Energy and exergy analysis of solar heat driven chiller under wide system boundary conditions

Accepted Manuscript Energy and exergy analysis of solar heat driven chiller under wide system boundary conditions

Karolina Petela, Andrzej Szlek PII:

S0360-5442(18)32279-5

DOI:

10.1016/j.energy.2018.11.067

Reference:

EGY 14165

To appear in:

Energy

Received Date:

25 June 2018

Accepted Date:

17 November 2018

Please cite this article as: Karolina Petela, Andrzej Szlek, Energy and exergy analysis of solar heat driven chiller under wide system boundary conditions, Energy (2018), doi: 10.1016/j.energy. 2018.11.067

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ACCEPTED MANUSCRIPT Energy and exergy analysis of solar heat driven chiller under wide system boundary conditions Karolina Petelaa *and Andrzej Szlek a a

Silesian University of Technology, Institute of Thermal Technology, Konarskiego 22, Gliwice 44-100, Poland

Abstract In the paper, a solar driven ammonia-water chiller is investigated, as one of the systems having potential for reduction of resources depletion. An energy and exergy analysis is proposed for correct diagnostics while designing and operating the cycle. The boundary conditions for the analyses are set in accordance with Professor Szargut’s primary instructions. They are however widened to solar collector component. Solar radiation is treated as the driving energy or exergy, respectively. The analyses are supplemented with a sensitivity diagnosis revealing the most significant parameters modifying the efficiency and irreversibilities distribution. According to the findings, design COP of the chiller equals 0.444 while its net exergy efficiency is 0.026. Solar collector component is the most burdened with exergy destruction and loss in the whole cycle.

Keywords Exergy analysis; solar radiation exergy; irreversibility; ammonia-water chiller; solar thermal collector

1. Introduction Despite deceiving commercial slogans, the truth that useful energy derived from renewable energy sources is burdened with high environmental and economic costs [1] is becoming wider socially accepted. It is due to the effort of researchers dealing with cumulative life cycle impact analyses. Environmental effect of a process mainly depends on the magnitude of non-renewable natural resources exhaustion. Presenting exergy as a proper measure allowing for evaluation of the usefulness of natural resources, Professor Jan Szargut introduced the term called “thermo-ecological cost” [2][3][4]. It provides the cumulative consumption of non-renewable exergy in all chains needed to obtain the final product. A thermo-ecological analysis of a solar collector presented in [5] revealed that the investment part (i.e. use of resources needed for the collector construction, thermo-ecological cost of auxiliary components) contributes to 40% of cumulative resources exergy consumption needed to deliver unit

*

Corresponding author: [email protected]

ACCEPTED MANUSCRIPT of exergy output. This conclusion should not discourage from making efforts to increase the share of renewable energy sources in the final energy consumption. In the end, there is no better method to minimize the consumption of non-renewable natural resources of exergy than to extract renewable energy from the nature [6]. At the same time, it is estimated that the share of energy demand for the cooling purposes on the services market of European countries will become equal to the heat demand share by 2030 [7]. It could be a motivation to drag some interest to renewable energy driven chillers having potential for reduction of resources depletion. An example is a solar thermal absorption chiller. Exergy analysis and life cycle assessment (LCA) of solar absorption cooling cycles indeed have been a topic for numerous research papers. Researchers in [8] performed an exergy and life cycle analysis of solar system for space heating, cooling and domestic hot water production. Already in the assumption phase, they stated that since almost all of the environmental impacts of the renewable energies are associated with the manufacturing process, the environmental impacts were analysed only at the manufacturing stage. In [9] authors performed an energy and exergy analysis of a 10 kW ammonia-water chiller and found that the cycle is more thermodynamically effective if the cooling system is using low-temperature heat sources rather than high-temperature heat sources. The highest exergy destructions were discovered in the absorber and generator (around 76%). An exergoeconomic analysis of a solar driven hybrid storage absorption cooling cycle was done by researchers in [10]. The exergoeconomic analysis was there performed to compare the components in the terms of the initial capital investment costs and the costs of irreversibilities. Generator and evaporator are here made mostly responsible for exergy destructions. However, the highest exergoeconomic cost is allocated to evaporator and solution heat exchanger. Authors noticed the improvement potential in optimizing the design variables of the system. Authors in [11] proposed a tool allowing for minimization of the total cost and the environmental impact of solar assisted absorption cooling systems. According to the findings it is recommended to increase the number of solar collectors installed. Increase of the solar fraction ensures reduction of environmental impact, although their cost allocation caused by manufacturing process is the highest. Although in [12] authors analyzed a compression chiller, they made a valuable distinction while performing the exergy analysis: they distinguished between avoidable and unavoidable exergy destructions (first can be considered in improvement phase, the latter cannot be reduced due to technological limitations) as well as between endogenous (connected only with the inefficiencies within the component) and exogenous parts (caused by the inefficiencies in the remaining components). It should help understanding the real potential for improving the components. This review leads to an obvious conclusion that the construction and decommission phases have a meaningful share while generally analysing the ecological impact of cold obtained from a solar

ACCEPTED MANUSCRIPT chiller. Nevertheless, one must not forget about the significance of the operational phase. Solar chiller relies on an exergy source with time-dependent availability. Moreover, it is a system, where a useful output (cryogenic exergy) is an effect of inevitable exergy destruction in preceding components of the cycle. It is of high importance to properly define the exergy streams and the boundary conditions. Only in that way it is possible to obtain correct operational indicators that could be taken into account in potential subsequent diagnostic LCA. Therefore, the aim of this research is an exergy analysis of a solar thermal chiller and discussion over its utilitarian aspects for the purpose of renewable energy driven system diagnostics. The same, the paper focuses on answering the following questions: what is the significance of exergy analysis applied for a system where exergy of thermal radiation coming from a very high-temperature source is transformed into heat exergy of cryogenic features? How does the choice of boundary conditions influence the assessment of solar chiller effectiveness? How does the definition of driving exergy affect the diagnostic conclusions? To what extent can the minimization of entropy generation within the solar collector have a positive impact on the exergy effectiveness indicators? The study covers energy and exergy analyses of a defined solar energy driven ammonia-water absorption chiller. Definitions of exergy, exergy of thermodynamic agent and solar radiation exergy are based on the primary literature sources available in [4] and scientific papers following this publication. These analyses were supplemented with a sensitivity diagnosis revealing the most significant parameters modifying the efficiency and the distribution of exergy destructions and losses. 2. Reference case presentation A single stage ammonia-water chiller has been taken into account. A simplified scheme of the cycle is presented in Figure 1.

ACCEPTED MANUSCRIPT

Figure 1 Technologic scheme of the single stage solar ammonia-water chiller.

The chiller is driven by a heat rate and electric power utilized by a circulation pump. The phenomena occurring in the chiller are as follows: ammonia-water solution is warmed up in the generator (1) by the heat rate coming from the solar collector field (8). Emerging ammonia vapour is subsequently purified in the rectifier (2). Ammonia vapour flows to condenser (3) where it is cooled down by external cooling water and by the rich solution coming from the absorber (3), producing waste heat. Rich solution passes through condenser, rectifier, preabsorber and reaches generator. The pressure of condensed ammonia is reduced by the intermediate throttling valve. Subcooler (4) reduces the temperature of the liquid, which is subsequently throttled to a lower pressure in evaporator (5) and then evaporated. Low-temperature evaporation process is responsible for providing the cooling power. After being warmed in subcooler, ammonia vapour enters preabsorber (6) where it is absorbed by the weak NH3-H2O solution from the generator. Rich solution is heated up to saturation conditions in the condenser-absorber vessel. 3. Methodology 3.1. Energy and Exergy analysis of ammonia-water chiller 

Energy analysis of chosen chiller

The method of theoretical chiller model preparation has been already thoroughly presented in [13]. The design model of the chiller is based on the application of mass and energy conservation equations to all components in accordance with the 1st law of thermodynamics. By the application of Peclet equation, a primary sizing of heat exchangers is allowed. In present work, it is important to be reminded that the coefficient of performance is calculated as in Eq. 1.

ACCEPTED MANUSCRIPT 𝐶𝑂𝑃 =

𝑚21(ℎ21 ‒ ℎ22)

(1)

𝑄𝐹 + 𝑁𝑝𝑢𝑚𝑝

Where 𝑁𝑝𝑢𝑚𝑝 is the electric power consumed by solution pump, while 𝑄𝐹 is the driving heat stream. It can be understood as useful heat gain from the solar collector (𝑄𝑔𝑒𝑛), or if the boundary was widened: as incoming solar radiation on aperture area. 

Exergy analysis for ammonia-water solution based cycle

Following the discussion available in [14], one can define the exergy balances of the components in such a way that only the increases of enthalpy, entropy and exergy will be calculated (incremental approach). Therefore, to calculate the specific reference enthalpy and entropy, any freely chosen reference conditions can be adapted. Moreover, while performing the analysis with incremental approach, chemical exergy balances are not obligatory. For this reason, the most comfortable way is to choose such reference conditions for which no negative values of enthalpy, entropy or exergy will be obtained. Authors decided to use similar approach and assumed that the reference parameters are that of water under triple point state conditions. Exergy of a j-th flow rate could be determined after [15][16] and is given in Eq. 2 Bj = 𝑚𝑗 ∙ (ℎ𝑗 ‒ ℎ0 ‒ 𝑇0 ∙ (𝑠𝑗 ‒ 𝑠0))

(2)

Exergy balance for each (i-th) component of the cycle can be written adapting Eq. 3, having in mind that the balance is always closed by exergy loss (∆BL,i) and/or exergy destruction (∆BD, i). An exergy loss is associated to exergy transfer to the surroundings, while an exergy destruction derives (for nonreactive systems such as the one here considered) from friction or irreversibility of heat transfer within a defined control volume. in

B i =B



out i + ∆BL,i + ∆BD,i

(3)

Exergy efficiency of an absorption chiller

Following the discussion in [4], one could be reminded that the temperatures of the bottom heat sources present in refrigeration cycles are lower than ambient temperature. In those cases, exergy is irreplaceable to reasonably judge the quality of withdrawn heat. The lower than ambient temperature is the chilled water temperature, the higher is its exergy, although its enthalpy decreases. It may happen that the change of exergy of the bottom heat source is much higher than amount of heat transferred from this source. Exergy analysis can help assess the reversibility of chiller processes. For its purposes, several system boundary conditions can be adopted. Szargut [4] suggested three sizes of the cycle boundary. The

ACCEPTED MANUSCRIPT first boundary separates the chiller itself without the evaporator component. Exergy efficiency of such a system provides a measure of how close the thermodynamic transformations in the chiller approach ideality. Exergy efficiency could be then treated as a gross efficiency (𝜂

𝑔𝑟𝑜𝑠𝑠 ), for cycle shown in Fig. 𝑏

1 following the Eq. 4. 𝜂

𝑔𝑟𝑜𝑠𝑠 𝑏 =

𝑚10(𝑏10 ‒ 𝑏11)

(4)

𝐵𝐹

In general, for thermal absorption chillers 𝐵𝐹 is the exergy of driving heat stream and the driving electric power of circulation pump inside the boundary. The second balance boundary also includes auxiliary components (chilled and cooling water pumping power Naux) and the change of chilled water exergy. Exergy efficiency can be then treated as net efficiency (𝜂

𝑛𝑒𝑡 ) 𝑏

and be calculated from Eq. 5. 𝜂

𝑛𝑒𝑡 𝑏 =

𝑚21(𝑏22 ‒ 𝑏21)

(5)

𝐵𝐹 + 𝑁𝑎𝑢𝑥

Szargut also singled out the third boundary which covers the whole package of thermal processes in the chiller. Exergy efficiency of the whole system may be called ‘general exergy efficiency’ and is given by Eq. 6. It takes into account the final useful effect of chiller operation, namely e.g. exergy increase of the chilled space or chilled matter (∆𝐵𝑐ℎ𝑖𝑙𝑙𝑒𝑑 𝑠𝑝𝑎𝑐𝑒). 𝜂

𝑔𝑒𝑛 𝑏 =

∆𝐵𝑐ℎ𝑖𝑙𝑙𝑒𝑑 𝑠𝑝𝑎𝑐𝑒

(6)

𝐵𝐹 + 𝑁𝑎𝑢𝑥

In the present work, authors analyse the solar ammonia-water chiller covered by a boundary of the second type. It is, however, modified: the boundary is widened by the exergy analysis of the solar collector. Consequently, the driving exergy becomes that of incoming solar radiation. At the same time, the change of cooling water exergy is treated as exergy loss (for the purpose of results presentation).

3.2. Energy and Exergy analysis of solar thermal collector In a solar thermal collector, solar radiation energy is converted into useful heat gain. Instantaneous energy efficiency of the collector is understood as a ratio between useful heat stream 𝑄𝑢 and driving energy stream 𝑄𝑠 being a multiplication of solar radiation energy on area unit (𝐺𝑠) and aperture area of the solar collector (A). It is written in Eq. 7. 𝜂𝑒𝑛 𝑠𝑐 =

𝑄𝑢 𝑄𝑠

=

𝑄𝑢 𝐺𝑠 ∙ 𝐴

(7)

ACCEPTED MANUSCRIPT Energy efficiency of the solar collector depends on its type (whether it can absorb diffused solar radiation), energy stream of the solar radiation, ambient temperature and average temperature of the heat transfer fluid. It can be estimated with the help of second order Bliss Eq. 8 [17]. Δ𝑇𝑚

𝜂𝑒𝑛 𝑆𝐶 = 𝜂𝑜𝑝𝑡 ‒ 𝑎1

𝐺𝑠

Δ𝑇𝑚

‒ 𝑎2

2

(8)

𝐺𝑠

where 𝜂𝑜𝑝𝑡 is the optical efficiency connected with transmissivity-absorptivity losses; whereas 𝑎1 and 𝑎2 are the heat loss coefficients (1st and 2nd order respectively) resulting from convective and radiative losses. Δ𝑇𝑚 is the mean arithmetic difference between heat transfer fluid average temperature and ambient temperature. Constants 𝜂𝑜𝑝𝑡, 𝑎1 and 𝑎2 are obtained experimentally and after certification are available in technical data sheets of a collector model. Similarly, solar collector exergy efficiency is the ratio between useful effect and driving exergy. The useful effect is understood as an increase in physical exergy stream of the heat transfer fluid (𝐵𝑠𝑐). It is presented in Eq. 9. 𝐵𝑠𝑐 = 𝑚17 ∙ (ℎ17 ‒ ℎ18 ‒ 𝑇0 ∙ (𝑠17 ‒ 𝑠18))

(9)

Where 𝑇0 is the ambient temperature (𝑇0 = 𝑇𝑎𝑚𝑏) Driving exergy stream is the solar radiation exergy stream 𝐵𝑠 discussed in next chapter. Collector exergy efficiency is obtained with Eq. 10. 𝜂𝑏 𝑠𝑐 =

𝐵𝑠𝑐

(10)

𝐵𝑠

Following the second law analysis of a solar collector, various approaches to the choice of optimal temperature can be found in the literature. An iterative control routine for finding optimal working parameters of solar collector has been described in [18][19], where the solar collector outlet temperature has been adapted to ensure maximum exergy efficiency of collector. Kalogirou [20] states that the process of solar energy collection is connected with the generation of entropy upstream, downstream of the collector and inside it. Thus, by minimizing the entropy generation one can maximize the power output. He delivered a formula for optimum collector temperature calculation being a geometric average of the maximum collector temperature and the ambient temperature ( 𝑇𝑜𝑝𝑡𝑖𝑚𝑢𝑚 = 𝑇𝑚𝑎𝑥𝑇0). The optimization problem has been considered in this way also by Bejan [21] or Torres-Reyes et al. [22]. However, Szargut argued with this approach in [5]. He motivated it saying that such kind of optimization does not take into account the entropy generation in the previous processes. What is more, and more accurate here, entropy generation in processes where renewable exergy is utilized should not be considered, since the irreversibility of such processes does not affect negatively the environment or other processes.

ACCEPTED MANUSCRIPT Authors follow the standpoint of Szargut and at the same time are paying attention to subsequent processes in solar chiller. The operational outlet temperature in the solar collector has been found using the procedure presented in [13]. It is based on the observation that although COP of the chiller increases together with the driving temperature, solar collector energy efficiency decreases if the temperature difference between heat transfer fluid and ambient becomes higher.

3.3. Solar radiation exergy definition According to the first and the second Law of Thermodynamics, energy cannot be spontaneously created or lost. However, the ability to perform work may become smaller because of the process irreversibility accompanied by entropy generation. This consideration led to defining exergy: as a maximum ability to perform work available during reversible transformations striving to equilibrium with the environment [23]. Unlike energy, exergy is not conserved, but it informs if there is a potential to improve the process, to minimize exergy loss. Exergy loss is defined by the Gouy-Stodola theorem

(∆𝐵 = 𝑇0∑∆𝑆). The question how to define the ability to perform work by solar radiation reaching given surface has already been raised in several research works. One should be reminded that exergy, like enthalpy or entropy, is a function of state and by thus the property of matter. Hence, instead of solar radiation exergy, one should rather speak about exergy change of radiation source. Nevertheless, the “solar radiation exergy” term is more common in the literature as an accepted form of concept shortcut. It will be also used in this work. Following the literature review, there are a few frames to define solar radiation exergy, relating to black body radiation [4][24][25], taking into consideration spectral radiation distribution [26], and declaring separately exergy for direct and diffuse radiation [27][28]. Szargut [4] and Petela [4][24][25] were one of the firsts to present a method to calculate exergy of undiluted thermal radiation. It can be recalled with an example of ideally reversible thermodynamic cycle. It is assumed the cycle is driven by an energy Es coming from a source (e.g. Sun) of temperature Ts (5780 K can be assumed for the Sun). Being driven by Es, the cycle can perform the maximum work Wmax. Maximum work is equal to source exergy of (solar) radiation Bs. At the same time, the cycle is losing heat to the ambient Q0 and is emitting radiation Ee. The energy balance for this ideal cycle is presented by Eq. 11. 𝐸𝑠 = 𝑊𝑚𝑎𝑥 + 𝑄0 + 𝐸𝑒

(11)

Knowing that maximum work is equal to source exergy, Eq. 11 is transformed to Eq. 12. 𝐸𝑠 = 𝐵𝑠 + 𝑄0 + 𝐸𝑒

(12)

ACCEPTED MANUSCRIPT In [4][24][25] Petela delivered a complete procedure to define entropy of thermal radiation. He introduced the ψ ratio for the maximum conversion efficiency indicating the maximum work to be obtained from radiation energy. Its formula is given in Eq. 13. It is commonly used to evaluate the solar radiation exergy value. 𝐵𝑠

(

)

4

(13)

4𝑇0 1𝑇0 𝜓= = 1‒ + 𝐺 3 𝑇𝑠 3𝑇4 𝑠

Where G can be treated as incoming solar radiation (𝐺𝑠) or, for cases other than solar, as thermal 4

radiation energy following Stefan-Boltzmann’s law (𝜎𝑇 𝑠 ). This formula was confirmed by other researchers: by Press in [29] or by Landsberg in [30]. In 1964 Spanner independently published a formula to calculate exergy of direct radiation [31]. It was partially in line with Petela’s considerations. However, it was assuming no emission from the theoretical thermodynamic cycle (Ee=0). Spanner obtained formula presented in Eq. 14.

(

4

𝐵𝑠 = 𝜎𝑇𝑠 1 ‒

)

4𝑇0 3 𝑇𝑠

(14)

20 years later, posing different assumptions, Jeter was proving that the Carnot cycle analysis can be utilized for the purpose of solar radiation exergy calculation [32]. Solar energy was then treated as heat. If solar radiation exergy was equal to work from heat engine, the maximum fuel conversion 𝑇0

efficiency would be 1-𝑇 . Consequently, solar radiation exergy could be given by Eq. 15. 𝑠

( )

𝐵𝑠 = 𝐺 1 ‒

𝑇0

(15)

𝑇𝑠

Petela himself thoroughly analysed the origin of differing formulas obtained [25]. These 3 approaches (Szargut and Petela’s, Spanner’s, Jeter’s) were investigated independently by Bejan [33]. He stated that the 3 theories do not exclude each other and if they are all individually correct, they may complement each other. The differences result from various assumptions: how the energy stream of which the useful effect we want to calculate is defined: whether it is heat or radiation and how the useful effect is understood. In 2009 Zamfirescu and Dincer provided their insight on exergy of incident solar radiation [34]. Their model rests on relating the exergy to the instantaneous insolation. They observed that if a thermodynamic model extracting maximum work (exergy) from solar radiation is analysed, the dissipation effects in the terrestrial atmosphere should be closer investigated. The dissipation effects in the atmosphere result from operating between Sun temperature and the solar collector temperature. The latter is constantly changed by the solar radiation intensity. Zamfirescu and Dincer finally proposed a new definition of solar maximum conversion coefficient - ψZD ratio presented in Eq. 16.

ACCEPTED MANUSCRIPT It takes into account that the solar radiation reaches the outer shell of atmosphere with an intensity given by solar constant 𝐼𝑠𝑐=1373 W/m2. 𝜓𝑍𝐷 =

𝐵𝑠 𝐺

(

= 1‒

(16)

)

𝑇0𝐼𝑠𝑐 𝑇𝑠 𝐺

Researchers were also pointing that one should differentiate between direct solar radiation exergy and diffused solar radiation exergy since scattered radiation is the source of higher entropy than direct radiation. Scattering is an irreversible process generating entropy. This definition was developed by Pons [27] and by Chu and Liu [26] who were defining solar radiation exergy using spectral distribution. Numerical difference resulting from adapting chosen model for solar radiation exergy calculation may be visualized while evaluating solar collector exergy efficiency. The difference was tested for an exemplary evacuated tube solar collector facing South with the slope of 45°, installed in Cracow, operated on an average day in July. Chart in Fig. 2 presents a daily distribution of solar collector exergy efficiency where incoming solar radiation exergy is calculated according to 3 methods: Petela’s, Jeter’s, Spanner’s and Zamfirescu’s. 0.12

1000 900 800 700 600 500 400 300 200 100 0 23, 0

0.08 0.06

G, W/m 2

ηex sc

0.1

0.04 0.02 0 6

7

8

9

10

11

12 13 14 15 hours of the day

16

17

18

19

G_dif

G_dir

Petela

Jeter

Spanner

Zamfirescu

20

Figure 2 Daily distribution of solar collector exergy efficiency following Petela’s, Jeter’s, Spanner’s and Zamfirescu’s approaches paired with solar radiation distribution (G_dir – direct, G_dif – diffused solar radiation).

It is visible that regardless of method applied, the shape of the curve remains the same. The Zamfirescu 𝜓𝑍𝐷 ratio is always smaller for the same analysed conditions. It leads to a smaller value

ACCEPTED MANUSCRIPT of solar radiation exergy and, the same, to a higher value of solar collector exergy efficiency, as shown in the figure. Exergy efficiency according to Spanner almost overlaps with the one calculated after Petela. Maximum difference between Jeter’s efficiency and Petela’s equals 0.002. The difference becomes visible if the temperature of the radiation source is close to ambient temperature. It is presented in Fig.3. According to Petela’s conclusion, Jeter’s and Spanner’s approach should not be used for cases below ambient temperature. Whereas at high source temperatures the numerical differences are negligible [25]. Since Zamfirescu’s 𝜓𝑍𝐷 also assumes dependence on incoming solar radiation G, it was not plotted on this chart.

Figure 3 Comparison of maximum conversion efficiency ψ according to Petela’s, Jeter’s and Spanner’s approaches in function of radiation source temperature.

Taking this whole discussion into account, it has been decided that for the purpose of incoming solar radiation exergy evaluation Petela’s approach will be utilized. 3.4. Sensitivity analysis Exergy analysis tool is aimed at detection of the weakest link, in the terms of irreversibility. It should help indicate components mostly responsible for low exergy efficiency indicators already in the designing phase. In order to be aware which parameters highly affect the exergy destruction and losses distribution, a sensitivity analysis has been proposed. The influence on the exergy efficiency of the chiller and on the distribution of exergy destructions or losses allocated to given component was investigated changing following parameters: 

Chilled water inlet temperature,



Cooling water inlet temperature,



Chilled water temperature decrease,

ACCEPTED MANUSCRIPT 

Cooling water temperature increase,



Solar collector energy efficiency.

4. Tools Thermodynamic model of the solar ammonia-water chiller was written within Engineering Equation Solver (EES) - a non-linear equation solver that can be used to solve sets of equations [36]. Thermodynamic properties of water were read from internal libraries provided by EES. Thermodynamic properties of ammonia-water solution were applied using an external routine available in EES. The thermodynamic data are based on the ammonia-water mixture equation of state described by Ibrahim O.M and Klein S.A. in [38]. 5. Calculations The assumptions made for the design point analysis of solar ammonia-water chiller are presented in Table 1. Table 1 Design point parameters assumptions

Parameter Symbol Solar collector model [37] Optical efficiency ηopt Linear het loss coefficient a1

Value

Unit

0.75 0.1123

W/(m2K)

0.00128

W/(m2K2)

73.3

m2

700

W/m2

10

K

25

°C

Cooling water inlet T19 Pinch point temperature difference in condenser 𝑇7 ‒ 𝑇19

35

°C

5

𝐾

chilled water inlet T21 Pinch point temperature difference in evaporator 𝑇22 ‒ 𝑇11

12

°C

7

K

5 0.995 0.22 0.94 0 0 0 1 1

K -

Quadratic heat loss coefficient a2 Aperture area A Total solar radiation Gs Heat transfer fluid temperature increase 𝑇17 ‒ 𝑇18 Ambient temperature Tamb Chiller model

temperature difference in generator 𝑇18 ‒ 𝑇14 x Concentration of ammonia-water solution 6 x1-x14 q11 q7 q Quality of ammonia-water solution 1 q14 q5 q6

ACCEPTED MANUSCRIPT For the purpose of exergy analysis, it was assumed that reference enthalpy and entropy are that of water under triple point conditions (Ttr = 0.01 °C, ptr = 0.6117 kPa). Ambient parameters are: Tamb = 25 °C, pamb =101.325 kPa. Exergy balance elements for each component of the cycle are presented in Table 2. Table 2 Set of exergy balance equations for each component of the chiller 𝐢𝐧

𝐨𝐮𝐭 𝐢

Component

i

𝐁𝐢

Generator

1

B17 + B4 + B16

B18 + B5 + B14

0

B1 ‒ B

Rectifier

2

B5 + B2

B16 + B3 + B6

0

B2 ‒ B

3

B6 + B13

B1 + B7

B20 ‒ B19

Subcooler

4

B8 + B11

B9 + B12

0

B4 ‒ B

Evaporator

5

B10

B11 + BP

0

B5 ‒ B

Preabsorber

6

B12 + B3 + B15

B4 + B13

0

B6 ‒ B

Pump

7

B1 + Npump,2

B2

0

B7 ‒ B

Solar collector

8

BF + B18

B17

Valve 9-10

9

B9

B10

0

B9 ‒ B

Valve 14-15

10

B14

B15

0

B10 ‒ B 10

Valve 7-8

11

B7

B8

0

B11 ‒ B 11

Condenser/Abs orber

𝐁

∆𝐁𝐋,𝐢

(

𝑄𝑔𝑒𝑛 1 ‒

∆𝐁𝐃,𝐢

𝑇0

in

out 1

in

out 2

in

B3 ‒ B

)

𝑇𝑐𝑜𝑙𝑙

out 3 ‒ ∆BL,3

in

out 4

in

out 5

in

out 6

in

out 7

in

B8 ‒ B

out 8 ‒ ∆BL,8

in

out 9

in

out

in

out

In order to maintain consistency with Eq. 5, the product exergy rate is that connected to change of exergy of chilled water (BP = 𝑚21(𝑏22 ‒ 𝑏21)), while the fuel exergy rate is that of incoming solar radiation (BF = BS). Authors proposed to separate the exergy loss for the solar collector component assuming that it is due to the irreversible heat loss from solar collector at temperature 𝑇𝑐𝑜𝑙𝑙 to the environment.

6. Results and discussion According to the energy analysis investigated ammonia-water chiller delivers 23 kW of cooling power with COP=0.632. If the incoming solar radiation was considered as the constituent of driving energy instead of solar collector useful heat gain, the COP under wide boundary conditions would have been 0.444. Energy analysis indicates that the condenser/absorber is mainly responsible for the heat loss, delivering 58.95 kW of waste heat, while there are no losses in generator or evaporator.

ACCEPTED MANUSCRIPT Net exergy efficiency calculated after Eq. 5 equals 2.62%. If the boundaries were narrowed and the driving exergy was understood as the exergy product rate from solar collector, the exergy efficiency of considered absorption chiller would equal 11.82%. It will be always lower than the exergy efficiency of a typical compression chiller (around 25% [14]), but one should remember that the advantage of absorption chiller is that it can be driven by a waste heat stream or, as in present case, by renewable energy. Exergy balance results are collected in Table 3. Percentage results are on purpose referred to driving solar radiation exergy as 100%. It is a replicated procedure of Professor Szargut presented in [4]. In that way one can refer all of the results only to the driving exergy from a renewable source. It indicates how much exergy from solar radiation is available to be converted into cooling effect, while the pump power input is already forced by the cycle operation. Table 3 Exergy balance results set for solar ammonia-water chiller

Name Solar radiation

kW

%

47.777

100

Name

Pump power

0.1167

0.24

Exergy destruction and losses

Driving exergy

exergy

kW

%

Generator

2.088

4.37

Rectifier

0.2465

0.52

Condenser/absorber

4.697

9.83

Subcooler

0.1091

0.23

Evaporator

0.866

1.81

Preabsorber

0.858

1.80

Pump

0.0224

0.05

Solar Collector

37.18

77.83

Valve 14-15

0.523

1.10

Valve 7-8

0.0008

0.002

Valve 9-10

0.0453

0.09

1.252

2.62

47.894

100.24

Exergetic useful effect from evaporator total

47.894

100.24

total

As expected, it is shown that solar collector and its efficiency parameters play the predominant role in the exergy destruction/losses allocation. Results distribution is consistent with those discussed in [4] or more recently in [9]. Apart from solar collector, highest exergy destruction and losses rates are assigned to generator and condenser/absorber components. The whole exergy balance from Table 3 is visualized in Fig. 4. This band chart shows how the driving exergy is step-by-step destroyed or lost to finally achieve the useful cooling effect.

Figure 4 Exergy balance- Sankey diagram of the solar driven ammonia-water chiller.

ACCEPTED MANUSCRIPT Partial results of the sensitivity analysis are shown in Fig. 5. It is shown how the ±30% change of the following parameters would affect the final value of chiller exergy efficiency: 5



Solar collector thermal efficiency (𝜂𝑒𝑛 𝑆𝐶 = 0.5 ÷ 0.9)



chilled water inlet temperature (𝑇21 = 8.5 ÷ 15.5℃)



cooling water inlet temperature (𝑇19 = 24.5 ÷ 45.5℃)



temperature decrease of chilled water (∆𝑇𝑐ℎ𝑖𝑙𝑙 = 3.5 ÷ 6.5℃)



temperature increase of cooling water (∆𝑇𝑐𝑤 = 7 ÷ 13℃)

10 Figure 5 Sensitivity of chiller exergy efficiency to ±30% change of chosen design parameters.

It is visible, that changing the design temperature differences of chilled or cooling water does not affect the exergy balance almost at all. On the other hand, if chilled water inlet temperature was decreased by 30% (to 8.5°C), the exergy efficiency of the chiller would increase by 5 percentage 15

points. It is even more positively affected by decreasing the cooling water temperature increase. If this temperature difference was decreased to 7°C, the efficiency would rise to 0.038. Non-linear behaviour of these curves may result from the built-in non-linearities (second order equation for solar collector efficiency calculation, ammonia-water solution as zeotropic mixture etc.). Potential 30% increase of solar collector efficiency (if e.g. enhanced construction was considered), could lead to

20

0.008 increase in exergy efficiency of the cycle. The sensitivity analysis allows to compare the influence of changing design operating conditions on COP calculated under wide boundary-balance conditions. This effect is shown in Fig. 6

ACCEPTED MANUSCRIPT

25

Figure 6 Sensitivity of chiller COP to ±30% change of chosen design parameters.

One can observe, that unlike chiller exergy efficiency, the COP of solar chiller becomes higher together with the increase of chilled water inlet temperature (𝑇21). It is directly connected with the quality approach. Less driving energy is needed to produce the same amount of cooling power but at higher temperature level. Exergy analysis, on the other hand, perceives the smaller usefulness of 30

cryogenic exergy as the chilled water approaches ambient temperature. From the energy analysis perspective, the COP is also more sensitive to modification of temperature decrease of chilled water. Fig. 7 shows how the same changes of operating conditions would affect the COP calculated under narrow balance-boundary.

ACCEPTED MANUSCRIPT

35 Figure 7 Sensitivity of chiller COP to ±30% change of chosen design parameters for narrow balance-boundary conditions.

The striking difference is no effect on COP if, potentially, the solar collector efficiency would be modified. It derives directly from the fact that this sensitivity analysis was done for narrow balance40

boundary and COP was calculated from Eq. 1, where the driving energy is understood as pump electricity consumption and useful heat gain from solar collector. Hence: it does not depend on solar collector efficiency coefficients. Fig. 8 visualized how the potential increase of solar collector efficiency affects the distribution of destruction (∆BD,i) and losses (∆BL,i) in the whole cycle. Indexed numbers are in accordance with

45

numbered components in Fig. 1.

ACCEPTED MANUSCRIPT

Figure 8 Distribution of exergy destructions and losses in the components of the cycle in the function of modified solar collector efficiency.

According to the exergy balance, there are no exergy losses in generator (1), rectifier (2), subcooler 50

(4), evaporator (5), preabsorber (6), pump (7) and valves. Exergy destructions in rectifier, subcooler, pump and valve (9) are so negligible that they were shown as sum in the chart. Fig. 6 helps realize that if solar collector efficiency parameters were potentially increased by 30%, the exergy destruction in solar collector component would have also drop by 30%. However, this modification of the design leads also to increase of exergy losses in solar collector component. Although much smaller than

55

destructions in solar collector, the exergy destruction in generator and absorber/condenser are doubled. Hence the processes are becoming more irreversible. If similar analysis was performed for the cooling water inlet temperature, it would turn out that although lowering this temperature decreases exergy loss and destruction in almost every component. However, it still induces higher exergy destructions in 2 parts. Exergy destruction increases in evaporator (higher mass flow rate) and

60

by 11% also in already the most burdened solar collector. It confirms the statement that exergy analysis should be used for diagnostic purposes where the whole cycle is treated as set of connected vessels.

ACCEPTED MANUSCRIPT 7. Conclusions 65

In the article energy and exergy analysis of a solar ammonia-water chiller was proposed. Solar collector component is included in the boundary for the analysis, thus solar radiation is understood as the driving energy or exergy respectively. The research covered discussion over proper boundary definition, proper treatment of exergy assigned to incoming solar radiation following Szargut’s and his co-authors’ guidelines. Coefficient of performance under wide boundary conditions of the system

70

equalled 0.444, while the net exergy efficiency was 0.026. On the other hand, if the driving exergy was defined as the exergy product rate from solar collector, the exergy efficiency of solar chiller would be 0.118. These apparent differences reveal, that not only the quality of energy matters, but also the definition of balance boundaries. They should be used wisely to avoid manipulation. It has been revealed that solar collector component is mostly responsible for the irreversibilities in

75

the cycle (0.778 of relative exergy destruction/loss product). The known approach of optimal collector temperature assuring entropy generation minimization was, however, not adapted to improve the balance, since this optimization method does not take into account preceding processes during e.g. construction phase. Enclosed energy and exergy analyses in this manuscript were meant to help identify location of losses

80

and irreversibilities. Discussion over sensitivity analysis provides an insight into which component could be redesigned and modified to enhance the cycle performance. One should observe that minimizing irreversibilities in one component could lead to deterioration of performance in another one. These aspects could be thoroughly addressed by an advanced exergy analysis on endo- and exogenous parts of irreversibilities. It is important to notice that obtained results should be furtherly

85

used for the purpose of thermoeconomic and thermoecological analysis and optimization.

Nomenclature Abbreviations 90

95

100

COP LCA RES TEC Symbols A 𝑎1 𝑎2 B 𝑏𝑖 𝐵𝑖 ∆BD,i ∆B𝐿,i

coefficient of performance life cycle assessment renewable energy sources thermo-ecological cost aperture total area, m2 linear het loss coefficient, W/(m2K) quadratic heat loss coefficient, W/(m2K2) exergy, kJ specific exergy, kJ/kg exergy of flow rate, kW exergy destruction rate in i-th component, kW exergy loss rate in i-th component, kW

ACCEPTED MANUSCRIPT

105

110

115

120

125

130

135

140

145

E 𝐸 G h𝑖 𝑚𝑖

energy, kJ energy rate, kW radiation, W/m2 enthalpy, kJ/kg

𝑁 p𝑖 q𝑖 𝑄𝑖 𝑄𝑖 𝑠𝑖 𝑇𝑖 x𝑖 subscripts 0 amb auxiliary chilled space comp dif dir e en ex F gen m opt pump s sc tr u superscripts gen gross net greek â^ † η ψ 𝜎

driving power, kW pressure, kPa quality, heat, kJ heat rate, kW entropy, kJ/(kgK) temperature, ºC concentration, -

mass flow rate, kg/s

reference ambient of auxiliary components of the chilled space component diffused solar direct solar emission energy exergy driving generator mean arithmetic optical of the pump sun/solar solar collector triple point useful gain general gross net delta – increase/loss efficiency maximum conversion efficiency Stefan-Boltzmann’s constant (5.670367∙10−8 W/(m2K4))

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ACCEPTED MANUSCRIPT Energy and exergy analysis of solar heat driven chiller under wide system boundary conditions Karolina Petelaa 1and Andrzej Szlek a a Silesian

University of Technology, Institute of Thermal Technology, Konarskiego 22, Gliwice 44-100, Poland

HIGHLIGHTS

1

  

Energy and exergy analysis of 23 kW solar NH3-H2O absorption chiller is performed Balance boundary is widened and includes solar collector field component 𝑛𝑒𝑡 Under wide balance boundary COP=0.444 and exergy efficiency (𝜂 𝑒𝑥 ) equals 0.0262



Lower cooling water temp. increases 𝜂 𝑒𝑥 but induces higher losses in evaporator and



sol. collector Decreasing exergy destruction in solar collector means higher irreversibilities in absorber

𝑛𝑒𝑡

Corresponding author: [email protected]