Abstract

In this paper, energy and exergy analyses of a new solar-driven triple-staged refrigeration cycle using Duratherm 600 oil as the heat transfer fluid are performed. The proposed cycle is an integration of absorption refrigeration cycle (ARC), ejector (EJE) refrigeration cycle (ERC), and ejector expansion Joule–Thomson (EJT) refrigeration cryogenic cycles which could produce refrigeration output of different magnitude at different temperature simultaneously. Both exergy destruction and losses in each component and hence in the overall system are determined to identify the causes and locations of the thermodynamic imperfection. Several design parameters, including the hot oil outlet temperature, refrigerant turbine inlet pressure, and the evaporator temperature of ERC and EJT cycle are also tested to evaluate their effects on energy and exergy performance. It is observed that largest contribution to cycle irreversibility comes from the central receiver and heliostat field with the heat recovery vapor generator (HRVG), condenser, and ejector of ERC itself also contributing considerably. The exergy efficiency of the solar-driven triple-staged refrigeration cycle is 4% which is much lower than its energy efficiency of 10%, respectively. The results clearly reveal that thermodynamic investigations based on energy analysis alone cannot legitimately be complete unless the exergy concept becomes a part of the analysis.

Introduction

For the last few years much research is devoted to the development of technologies that can offer reductions in energy consumption, peak electrical demand, and energy costs without lowering the desired level of comfort conditions. Solar energy refrigeration technologies have the advantage of removing the majority of harmful effects of traditional refrigeration machines and that the peaks of requirements in cold coincide most of the time with the availability of solar radiation. The development of solar refrigeration technologies became the worldwide focal point for concern again [1].

In order to utilize the solar energy for its potential in reducing fossil fuel consumption and alleviating environmental problem, more interests have been paid to the solar thermal-driven refrigeration technologies like solar ejector cooling, solar powered absorption refrigeration, and solar energy driven combined ejector-absorption cooling cycles. Detailed discussion on the thermodynamic performance of these refrigeration cycles is recently published. Priasawas and Lundqvist [2] studied the solar-driven ejector system and calculated the irreversibilities in each component of the system to find the optimum operating conditions. Their results indicate that most significant destruction/losses occur in the solar collector and ejector. Hernandez et al. [3] showed that for an evaporator temperature of −10 °C, an ejector refrigeration system employing R134a can operate at a generator temperature of 85 °C with average energy efficiencies between 21% and 58%, depending on the condenser temperature. Alexis and Katsanis [4] obtained similar results for methanol. Varga et al. [5] carried out a theoretical study to asses system and refrigeration efficiencies of a solar-assisted ejector cycle using water as the operating fluid. Their analysis indicated that in order to achieve an acceptable coefficient of performance, generator temperatures should not fall below 90 °C. Evaporator temperatures below 10 °C and condenser temperatures over 35 °C resulted in a significant drop in system efficiency. Solar-driven absorption refrigeration systems are suitable for use with solar energy and existing absorption system show limitations in the evaporator range −20 °C to +10 °C. It is widely realized that now refrigerant-absorbent combinations may be more suitable than the most commonly used solutions (LiBr-H2O and NH3-H2O solutions). In this context, Pierres et al. [6] examined the possibility to design a new deep freezing process to produce cold at low temperature (−40 °C) from low grade heat source (80 °C) using absorption thermochemical technology. They reported that the exergies involved in thermochemical process for cold production distinguish between the quantity and quality of the inlet and outlet energies. Dincer et al. [7] used a mixture of R-22 and dimethyl ether tetra ethylene glycol as the working fluid. The coefficient of performance (COP) for theory and experiment was found to be 0.6 and 0.4, respectively, at a generator temperature of 90 °C. Das and Mani [8] recommended the use of R22-N,N-dimethyl formamide. Another attempt towards the improving of the performance of solar-driven absorption cycle is to improve the performance of the solar collection by using glazed collectors/generators [9]. Atmaca and Yigit [10] carried out a thermodynamic optimization of solar powered absorption cycle using NH3-H2O mixture as a working fluid. Ziegler et al. [11] introduced the multieffect absorption cycles to yield better cooling performances using low grade heat. Sozen et al. [12] highlighted the prospects for utilization of solar-driven ejector-absorption cooling system and reported that there is a great potential for utilization of solar cooling system for domestic heating/cooling applications in Turkey. Wang et al. [13] dealt with a solar-driven ejector-absorption refrigeration cycle with re-absorption of the strong solution and pressure boost of the weak solution (NH3-LiNO3). It is demonstrated that the cycle has obvious advantages as compared with the conventional absorption refrigeration cycle. Fan et al. [14] shows that solar power ejector-absorption technologies are attractive alternatives that not only can serve the needs of air conditioning and refrigeration purposes but also can meet demand for energy conservation and environmental protection. Solar operated ejector and absorption refrigeration systems are limited in their ability to produce cooling in the range of 250 K–290 K. These systems were found suitable for refrigeration and air conditioning purpose. There are many applications, where cooling in the cryogenic range (80 K–220 K) is needed, like infrared detector, gas chillers or liquefaction, cryosurgery, cryopreservation, water vapor cryotrapping, and astronautical application, etc. To meet out such a cooling demand, the EJT cryogenic cycle has been explored and various investigations related to this cycle are reported in the literature. At this onset, Naer and Rozhentsev [15] conducted the experimental investigation with Joule–Thomson microcoolers in the range of 90–200 K for hydrocarbon mixtures. Yu et al. [16] performed a component level exergy analysis, for the ejector Joule–Thomson cycle using the two component refrigerant mixture N2-CH4 and showed that the ejector Joule–Thomson cycle exhibits a clear increase in exergetic efficiency compared to the basic Joule–Thomson refrigeration cycle. Recently, Rashidi et al. [17] applied the first-law and second-law approach to study an ejector Joule–Thomson cryogenic refrigeration cycle. Their investigations show that COP and exergy efficiency increase with increasing evaporator temperature and ejector pressure. More recently, Gong et al. [18] developed the dual mixed gases Joule–Thomson refrigeration system for −186 °C cryogenic preservation. Their investigations show that the dual mixture refrigeration cycle has a good performance for low temperature applications. For the effective exploitation of solar energy and to provide cooling for refrigeration and space conditioning in various ranges of operating temperature for domestic, commercial, and industrial applications, an emergence of hybrid cycle combining the various solar powered refrigeration cycles has become an imperative need to overcome with the twin menace of increasing energy demand and environmental degradation through fossil fuel consumption for cooling applications.

The literature review indicates that the energy and exergy analyses of solar energy driven hybrid cycle for triple-staged refrigeration, which use heliostat field and central receiver as the concentrator-receiver system, have not been reported till now. In this regard, the objective of this article is to construct a theoretical framework for the energy and exergy analysis of solar powered triple-staged refrigeration cycle using Duratherm 600 oil as the heat transfer fluid. The proposed cycle is the integration of LiBr-H2O ARC which may be used for space conditioning of 4 °C to 10 °C, ERC which provides cooling for refrigeration in the range of −9 °C to −1 °C (264 K–272 K), and EJT cryogenic cycle which is effectively applicable for cryogenic cooling in the range of −193 °C to −143 °C (80 K–130 K). The proposed cycle is an effort for the effective exploitation of solar energy to meet out the cooling demands of various industries like space conditioning, cold storages, pharmaceuticals, infrared detectors, cryosurgical probes, and vaccine preservation, etc. Parallel to the advancement in refrigeration systems for the effective exploitation of waste heat, second law of thermodynamics along with the traditional first law approach, is highly desirable in order to make the theoretical treatment of the proposed cycle in general and to identify and quantify the sources of losses for evaluating its true efficiency in particular. A reduction in thermodynamic losses in its various components will lead to its effective exploitation through efficient and environmentally benign operation. The effect of most influenced parameters has been observed on the energy and exergy efficiency of the proposed cycle along with the exergy destruction in its various components. Numerical results are graphed and commented upon.

Description of the Proposed Cycle

The proposed system consists of Rankine cycle (RC), ERC, ARC, and EJT cycle with only solar heat source. Figure 1 shows the simplified RC, ERC, ARC, and EJT cycle, while Fig. 1(a) depicts the corresponding T-s diagram. Solar energy falls on the heliostat field and reflected on the aperture area of central receiver which is located at the top of the tower. The concentrated rays, which fall onto the receiver results in high temperature of the central receiver is used to heat the oil (Duratherm 600). The oil is flowing through the pipes which transfer the thermal energy from central receiver to the HRVG (1–2) and generator (2–12). Superheated vapor of R141b (4) is expanded in a turbine to generate work. The turbine exhaust (5) passes through converging diverging supersonic nozzle of EJE1. The very high velocity refrigerant vapor at the exit of the nozzle creates a very high vacuum at the inlet of the mixing chamber and extract secondary vapor (11) into the chamber from the evaporator-1 (E1) of ERC and this causes cooling effect at E1 of ERC. The primary vapor (5) and secondary vapor (11) are mixed in the mixing chamber. The mixed stream (6) is cooled in condenser-1 (C1). The saturated liquid (7) is divided into two parts (8, 9), one part (9) is passed through throttling valve-1 (TV1) where pressure is reduced to evaporator pressure (10) and feed to E1, and second part (8) is pumped by pump-1 (P1) to the HRVG of RC cycle. The solar thermal energy (2) coming out from HRVG passes through the generator of ARC and finally recirculated to the central receiver. The saturated pure water vapor (13) coming from generator is cooled in C2. Saturated liquid (14) at condenser pressure passes through TV2 to generate saturated liquid (15) at reduced pressure, i.e., evaporator pressure. Saturated vapor (16) after receiving heat from E2 enters the absorber (A). Solution (20) which is a mixture of LiBr-H2O passes through solution heat exchanger (SHX) and cooled to (21) and then passes through throttle valve to reduce its pressure, i.e., absorber pressure. Absorber is maintained at 35 °C at E2 pressure. Two streams (16, 22) mixed at absorber (A) and form a new mixture (17), which passes through P2 and SHX and then finally enters to the generator (G).

Fig. 1
Fig. 1
Close modal
Fig. 1(a)
Fig. 1(a)
Close modal

The work output from turbine is fed as input to the compressor of EJT cycle. The working fluid (propane) compressed from state 23 to 24 isothermally. Next, the high-pressure vapor enters the heat exchanger-1 (HX1) and cooled to 25. Subsequently, the flow is divided into two streams; one stream leaves the HX1 and enters the EJE2, the other stream enters the HX2 and is further subcooled to 26. The vapor in HX1 and HX2 is subcooled (25–26) by the returning low-pressure gas stream from the EJE2. The subcooled refrigerant transforms to two-phase flow after the TV4 at state 27. The low pressure and temperature flow that enter the E3 are vaporized by absorbing heat from cooling media and produces the necessary cooling effect and exits the evaporator in a two-phase flow at state 28.

The extracted vapor (25) from the HX1 enters the nozzle of the EJE2 as the primary fluid. The very high velocity vapor at the exit of the nozzle produces vacuum at the inlet of mixing chamber and entrains the two-phase flow (secondary fluid) from the E3. The two streams are mixed in the mixing chamber and the mixed stream discharges from the EJE2 to the HX2 at state 29. The temperature of vapor increases while passing through HX1 and HX2 and in due course superheated vapor enters the compressor at state 23.

The following assumptions are made for the analysis of the proposed cycle:

• the components of the cycle are in steady state with constant solar radiation, and pressure drop in pipes and heat losses to the environment in the HRVG, turbine, condensers, and evaporators are neglected

• the flow through the throttle valve is isenthalpic

• the condenser outlet state is saturated liquid

• the evaporator outlet state is saturated vapor

• only physical exergies are used for the industrial waste heat source and vapor flows

• kinetic, potential, and chemical exergies of the substances are neglected

• lithium bromide solutions in the generator and absorber are in equilibrium state at their respective temperature and pressure

• the water refrigerant at condenser and evaporator exit is at saturated state

• the strong solution leaving the absorber and the weak solution leaving the generator are saturated

• to avoid crystallization of the solution in ARC, the temperature of the solution entering the TV3 should be at least 7 °C–8 °C above the crystallization temperature

• amount of power consumed by refrigerant pump and solution pump is found to be negligible, hence it is assumed to be zero

For the analysis, the specifications of the combined RC, ERC, ARC and EJT cycle are given in Table 1.

Table 1

Main parameters considered for the analysis [22,25]

 Environment temperature (°C) 15 Environment pressure (MPa) 0.10135 Turbine inlet pressure range (MPa) 0.9–1.7 Hot oil outlet temperature (°C) 160–180 Hot oil inlet temperature (°C) 85 Solar radiation received per unit area (W m−2) 850 Apparent sun temperature (K) 4500 Heliostat aperture area (m2) 3000 Turbine back pressure range (MPa) 0.22–0.3 Turbine isentropic efficiency (%) 85 Isothermal efficiency of compressor (%) 55 ARC evaporator temperature (°C) 5 ERC evaporator temperature range (°C) (−1 to −9) or (264 K–272 K) EJT evaporator temperature range (°C) (−193 to −143) or (80 K–130 K) Condenser-2 temperature (°C) 35 Hot oil mass flow rate (kg s−1) 8.0 Pump isentropic efficiency (%) 70 HRVG efficiency (%) 100 Pinch point temperature difference (°C) 10.0 Nozzle efficiency (%) 90 Mixing chamber efficiency (%) 85 Diffuser efficiency (%) 85 Energy efficiency of heliostat field (%) 75 Energy efficiency of central receiver (%) 90 Exergy efficiency of heliostat field (%) 75 Exergy efficiency of central receiver (%) 30 View factor of central receiver 0.8 Emissivity of central receiver 0.8 Reflectivity of central receiver 0.04
 Environment temperature (°C) 15 Environment pressure (MPa) 0.10135 Turbine inlet pressure range (MPa) 0.9–1.7 Hot oil outlet temperature (°C) 160–180 Hot oil inlet temperature (°C) 85 Solar radiation received per unit area (W m−2) 850 Apparent sun temperature (K) 4500 Heliostat aperture area (m2) 3000 Turbine back pressure range (MPa) 0.22–0.3 Turbine isentropic efficiency (%) 85 Isothermal efficiency of compressor (%) 55 ARC evaporator temperature (°C) 5 ERC evaporator temperature range (°C) (−1 to −9) or (264 K–272 K) EJT evaporator temperature range (°C) (−193 to −143) or (80 K–130 K) Condenser-2 temperature (°C) 35 Hot oil mass flow rate (kg s−1) 8.0 Pump isentropic efficiency (%) 70 HRVG efficiency (%) 100 Pinch point temperature difference (°C) 10.0 Nozzle efficiency (%) 90 Mixing chamber efficiency (%) 85 Diffuser efficiency (%) 85 Energy efficiency of heliostat field (%) 75 Energy efficiency of central receiver (%) 90 Exergy efficiency of heliostat field (%) 75 Exergy efficiency of central receiver (%) 30 View factor of central receiver 0.8 Emissivity of central receiver 0.8 Reflectivity of central receiver 0.04
The key component of this combined cycle is ejector and its performance is dependent upon entrainment ratio which determines the magnitude of mass flow rate of secondary refrigerant in terms of mass flow rate of primary refrigerant coming out from the turbine. The basic principle of the model was introduced by Keenan et al. [19] based on gas dynamics and formulated by Huang et al. [20] and Ouzzane and Aidoun [21]. The formulation and assumption of entrainment ratio are based on mass, momentum, and energy equations which is recently developed by Dai et al. [22] and may be reported as
$μ=ηnηmηd(hpf,n1-hpf,n2,s)/(hmf,d,s-hmf,m)-1$
(1)

Note that, the properties of the heliostat, central receiver, nozzle, mixing chamber, and diffuser are reported in Table 1 and the required enthalpy values at various state points of the ejector cycle for a given refrigerant are taken from REFPROP 6.01 [23]

The ejector mainly consists of three sections, that is, nozzle, mixing, and diffuser section. In the nozzle section, the energy conservation equation for the adiabatic and steady primary flow is given as
$m·pfhpf,n2+m·pfupf,n222=m·pfhpf,n1+m·pfupf,n122$
(2)
The nozzle efficiency may be defined as
$ηn=hpf,n1-hpf,n2hpf,n1-hpf,n2,s$
(3)
In the mixing section, the momentum conservation equation is given as
$m·pfupf,n2+m·sfusf,n2=(m·pf+m·sf)umf,m,s$
(4)
In the diffuser section, the energy equation is given as
$12(umf,m2-umf,d,s2)=hmf,d,s-hmf,m$
(5)
The diffuser efficiency is given as
$ηd=hmf,d,s-hmf,mhmf,d-hmf,m$
(6)

Thermodynamic Analysis

A thermodynamic analysis considering both the first and the second laws of thermodynamics provide an opportunity to evaluate the theoretical performance of the proposed cycle. The model based on thermodynamic analysis able to predict the cycle performance, efficiency, and emissions. Theoretical analysis minimize the number of experimental tests that have conducted, which are usually costly and time consuming when new thermodynamic cycle technologically advanced are appraised. Exergy analysis which is the combined application of both first and second laws of thermodynamics determines the system performance based on exergy which is defined as the maximum amount of work produced during the reversible transition of a stream of matter from its given thermodynamic state to the restricted dead state where the stream of matter will only be in thermal and mechanical equilibrium with the environment not in chemical equilibrium, hence the exergy obtained during this process will be the physical exergy.

Mathematically
$E·=m·[(h-h0)-T0(s-s0)]$
(7)
According to Bejan [24], the entropy generation over a control volume is given by
$S·gen=dSdt-∑i=0nQ·iTi-∑inm·s+∑outm·s≥0$
(8)
The exergy destruction and entropy generation are related as
$E·D=T0S·gen$
(9)

Energy Efficiency (ηenergy).

It can be defined as the ratio of the desired effect ($Q·E1,Q·E2,Q·E3$) to the thermal energy of solar input ($Q·Solar$). The energy efficiency of the triple-staged refrigeration cycle is then given by
$ηenergy=Q·E1+Q·E2+Q·E3Q·Solar$
(10)

Note that the basic equations obtained from the law of conservation of energy in the components of RC, ERC, ARC, and EJT may be written as follows:

For heliostat: A part of thermal energy received by heliostat is delivered to the central receiver and rest is lost to the environment [25]
$Q·Solar=Ahq$
(11)
where Ah and q are the aperture area and solar radiation per unit area
$Q·Solar=Q·CR+Q·lost,heliostat$
(12)
So,
$ηenergy,heliostat=Q·CRQ·Solar$

Exergy Efficiency (ηexergy).

Since exergy is more valuable than energy according to the second law of thermodynamics, it is useful to consider both output and input in terms of exergy. The amount of exergy supplied in the product to the amount of exergy associated with the fuel is more accurate measure of the thermodynamic performance of the system which is defined as the ratio of exergy contained in the product to the exergy associated with the fuel input and the exergy efficiency of combined cycle may be reported as
$ηexergy=ΔE·E1+ΔE·E2+ΔE·E3E·Solar$
(13)

where $ΔE·E1$ is the change in exergy at evaporator of ERC, $ΔE·E2$ is the change in exergy at evaporator of ARC, $ΔE·E3$ is the change in exergy at evaporator of EJT cycles, and $E·Solar$ is the exergy associated with solar radiation falling on heliostat.

Equations (7)–(9) have been applied to evaluate the energy and exergy balances and hence the equations for exergy destruction in each component of the proposed solar-driven triple-staged refrigeration cycle are provided in the Appendix.

Results and Discussion

A parametric study is carried out to identify the effect of various parameters on the performance of the solar-driven triple-staged refrigeration system. Following parameters have been chosen in the typical range of its operation: hot oil temperature at the exit of central receiver, turbine inlet pressure (0.9–1.7 MPa), evaporator temperature of ERC (264 K–272 K), and evaporator temperature of EJT cycle (80 K–130 K). The parameter under consideration is varied over a given typical range while values of other parameters are kept constant at the level of base case values.

The energy efficiency and energy distribution of solar heat source are obtained by energy balance approach or first law analysis of the cycle. However, the exergy destruction or irreversibility in each component, and the exergy efficiency are investigated under the exergy balance approach or second-law analysis of the cycle. The exergy destruction in each component of the cycle as a whole is nondimensional by expressing it as a percentage of the exergy of solar heat source. The distribution of heat source exergy among the components, exergy destruction due to irreversibility of the components of the cycle, useful energy output (refrigeration capacity of ERC, ARC, and EJT cycle) is clearly depicted. Inclusion of losses in an irreversibility analysis approaches the performance of real cycle. The thermodynamic properties of R141b of ERC, refrigerant of EJT cycle (Propane) were calculated by REFPROP 6.01 (1998) and thermodynamic properties of LiBr/H2O mixture for the operation of ARC are taken from Chua et al. [26]. First law analysis simply provides the overall performance of the cycle. On the other hand, second-law analysis identifies and quantifies the sources of losses in the system and hence helps in to gain an insight into the system performance, therefore, both energy and exergy distribution of proposed cycle are shown in Figs. 2 and 3.

Fig. 2
Fig. 2
Close modal
Fig. 3
Fig. 3
Close modal

Figure 2 indicates that out of 100% solar energy supplied to the system, around 9.23% is available as useful energy output (refrigeration capacity of ARC, ERC, and EJT cycle), 109.23% is lost to the environment via thermal energy exhaust from the system. Application of second-law analysis to the proposed cycle leads to the exergy distribution in the system. It is found that around 3.5% of the total input exergy is available as an exergy output (amount of exergy associated with the cooling produced at the evaporator of ARC, exergy associated with the cooling effect at the evaporator of ERC, and amount of exergy associated at the evaporator of EJT cycle) and 96.5% of the input (solar heat) exergy is destructed and lost due to irreversibilities occurred in various components of the proposed cycle and exergy carried away by the cooling water at absorber and condensers as shown in Fig. 3.

The energy and exergy efficiency of the heliostat field are 75% which indicates 25% loss at the heliostat. The exergy efficiency of central receiver is 30% which is much lower than its energy efficiency which is around 90%. This is an evidence of the deeper insight provided from second-law analysis compared to the performance obtained from first law. Therefore, performance evaluation of solar-driven refrigeration system based on first-law analysis is inadequate and hence more meaningful evaluation must include second-law analysis. The second-law analysis aids to pinpoint the cycle component of maximum irreversibility. It is observed that percentage of exergy destruction is highest in central receiver which is around 52.5%. The next largest exergy destruction was observed in the C1 of the ERC, heat recovery vapor generator, and ejector of ERC which were in the range of (4–5%) as shown in Fig. 3. Less than 1% exergy destructions were observed in other components of the cycle in question. Exergy destruction of 3.7% is observed in the EJT cycle. This is because the ejector of both ERC and EJT cycle comprises the various processes of entropy generation like mixing, normal shock formation, and friction which are the main sources of entropy generation. Therefore, from second-law point of view central receiver, heliostat, HRVG, ejector, condenser of the ERC, and EJT cycle need special attention in order to improve the overall performance of the proposed solar-driven triple-staged refrigeration cycle.

Figure 4 shows the variation of the refrigeration output of three refrigeration cycles individually as well as its combined refrigeration output of the proposed triple-staged refrigeration cycle. It is observed that output of ERC and EJT cycle increases with the increase in hot oil outlet temperature. This is due to the fact that the quality of vaporized refrigerant at the turbine inlet which is a prime mover for both the ejector cycles will be improved with the increase in hot oil outlet temperature. When refrigerant at significant pressure and temperature passes though the nozzle section of the ejector, it will increase mass flow rate of the secondary refrigerant which will result in larger refrigerating effect at the evaporator of the EJT cycle because increase in turbine power output due to increased hot oil outlet temperature enhances mass flow rate of refrigerant (propane) across the compressor which indirectly results in larger cooling effect produced at the evaporator of EJT cycle. It is further observed that increase in hot oil outlet temperature causes a lower refrigerating effect at the evaporator of ARC. This is due to the reason that increase in hot oil outlet temperature results in lower temperature at the exit of HRVG which causes a low mass flow rate of water refrigerant goes to the C2, and hence a lower refrigerating effect at the evaporator of ARC. Since the refrigeration output of ARC is much higher than the refrigeration output of ERC and EJT cycle, therefore the total refrigeration output is also showing the same trend of decreasing with the increase in hot oil outlet temperature.

Fig. 4
Fig. 4
Close modal

In order to observe a complete thermodynamic view of proposed cooling cycle, energy efficiency based on first law and exergy efficiency based on second law is also evaluated and their representation against the hot oil outlet temperature is shown in Fig. 5. Energy analysis of the cycle reveals that the refrigeration capacity of ARC decreases significantly with increase in oil temperature, while the refrigeration capacity of ERC and EJT cycle increases marginally with the same. Since the refrigeration capacity of ARC dominates over refrigeration capacity of other two cycles, therefore, the energy efficiency of proposed triple-effect refrigeration cycle decreases considerably with the increase in oil temperature. On the other hand, the exergy efficiency which is defined as the ratio of amount of exergy associated with the refrigeration capacity to the amount of exergy associated with the solar heat input. Exergy associated with refrigeration capacity is the ratio of refrigeration capacity to the Carnot COP of a refrigerator operates between the evaporator temperature and ambient. Since the evaporator temperature of ARC is closer to the ambient temperature, therefore, the exergy output of ARC decreases considerably similar to its refrigeration capacity. The exergy associated with the ERC increases marginally while the exergy associated with the EJT cycle increases significantly due to the fact that the difference of temperature between the evaporator of ERC and ambient is not of larger magnitude but the difference of temperature between the evaporator of EJT cycle and ambient is very large. Due to these reasons, the exergy output of ERC cycle increases marginally while the exergy output of EJT cycle increases significantly. Overall, the exergy output of triple-staged refrigeration cycle increases marginally with the increase in hot oil outlet temperature which results in the marginal overall increase in its exergy efficiency.

Fig. 5
Fig. 5
Close modal

Figure 6 shows the effect of refrigerant turbine inlet pressure on the individual as well as combined output of proposed triple-staged refrigeration cycle. It is observed that refrigeration capacity of ERC and EJT cycle decreases with the increase in turbine inlet pressure while the refrigeration capacity of ARC increases significantly with the same. The reason for this is that increase in turbine inlet pressure results in lower mass flow of refrigerant vapor produced in the HRVG and a lower turbine exit temperature which further results in reduction of velocity at the ejector nozzle which causes a reduced mass flow rate of secondary refrigerant through ejector evaporator. Refrigeration capacity of ARC increases significantly due to fact that increase in turbine inlet pressure which lowers the mass flow rate of refrigerant vapor will result in a reduced absorption of heat from the exhaust gases through the HRVG which leads to the higher value of HRVG exit temperature. This higher temperature at the inlet of generator causes a significant increase in the capacity of ARC due to increased mass flow rate of water refrigerant. The decrease in refrigerating capacity of EJT cycle is observed due to the reduced mass flow rate of refrigerant (propane) across the compressor which is caused because of reduced mass flow rate of R141b across the turbine. The reduced mass flow rate will decrease the refrigerating capacity of EJT cycle due to overall reduced mass flow rate across the cycle. The effect of change in turbine inlet pressure on energy and exergy efficiency of triple-staged refrigeration cycle is clearly shown in Fig. 7. The energy efficiency found to be increased significantly with the increase in turbine inlet pressure while its exergy efficiency decreases with the same. This is due to the reason that increase in turbine inlet pressure causes a significant improvement in refrigeration output of ARC and reduction in refrigeration output of ERC and EJT cycle. Since the rate of enhancement in the refrigeration capacity of ARC is much greater than the rate of reduction in the refrigerating capacity of ERC and EJT cycle, therefore, the overall energy efficiency of triple-staged refrigeration cycle increases with the increase in turbine inlet pressure. The exergy efficiency of the proposed triple-staged refrigeration cycle shows the trend of increasing with increase in turbine inlet pressure to some extent and then it starts decreasing with the same. This is because initially the rate of increase in exergy output of ARC is greater than the rate of decrease in exergy output of ERC and EJT cycle becomes greater than the rate of increase in exergy output of ARC.

Fig. 6
Fig. 6
Close modal
Fig. 7
Fig. 7
Close modal

In order to highlight the importance of employment of EJT cycle, the effects of change in the evaporator temperature of ERC and evaporator temperature of EJT cycle are observed on the refrigeration capacity of individual refrigeration cycles and combined triple-staged refrigeration cycle. It is shown that refrigeration capacity of ERC and combined refrigeration cycle increases considerably with the increase in evaporator temperature of ERC while insignificant variation is observed in the refrigeration capacity of EJT cycle and ARC, respectively, as shown in Fig. 8. The effect of change in evaporator temperature of ERC on energy and exergy efficiency of the triple-staged refrigeration cycle is shown in Fig. 9 and it is found that energy efficiency increases significantly with the increase in evaporator temperature of ERC while the exergy efficiency of the combined refrigeration cycle increases marginally with the same. It is further observed that increase in evaporator temperature of EJT cycle causes a marginal increase in the energy and exergy efficiency of combined triple-staged refrigeration cycle as shown in Fig. 10.

Fig. 8
Fig. 8
Close modal
Fig. 9
Fig. 9
Close modal
Fig. 10
Fig. 10
Close modal

Conclusion

A new solar-driven triple-staged refrigeration cycle is proposed for the production of cooling from air conditioning to cryogenic range. Energy and exergy methods are employed which enable us to develop a systematic approach that can be used to identify the sites of the real destructions/losses of valuable energy in thermal devices. The effect of several design parameters was observed on energy and exergy performance of the proposed cycle. The conclusions of the present analysis can be summarized as follows:

• Out of 100% energy (solar heat source) supplied to the system around 9.23% is produced as refrigeration capacity and 109.23% is lost to the environment.

• About 3.5% of the input exergy is available as exergetic refrigeration output and 96.5% is lost due to irreversibilities in the components and via thermal lost to the ambient.

• For a given solar heat source, the exergy output of EJT cycle is around 2.96% which is significantly higher than the exergy outputs of ARC and ERC of 0.27% and 0.124%, respectively.

• The largest contribution to cycle irreversibility comes from central receiver and heliostat field of 52.5% and 25%, respectively.

• The irreversibility of the order of 4–5% is observed in the HRVG, ejector and condenser of the ERC.

• The exergy efficiency of around 4% for solar-driven triple-effect cycle is obtained which is much lower than its energy efficiency of 10%.

This comprehensive thermodynamic analysis provides a powerful and systematic tool for identifying the sources of real losses in solar-driven triple-staged refrigeration cycle and guided for the effective exploitation of solar thermal energy using an integrated refrigeration system.

Nomenclature
Ah =

aperture area of heliostat (m−2)

ARC =

absorption refrigeration cycle

COMP =

compressor

$E·$ =

exergy rate (kJ s−1)

$ΔE·$ =

exergy change (kJ s−1)

EJT =

ejector expansion Joule–Thomson cryogenic

ERC =

ejector refrigeration cycle

LiBr-H2O =

lithium bromide-water

$Q·$ =

energy rate (kJ s−1)

R141b =

1,1-dichloro-1-fluoroethane

RC =

Rankine cycle

T =

absolute temperature (K), Turbine

$W·$ =

work output (kJ s−1)

h =

enthalpy (kJ kg−1)

$m·$ =

mass flow rate (kg s−1)

q =

s =

entropy (kJ kg−1 K−1)

u =

velocity of flow in nozzle and diffuser (m s−1)

Greek Symbols
μ =

entrainment ratio

η =

efficiency (%)

Subscripts
A =

absorber

C1 =

condenser-1

C2 =

condenser-2

CR =

D =

destruction

E =

evaporator

E1 =

evaporator-1

E2 =

evaporator-2

E3 =

evaporator-3

EJE1 =

ejector-1

EJE2 =

ejector-2

G =

generator

HRVG =

heat recovery vapor generator

HX1 =

heat exchanger-1

HX2 =

heat exchanger-2

P1 =

pump-1

P2 =

pump-2

SHX =

solution heat exchanger

T =

turbine

TV1 =

throttle valve-1

TV2 =

throttle valve-2

TV3 =

throttle valve-3

TV4 =

throttle valve-4

d =

diffuser

ejt =

ejector expansion Joule–Thomson cryogenic

f =

refrigerant fluid

h =

heliostat field

m =

mixing chamber

n =

nozzle

n1 =

inlet of nozzle

n2 =

outlet of nozzle

oil =

hot oil (Duratherm 600)

pf =

primary flow

r =

water refrigerant

s =

solution mixture of LiBr/H2O, isentropic

sf =

secondary flow

1, 2, 3… a, b, c… =

state points in Fig. 1

Appendix

Energy Balance Equations.
For central receiver (CR): A part of thermal energy received by central receiver is absorbed by oil (Duratherm 600) and rest is lost to the environment
$Q·CR=Q·oil+Q·lost,CR=m·oil(h1-h12)+Qlost,CR$
(A1)
and
$ηenergy,CR=Q·oilQ·CR$
For HRVG
$m·oil(h1-h2)=m·pf(h4-h3)$
(A2)
For turbine
$W·T=m·pf(h4-h5)$
(A3)
For pump-1
$W·P1=m·pf(h3-h8)$
(A4)
For ejector-1
$m·pfh5+m·sfh11=h6(m·pf+m·sf)$
(A5)
For condenser-1
$Q·C1=m·C1(hd-hc)=(m·pf+m·sf)(h6-h7)$
(A6)
For throttle valve-1
$h9=h10$
(A7)
For evaporator-1
$Q·E1=m·E1(ha-hb)=m·sf(h11-h10)$
(A8)
For generator
$Q·G=m·oil(h2-h12)=(m·s-m·r)h20+m·rh13-m·sh19$
(A9)
For condenser-2
$Q·C2=m·C2(hf-he)=m·r(h13-h14)$
(A10)
For throttle valve-2
$h14=h15$
(A11)
For evaporator-2
$Q·E2=m·E2(hi-hj)=m·r(h16-h15)$
(A12)
For absorber
$Q·A=m·A(hh-hg)=(m·s-m·r)h22+m·rh16-m·sh17$
(A13)
For pump-2
$W·P2=m·s(h18-h17)$
(A14)
For solution heat exchanger
$m·sh18+(m·s-m·r)h20=m·sh19+(m·s-m·r)h21$
(A15)
For throttle valve-3
$h21=h22$
(A16)
For compressor:
$W·comp=W·T=m·ejt[(h24-h23)-T23(s24-s23)]/ηc$
(A17)
For heat exchanger-1
$m·ejt(h24-h25)=m·ejt(h23-h30)$
(A18)
For heat exchanger-2
$m·ejt,sf(h25-h26)=m·ejt(h30-h29)$
(A19)
For throttle valve-4
$h26=h27$
(A20)
For evaporator-3
$Q·E3=m·E3(hk-hl)=m·ejt,sf(h28-h27)$
(A21)
For ejector-2
$m·ejt,pfh25+m·ejt,sfh28=m·ejth29$
(A22)
Exergy Destruction Equations
$ΔE·E1=m·sf[(h10-h11)-T0(s10-s11)]$
(A23)
$ΔE·E2=m·r[(h15-h16)-T0(s15-s16)]$
(A24)
$ΔE·E3=m·ejt,sf[(h27-h28)-T0(s27-s28)]$
(A25)
$E·Solar=Q·Solar(1-T0TS)$
where Ts the apparent sun temperature taken as 4500 K.
$E·1=m·oil[(h1-h0)-T0(s1-s0)]$
(A26)
$E·12=m·oil[(h12-h0)-T0(s12-s0)]$
(A27)

$E·1$ is the exergy associated with incoming hot oil from receiver while $E·12$ is the exergy associated with outgoing hot oil to the receiver.

The basic equations of exergy destruction rate in the components of RC, ERC, ARC, and EJT are written as follows:

For heliostat: A part of exergy received by heliostat is delivered to the central receiver and rest is destructed (irreversibility)
$ESolar=E·CR+ Elost,heliostat$
(A28)
and
$ηexergy,heliostat=E·CRE·Solar$
For CR: A part of exergy received by central receiver is absorbed by oil (Duratherm 600) and rest is lost to the environment (irreversibility)
$E·CR=E·oil+E·lost,CR=m·oil cp,oil[T1-T12-T0ln(T1T12)]+E·lost,CR$
(A29)
and
$ηexergy,CR=E·oilE·CR$
For HRVG
$E·D,HRVG=T0[m·oil(s2-s1)+m·pf(s4-s3)]$
(A30)
For turbine
$E·D,T=T0[m·pf(s5-s4)]$
(A31)
For ejector-1
$E·D,EJE1=T0[(m·pf+m·sf)s6-m·pfs5-m·sfs11]$
(A32)
For condenser-1
$E·D,C1=T0(m·pf+m·sf)(s7-s6)$
(A33)
For throttle valve-1
$E·D,TV1=T0m·sf(s10-s9)$
(A34)
For generator
$E·D,G=T0[m·r(s13-s20)+m·s(s20-s19)+m·oil(s12-s2)]$
(A35)
For solution heat exchanger
$E·D,SHX=T0[m·s(s19-s18)+(m·s-m·r)(s21-s20)]$
(A36)
For pump-2
$E·D,P2=T0[m·s(s18-s17)]$
(A37)
For throttle valve-3
$E·D,TV3=T0[(m·s-m·r)(s22-s21)]$
(A38)
For absorber
$E·D,A=T0[m·r(s22-s16)+m·s(s17-s22)+m·A(sh-sg)]$
(A39)
For condenser-2
$E·D,C2=T0[m·r(s14-s13)+m·C2(sf-se)]$
(A40)
For throttle valve-2
$E·D,TV2=T0[m·r(s15-s14)]$
(A41)
For compressor
$E·D,comp=m·ejt[(h23-h24)(1-1ηc)+(s23-s24)(T23ηc-T0)]$
(A42)
For ejector-2
$E·D,EJE2=T0[m·ejt(s29)-m·ejt,pf(s25)-m·ejt,sf(s28)]$
(A43)
For throttle valve-4
$E·D,TV4=T0[m·ejt,sf(s27-s26)]$
(A44)
For heat exchanger-1
$E·D,HX1=m·ejtT0[(s25-s24)+(s23-s30)]$
(A45)
For heat exchanger-2
$E·D,HX2=T0[m·ejt,sf(s26-s25)+m·ejt(s30-s29)]$
(A46)

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