults the solar in a collector.higher temperature Additionally, difference the decline between of efficiency the metal at tube the DNI and ofthe 300 HCO W/m and2 from enhances 65.5% the to 57.7%heat transfer exceeds of that the atsolar 700 collector. W/m2 from Additionally, 66.0% to 61.8%. the decline This indicates of efficiency that at the the higher DNI of inlet 300 temperature W/m2 from Energiesof65.5% HCO 2018to influences 57.7%, 11, x FOR exceeds PEER the thermal REVIEW that at efficiency 700 W/m more2 from evidently 66.0% toat 61.8%. the low This DNI. indicates that the higher10 ofinlet 17 temperature of HCO influences the thermal efficiency more evidently at the low DNI. 68.0

66.0 ％ 64.0

62.0

300W/m2 60.0

Thermal , efficiency Thermal 500W/m2 58.0 700W/m2

56.0 100 125 150 175 200 225 250 275 300 Temperature of HCO, ℃

FigureFigure 5. 5. VariationsVariations in in heat heat collecting collecting efficiency efﬁciency of of the the LS-2 LS-2 PTC PTC with with the the different different DNI DNI and and HCO HCO temperaturetemperature (the (the mass mass flow ﬂow of of the the HCO HCO is is 47.8 47.8 L/min). L/min).

When the inlet temperature of the HCO is 151 °C and the other parameters remain unchanged, the variations in the thermal efficiency of the PTC with the DNI and HCO flow rate are displayed in Figure 6 It is observed that the higher flow rate of the HCO results in a higher collecting efficiency of solar heat. At a constant DNI, the higher flow rate decreases the outlet temperature of the HCO, and then the average temperature of the HCO naturally declines. However, the total temperature difference between the HCO and metal wall increases, and this enhances the heat transfer and increases the collection efficiency. At a higher flow rate, the changes in the average temperature of the HCO are low, such that the increasing rate in the thermal efficiency also becomes slow. When the DNI is 700 W/m2 and the flow rate of HCO increases from 20 L/min to 35 L/min, the collector efficiency increases from 63.98% to 64.96%. However, the thermal efficiency increases slowly at a higher flow rate, and it increases by only 0.43% when the flow rate increases to 55 L/min.

65.5 300W/m2 500W/m2 65.0 700W/m2 ％

64.5

64.0 Thermal efficiency, efficiency, Thermal 63.5

63.0 20 25 30 35 40 45 50 55 Flow rate, L/min Figure 6. Variations in heat collecting efficiency of the LS-2 PTC with the different DNI and HCO flow rate (the inlet temperature of the HCO is 151 °C).

Energies 2018, 11, x FOR PEER REVIEW 10 of 17

68.0

66.0 ％ 64.0

62.0

300W/m2 60.0

Thermal , efficiency Thermal 500W/m2 58.0 700W/m2

56.0 100 125 150 175 200 225 250 275 300 Temperature of HCO, ℃

EnergiesFigure2018, 115., 2679Variations in heat collecting efficiency of the LS-2 PTC with the different DNI and HCO10 of 17 temperature (the mass flow of the HCO is 47.8 L/min).

WhenWhen thethe inletinlet temperaturetemperature ofof thethe HCOHCO isis 151151 ◦°CC and the other parameters remain unchanged, thethe variationsvariations inin thethe thermalthermal efficiencyefficiency ofof thethe PTCPTC withwith thethe DNIDNI andand HCOHCO flowflow raterate areare displayeddisplayed inin FigureFigure6 6 It It isis observedobserved that the higher flow flow rate rate of of the the HCO HCO results results in in a ahigher higher collecting collecting efficiency efficiency of ofsolar solar heat. heat. At Ata constant a constant DNI, DNI, the thehigher higher flow flow rate rate decreases decreases the ou thetlet outlet temperature temperature of the of HCO, the HCO, and andthen thenthe theaverage average temperature temperature of ofthe the HCO HCO natura naturallylly declines. declines. However, However, the the total temperaturetemperature differencedifference betweenbetween the the HCO HCO and and metal metal wall wall increases, increases, and this and enhances this enhances the heat the transfer heat andtransfer increases and theincreases collection the collection efficiency. efficiency. At a higher At flow a higher rate, flow the changes rate, the in changes the average in the temperature average temperature of the HCO of arethe low,HCO such are low, that such the increasing that the incr rateeasing in the rate thermal in the efficiencythermal efficiency also becomes also becomes slow. When slow. the When DNI the is 700DNI W/m is 7002 and W/m the2 and flow the rate flow of HCO rate increasesof HCO increases from 20 L/min from 20 to 35L/min L/min, to 35 the L/min, collector the efficiency collector increasesefficiency fromincreases 63.98% from to 64.96%.63.98% However,to 64.96%. theHowever, thermal the efficiency thermal increases efficiency slowly increases at a higherslowly flowat a rate,higher and flow it increases rate, and by it increases only 0.43% by when only the0.43% flow when rate the increases flow rate to 55increases L/min. to 55 L/min.

65.5 300W/m2 500W/m2 65.0 700W/m2 ％

64.5

64.0 Thermal efficiency, efficiency, Thermal 63.5

63.0 20 25 30 35 40 45 50 55 Flow rate, L/min FigureFigure 6. Variations inin heat collecting efﬁciencyefficiency ofof thethe LS-2 PTC with the different DNI and HCO ﬂowflow ◦ raterate (the(the inletinlet temperaturetemperature ofof thethe HCOHCO isis 151151 °CC).). 3.3. Performances of Absorption Chiller

An absorption chiller with a 1000-kW cooling output is simulated using the model constructed above. The design parameters and their performance with respect to the design work conditions are listed in Table4. It is observed that the COP is approximately 1.332. The performances of the absorption chiller change when a few parameters, including cooling load, temperature, or flow rate of cooling water, are different from the design work conditions during the actual operation. Figure7 shows the variations in the cooling load and COP with the steam flow rate. The COP increases from 0.893 to 1.332 when the cooling load factor increases from 20% to 100%, which is similar to the changing trend of the absorption chiller driven by high temperature exhausted gas in the literature [33]. The reason for the decreasing COP with the decreasing steam flow rate is that the temperature, pressure, and concentration LiBr solution in the HG decline with the decreasing steam flow rate; the flow rate of H2O steam naturally becomes less; the circulating ratio will increase quickly; and these influences result in the decline of COP. Energies 2018, 11, 2679 11 of 17

Table 4. Design parameters and performances of the absorption chiller on the work conditions. HG—high-pressure generator; HX—high temperature exchanger; LG—low-pressure generator; LX—low temperature heat exchanger; COP—coefﬁcient of performance.

Parameter Value Parameter Value Steam temperature, ◦C 158 Heat efficiency of HX, % 85 Steam pressure, MPa 0.6 Heat efficiency of LX, % 85 Steam flow rate, kg/s 0.3 Condensate temperature, ◦C 71 kA a of HG, kW/K 36.48 Condensate pressure, MPa 0.1 kA of LG, kW/K 111.7 Temperature of chilled water, ◦C 7/12 kA of the evaporator, kW/K 191.2 Temperature of cooling water, ◦C 35/30 kA of the condenser, kW/K 113.9 Evaporating temperature, ◦C 3.878 kA of the absorber, kW/K 238 Condensing temperature, ◦C 39 COP 1.332 a: kA is the product of the heat transfer area and the thermal conductivity coefficient of the equipment.

The reduction of steam ﬂow rate leads to a decrease in the intermediate solution temperature. Subsequently, the high-pressure refrigerant vapor decreases and the concentration of the intermediate solution decreases. With the decreases in the high-pressure refrigerant vapor, the absorbed heat in the LG is reduced. Consequently, the outlet temperature of concentrated solution reduces, the concentration of the concentrated solution decreases, and the cooling capacity reduces. With the increase in steam ﬂow rate, the temperature, pressure, and concentration of the HG increase to the limits of the unit itself. During the increase, the COP increases rapidly at the initial increasing stage Energiesbecause 2018 of, the11, xhigher FOR PEER difference, REVIEW and the increasing speed of COP then decreases. 12 of 17

1.4 1200

Cooling energy 1.3 1000 COP

1.2 800

1.1 600 COP

1 400 Cooling energy/kW Cooling

0.9 200

0.8 0 0.09 0.11 0.13 0.15 0.17 0.20 0.22 0.25 0.28 0.30 Steam flow rate, kg/s

FigureFigure 7. 7. VariationsVariations in in the the cooling cooling load and CO COPP with respect to the steam flow ﬂow rate.

3.4. Systemic Performances In order to analyze the performances of the complete system including solar collecting subsystem and absorption chiller, a hotel building in Beijing (north latitude 40° and east longitude 116°) is selected as a case study [35]. The hourly cooling loads were simulated using the Software DeST through setting the occupancy schedules of people, electric equipment, and light, among others. The hourly cooling loads and solar irradiance in a typical day (15 July) are shown in Figure 8.

1000 1200 Direct normal irradiance 2 900 Cooling load 1000 800 700 800 600 500 600 400 400 300 kW load, Cooling 200 Direct normal irradiance, W/m 200 100 0 0 0 2 4 6 8 10 12 14 16 18 20 22 Time, h Figure 8. Hourly cooling loads and solar DNI in a typical day.

In order to satisfy the cooling loads of a complete day, the collection area of the PTC is 2886 m2, and 74 sets of LS-2 collectors based on the calculation methods in Equations (8) and (9) are used. In order to match the flow rate of the HCO and the requirement of absorption chiller, the 74 sets of collectors are divided into 8 rows that include 7 rows with 11 collectors and 1 row with 8 collectors in a series. At the base design work conditions, the design parameters and system performances are listed into Table 5.

Energies 2018, 11, x FOR PEER REVIEW 12 of 17

1.4 1200

Cooling energy 1.3 1000 COP

1.2 800

1.1 600 COP

1 400 Cooling energy/kW Cooling

0.9 200

0.8 0 0.09 0.11 0.13 0.15 0.17 0.20 0.22 0.25 0.28 0.30 Steam flow rate, kg/s

Energies 2018Figure, 11, 2679 7. Variations in the cooling load and COP with respect to the steam flow rate. 12 of 17

3.4. Systemic Performances 3.4. Systemic Performances In order to analyze the performances of the complete system including solar collecting subsystemIn and order absorption to analyze thechiller, performances a hotel building of the complete in Beijing system (north including latitude solar 40° collecting and east subsystem longitude and absorption chiller, a hotel building in Beijing (north latitude 40◦ and east longitude 116◦) is selected 116°) is selected as a case study [35]. The hourly cooling loads were simulated using the Software as a case study [35]. The hourly cooling loads were simulated using the Software DeST through setting DeSTthe through occupancy setting schedules the occupanc of people,y electric schedules equipment, of people, and light, electric among equipment, others. The and hourly light, cooling among others.loads The and hourly solar cooling irradiance loads in a and typical solar day irradiance (15 July) are in showna typical in Figure day (158. July) are shown in Figure 8.

1000 1200 Direct normal irradiance 2 900 Cooling load 1000 800 700 800 600 500 600 400 400 300 kW load, Cooling 200 Direct normal irradiance, W/m 200 100 0 0 0 2 4 6 8 10 12 14 16 18 20 22 Time, h FigureFigure 8. Hourly 8. Hourly cooling cooling loads loads and and solar solar DNI inina a typical typical day. day.

In order to satisfy the cooling loads of a complete day, the collection area of the PTC is 2886 m2, In order to satisfy the cooling loads of a complete day, the collection area of the PTC is 2886 m2, and 74 sets of LS-2 collectors based on the calculation methods in Equations (8) and (9) are used. and 74In sets order of to LS-2 match collectors the ﬂow based rate of on the the HCO calcul andation the requirement methods in of Equations absorption (8) chiller, and the(9) 74are sets used. of In ordercollectors to match are the divided flow rate into 8of rows the thatHCO include and the 7 rows requirement with 11 collectors of absorption and 1 row chiller, with 8the collectors 74 sets of collectorsin a series. are divided At the baseinto design8 rows work that conditions, include 7 therows design with parameters 11 collectors and and system 1 row performances with 8 collectors are in a series.listed intoAt the Table base5. design work conditions, the design parameters and system performances are listed into Table 5. Table 5. Design parameters of the case study in the typical day.

Parameter Value Solar collector area, m2 2886 Sets of collectors 74 Arrangements (row/column) 7/11 Inlet temperature of HCO, ◦C 160 Outlet temperature of HCO, ◦C 300 Cooling capacity of absorption chiller, kW 1000 Pressure of steam, Mpa 0.6 Steam temperature, ◦C 158 Condensed water temperature, ◦C 71

In the solar collect system, adjustments in the flow rate of the HCO are employed to suit to the variation in DNI and maintain the constant outlet temperature of the HCO. Similarly, the cooling output is adjusted by changing the flow rate of steam into the absorption chiller and maintaining the constant inlet temperature of HG. Consequently, the inlet and outlet temperatures of the HCO and the HG in Table5 are always kept constant. The hourly flow rate and transient collecting efficiency of PTC and COP of the absorption chiller are shown in Figures9 and 10, respectively. Energies 2018, 11, x FOR PEER REVIEW 13 of 17

Table 5. Design parameters of the case study in the typical day. Energies 2018, 11, x FOR PEER REVIEW 13 of 17 Parameter Value Table 5. Design parameters of the case study in the typical day. Solar collector area, m2 2886 Sets ofParameter collectors Value 74 ArrangementsSolar collector (row/column) area, m2 7/112886 Inlet temperatureSets of collectors of HCO, °C 160 74

OutletArrangements temperature (row/column) of HCO, °C 3007/11 Inlet temperature of HCO, °C 160 Cooling capacity of absorption chiller, kW 1000 Outlet temperature of HCO, °C 300 Pressure of steam, Mpa 0.6 Cooling capacity of absorption chiller, kW 1000 SteamPressure temperature, of steam, °CMpa 158 0.6 CondensedSteam water temperature, temperature, °C °C 15871 Condensed water temperature, °C 71 In the solar collect system, adjustments in the flow rate of the HCO are employed to suit to the variation inIn DNI the solarand collectmaintain system, the adjustmentsconstant outlet in the temperature flow rate of theof theHCO HCO. are employed Similarly, to suitthe tocooling the output variationis adjusted in DNIby changing and maintain the flow the constantrate of steam outlet intotemperature the absorption of the HCO. chiller Similarly, and maintaining the cooling the constantoutput inlet istemperature adjusted by changingof HG. Consequently, the flow rate of steamthe inlet into and the absorptionoutlet temperatures chiller and maintainingof the HCO the and the HGconstant in Table inlet 5 are temperature always kept of HG. constant. Consequently, The hour thlye inlet flow and rate outlet and temperaturestransient collecting of the HCO efficiency and Energiesthe HG2018 in, 11 Table, 2679 5 are always kept constant. The hourly flow rate and transient collecting efficiency13 of 17 of PTC and COP of the absorption chiller are shown in Figures 9 and 10, respectively. of PTC and COP of the absorption chiller are shown in Figures 9 and 10, respectively.

1.2 1.2

1 1 HCO flowHCO rateflow rate 0.8 0.8 SteamSteam flow rateflow rate

0.6 0.6

Flow rate,kg/s Flow 0.4

0.2 0.2

0 0 0246810121416182022 0246810121416182022 Time, h Time, h Figure 9. Variations in the flow rates of HCO and steam. FigureFigure 9. Variations 9. Variations in inthe the flow ﬂow rates rates of of HCO andand steam. steam. 1.4 70 1.4 7069 1.2 6968

1.2 % 1.0 67 68 ， 1.0 6766 %

0.8 ， 65

COP 66 0.8 0.6 64 65 COP 0.6 0.4 63

64 Thermal efficiency COP Transient thermal efficiency of PTC 62 0.2 63 0.4 61 Thermal Thermal efficiency 0.0 COP Transient thermal efficiency of PTC 6260 0.2 024681012141618202261 Time, h 0.0 60 Figure 10. Variations0246810121416182022 in coefficient of performance (COP) and collecting efficiency of solar collector. Figure 10. Variations in coefficient of performance (COP) and collecting efficiency of solar collector. Time, h From Figure9, it is observed that the variation curve of steam flow rate shows a trend similar From Figure 9, it is observed that the variation curve of steam flow rate shows a trend similar to Figureto the variation10. Variations in the in cooling coefficient load of in performance Figure8. Additionally, (COP) and collecting the flow rateefficiency of the of HCO solar matches collector. the the variation in the cooling load in Figure 8. Additionally, the flow rate of the HCO matches the change in the DNI to stratify the constant outlet temperature of PTC. When the solar DNI is below change in the DNI to stratify the constant outlet temperature of PTC. When the solar DNI is below From400 W/m Figure2, the 9, solarit is observed collector does that notthe work, variation and thecurve solar of collector steam fl worksow rate for shows nine hours a trend from similar 08:00 to 400 W/m2, the solar collector does not work, and the solar collector works for nine hours from 08:00 the variationto 16:00 inin a the typical cooling day. Duringload in other Figure times, 8. Additionally, the collector system the flow is unable rate toof collect the HCO the heat matches for the the changerefrigeration in the DNI cycle, to stratify and the the HST constant supplements outlet the temperature heat demands of as PTC. the heat When source. the solar DNI is below 400 W/m2,As the shown solar incollector in Figure does 10, the not collector work, and efficiency the so reacheslar collector a maximum works value for ofnine 65% hours at the from highest 08:00 DNI, and the collector efficiency does not exhibit significant changes during its work time. The heat collected is used to produce the cooling energy in its work time and is stored in the HST to drive the absorption chiller in its non-work time. Thus, there are nine hours (from 08:00 to 16:00) to collect heat for the 24 h of cooling demands shown in Figure8, and the results indicate that approximately 73% of the collected heat of the PTC is stored in the HST for heat demands in the night or daytime with no solar radiation (from 15:00 to 07:00). As discussed in the section on the COP variations with the steam flow rate in Figure7, the COP also exhibits a trend similar to the cooling loads. The minimum COP is approximately 0.884 at the lowest cooling load, while the maximum COP reaches 1.332 at the highest cooling load. Thus, the utilization efficiency of solar energy is 61.98% in a typical day in which the average COP of absorption chiller is approximately 1.195, and the average collection efficiency of solar collector is 64.4%, as shown in Table5. Energies 2018, 11, x FOR PEER REVIEW 14 of 17 to 16:00 in a typical day. During other times, the collector system is unable to collect the heat for the refrigeration cycle, and the HST supplements the heat demands as the heat source. As shown in in Figure 10, the collector efficiency reaches a maximum value of 65% at the highest DNI, and the collector efficiency does not exhibit significant changes during its work time. The heat collected is used to produce the cooling energy in its work time and is stored in the HST to drive the absorption chiller in its non-work time. Thus, there are nine hours (from 08:00 to 16:00) to collect heat for the 24 h of cooling demands shown in Figure 8, and the results indicate that approximately 73% of the collected heat of the PTC is stored in the HST for heat demands in the night or daytime with no solar radiation (from 15:00 to 07:00). As discussed in the section on the COP variations with the steam flow rate in Figure 7, the COP also exhibits a trend similar to the cooling loads. The minimum COP is approximately 0.884 at the lowest cooling load, while the maximum COP reaches 1.332 at the highest cooling load. Thus, the utilization efficiency of solar energy is 61.98% in a typical day in which the average COP of absorption chiller is approximately 1.195, and the average collection efficiency of solar collector is 64.4%, as shown in Table 5.

Energies 2018, 11, 2679 14 of 17 3.5. Applicability of the Solar Cooling System The input of the cooling system is solar energy, and its output is the chilled water for building 3.5. Applicability of the Solar Cooling System the cooling load. Both of these are uncertain and time variant. When they match well, the systemic performancesThe input including of the cooling energy system and economy is solar energy, improve. and In its order output to demonstrate is the chilled their water correlations, for building a thecorrelation cooling coefficient load. Both between of these arehourly uncertain cooling and load time and variant. hourly When DNI theyis introduced match well, to compare the systemic the performances and including to analyze energy two and or more economy variable improve. elements In orderwith relativity to demonstrate and measure their correlations, the relative adegree correlation of correlation coefﬁcient between between the hourlytwo variables. cooling Th loade correlation and hourly coefficient DNI is introduced between variable to compare arrays the I performancesand QC , rIQ(, andC ) to is analyzeexpressed two asor follows: morevariable elements with relativity and measure the relative degree of correlation between the two variables. The correlation coefﬁcient between variable arrays I Cov(, I Q ) and QC, r(I, QC) is expressed as follows:rIQ(, )= C C ⋅ (16) Var[] I Var [ QC ] Cov(I, QC) r(I, QC) = p (16) where Cov(, I Q ) is the covariance of I and Q [and] · Var[ [] I ] and Var[] Q are the variances of C VarC I Var QC C

I and QC , respectively. The higher correlation coefficient implies increased consistency between where Cov(I, QC) is the covariance of I and QC and Var[I] and Var[QC] are the variances of I and QC, the two variables. respectively. The higher correlation coefﬁcient implies increased consistency between the two variables. Two additional buildings in Beijing, namely a shopping mall and an office building, are selected Two additional buildings in Beijing, namely a shopping mall and an ofﬁce building, are selected for comparison with the hotel building and for analyzing the application of the solar cooling system for comparison with the hotel building and for analyzing the application of the solar cooling system in in different buildings. The hourly cooling loads are shown in Figure 11, and the simulation results different buildings. The hourly cooling loads are shown in Figure 11, and the simulation results are are listed in Table 6. listed in Table6.

1200 Mall Hotel 1000 Office

800

600

400 Cooling kW Cooling load,

200

0 0246810121416182022 Time, h Figure 11. Hourly cooling loads for different buildings. Table 6. Performance comparisons of solar cooling systems in different buildings. HST—heat storage tank.

Item Hotel Shopping Mall Office Cooling capacity, kW 1000 1000 750 Correlation coefficient 0.16 0.72 0.80 Area of the PTC, m2 2886 2184 1716 Number of LS-2 solar collector 74 56 44 Thermal storage ratio 0.73 0.39 0.32 Capacity of HST, kWh 8995 3633 2354 Thermal efficiency, % 61.98 68.73 69.47

As shown in Table6, the correlation coefficient in the office building (0.80) is the highest, while that in the hotel (0.16) is the lowest. This point implies that the solar DNI is more similar to the cooling load in the office building. Correspondingly, the thermal efficiency in the office building (69.47%) is the highest, while that in hotel (61.98%) is the lowest. Consequently, it is concluded that the increased Energies 2018, 11, 2679 15 of 17 correlation coefficient between solar DNI and cooling load allows the solar cooling system to achieve increased benefits and leads to increased thermal efficiency. The relationship between hourly solar DNI and cooling load is analyzed, and the increased correlation coefficient implies more similar changing trends between system input, solar energy and system output, cooling energy. When the input completely matches the output, then the correlation coefficient is equal to 1.0 and the heat storage system as a balance segment for input and output is not necessary. Table5 shows a comparison of the thermal storage ratios (which are defined as the ratios of the total stored heat to the total collected solar heat), and it is observed that the office building with the highest correlation coefficient and the highest thermal efficiency exhibits the lowest thermal storage ratio. The installation capacity of the HST in the office building is the lowest (2354 kWh), while that in the hotel building is the largest (8995 kWh). Consequently, the heat loss during heat storage and release decreases and the systemic thermal efficiency naturally increases.

4. Conclusions

The study proposed a double-effect LiBr–H2O absorption chiller based on solar PTC, constructed the thermodynamic model, and presented the thermodynamic performance analysis on the design and off-design work conditions. The following conclusions are obtained: The comparisons of the simulation results from the constructed thermodynamic models and the experimental data indicated that the maximum relative error of solar PTC model is approximately 1.29% and the maximum error of the absorption chiller model is only 0.056%, which satisfied the requirements of thermodynamic simulation. The influence analysis of uncertain factors on solar PTC indicated that the outlet temperature of collector will increase by approximately 2 ◦C when the DNI increases by 100 W/m2 in the case study. The solar irradiance has a strong effect on the collecting thermal efficiency. As for the absorption chiller, the influence of steam flow rate on its COP demonstrates that the COP increases rapidly with the increasing steam flow rate at a lower cooling load, and the increasing rate of COP then becomes slow with increases in the cooling load. In total, the combination of solar PTC and steam LiBr–H2O absorption chiller is a good method to match the energy level of medium temperature solar energy. The solar energy utilization efficiency reaches approximately 61.98% in the hotel building. A correlation coefficient between solar irradiance and cooling load is proposed to quantify the applicability of the solar cooling system in the buildings. The performance comparison of the solar cooling system in different types of building indicates that better matching and a higher correlation coefficient between the transient solar DNI and cooling load is helpful in decreasing the heat loss and improving the systemic performance. The solar cooling system in the office building with a correlation coefficient of approximately 0.81 achieves 69.47% systemic thermal efficiency. The thermodynamic performance of the solar cooling system on the design and off-design work conditions were only analyzed in this paper, while other performances such as economic feasibility, reliability, and availability are not considered. These aspects should be studied to promote the development of solar cooling systems in future research.

Author Contributions: Formal analysis, Z.W.; Methodology, R.Y.; Project administration, J.W.; Software, X.Z.; Writing–original draft, J.W.; Writing–review & editing, G.S. Funding: This study was supported by the National Natural Science Foundation of China (Grant No. 51876064) and the Fundamental Research Funds for the Central Universities (2018MS098). Acknowledgments: We gratefully acknowledge the anonymous reviewers for their insightful comments on the manuscript. Conﬂicts of Interest: The authors declare no conﬂicts of interest. Energies 2018, 11, 2679 16 of 17

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